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Computational Exploration of Ambiphilic Reactivity of Azides and Sustmann’s Paradigmatic Parabola
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  • Pan-Pan Chen
    Pan-Pan Chen
    Department of Chemistry and Biochemistry, University of California, Los Angeles, California 90095-1569, United States
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  • Pengchen Ma
    Pengchen Ma
    Department of Chemistry and Biochemistry, University of California, Los Angeles, California 90095-1569, United States
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  • Xue He
    Xue He
    College of Sciences, Nanjing Agricultural University, Nanjing 210095, China
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  • Dennis Svatunek
    Dennis Svatunek
    Department of Chemistry and Biochemistry, University of California, Los Angeles, California 90095-1569, United States
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    Orcidhttps://orcid.org/0000-0003-1101-2376
  • Fang Liu*
    Fang Liu
    College of Sciences, Nanjing Agricultural University, Nanjing 210095, China
    *Email: [email protected]
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  • Kendall N. Houk*
    Kendall N. Houk
    Department of Chemistry and Biochemistry, University of California, Los Angeles, California 90095-1569, United States
    *Email: [email protected]
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    Orcidhttps://orcid.org/0000-0002-8387-5261
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The Journal of Organic Chemistry

Cite this: J. Org. Chem. 2021, 86, 8, 5792–5804
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https://doi.org/10.1021/acs.joc.1c00239
Published March 26, 2021

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Abstract

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We examine the theoretical underpinnings of the seminal discoveries by Reiner Sustmann about the ambiphilic nature of Huisgen’s phenyl azide cycloadditions. Density functional calculations with ωB97X-D and B2PLYP-D3 reproduce the experimental data and provide insights into ambiphilic control of reactivity. Distortion/interaction-activation strain and energy decomposition analyses show why Sustmann’s use of dipolarophile ionization potential is such a powerful predictor of reactivity. We add to Sustmann’s data set several modern distortion-accelerated dipolarophiles used in bioorthogonal chemistry to show how these fit into the orbital energy criteria that are often used to understand cycloaddition reactivity. We show why such a simple indicator of reactivity is a powerful predictor of reaction rates that are actually controlled by a combination of distortion energies, charge transfer, closed-shell repulsion, polarization, and electrostatic effects.

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Introduction

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Sustmann and Trill published a landmark paper in 1972 about reactivity of phenyl azide in 1,3-dipolar cycloadditions. (1a) At that time, an iconic parabola (Figure 1a) presented for the first time a memorable summary of how the electronic nature of a dipolarophile, relative to that of the 1,3-dipole, determines the rate of reaction. This parabola, based on second-order perturbation theory, (2) shows the correlation of the second-order rate constant k for cycloadditions of phenyl azide to a series of dipolarophiles and the experimental ionization potential (IP) of these dipolarophiles. (1b) The IP is related by Koopmans’ theorem to the negative of the highest occupied molecular orbital (HOMO) energy and serves as a measure of both the HOMO and lowest unoccupied molecular orbital (LUMO) energies: a low-energy HOMO is usually accompanied with a low-energy LUMO and vice versa.

Figure 1

Figure 1. (a) Plot of reactivity (lnk2) vs IP. Replotted in the same style as Sustmann’s original figure in ref (1). Copyright 1972 by Verlag Chemie GmbH, Germany. (b) Schematic of the azide HOMO and LUMO vs those of donor-substituted dipolarophiles, ethylene, and acceptor-substituted dipolarophiles.

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Figure 1b shows how donor (D) and acceptor (A) substituents alter the frontier molecular orbital (FMO) energies of a dipolarophile. (1c) In the reaction of phenyl azide with ethylene (Figure 1b, middle), two sets of interactions contribute: the HOMO of azide with the LUMO of ethylene and the HOMO of ethylene with the LUMO of azide. An electron donor (Figure 1b, left) raises the ethylene HOMO and LUMO energies, which leads to better interaction between the HOMO of ethylene and the LUMO of azide, resulting in stronger stabilization and higher reactivity. An electron acceptor (Figure 1b, right) enhances the reactivity of ethylene in the same manner by lowering the HOMO and LUMO energies. With this FMO model, Sustmann qualitatively explained the effect of different substituents on reactivities in 1,3-dipolar cycloadditions.
The Sustmann paper quantified what we now describe as the ambiphilic character of aryl and alkyl azides, a feature that was revealed by comparisons of Huisgen’s experimental measurements (3) to the many ionization potentials that became available from Heilbronner et al. (4) and Sustmann et al.’s work, (5) as well as ours (6) and others (7) through the commercialization of the PerkinElmer UV photoelectron spectrometer in 1967. (8)
Ever since that time, Fukui’s FMO theory has provided a powerful model for a qualitative understanding of reactivity and regioselectivity in reactions of various 1,3-dipoles with alkenes. (9) We recently proposed a general distortion/interaction (D/I) model for cycloaddition reactivity, (10a−d) and Bickelhaupt proposed the equivalent activation strain (AS) model. (10e,f) The D/I-AS model has been applied to 1,3-dipolar cycloadditions and shows that there are correlations between distortion energies and the activation barriers for 1,3-dipolar cycloadditions of various 1,3-dipoles with alkenes and alkynes. The reactivity differences between dipoles are often controlled by the distortion energies of the 1,3-dipoles (the energy required to distort the ground state of the 1,3-dipoles to their transition state geometries), rather than by FMO interactions or reaction thermodynamics. However, the reactivity of dipolarophiles with a given dipole correlates with orbital interactions and can be understood with FMO analysis. (10a) Energy decomposition analyses have shown that a variety of other factors, like closed-shell repulsion, electrostatic effects, and polarization, may also influence reactivity. (10e) A different approach based on electron density analyses was proposed by Domingo. (11) Domingo’s approach, molecular electron density theory (MEDT), is based on conceptual density functional theory, in which reactivity parameters are obtained by computations of changes in electron density upon electron removal or addition. This obviously ties in closely with Sustmann’s ionization potential as an indicator of reactivity, although Domingo criticizes severely any discussion of reactivity in terms of orbitals. (11) The MEDT approach was applied to azide cycloadditions and many other cycloadditions. (11b) In addition, Cremer et al. performed computational studies of ten different cycloadditions of 1,3-dipoles XYZ (diazonium betaines, nitrilium betaines, azomethines, and nitryl hydride) to acetylene with B3LYP/6-31G(d,p) geometries and CCSD(T)-F12/aug-cc-pVTZ energetics, employing their unified reaction valley approach (URVA) (12) on the concerted processes, and Breugst, with Huisgen and Reissig, conducted calculations with M06-2X geometries and DLPNO-CCSD(T) (13) energies for the concerted 1,3-dipolar cycloadditions of diazomethane with many model-substituted alkynes. (14) Because few recent high-accuracy calculations have explored the full range of azide cycloadditions to the alkene dipolarophiles studied experimentally by Huisgen, we carried out an analysis of the Sustmann relationship for this important class of reactions. (15)

Computational Methods

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All density functional theory (DFT) calculations were performed with Gaussian 16. (16) Geometry optimizations of all stationary points were performed with the long-range corrected hybrid functional, ωB97X-D (17) with the 6-31+G(d,p) basis set in solution. Solvents were chosen according to what was used in the experiment. Vibrational frequencies were calculated at the same level of theory to evaluate the zero-point vibrational energy (ZPVE) and thermal corrections at 298.15 K. The single-point energies were computed using ωB97X-D and the double hybrid B2PLYP-D3 (18) functional with the aug-cc-pVTZ (19) basis set; solvation energy corrections were evaluated with the CPCM model. (20) The Hirshfeld charges of the transition states were analyzed at the ωB97X-D/6-31+G(d,p) level of theory on the optimized structures to determine the direction and extent of charge transfer. Frontier molecular orbitals were calculated on DFT-optimized structures at the HF level of theory with the 6-31G(d) basis set and visualized with Multiwfn (21) and VMD. (22) Fragment distortion and interaction energies were calculated with autoDIAS (23) at the ωB97X-D level of theory with the aug-cc-pVTZ basis set in the gas phase. Energy decomposition analyses were performed in ADF 2019.304 (24) at the ωB97X-D3/TZ2P (25) level of theory using PyFrag 2019. (26) The orbital coefficients were calculated using the NBO (27) module of Gaussian 16 and Multiwfn. Extensive conformational searches for the intermediates and transition states have been carried out to ensure that the lowest energy conformers were located. The 3D images of molecules were generated using CYLView. (28)

Results and Discussion

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We investigated the reactivity of phenyl azide in the context of modern density functional theory and the distortion/interaction-activation strain model and analyzed the interactions of phenyl azide and dipolarophiles with an energy decomposition analysis. We describe the factors that control reactivity and show why Sustmann’s parabola provides such a powerful model for ambiphilic cycloaddition reactivity, despite the many factors that contribute to reactivity.
We computed the transition states of the 1,3-dipolar cycloadditions between phenyl azide and 27 dipolarophiles. The first 21 dipolarophiles, which are included in Sustmann’s plot, are listed in Scheme 1. Table 1 shows the energetics computed with two functionals (method A and method B). The same trend of reactivity was obtained from the two methods (Figure 2). The computed rate constants (by applying the Eyring equation to activation free energies) (29) given by the double hybrid functional (method B) agree somewhat better with measured rate constants (30) (Table 1 and Figure 3). For all dipolarophiles studied, there is a good linear correlation between the variables. In the following discussion, we report the values of energetics calculated by B2PLYP-D3, unless otherwise specified.

Figure 2

Figure 2. Correlation of aΔGA‡ with bΔGB‡ for the cycloadditions between phenyl azide and 21 dipolarophiles. aωB97X-D/aug-cc-pVTZ-CPCM(solvent)//ωB97X-D/6-31+G(d,p)-CPCM(solvent); bB2PLYP-D3/aug-cc-pVTZ-CPCM(solvent)//ωB97X-D/6-31+G(d,p)-CPCM(solvent).

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Figure 3

Figure 3. Correlation of logarithms of the experimental rate constants with the calculated rate constants (method B) for the cycloadditions between phenyl azide and 21 dipolarophiles.

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Scheme 1

Scheme 1. The 1,3-Dipolar Cycloaddition between Phenyl Azide and Different Dipolarophiles Studied by Sustmann and in This Paper
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Table 1. Experimental Rate Constantsa and Calculated Reaction Barriers and Rate Constantsb
  method Acmethod Bd
dipolarophilelog(kexp × 109)ΔGA‡ (kcal/mol)log(kcal × 109)ΔGB‡ (kcal/mol)log(kcal × 109)
R1e7.0623.14.8518.38.37
R2e6.0025.63.0220.86.54
R3e5.4124.33.9719.67.42
R4e4.4029.60.0923.74.41
R54.2930.0–0.2123.94.27
R6e2.3832.5–2.0426.42.43
R71.9532.9–2.3326.72.21
R81.6032.3–1.9027.81.41
R91.3833.8–3.0028.40.97
R101.1833.3–2.6327.61.55
R110.5235.0–3.8828.90.60
R121.4333.4–2.7027.91.33
R131.4633.5–2.7827.71.48
R141.5332.5–2.0426.32.51
R151.6033.3–2.6327.01.99
R161.8633.4–2.7027.31.77
R172.0332.7–2.1928.01.26
R182.9231.7–1.4625.92.80
R192.9931.5–1.3126.42.43
R203.0231.5–1.3126.62.29
R213.4031.3–1.1625.63.02
a

For different dipolarophiles, the corresponding cycloaddition was performed in a particular solvent (carbon tetrachloride or benzene) at 25 °C. (30)

b

For different dipolarophiles, the calculated reaction barriers and rate constants are values in a specific solvent (carbon tetrachloride or benzene), which was chosen according to what was used in the experiment. (30)

c

ωB97X-D/aug-cc-pVTZ-CPCM(solvent)//ωB97X-D/6-31+G(d,p)-CPCM(solvent).

d

B2PLYP-D3/aug-cc-pVTZ-CPCM(solvent)//ωB97X-D/6-31+G(d,p)-CPCM(solvent).

e

In the experimental study, the reaction solvent was benzene for these dipolarophiles and carbon tetrachloride for the other dipolarophiles. (30)

We compared our predicted ionization potentials (IP) based on Koopmans’ theorem (31) to those measured experimentally by photoelectron spectroscopy and found that the theoretical value is in good agreement with the experimental value (Figure S1). In Sustmann’s plot, a key concept is that the HOMO and LUMO of the substituted dipolarophiles will be shifted in the same direction. Therefore, the variation of HOMO energy should reflect corresponding shifts of LUMO energy. We indeed found a correlation between predicated ionization potential and electron affinity (EA) for different dipolarophiles (Figure S2), indicating that the change of LUMO energy can be semi-quantitatively characterized by the variation of HOMO energy.
We also plotted the predicted log k values for the 1,3-dipolar cycloadditions versus the calculated ionization potentials of a number of dipolarophiles. Figure 4 is a theoretical version of Sustmann’s plot. The parabolic relationship of reactivity with dipolarophile ionization potential is nicely consistent with Sustmann’s results. (1a) Additionally, we plotted the relationship between logarithms of the predicted rate constants of 1,3-dipolar cycloadditions and calculated Mulliken electronegativities (χ) for all dipolarophiles, and we obtained a similar parabola (Figure S3). This indicates that there is a relationship between the ionization potential used by Sustmann and the electronegativity, which is the average of the ionization energy and the electron affinity (Figure S4). It is worth noting that the correlation with Mulliken’s electronegativity is only a slight modification of the poor correlation between IP and EA (compare Figures S2 and S4) because Mulliken’s electronegativties (χ = IP/2 + EA/2) superimpose half of the EA values on the identity correlation IP/2 vs IP and thus reduce the magnitude of the deviations while simultaneously increasing the slope.

Figure 4

Figure 4. Theoretical version of Sustmann’s plot with charge transfer (e), using B2PLYP-D3/aug-cc-pVTZ-CPCM(solvent)//ωB97X-D/6-31+G(d,p)-CPCM(solvent)-predicted rate constants and HF/6-31G(d)-calculated ionization potentials (eV). The three purple points, for which experimental rate constants have been given in Huisgen’s experimental study (30) but were not included in Sustmann’s analysis, are qualitatively in line with the parabolic trend. The three points in red are added to the original plot to show how distortion-accelerated dipolarophiles fit on the correlation, and the point in orange is added to the original plot to show the enormous acceleration that occurs with Cu catalysis. Data in blue (negative number) shows charge transfer from dipolarophiles to azide; data in green (positive number) shows charge transfer from azide to dipolarophiles; data in black shows charge transfer of 0.05 e or less between reactants, essentially zero.

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We have, in addition to the 21 dipolarophiles reported in Sustmann’s analysis, studied the cycloadditions of phenyl azide with other dipolarophiles, such as 1-methoxycyclopentene, (32) maleic anhydride, and N-phenylmaleimide, for which experimental rate constants were given in Huisgen et al.’s 1967 paper. (30) The reactivities for these three species (Figure 4, purple) are qualitatively in line with the parabolic trend. Moreover, we have incorporated the results for distortion-activated (or strain-promoted) dipolarophiles, (33) e.g., trans-cyclooctene, cyclooctyne, and cyclopropene, which are of interest in bioorthogonal chemistry (Figure 4, red). (34) It is shown that trans-cyclooctene actually fits very nicely on the parabola since the distortion of the alkene increases the HOMO energy to be about the same as pyrrolidinocyclohexene (R2). However, cyclooctyne has a slightly lowered ionization potential (9.4 eV) as compared to 2-butyne (9.6 eV) (35) but is anomalously reactive, as expected for a distortion-accelerated dipolarophile. (33,36) Cyclopropenes have been used as dienophiles in bioorthogonal chemistry by the Prescher (34d) and Devaraj groups (34e) and studied theoretically. (34f) Cyclopropene is somewhat more reactive than reactive norbornene. To support our statement that trans-cyclooctene, cyclooctyne, and cyclopropene are all distortion-promoted dipolarophiles, we performed distortion/interaction-activation strain analysis on the transition states of their cycloaddition reactions with phenyl azide (Figure S5). The corresponding results confirmed our inference (Table S1). Finally, we add the famous Sharpless Cu-catalyzed click reaction of azide with terminal alkyne (Figure 4, orange) to the graph to emphasize the enormous acceleration that occurs with Cu catalysis. (37)
We have also calculated the charge transfer for all cycloaddition transition states, and values are shown in Figure 4. In general, the fast reactions involve significant (δq > 0.05 e) charge transfer, which is consistent with the general idea that orbital interactions are influential on reactivity.
We performed distortion/interaction-activation strain analyses on these cycloaddition transition states to evaluate other factors that influence reactivities. This involves decomposition of the electronic energy (ΔE) into two terms: the distortion energy (ΔEdist) that results from the distortion of the individual reactants and the interaction (ΔEint) between the deformed reactants. Based on our study, we find that there is a rough relationship between distortion energy and cycloaddition reactivity (Figure 5a). However, the interaction energy surprisingly has little correlation with the reactivity (Figure 5b). This is, of course, in apparent contrast to Sustmann’s conclusion and that from charge transfer assessments that suggest that FMO interactions control cycloaddition reactivity. As shown in Figure 5a, nucleophilic dipolarophiles (R1–R5, red dots) show low distortion energies and higher reactivities; electrophilic dipolarophiles (R14 and R17–R21, blue dots) show moderate distortion energies and reactivities; neutral or ambiphilic dipolarophiles (R6–R13, R15, and R16, green dots) show the greatest distortion energies and the lowest reactivities. The cycloaddition reactivity as a whole is related to the distortion energy. There is a close relationship between FMO interactions, the position of the transition state, and distortion energies. For nucleophilic dipolarophiles, the HOMO-LUMO interaction is stronger (smaller FMO gap), so the transition state is earlier, corresponding to less distortion. For electrophilic dipolarophiles, the HOMO-LUMO interaction is weak (larger FMO gap), so the transition state is later, corresponding to greater distortion. In other words, the orbital interactions are related to the transition state position and therefore the distortion energies. Although Sustmann’s parabola provided a great qualitative guide to the reactivity trends for an ambiphilic 1,3-dipole, it is because the IP reflects not only changes in HOMO or LUMO energy but also distortion energy differences. (38)

Figure 5

Figure 5. Plots of logarithms of the experimental rate constants versus (a) distortion and (b) interaction energies for the cycloadditions between phenyl azide and dipolarophiles. Energies are in kcal/mol.

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Figure 6 shows a plot of the optimum FMO gaps between dipole and 21 dipolarophiles (the FMOs used here are those involved in the formation of new bonds, not the actual HOMOs and LUMOs) versus the calculated ionization potentials of these dipolarophiles. There is an excellent linear correlation between IP and the energy gap. For the electron-rich (R1–R5, red dots) and neutral or ambiphilic dipolarophiles (R6–R13, R15, and R16, green dots), lower IP and a smaller FMO gap correlate with higher reactivity. However, with the electron-deficient dipolarophiles, R14 and R17–R21 (blue dots), there must be other factors that compensate the unfavorable FMO gaps, leading to high reactivity.

Figure 6

Figure 6. Plot of optimum FMO gaps (eV) between dipole and dipolarophiles versus calculated ionization potentials (eV) of a number of dipolarophiles.

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A plot of the IP of the dipolarophiles versus both FMO gaps (the FMOs used here are those involved in the formation of new bonds, not the actual HOMOs and LUMOs) is provided in Figure S6. As expected, the HOMOdipolarophile-(LUMO+2)azide gap of electron-rich dipolarophiles (IP < 10 eV) accounts for the left arm of the parabola. For dipolarophiles with IP around 10 eV, HOMOdipolarophile-(LUMO+2)azide and (HOMO-3)azide-LUMOdipolarophile gaps become comparable; for dipolarphiles with IP greater than 11 eV, the (HOMO-3)azide-LUMOdipolarophile gap becomes determinant and corresponds with the right arm of the parabola. This is the basic idea that Sustmann proposed and is now quantitatively shown in Figure S6.
To gain more insights into the physical factors leading to the reactivity trend, we studied the cycloadditions between phenyl azide and five representative dipolarophiles, including the most reactive and electron-rich R1 and R4, neutral R11, and electron-deficient R17 and R21. The corresponding transition states are shown in Figure 7. The forming C–N bond ranges from 2.0 to 2.8 Å, and the transition state structure varies from nearly synchronous to highly asynchronous, with an average of the two forming C–N bonds being 2.2–2.4 Å.

Figure 7

Figure 7. DFT-optimized transition structures for cycloadditions between phenyl azide and five representative dipolarophiles. TS1 and TS17 are for the experimentally observed regioselectivity.

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Figure 8 shows the orbital interaction diagrams of the selected reactions. As noted above, these diagrams show the FMOs that are involved in the formation of new bonds, not the actual HOMOs and LUMOs. For the cycloaddition between phenyl azide and R1, the dominant orbital interaction is between the HOMO of R1 and the LUMO+2 of phenyl azide (the LUMO+2 is slightly higher than the perpendicular LUMO, which conjugates with the phenyl group and is not involved in bond formation). This is the same with R4, R11, and R17. Along the series, as the HOMO energy of a dipolarophile decreases (the nucleophilicity of the dipolarophile decreases), the energy gap increases (11.1, 12.7, 12.8, and 14.4 eV for R1, R4, R11, and R17, respectively). For R21, the interaction between HOMO-3 of phenyl azide (the higher energy orbitals are not involved in bond formation) and the LUMO of R21 dominates. Phenyl azide is somewhat electron-deficient and thus gives stronger interactions and faster rates with the electron-rich dipolarophiles.

Figure 8

Figure 8. Orbital interaction diagrams for the cycloadditions between phenyl azide and selected dipolarophiles. In order to justify that HOMO-3 and LUMO+2 of phenyl azide are the effective orbitals involved in the orbital interactions between phenyl azide and dipolarophiles, we show the HOMO, HOMO-1, and HOMO-2 as well as the LUMO and LUMO+1 of phenyl azide in the upper left corner for comparison.

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A distortion/interaction-activation strain analysis was performed along the reaction coordinate (defined by the bond length of the shorter forming C–N bond) for the five reactions in discussion (Figure 9). The transition states of cycloadditions between phenyl azide and symmetric dipolarophiles (R4, R11, and R21) are nearly synchronous, corresponding to generally higher distortion energies. Asymmetric dipolarophiles (R1 and R17) have asynchronous transition states (bond formation mainly at one center) and lower distortion energies at a given forming bond length (Figure 9b). We interpret this as a result of the stronger HOMO-LUMO interactions in the asynchronous transition states: strong asynchronicity is related to lower distortion energies and to much greater overlap at the shorter forming bond.

Figure 9

Figure 9. Distortion/interaction-activation strain (DIAS) analysis for selected cycloaddition reactions. Reactant distortion and interaction energies were calculated at the ωB97X-D level of theory with the aug-cc-pVTZ basis set, in the gas phase. (a) Electronic energies (ΔE). (b) Distortion energies (ΔEdist). (c) Interaction energies (ΔEint).

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The interaction energies (Figure 9c) are higher for very electron-rich enamine (R1) and very electron-deficient dimethyl acetylenedicarboxylate (R21). Interaction energies involve more than the commonly cited frontier orbital interactions represented in Figure 8, and we performed an energy decomposition analysis to determine the origins of the different interaction energies (Figure S7). The interaction energy in transition states (−8 to −14 kcal/mol) is a combination of Pauli repulsion (70 to 100 kcal/mol), orbital interactions (around −40 kcal/mol), and electrostatic interactions (around −40 kcal/mol). No clear pattern in the energy components was found. The origin of these very large individual interactions is that covalent bonds are being formed and very large changes in potential and kinetic energies occur as a result. We caution against simple interpretations of the very large changes in all energy components that occur in partial covalent bond formation; nevertheless, details of the energy decomposition analysis are given in the Supporting Information (Figure S7).
We also investigated the regioselectivity of the 1,3-dipolar cycloadditions for five unsymmetrical alkenes, R2, R8, R9, R15, and R17. Orbital interaction diagrams for the corresponding cycloaddition reactions are shown in Figure 10. The regioselectivity has been rationalized traditionally by frontier molecular orbital interactions, and in general, the preferred product is indeed the one in which the favored product results from the union of the larger terminal coefficients of azide (the nucleophilic substituted terminus of azide in the HOMO-3 and the electrophilic unsubstituted terminus in the LUMO+2, see Figure 8) with the larger terminal coefficients in the complementary FMO of the dipolarophile. (9)

Figure 10

Figure 10. Orbital interaction diagrams for the cycloadditions between phenyl azide and selected dipolarophiles. We added orbital coefficients for the interacting orbitals. For phenyl azide, N1 is the nitrogen attached to the phenyl group, and N2 is the terminal-unsubstituted nitrogen. For dipolarophiles, C3 is the carbon attached to the substituent, and C4 is the terminal-unsubstituted carbon. In order to justify that HOMO-3 and LUMO+2 of phenyl azide are the effective orbitals involved in the orbital interactions between phenyl azide and dipolarophiles, we show the HOMO, HOMO-1, and HOMO-2 as well as the LUMO and LUMO+1 of phenyl azide in the upper left corner of Figure 10 for comparison.

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To achieve a more quantitative view, we performed a distortion/interaction-activation strain analysis (Figure 11) to explore the origins of regioselectivity of the 1,3-dipolar cycloadditions for the five asymmetrical alkenes in discussion. For R2, both the distortion and interaction energies determine the regioselectivity. TS2 is more asynchronous compared to TS2*. Therefore, it has lowered distortion energies for both azide and alkene. Additionally, there are more favorable interactions for TS2 due to the orbital interactions (the combination between the terminal with the larger HOMO coefficient of alkene and the terminal with the larger LUMO+2 coefficient of azide leads to more favorable orbital interaction), corresponding to a larger charge transfer (Table S2, entry 1). Thus, the cycloaddition occurs via TS2 with higher selectivity.

Figure 11

Figure 11. Distortion/interaction-activation strain (DIAS) analysis of the cycloaddition transition states to reveal the origins of regioselectivity. Free energies were calculated at the ωB97X-D/aug-cc-pVTZ-CPCM(solvent)//ωB97X-D/6-31+G(d,p)-CPCM(solvent) level of theory. Fragment distortion and interaction energies were calculated at the ωB97X-D level of theory with the aug-cc-pVTZ basis set, without the inclusion of solvation energy corrections (black, activation energies; blue, distortion energies of azide; green, distortion energies of dipolarophiles; red, interaction energies). Energies are in kcal/mol. The starred transition state is the regioisomeric transition state, which is unfavorable compared to the one without an asterisk.

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For R8, R9, and R15, it is the interaction energy that determines the regioselectivity. There are stronger interactions between phenyl azide and alkenes in the favorable transition states (TS8, TS9, and TS15) compared to unfavorable ones (TS8*, TS9*, and TS15*) due to orbital interactions, and correspondingly, more significant charge transfer occurs in favorable transition states (Table S2, entries 2–4). As for R17, it is the distortion of azide that determines the regioselectivity. TS17 has a smaller distortion energy of azide compared to TS17*. In terms of interaction energy, TS17* is more favorable than TS17 due to orbital interactions (Table S2, entry 5). However, the interaction energy contributes less to regioselectivity than the distortion energy. Therefore, the cycloaddition between phenyl azide and R17 occurs via TS17 selectively.
Based on the above analysis, we found that, in general, a combination of interaction energies and distortion energies parallels those interactions predicated by the FMO model, and the FMO models developed some time ago to rationalize and predict 1,3-dipolar cycloaddition regioselectivity are supported by this analysis. (9)

Conclusions

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As Sustmann showed in the 70s, the IP of dipolarophiles is a powerful indicator of reactivity. A low IP (high HOMO) indicates a very nucleophilic molecule, an electron-rich dipolarophile in our case, which reacts very rapidly with azide. A high IP suggests lowering of the HOMO (and LUMO at the same time); as the dipolarophile becomes more electrophilic, its reactivity with azide rises. We have also analyzed how the IP (minus of HOMO energy) relates to distortion, the FMO gap, closed-shell repulsions, and electrostatic and charge-transfer interactions. All of these are involved in controlling reactivity.
Distortion energies are related to the HOMO-LUMO gap of individual molecules through the “second-order Jahn–Teller effect”, which states that distortions are made easier by the mixing of the HOMO and LUMO of a molecule upon distortion; this becomes more effective when the HOMO-LUMO gap is small. (38) A donor raises the HOMO energy (low IP), generally more than it raises the LUMO, which leads to a small HOMO-LUMO gap. Alternatively, an electron acceptor lowers the HOMO energy (high IP), generally less than it lowers the LUMO, which also narrows the HOMO-LUMO gap. Thus, for the dipolarophiles with either low or high IPs, the HOMO-LUMO gaps are small and distortion energies are small, at the same time that they are reactive nucleophiles or electrophiles.
Fukui’s frontier molecular orbital theory based only on HOMO-LUMO interactions is very successful, despite the variety of interactions that influence reactivity. (39) The FMO gap is not only related to distortion energies but to electrostatic interactions as well. As orbital interactions increase, charge transfer increases, causing electrostatic interactions between the reactants to increase. Thus, the degree of electrostatic interactions is also related to charge transfer, which is the result primarily of FMO interactions.
Closed-shell repulsion is also related to FMO interactions. Strong HOMO-LUMO interactions between molecules are generally accompanied by low closed-shell repulsions between HOMOs of the two molecules. A reduction in closed-shell repulsion increases reactivity. (40) The primary example of this relationship is found in the orbital symmetry relationships. An orbital symmetry-allowed reaction has strong HOMO-LUMO interactions between reactants because the HOMO of one molecule has the same symmetry as the LUMO of the other. For such a case, the HOMOs of the two molecules have opposite symmetries and do not interact, and there is no destabilizing closed-shell repulsion between them. Donor and acceptor substituents polarize the HOMO and LUMO of molecules in opposite directions, so there is always an opposite relationship between stabilizing HOMO-LUMO and destabilizing HOMO-HOMO interactions.
This intimate relationship between the IPs of a series of molecules and the LUMO energies, HOMO-LUMO gaps in a molecule, and distortion, charge transfer, electrostatic, and closed-shell repulsion effects accounts for the ability of IP to be such a simple and valuable indicator of reactivity. As the power of analysis increases, we have learned the profound prescience of the Sustmann parabola.
Looking back from the 2021 perspective at Sustmann’s conclusion almost 50 years ago, we are struck by how insightful and influential they were for the organic community, despite the lack of computers of much consequence when he published the paper (at least a billion times less powerful than today’s computers). The real chemical reaction system is complex, and one parameter can never be quantitatively related to reactivity. Nevertheless, chemists appreciate models that give a qualitative guide to reactivity. Nowadays, armed with sophisticated methods of theoretical calculation and analysis, we can provide intimate and complicated details about mechanisms and reactivity. Nevertheless, we acknowledge and admire Sustmann’s insight that the IP of dipolarophiles is a good guide to reactivities of dipolarophiles toward ambiphilic azides.

Supporting Information

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The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.joc.1c00239.

  • Optimized geometries and energies of all computed species (PDF)

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Author Information

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  • Corresponding Authors
  • Authors
    • Pan-Pan Chen - Department of Chemistry and Biochemistry, University of California, Los Angeles, California 90095-1569, United States
    • Pengchen Ma - Department of Chemistry and Biochemistry, University of California, Los Angeles, California 90095-1569, United States
    • Xue He - College of Sciences, Nanjing Agricultural University, Nanjing 210095, China
    • Dennis Svatunek - Department of Chemistry and Biochemistry, University of California, Los Angeles, California 90095-1569, United States;  Orcidhttps://orcid.org/0000-0003-1101-2376
  • Author Contributions

    P.-P.C. and P.M. contributed equally to this manuscript.

  • Notes
    The authors declare no competing financial interest.

Acknowledgments

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We are grateful to the Natural Science Foundation of Jiangsu Province, China (BK20190505 to FL) and the National Science Foundation (CHE-1764328 to KNH) for financial support of this research. D.S. is grateful to the Austrian Science Funds (FWF, grant number J4216-N28) and the city of Vienna (H-331849/2018) for financial support. Calculations were performed on the IDRE Hoffman2 cluster at the University of California, Los Angeles, and the Vienna Scientific Cluster.

References

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This article references 40 other publications.

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    The transition states and activation barriers of the 1,3-dipolar cycloaddns. of azides with cycloalkynes and cycloalkenes were explored using B3LYP d. functional theory (DFT) and spin component scaled SCS-MP2 methods. A survey of benzyl azide cycloaddns. to substituted cyclooctynes (OMe, Cl, F, CN) showed that fluorine substitution has the most dramatic effect on reactivity. Azide cycloaddns. to 3-substituted cyclooctynes prefer 1,5-addn. regiochem. in the gas phase, but CPCM solvation abolishes the regioselectivity preference, in accord with expts. in soln. The activation energies for Ph azide addn. to cycloalkynes decrease considerably as the ring size is decreased (cyclononyne ΔG⧧ = 29.2 kcal/mol, cyclohexyne ΔG⧧ = 14.1 kcal/mol). The origin of this trend is explained by the distortion/interaction model. Cycloalkynes are predicted to be significantly more reactive dipolarophiles than cycloalkenes. The activation barriers for the cycloaddns. of Ph azide and picryl azide (2,4,6-trinitrophenyl azide) to five- through nine-membered cycloalkenes were also studied and compared to expt. Picryl azide has considerably lower activation barriers than Ph azide. Dissection of the transition state energies into distortion and interaction energies revealed that "strain-promoted" cycloalkyne and cycloalkene cycloaddn. transition states must still pay an energetic penalty to achieve their transition state geometries, and the differences in reactivity are more closely related to differences in distortion energies than the amt. of strain released in the product. Trans-cycloalkene dipolarophiles have much lower barriers than cis-cycloalkenes.
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    (d) Gordon, C. G.; Mackey, J. L.; Jewett, J. C.; Sletten, E. M.; Houk, K. N.; Bertozzi, C. R. Reactivity of Biarylazacyclooctynones in Copper-Free Click Chemistry. J. Am. Chem. Soc. 2012, 134, 9199– 9208,  DOI: 10.1021/ja3000936
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    10d
    Reactivity of Biarylazacyclooctynones in Copper-Free Click Chemistry
    Gordon, Chelsea G.; Mackey, Joel L.; Jewett, John C.; Sletten, Ellen M.; Houk, K. N.; Bertozzi, Carolyn R.
    Journal of the American Chemical Society (2012), 134 (22), 9199-9208CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
    The 1,3-dipolar cycloaddn. of cyclooctynes with azides, also called "copper-free click chem.", is a bioorthogonal reaction with widespread applications in biol. discovery. The kinetics of this reaction are of paramount importance for studies of dynamic processes, particularly in living subjects. Here we performed a systematic anal. of the effects of strain and electronics on the reactivity of cyclooctynes with azides through both exptl. measurements and computational studies using a d. functional theory (DFT) distortion/interaction transition state model. In particular, we focused on biarylazacyclooctynone (BARAC) because it reacts with azides faster than any other reported cyclooctyne and its modular synthesis facilitated rapid access to analogs. We found that substituents on BARAC's aryl rings can alter the calcd. transition state interaction energy of the cycloaddn. through electronic effects or the calcd. distortion energy through steric effects. Exptl. data confirmed that electronic perturbation of BARAC's aryl rings has a modest effect on reaction rate, whereas steric hindrance in the transition state can significantly retard the reaction. Drawing on these results, we analyzed the relationship between alkyne bond angles, which we detd. using X-ray crystallog., and reactivity, quantified by exptl. second-order rate consts., for a range of cyclooctynes. Our results suggest a correlation between decreased alkyne bond angle and increased cyclooctyne reactivity. Finally, we obtained structural and computational data that revealed the relationship between the conformation of BARAC's central lactam and compd. reactivity. Collectively, these results indicate that the distortion/interaction model combined with bond angle anal. will enable predictions of cyclooctyne reactivity and the rational design of new reagents for copper-free click chem.
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    (e) Bickelhaupt, F. M.; Houk, K. N. Analyzing Reaction Rates with the Distortion/Interaction-Activation Strain Model. Angew. Chem. Int. Ed. 2017, 56, 10070– 10086,  DOI: 10.1002/anie.201701486
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    10e
    Analyzing Reaction Rates with the Distortion/Interaction-Activation Strain Model
    Bickelhaupt, F. Matthias; Houk, Kendall N.
    Angewandte Chemie, International Edition (2017), 56 (34), 10070-10086CODEN: ACIEF5; ISSN:1433-7851. (Wiley-VCH Verlag GmbH & Co. KGaA)
    The activation strain or distortion/interaction model is a tool to analyze activation barriers that det. reaction rates. For bimol. reactions, the activation energies are the sum of the energies to distort the reactants into geometries they have in transition states plus the interaction energies between the two distorted mols. The energy required to distort the mols. is called the activation strain or distortion energy. This energy is the principal contributor to the activation barrier. The transition state occurs when this activation strain is overcome by the stabilizing interaction energy. Following the changes in these energies along the reaction coordinate gives insights into the factors controlling reactivity. This model has been applied to reactions of all types in both org. and inorg. chem., including substitutions and eliminations, cycloaddns., and several types of organometallic reactions.
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    (f) Hamlin, T. A.; Svatunek, D.; Yu, S.; Ridder, L.; Infante, I.; Visscher, L.; Bickelhaupt, F. M. Elucidating the Trends in Reactivity of Aza-1,3-Dipolar Cycloadditions. Eur. J. Org. Chem. 2019, 378– 386,  DOI: 10.1002/ejoc.201800572
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    10f
    Elucidating the Trends in Reactivity of Aza-1,3-Dipolar Cycloadditions
    Hamlin, Trevor A.; Svatunek, Dennis; Yu, Song; Ridder, Lars; Infante, Ivan; Visscher, Lucas; Bickelhaupt, F. Matthias
    European Journal of Organic Chemistry (2019), 2019 (2-3), 378-386CODEN: EJOCFK; ISSN:1099-0690. (Wiley-VCH Verlag GmbH & Co. KGaA)
    This report describes a d. functional theory investigation into the reactivities of a series of aza-1,3-dipoles with ethylene at the BP86/TZ2P level. A benchmark study was carried out using QMflows, a newly developed program for automated workflows of quantum chem. calcns. In total, 24 1,3-dipolar cycloaddn. (1,3-DCA) reactions were benchmarked using the highly accurate G3B3 method as a ref. We screened a no. of exchange and correlation functionals, including PBE, OLYP, BP86, BLYP, both with and without explicit dispersion corrections, to assess their accuracies and to det. which of these computationally efficient functionals performed the best for calcg. the energetics for cycloaddn. reactions. The BP86/TZ2P method produced the smallest errors for the activation and reaction enthalpies. Then, to understand the factors controlling the reactivity in these reactions, seven archetypal aza-1,3-dipolar cycloaddns. were investigated using the activation strain model and energy decompn. anal. Our investigations highlight the fact that differences in activation barrier for these 1,3-DCA reactions do not arise from differences in strain energy of the dipole, as previously proposed. Instead, relative reactivities originate from differences in interaction energy. Anal. of the 1,3-dipole-dipolarophile interactions reveals the reactivity trends primarily result from differences in the extent of the primary orbital interactions.
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  11. 11
    (a) Domingo, L. R. Molecular Electron Density Theory: A Modern View of Reactivity in Organic Chemistry. Molecules 2016, 21, 1319,  DOI: 10.3390/molecules21101319
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    11a
    Molecular electron density theory: a modern view of reactivity in organic chemistry
    Domingo, Luis R.
    Molecules (2016), 21 (10), 1319/1-1319/15CODEN: MOLEFW; ISSN:1420-3049. (MDPI AG)
    A review. A new theory for the study of the reactivity in Org. Chem., named Mol. Electron D. Theory (MEDT), is proposed herein. MEDT is based on the idea that while the electron d. distribution at the ground state is responsible for phys. and chem. mol. properties, as proposed by the D. Functional Theory (DFT), the capability for changes in electron d. is responsible for mol. reactivity. Within MEDT, the reactivity in Org. Chem. is studied through a rigorous quantum chem. anal. of the changes of the electron d. as well as the energies assocd. with these changes along the reaction path in order to understand exptl. outcomes. Studies performed using MEDT allow establishing a modern rationalisation and to gain insight into mol. mechanisms and reactivity in Org. Chem.
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    Applications to azide cycloadditions:

    (b) Ben El Ayouchia, H.; Lahoucine, B.; Anane, H.; Ríos-Gutiérrez, M.; Domingo, L. R.; Stiriba, S.-E. Experimental and Theoretical MEDT Study of the Thermal [3+2] Cycloaddition Reactions of Aryl Azides with Alkyne Derivatives. ChemistrySelect 2018, 3, 1215– 1223,  DOI: 10.1002/slct.201702588
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    11b
    Experimental and Theoretical MEDT Study of the Thermal [3+2] Cycloaddition Reactions of Aryl Azides with Alkyne Derivatives
    Ben El Ayouchia, Hicham; Lahoucine, Bahsis; Anane, Hafid; Rios-Gutierrez, Mar; Domingo, Luis R.; Stiriba, Salah-Eddine
    ChemistrySelect (2018), 3 (4), 1215-1223CODEN: CHEMUD; ISSN:2365-6549. (Wiley-VCH Verlag GmbH & Co. KGaA)
    The reactivity and regioselectivity of the [3+2] cycloaddn. (32CA) reactions of a series of 4-substituted-aryl azides/alkynes in toluene have been explored exptl. These 32CA reactions have been also studied within the Mol. Electron D. Theory (MEDT) using D. Functional Theory (DFT) calcns. at the B3LYP/6-31G(d) computational level. The computed activation energies, in gas phase and in toluene, show that the 1,5-regioisomeric channels are slightly favored kinetically as found exptl. The topol. anal. of the electron localization function (ELF) of some relevant points of the regioisomeric reaction paths shows that while the formation of the 1,4-diaryl triazoles takes place via a low asynchronous C-N bond formation process, the formation of the favored 1,5-diaryl triazoles takes place via a two-stage one-step mechanism, as the result of the attack of the most nucleophilic center of the aryl alkyne on the most electrocyclic center of aryl azide.
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    Domingo, L. R.; Acharjee, N. Unravelling the Strain-Promoted [3+2] Cycloadditi on Reactions of Phenyl Azide with Cycloalkynes from the Molecular Electron Density Theory Perspective. New J. Chem. 2020, 44, 13633-13643.

  12. 12
    Freindorf, M.; Sexton, T.; Kraka, E.; Cremer, D. The Mechanism of the Cycloaddition Reaction of 1,3-Dipole Molecules with Acetylene: An Investigation with the Unified Reaction Valley Approach. Theoret. Chem. Acc. 2014, 133, 1423,  DOI: 10.1007/s00214-013-1423-z
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  13. 13
    (a) Riplinger, C.; Neese, F. An Efficient and Near Linear Scaling Pair Natural Orbital Based Local Coupled Cluster Method. J. Chem. Phys. 2013, 138, 034106  DOI: 10.1063/1.4773581
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    13a
    An efficient and near linear scaling pair natural orbital based local coupled cluster method
    Riplinger, Christoph; Neese, Frank
    Journal of Chemical Physics (2013), 138 (3), 034106/1-034106/18CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
    In previous publications, it was shown that an efficient local coupled cluster method with single- and double excitations can be based on the concept of pair natural orbitals (PNOs) . The resulting local pair natural orbital-coupled-cluster single double (LPNO-CCSD) method has since been proven to be highly reliable and efficient. For large mols., the no. of amplitudes to be detd. is reduced by a factor of 105-106 relative to a canonical CCSD calcn. on the same system with the same basis set. In the original method, the PNOs were expanded in the set of canonical virtual orbitals and single excitations were not truncated. This led to a no. of fifth order scaling steps that eventually rendered the method computationally expensive for large mols. (e.g., >100 atoms). In the present work, these limitations are overcome by a complete redesign of the LPNO-CCSD method. The new method is based on the combination of the concepts of PNOs and projected AOs (PAOs). Thus, each PNO is expanded in a set of PAOs that in turn belong to a given electron pair specific domain. In this way, it is possible to fully exploit locality while maintaining the extremely high compactness of the original LPNO-CCSD wavefunction. No terms are dropped from the CCSD equations and domains are chosen conservatively. The correlation energy loss due to the domains remains below <0.05%, which implies typically 15-20 but occasionally up to 30 atoms per domain on av. The new method has been given the acronym DLPNO-CCSD ("domain based LPNO-CCSD"). The method is nearly linear scaling with respect to system size. The original LPNO-CCSD method had three adjustable truncation thresholds that were chosen conservatively and do not need to be changed for actual applications. In the present treatment, no addnl. truncation parameters have been introduced. Any addnl. truncation is performed on the basis of the three original thresholds. There are no real-space cutoffs. Single excitations are truncated using singles-specific natural orbitals. Pairs are prescreened according to a multipole expansion of a pair correlation energy est. based on local orbital specific virtual orbitals (LOSVs). Like its LPNO-CCSD predecessor, the method is completely of black box character and does not require any user adjustments. It is shown here that DLPNO-CCSD is as accurate as LPNO-CCSD while leading to computational savings exceeding one order of magnitude for larger systems. The largest calcns. reported here featured >8800 basis functions and >450 atoms. In all larger test calcns. done so far, the LPNO-CCSD step took less time than the preceding Hartree-Fock calcn., provided no approxns. have been introduced in the latter. Thus, based on the present development reliable CCSD calcns. on large mols. with unprecedented efficiency and accuracy are realized. (c) 2013 American Institute of Physics.
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    (b) Riplinger, C.; Sandhoefer, B.; Hansen, A.; Neese, F. Natural Triple Excitations in Local Coupled Cluster Calculations with Pair Natural Orbitals. J. Chem. Phys. 2013, 139, 134101,  DOI: 10.1063/1.4821834
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    13b
    Natural triple excitations in local coupled cluster calculations with pair natural orbitals
    Riplinger, Christoph; Sandhoefer, Barbara; Hansen, Andreas; Neese, Frank
    Journal of Chemical Physics (2013), 139 (13), 134101/1-134101/13CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
    In this work, the extension of the previously developed domain based local pair-natural orbital (DLPNO) based singles- and doubles coupled cluster (DLPNO-CCSD) method to perturbatively include connected triple excitations is reported. The development is based on the concept of triples-natural orbitals that span the joint space of the three pair natural orbital (PNO) spaces of the three electron pairs that are involved in the calcn. of a given triple-excitation contribution. The truncation error is very smooth and can be significantly reduced through extrapolation to the zero threshold. However, the extrapolation procedure does not improve relative energies. The overall computational effort of the method is asymptotically linear with the system size O(N). Actual linear scaling has been confirmed in test calcns. on alkane chains. The accuracy of the DLPNO-CCSD(T) approxn. relative to semicanonical CCSD(T0) is comparable to the previously developed DLPNO-CCSD method relative to canonical CCSD. Relative energies are predicted with an av. error of approx. 0.5 kcal/mol for a challenging test set of medium sized org. mols. The triples correction typically adds 30%-50% to the overall computation time. Thus, very large systems can be treated on the basis of the current implementation. In addn. to the linear C150H302 (452 atoms, >8800 basis functions) we demonstrate the first CCSD(T) level calcn. on an entire protein, Crambin with 644 atoms, and more than 6400 basis functions.
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    (c) Liakos, D. G.; Neese, F. Is It Possible To Obtain Coupled Cluster Quality Energies at near Density Functional Theory Cost? Domain-Based Local Pair Natural Orbital Coupled Cluster vs. Modern Density Functional Theory. J. Chem. Theory Comput. 2015, 11, 4054– 4063,  DOI: 10.1021/acs.jctc.5b00359
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    13c
    Is It Possible To Obtain Coupled Cluster Quality Energies at near Density Functional Theory Cost? Domain-Based Local Pair Natural Orbital Coupled Cluster vs Modern Density Functional Theory
    Liakos, Dimitrios G.; Neese, Frank
    Journal of Chemical Theory and Computation (2015), 11 (9), 4054-4063CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
    The recently developed domain-based local pair natural orbital coupled cluster theory with single, double, and perturbative triple excitations (DLPNO-CCSD(T)) delivers results that are closely approaching those of the parent canonical coupled cluster method at a small fraction of the computational cost. A recent extended benchmark study established that, depending on the three main truncation thresholds, it is possible to approach the canonical CCSD(T) results within 1 kJ (default setting, TightPNO), 1 kcal/mol (default setting, NormalPNO), and 2-3 kcal (default setting, LoosePNO). Although thresholds for calcns. with TightPNO are 2-4 times slower than those based on NormalPNO thresholds, they are still many orders of magnitude faster than canonical CCSD(T) calcns., even for small and medium sized mols. where there is little locality. The computational effort for the coupled cluster step scales nearly linearly with system size. Since, in many instances, the coupled cluster step in DLPNO-CCSD(T) is cheaper or at least not much more expensive than the preceding Hartree-Fock calcn., it is useful to compare the method against modern d. functional theory (DFT), which requires an effort comparable to that of Hartree-Fock theory (at least if Hartree-Fock exchange is part of the functional definition). Double hybrid d. functionals (DHDF's) even require a MP2-like step. The purpose of this article is to evaluate the cost vs accuracy ratio of DLPNO-CCSD(T) against modern DFT (including the PBE, B3LYP, M06-2X, B2PLYP, and B2GP-PLYP functionals and, where applicable, their van der Waals cor. counterparts). To eliminate any possible bias in favor of DLPNO-CCSD(T), we have chosen established benchmark sets that were specifically proposed for evaluating DFT functionals. It is demonstrated that DLPNO-CCSD(T) with any of the three default thresholds is more accurate than any of the DFT functionals. Furthermore, using the aug-cc-pVTZ basis set and the LoosePNO default settings, DLPNO-CCSD(T) is only about 1.2 times slower than B3LYP. With NormalPNO thresholds, DLPNO-CCSD(T) is about a factor of 2 slower than B3LYP and shows a mean abs. deviation of less than 1 kcal/mol to the ref. values for the four different data sets used. Our conclusion is that coupled cluster energies can indeed be obtained at near DFT cost.
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  14. 14
    (a) Breugst, M.; Huisgen, R.; Reissig, H.-U. Regioselective 1,3-Dipolar Cycloadditions of Diazoalkanes with Heteroatom-Substituted Alkynes: Theory and Experiment. Eur. J. Org. Chem. 2018, 2477– 2485,  DOI: 10.1002/ejoc.201800100
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    14a
    Regioselective 1,3-Dipolar Cycloadditions of Diazoalkanes with Heteroatom-Substituted Alkynes: Theory and Experiment
    Breugst, Martin; Huisgen, Rolf; Reissig, Hans-Ulrich
    European Journal of Organic Chemistry (2018), 2018 (20-21), 2477-2485CODEN: EJOCFK; ISSN:1099-0690. (Wiley-VCH Verlag GmbH & Co. KGaA)
    The 1,3-dipolar cycloaddns. of diazomethane and diazoethane with Me 3-(diethylamino)propiolate were investigated exptl. and computationally by employing d. functional theory (DFT). The expts. provided Me 3-(diethylamino)-pyrazole-4-carboxylates as the only isolated regioisomers. The constitution of these cycloadducts was secured by independent synthesis and decarboxylation to 3-(diethylamino)pyrazoles. The calcns. fully support the exptl. findings. For the preferred pathway of the diazomethane cycloaddn. with the alkyne, a kinetic preference of 9.6 kJ mol-1 was calcd. in Et2O soln. The computational anal. was extended to other alkynes, for instance to heteroatom-substituted alkynes such as ethoxyethyne and (ethylthio)ethyne. Again, the calcns. nicely explain the switch in regioselectivity of the 1,3-dipolar cycloaddns. of diazomethane with these two alkynes, which has been reported earlier by the group of Arens.
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    (b) Breugst, M.; Reissig, H.-U. The Huisgen Reaction: Milestones of the 1,3-Dipolar Cycloaddition. Angew. Chem. Int. Ed. 2020, 59, 12293– 12307,  DOI: 10.1002/anie.202003115
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    14b
    The Huisgen Reaction: Milestones of the 1,3-Dipolar Cycloaddition
    Breugst, Martin; Reissig, Hans-Ulrich
    Angewandte Chemie, International Edition (2020), 59 (30), 12293-12307CODEN: ACIEF5; ISSN:1433-7851. (Wiley-VCH Verlag GmbH & Co. KGaA)
    A review. The concept of 1,3-dipolar cycloaddns. was presented by Rolf Huisgen 60 years ago. Previously unknown reactive intermediates, for example azomethine ylides, were introduced to org. chem. and the (3+2) cycloaddns. of 1,3-dipoles to multiple-bond systems (Huisgen reaction) developed into one of the most versatile synthetic methods in heterocyclic chem. In this Review, the authors present the history of this research area, highlight important older reports, and describe the evolution and further development of the concept. The most important mechanistic and synthetic results are discussed. Quantum-mech. calcns. support the concerted mechanism always favored by R. Huisgen; however, in extreme cases intermediates may be involved. The impact of 1,3-dipolar cycloaddns. on the click chem. concept of K. B. Sharpless will also be discussed.
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  15. 15

    For some selected computational studies on the reactivity of azides in 1,3-dipolar cycloadditions, see:

    (a) Hamlin, T. A.; Levandowski, B. J.; Narsaria, A. K.; Houk, K. N.; Bickelhaupt, F. M. Structural Distortion of Cycloalkynes Influences Cycloaddition Rates both by Strain and Interaction Energies. Chem. Eur. J. 2019, 25, 6342– 6348,  DOI: 10.1002/chem.201900295
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    15a
    Structural Distortion of Cycloalkynes Influences Cycloaddition Rates both by Strain and Interaction Energies
    Hamlin, Trevor A.; Levandowski, Brian J.; Narsaria, Ayush K.; Houk, Kendall N.; Bickelhaupt, F. Matthias
    Chemistry - A European Journal (2019), 25 (25), 6342-6348CODEN: CEUJED; ISSN:0947-6539. (Wiley-VCH Verlag GmbH & Co. KGaA)
    The reactivities of 2-butyne, cycloheptyne, cyclooctyne, and cyclononyne in the 1,3-dipolar cycloaddn. reaction with Me azide were evaluated through DFT calcns. at the M06-2X/6-311++G(d)//M06-2X/6-31+G(d) level of theory. Computed activation free energies for the cycloaddns. of cycloalkynes are 16.5-22.0 kcal mol-1 lower in energy than that of the acyclic 2-butyne. The strained or predistorted nature of cycloalkynes is often solely used to rationalize this significant rate enhancement. Our distortion/interaction-activation strain anal. has been revealed that the degree of geometrical predistortion of the cycloalkyne ground-state geometries acts to enhance reactivity compared with that of acyclic alkynes through three distinct mechanisms, not only due to (i) a reduced strain or distortion energy, but also to (ii) a smaller HOMO-LUMO gap, and (iii) an enhanced orbital overlap, which both contribute to more stabilizing orbital interactions.
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    (b) Dommerholt, J.; van Rooijen, O.; Borrmann, A.; Fonseca Guerra, C.; Bickelhaupt, F. M.; van Delft, F. L. Highly Accelerated Inverse Electron-Demand Cycloaddition of Electron-Deficient Azides with Aliphatic Cyclooctynes. Nat. Commun. 2014, 5, 5378,  DOI: 10.1038/ncomms6378
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    15b
    Highly accelerated inverse electron-demand cycloaddition of electron-deficient azides with aliphatic cyclooctynes
    Dommerholt, Jan; van Rooijen, Olivia; Borrmann, Annika; Guerra, Celia Fonseca; Bickelhaupt, F. Matthias; van Delft, Floris L.
    Nature Communications (2014), 5 (), 5378CODEN: NCAOBW; ISSN:2041-1723. (Nature Publishing Group)
    Strain-promoted azide-alkyne cycloaddn. (SPAAC) as a conjugation tool has found broad application in material sciences, chem. biol. and even in vivo use. However, despite tremendous effort, SPAAC remains fairly slow (0.2-0.5 M-1 s-1) and efforts to increase reaction rates by tailoring of cyclooctyne structure have suffered from a poor trade-off between cyclooctyne reactivity and stability. We here wish to report tremendous acceleration of strain-promoted cycloaddn. of an aliph. cyclooctyne (bicyclo[6.1.0]non-4-yne, BCN) with electron-deficient aryl azides, with reaction rate consts. reaching 2.0-2.9 M-1 s-1. A remarkable difference in rate consts. of aliph. cyclooctynes vs. benzoannulated cyclooctynes is noted, enabling a next level of orthogonality by a judicious choice of azide-cyclooctyne combinations, which is inter alia applied in one-pot three-component protein labeling. The pivotal role of azide electronegativity is explained by d.-functional theory calcns. and electronic-structure analyses, which indicates an inverse electron-demand mechanism is operative with an aliph. cyclooctyne.
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    (c) Lopez, S. A.; Munk, M. E.; Houk, K. N. Mechanisms and Transition States of 1,3-Dipolar Cycloadditions of Phenyl Azide with Enamines: A Computational Analysis. J. Org. Chem. 2013, 78, 1576– 1582,  DOI: 10.1021/jo302695n
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    15c
    Mechanisms and Transition States of 1,3-Dipolar Cycloadditions of Phenyl Azide with Enamines: A Computational Analysis
    Lopez, Steven A.; Munk, Morton E.; Houk, K. N.
    Journal of Organic Chemistry (2013), 78 (4), 1576-1582CODEN: JOCEAH; ISSN:0022-3263. (American Chemical Society)
    The transition structures for the 1,3-dipolar cycloaddns. of Ph azide to enamines derived from acetophenone or phenylacetaldehyde and piperidine, morpholine, or pyrrolidine were located using quantum mech. methods. These cycloaddns. were studied exptl. in 1975 by Meilahn, Cox, and Munk (J. Org. Chem.1975, 40, 819-823). Calcns. were carried out with M06-2X/6-311+G(d,p), SCS-MP2/6-311+G(d,p)//M06-2X/6-311+G(d,p), and B97D/6-311+G(d,p) methods with the IEF-PCM solvation model for chloroform and ethanol. The distortion/interaction model was utilized to understand mechanisms, reactivities, and selectivities.
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    (d) Lopez, S. A.; Houk, K. N. Alkene Distortion Energies and Torsional Effects Control Reactivities, and Stereoselectivities of Azide Cycloadditions to Norbornene and Substituted Norbornenes. J. Org. Chem. 2013, 78, 1778– 1783,  DOI: 10.1021/jo301267b
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    15d
    Alkene Distortion Energies and Torsional Effects Control Reactivities, and Stereoselectivities of Azide Cycloadditions to Norbornene and Substituted Norbornenes
    Lopez, Steven A.; Houk, K. N.
    Journal of Organic Chemistry (2013), 78 (5), 1778-1783CODEN: JOCEAH; ISSN:0022-3263. (American Chemical Society)
    The transition structures for 1,3-dipolar cycloaddns. of Ph azide to norbornene derivs. were located with quantum mech. methods. Calcns. were carried out with M06-2X/6-311G(d,p) and SCS-MP2/6-311G(d,p)//M06-2X/6-311G(d,p) methods. The calcd. activation barriers strongly correlate with transition state distortion energies (ΔEd‡) but not with the reaction energies. Strain-promoted reactions are accelerated because it is easy to distort the strained reactants to a pyramidalized transition state geometry; a correlation of cycloaddn. rates with substrate distortion was found for the bicyclic and tricyclic alkenes studied here. The stereoselectivities of reactions of norbornene derivs. are controlled primarily by torsional effects that also influence alkene pyramidalization. These reactions are distortion-accelerated.
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  16. 16
    Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Petersson, G. A.; Nakatsuji, H.; Li, X.; Caricato, M.; Marenich, A. V.; Bloino, J.; Janesko, B. G.; Gomperts, R.; Mennucci, B.; Hratchian, H. P.; Ortiz, J. V.; Izmaylov, A. F.; Sonnenberg, J. L.; Williams; ; Ding, F.; Lipparini, F.; Egidi, F.; Goings, J.; Peng, B.; Petrone, A.; Henderson, T.; Ranasinghe, D.; Zakrzewski, V. G.; Gao, J.; Rega, N.; Zheng, G.; Liang, W.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Vreven, T.; Throssell, K.; Montgomery, J. A., Jr.; Peralta, J. E.; Ogliaro, F.; Bearpark, M. J.; Heyd, J. J.; Brothers, E. N.; Kudin, K. N.; Staroverov, V. N.; Keith, T. A.; Kobayashi, R.; Normand, J.; Raghavachari, K.; Rendell, A. P.; Burant, J. C.; Iyengar, S. S.; Tomasi, J.; Cossi, M.; Millam, J. M.; Klene, M.; Adamo, C.; Cammi, R.; Ochterski, J. W.; Martin, R. L.; Morokuma, K.; Farkas, O.; Foresman, J. B.; Fox, D. J. Gaussian 16, Rev. A.03, Wallingford, CT, 2016.
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    Chai, J.-D.; Head-Gordon, M. Long-Range Corrected Hybrid Density Functionals with Damped Atom–Atom Dispersion Corrections. Phys. Chem. Chem. Phys. 2008, 10, 6615– 6620,  DOI: 10.1039/b810189b
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    Long-range corrected hybrid density functionals with damped atom-atom dispersion corrections
    Chai, Jeng-Da; Head-Gordon, Martin
    Physical Chemistry Chemical Physics (2008), 10 (44), 6615-6620CODEN: PPCPFQ; ISSN:1463-9076. (Royal Society of Chemistry)
    We report re-optimization of a recently proposed long-range cor. (LC) hybrid d. functional [J.-D. Chai and M. Head-Gordon, J. Chem. Phys., 2008, 128, 084106] to include empirical atom-atom dispersion corrections. The resulting functional, ωB97X-D yields satisfactory accuracy for thermochem., kinetics, and non-covalent interactions. Tests show that for non-covalent systems, ωB97X-D shows slight improvement over other empirical dispersion-cor. d. functionals, while for covalent systems and kinetics it performs noticeably better. Relative to our previous functionals, such as ωB97X, the new functional is significantly superior for non-bonded interactions, and very similar in performance for bonded interactions.
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    (a) Grimme, S. Semiempirical Hybrid Density Functional with Perturbative Second-order Correlation. J. Chem. Phys. 2006, 124, 034108  DOI: 10.1063/1.2148954
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    18a
    Semiempirical hybrid density functional with perturbative second-order correlation
    Grimme, Stefan
    Journal of Chemical Physics (2006), 124 (3), 034108/1-034108/16CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
    A new hybrid d. functional for general chem. applications is proposed. It is based on a mixing of std. generalized gradient approxns. (GGAs) for exchange by Becke (B) and for correlation by Lee, Yang, and Parr (LYP) with Hartree-Fock (HF) exchange and a perturbative second-order correlation part (PT2) that is obtained from the Kohn-Sham (GGA) orbitals and eigenvalues. This virtual orbital-dependent functional contains only two global parameters that describe the mixt. of HF and GGA exchange (ax) and of the PT2 and GGA correlation (c), resp. The parameters are obtained in a least-squares-fit procedure to the G2/97 set of heat of formations. Opposed to conventional hybrid functionals, the optimum ax is found to be quite large (53% with c = 27%) which at least in part explains the success for many problematic mol. systems compared to conventional approaches. The performance of the new functional termed B2-PLYP is assessed by the G2/97 std. benchmark set, a second test suite of atoms, mols., and reactions that are considered as electronically very difficult (including transition-metal compds., weakly bonded complexes, and reaction barriers) and comparisons with other hybrid functionals of GGA and meta-GGA types. According to many realistic tests, B2-PLYP can be regarded as the best general purpose d. functional for mols. (e.g., a mean abs. deviation for the two test sets of only 1.8 and 3.2 kcal/mol compared to about 3 and 5 kcal/mol, resp., for the best other d. functionals). Very importantly, also the max. and minium errors (outliers) are strongly reduced (by about 10-20 kcal/mol). Furthermore, very good results are obtained for transition state barriers but unlike previous attempts at such a good description, this definitely comes not at the expense of equil. properties. Preliminary calcns. of the equil. bond lengths and harmonic vibrational frequencies for diat. mols. and transition-metal complexes also show very promising results. The uniformity with which B2-PLYP improves for a wide range of chem. systems emphasizes the need of (virtual) orbital-dependent terms that describe nonlocal electron correlation in accurate exchange-correlation functionals. From a practical point of view, the new functional seems to be very robust and it is thus suggested as an efficient quantum chem. method of general purpose.
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    (b) Grimme, S. Semiempirical GGA-Type Density Functional Constructed with A Long-Range Dispersion Correction. J. Comput. Chem. 2006, 27, 1787– 1799,  DOI: 10.1002/jcc.20495
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    18b
    Semiempirical GGA-type density functional constructed with a long-range dispersion correction
    Grimme, Stefan
    Journal of Computational Chemistry (2006), 27 (15), 1787-1799CODEN: JCCHDD; ISSN:0192-8651. (John Wiley & Sons, Inc.)
    A new d. functional (DF) of the generalized gradient approxn. (GGA) type for general chem. applications termed B97-D is proposed. It is based on Becke's power-series ansatz from 1997 and is explicitly parameterized by including damped atom-pairwise dispersion corrections of the form C6·R-6. A general computational scheme for the parameters used in this correction has been established and parameters for elements up to xenon and a scaling factor for the dispersion part for several common d. functionals (BLYP, PBE, TPSS, B3LYP) are reported. The new functional is tested in comparison with other GGAs and the B3LYP hybrid functional on std. thermochem. benchmark sets, for 40 noncovalently bound complexes, including large stacked arom. mols. and group II element clusters, and for the computation of mol. geometries. Further cross-validation tests were performed for organometallic reactions and other difficult problems for std. functionals. In summary, it is found that B97-D belongs to one of the most accurate general purpose GGAs, reaching, for example for the G97/2 set of heat of formations, a mean abs. deviation of only 3.8 kcal mol-1. The performance for noncovalently bound systems including many pure van der Waals complexes is exceptionally good, reaching on the av. CCSD(T) accuracy. The basic strategy in the development to restrict the d. functional description to shorter electron correlation lengths scales and to describe situations with medium to large interat. distances by damped C6·R-6 terms seems to be very successful, as demonstrated for some notoriously difficult reactions. As an example, for the isomerization of larger branched to linear alkanes, B97-D is the only DF available that yields the right sign for the energy difference. From a practical point of view, the new functional seems to be quite robust and it is thus suggested as an efficient and accurate quantum chem. method for large systems where dispersion forces are of general importance.
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    (a) Dunning, T. H. Gaussian-Basis Sets for Use in Correlated Molecular Calculations. I. The Atoms Boron through Neon and Hydrogen. J. Chem. Phys. 1989, 90, 1007– 1023,  DOI: 10.1063/1.456153
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    Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogen
    Dunning, Thom H., Jr.
    Journal of Chemical Physics (1989), 90 (2), 1007-23CODEN: JCPSA6; ISSN:0021-9606.
    Guided by the calcns. on oxygen in the literature, basis sets for use in correlated at. and mol. calcns. were developed for all of the first row atoms from boron through neon, and for hydrogen. As in the oxygen atom calcns., the incremental energy lowerings, due to the addn. of correlating functions, fall into distinct groups. This leads to the concept of correlation-consistent basis sets, i.e., sets which include all functions in a given group as well as all functions in any higher groups. Correlation-consistent sets are given for all of the atoms considered. The most accurate sets detd. in this way, [5s4p3d2f1g], consistently yield 99% of the correlation energy obtained with the corresponding at.-natural-orbital sets, even though the latter contains 50% more primitive functions and twice as many primitive polarization functions. It is estd. that this set yields 94-97% of the total (HF + 1 + 2) correlation energy for the atoms neon through boron.
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    (b) Kendall, R. A.; Dunning Jr, T. H.; Harrison, R. J. Electron Affinities of the First-Row Atoms Revisited. Systematic Basis Sets and Wave Functions. J. Chem. Phys. 1992, 96, 6796– 6806,  DOI: 10.1063/1.462569
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    Electron affinities of the first-row atoms revisited. Systematic basis sets and wave functions
    Kendall, Rick A.; Dunning, Thom H., Jr.; Harrison, Robert J.
    Journal of Chemical Physics (1992), 96 (9), 6796-806CODEN: JCPSA6; ISSN:0021-9606.
    The authors describe a reliable procedure for calcg. the electron affinity of an atom and present results for H, B, C, O, and F (H is included for completeness). This procedure involves the use of the recently proposed correlation-consistent basis sets augmented with functions to describe the more diffuse character of the at. anion coupled with a straightforward, uniform expansion of the ref. space for multireference singles and doubles configuration-interaction (MRSD-CI) calcns. A comparison is given with previous results and with corresponding full CI calcns. The most accurate EAs obtained from the MRSD-CI calcns. are (with exptl. values in parentheses): H 0.740 eV (0.754), B 0.258 (0.277), C 1.245 (1.263), O 1.384 (1.461), and F 3.337 (3.401). The EAs obtained from the MR-SDCI calcns. differ by less than 0.03 eV from those predicted by the full CI calcns.
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    Cossi, M.; Rega, N.; Scalmani, G.; Barone, V. Energies, Structures, and Electronic Properties of Molecules in Solution with the C-PCM Solvation Model. J. Comput. Chem. 2003, 24, 669– 681,  DOI: 10.1002/jcc.10189
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    Energies, structures, and electronic properties of molecules in solution with the C-PCM solvation model
    Cossi, Maurizio; Rega, Nadia; Scalmani, Giovanni; Barone, Vincenzo
    Journal of Computational Chemistry (2003), 24 (6), 669-681CODEN: JCCHDD; ISSN:0192-8651. (John Wiley & Sons, Inc.)
    The conductor-like solvation model, as developed in the framework of the polarizable continuum model (PCM), has been reformulated and newly implemented in order to compute energies, geometric structures, harmonic frequencies, and electronic properties in soln. for any chem. system that can be studied in vacuo. Particular attention is devoted to large systems requiring suitable iterative algorithms to compute the solvation charges: the fast multipole method (FMM) has been extensively used to ensure a linear scaling of the computational times with the size of the solute. A no. of test applications are presented to evaluate the performances of the method.
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    (a) Lu, T.; Chen, F. Multiwfn: A Multifunctional Wavefunction Analyzer. J. Comput. Chem. 2012, 33, 580– 592,  DOI: 10.1002/jcc.22885
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    Multiwfn: A multifunctional wavefunction analyzer
    Lu, Tian; Chen, Feiwu
    Journal of Computational Chemistry (2012), 33 (5), 580-592CODEN: JCCHDD; ISSN:0192-8651. (John Wiley & Sons, Inc.)
    Multiwfn is a multifunctional program for wavefunction anal. Its main functions are: (1) Calcg. and visualizing real space function, such as electrostatic potential and electron localization function at point, in a line, in a plane or in a spatial scope. (2) Population anal. (3) Bond order anal. (4) Orbital compn. anal. (5) Plot d.-of-states and spectrum. (6) Topol. anal. for electron d. Some other useful utilities involved in quantum chem. studies are also provided. The built-in graph module enables the results of wavefunction anal. to be plotted directly or exported to high-quality graphic file. The program interface is very user-friendly and suitable for both research and teaching purpose. The code of Multiwfn is substantially optimized and parallelized. Its efficiency is demonstrated to be significantly higher than related programs with the same functions. Five practical examples involving a wide variety of systems and anal. methods are given to illustrate the usefulness of Multiwfn. The program is free of charge and open-source. Its precompiled file and source codes are available from http://multiwfn.codeplex.com. © 2011 Wiley Periodicals, Inc. J Comput Chem, 2011.
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    (b) Lu, T.; Chen, F. Quantitative Analysis of Molecular Surface Based on Improved Marching Tetrahedra Algorithm. J. Mol. Graphics Model. 2012, 38, 314– 323,  DOI: 10.1016/j.jmgm.2012.07.004
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    Quantitative analysis of molecular surface based on improved Marching Tetrahedra algorithm
    Lu, Tian; Chen, Feiwu
    Journal of Molecular Graphics & Modelling (2012), 38 (), 314-323CODEN: JMGMFI; ISSN:1093-3263. (Elsevier Ltd.)
    Quant. anal. of mol. surface is a valuable technique for analyzing non-covalent interaction, studying mol. recognition mode, predicting reactive site and reactivity. An efficient way to realize the anal. was first proposed by Bulat et al. (J. Mol. Model., 16, 1679), in which Marching Tetrahedra (MT) approach commonly used in computer graphics is employed to generate vertices on mol. surface. However, it has been found that the computations of the electrostatic potential in the MT vertices are very expensive and some artificial surface extremes will be presented due to the uneven distribution of MT vertices. In this article, we propose a simple and reliable method to eliminate these unreasonably distributed surface vertices generated in the original MT. This treatment can save more than 60% of total anal. time of electrostatic potential, yet the loss in accuracy is almost negligible. The artificial surface extremes are also largely avoided as a byproduct of this algorithm. In addn., the bisection iteration procedure has been exploited to improve accuracy of linear interpolation in MT. The most appropriate grid spacing for surface anal. has also been investigated. 0.25 and 0.20 bohr are recommended to be used for surface anal. of electrostatic potential and av. local ionization energy, resp.
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    Humphrey, W.; Dalke, A.; Schulten, K. VMD: Visual Molecular Dynamics. J. Mol. Graphics. 1996, 14, 33– 38,  DOI: 10.1016/0263-7855(96)00018-5
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    VDM: visual molecular dynamics
    Humphrey, William; Dalke, Andrew; Schulten, Klaus
    Journal of Molecular Graphics (1996), 14 (1), 33-8, plates, 27-28CODEN: JMGRDV; ISSN:0263-7855. (Elsevier)
    VMD is a mol. graphics program designed for the display and anal. of mol. assemblies, in particular, biopolymers such as proteins and nucleic acids. VMD can simultaneously display any no. of structures using a wide variety of rendering styles and coloring methods. Mols. are displayed as one or more "representations," in which each representation embodies a particular rendering method and coloring scheme for a selected subset of atoms. The atoms displayed in each representation are chosen using an extensive atom selection syntax, which includes Boolean operators and regular expressions. VMD provides a complete graphical user interface for program control, as well as a text interface using the Tcl embeddable parser to allow for complex scripts with variable substitution, control loops, and function calls. Full session logging is supported, which produces a VMD command script for later playback. High-resoln. raster images of displayed mols. may be produced by generating input scripts for use by a no. of photorealistic image-rendering applications. VMD has also been expressly designed with the ability to animate mol. dynamics (MD) simulation trajectories, imported either from files or from a direct connection to a running MD simulation. VMD is the visualization component of MDScope, a set of tools for interactive problem solving in structural biol., which also includes the parallel MD program NAMD, and the MDCOMM software used to connect the visualization and simulation programs, VMD is written in C++, using an object-oriented design; the program, including source code and extensive documentation, is freely available via anonymous ftp and through the World Wide Web.
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    VMD Official website. http://www.ks.uiuc.edu/Research/ vmd/.

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    Svatunek, D.; Houk, K. N. autoDIAS: A Python Tool for an Automated Distortion/Interaction Activation Strain Analysis. J. Comput. Chem. 2019, 40, 2509– 2515,  DOI: 10.1002/jcc.26023
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    autoDIAS: a python tool for an automated distortion/interaction activation strain analysis
    Svatunek, Dennis; Houk, Kendall N.
    Journal of Computational Chemistry (2019), 40 (28), 2509-2515CODEN: JCCHDD; ISSN:0192-8651. (John Wiley & Sons, Inc.)
    The distortion/interaction activation strain (DIAS) anal. is a powerful tool for the investigation of energy barriers. However, setup and data anal. of such a calcn. can be cumbersome and requires lengthy intervention of the user. We present autoDIAS, a python tool for the automated setup, performance, and data extn. of the DIAS anal., including automated detection of fragments and relevant geometric parameters. © 2019 Wiley Periodicals, Inc.
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    te Velde, G.; Bickelhaupt, F. M.; Baerends, E. J.; Fonseca Guerra, C.; van Gisbergen, S. J. A.; Snijders, J. G.; Ziegler, T. Chemistry with ADF. J. Comput. Chem. 2001, 22, 931– 967,  DOI: 10.1002/jcc.1056
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    Chemistry with ADF
    Te Velde, G.; Bickelhaupt, F. M.; Baerends, E. J.; Fonseca Guerra, C.; Van Gisbergen, S. J. A.; Snijders, J. G.; Ziegler, T.
    Journal of Computational Chemistry (2001), 22 (9), 931-967CODEN: JCCHDD; ISSN:0192-8651. (John Wiley & Sons, Inc.)
    A review with 241 refs. We present the theor. and tech. foundations of the Amsterdam D. Functional (ADF) program with a survey of the characteristics of the code (numerical integration, d. fitting for the Coulomb potential, and STO basis functions). Recent developments enhance the efficiency of ADF (e.g., parallelization, near order-N scaling, QM/MM) and its functionality (e.g., NMR chem. shifts, COSMO solvent effects, ZORA relativistic method, excitation energies, frequency-dependent (hyper)polarizabilities, at. VDD charges). In the Applications section we discuss the phys. model of the electronic structure and the chem. bond, i.e., the Kohn-Sham MO (MO) theory, and illustrate the power of the Kohn-Sham MO model in conjunction with the ADF-typical fragment approach to quant. understand and predict chem. phenomena. We review the "Activation-strain TS interaction" (ATS) model of chem. reactivity as a conceptual framework for understanding how activation barriers of various types of (competing) reaction mechanisms arise and how they may be controlled, for example, in org. chem. or homogeneous catalysis. Finally, we include a brief discussion of exemplary applications in the field of biochem. (structure and bonding of DNA) and of time-dependent d. functional theory (TDDFT) to indicate how this development further reinforces the ADF tools for the anal. of chem. phenomena.
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    Baerends, E. J.; Ellis, D. E.; Ros, P. Self-Consistent Molecular Hartree-Fock-Slater Calculations I. The Computational Procedure. Chem. Phys. 1973, 2, 41– 51,  DOI: 10.1016/0301-0104(73)80059-X
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    Self-consistent molecular Hartree-Fock-Slater calculations. I. Computational procedure
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    Chemical Physics (1973), 2 (1), 41-51CODEN: CMPHC2; ISSN:0301-0104.
    A numerical-variational computational scheme is presented for making SCF-LCAO-MO calcns. with the Hartree-Fock-Slater model (e.g., J. C. Slater and K. H. Johnson, 1972). The local exchange approxn. is used, but the usual muffin-tin approxn. for the potentials or ds. (e.g., J. and F. C. Smith Jr., 1972) is avoided. Procedures are given that are specifically optimized for treating large systems such as transition-metal complexes. Illustrative calcns. are given of the electronic structure of mol. CO, and the bond lengths of LiF, NO, N2, O2, and C2H4. The 1-electron energies and the charge distributions can be calcd. rapidly, whereas the total energies, and therefore the optimized mol. geometries, require more computation time.
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    Sun, X.; Soini, T. M.; Poater, J.; Hamlin, T. A.; Bickelhaupt, F. M. PyFrag 2019-Automating the Exploration and Analysis of Reaction Mechanisms. J. Comput. Chem. 2019, 40, 2227– 2233,  DOI: 10.1002/jcc.25871
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    PyFrag 2019-Automating the exploration and analysis of reaction mechanisms
    Sun, Xiaobo; Soini, Thomas M.; Poater, Jordi; Hamlin, Trevor A.; Bickelhaupt, F. Matthias
    Journal of Computational Chemistry (2019), 40 (25), 2227-2233CODEN: JCCHDD; ISSN:0192-8651. (John Wiley & Sons, Inc.)
    We present a substantial update to the PyFrag 2008 program, which was originally designed to perform a fragment-based activation strain anal. along a provided potential energy surface. The original PyFrag 2008 workflow facilitated the characterization of reaction mechanisms in terms of the intrinsic properties, such as strain and interaction, of the reactants. The new PyFrag 2019 program has automated and reduced the time-consuming and laborious task of setting up, running, analyzing, and visualizing computational data from reaction mechanism studies to a single job. PyFrag 2019 resolves three main challenges assocd. with the automated computational exploration of reaction mechanisms: it (1) computes the reaction path by carrying out multiple parallel calcns. using initial coordinates provided by the user; (2) monitors the entire workflow process; and (3) tabulates and visualizes the final data in a clear way. The activation strain and canonical energy decompn. results that are generated relate the characteristics of the reaction profile in terms of intrinsic properties (strain, interaction, orbital overlaps, orbital energies, populations) of the reactant species.
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  27. 27
    (a) Foster, J. P.; Weinhold, F. Natural Hybrid Orbitals. J. Am. Chem. Soc. 1980, 102, 7211– 7218,  DOI: 10.1021/ja00544a007
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    27a
    Natural hybrid orbitals
    Foster, J. P.; Weinhold, F.
    Journal of the American Chemical Society (1980), 102 (24), 7211-18CODEN: JACSAT; ISSN:0002-7863.
    From the information contained in the (exact or approx.) 1st-order d. matrix, a method is described for extg. a unique set of at. hybrids and bond orbitals for a given mol., thereby constructing its Lewis structure in an a priori manner. The natural hybrids are optimal in a certain sense, they are efficiently computed, and agree with chem. intuition (as summarized, for example, in H. A. Bent's Rule (1961) and with hybrids obtained by other procedures). By using simple INDO-SCF-MO wave functions, applications are given of the natural hybrid orbital anal. to mols. exhibiting a variety of bonding features, including lone pairs, multiple bonds, strained rings and bent bonds, multiple resonance structures, H-bonds, and 3-center bonds. Three examples are given: (1) orbital following during NH3 umbrella inversion, (2) dimerization of water mols., and (3) the H-bridged bonds of diborane.
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    (b) Reed, A. E.; Weinstock, R. B.; Weinhold, F. Natural Population Analysis. J. Chem. Phys. 1985, 83, 735– 746,  DOI: 10.1063/1.449486
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    27b
    Natural population analysis
    Reed, Alan E.; Weinstock, Robert B.; Weinhold, Frank
    Journal of Chemical Physics (1985), 83 (2), 735-46CODEN: JCPSA6; ISSN:0021-9606.
    A method of "natural population anal." was developed to calc. at. charges and orbital populations of mol. wave functions in general AO basis sets. The natural anal. is an alternative to the conventional Mulliken population anal., and seems to exhibit improved numerical stability, and to describe better the electron distribution in compds. of high ionic character, such as those contg. metal atoms. Ab-initio SCF-MO wave functions were calcd. for compds. of type CH3X and LiX (X = F, OH, NH2, CH3, BH2, BeH, Li, H) in a variety of basis sets to illustrate the generality of the method, and to compare the natural populations with results of Mulliken anal., d. integration, and empirical measures of ionic character. Natural populations gave a satisfactory description of these mols., and provided a unified treatment of covalent and extreme ionic limits at modest computational cost.
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  28. 28
    Legault, C. Y. CYLview; version 1.0b; Université de Sherbrooke: 2009 (http://www.cylview.org).
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  29. 29
    We calculated the rate constants from the activation barriers based on Eyring Equation, which follows from the transition state theory, also known as activated-complex theory.
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  30. 30
    Huisgen, R.; Szeimie, G.; Möbius, L. 1.3-Dipolare Cycloadditionen, XXXII. Kinetik der Additionen organischer Azide an CC-Mehrfachbindungen. Chem. Ber. 1967, 100, 2494– 2507,  DOI: 10.1002/cber.19671000806
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    30
    1,3-Dipolar cycloadditions. XXXII. Kinetics of the addition of organic azides to carbon-carbon multiple bonds
    Huisgen, Rolf; Szeimies, Guenter; Moebius, Leander
    Chemische Berichte (1967), 100 (8), 2494-507CODEN: CHBEAM; ISSN:0009-2940.
    cf. preceding abstr. The ir spectrophotometrically-detd. addn. consts. of phenyl azide to 27 olefinic and 4 acetylenic dipolarophiles at 25° are of the 107 order of magnitude. The interaction between electronic and steric substitution effects on the dipolarophiles is discussed. The addn. rates of the ring-substituted phenyl azides obeyed the Hammett equation; the ρ values depended on the dipolarophile, and are as follows: maleic anhydride -1.1, N-phenylmaleimide -0.8, norbornene 0.88, cyclopentene 0.9, 1-pyrrolidinocyclohexene 2.5. The activation entropies for cycloaddn. of the 4 azides are -26 to -36 cal./mole degree. The addn. const. of phenyl azide to pyrrolidinocyclopentane depends only slightly on the polarity of the solvent. The cycloaddn. of azides seems to be a multicenter reaction.
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  31. 31
    Koopmans, T. Über die Zuordnung von Wellenfunktionen und Eigenwerten zu den einzelnen Elektronen eines Atoms. Physica. 1934, 1, 104– 113,  DOI: 10.1016/S0031-8914(34)90011-2
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  32. 32

    The exact dipolarophile used in the experiment is 1-ethoxycyclopentene. (30) In the calculation, 1-methoxycyclopentene is substituted for 1-ethoxycyclopentene in order to simplify the calculation model.

    There is no corresponding record for this reference.
  33. 33
    Liu, F.; Liang, Y.; Houk, K. N. Theoretical Elucidation of the Origins of Substituent and Strain Effects on the Rates of Diels–Alder Reactions of 1,2,4,5-Tetrazines. J. Am. Chem. Soc. 2014, 136, 11483– 11493,  DOI: 10.1021/ja505569a
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    33
    Theoretical Elucidation of the Origins of Substituent and Strain Effects on the Rates of Diels-Alder Reactions of 1,2,4,5-Tetrazines
    Liu, Fang; Liang, Yong; Houk, K. N.
    Journal of the American Chemical Society (2014), 136 (32), 11483-11493CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
    The Diels-Alder reactions of seven 1,2,4,5-tetrazines with unstrained and strained alkenes and alkynes were studied with quantum mech. calcns. (M06-2X d. functional theory) and analyzed with the distortion/interaction model. The higher reactivities of alkenes compared to alkynes in the Diels-Alder reactions with tetrazines arise from the differences in both interaction and distortion energies. Alkenes have HOMO energies higher than those of alkynes and therefore stronger interaction energies in inverse-electron-demand Diels-Alder reactions with tetrazines. We have also found that the energies to distort alkenes into the Diels-Alder transition-state geometries are smaller than for alkynes in these reactions. The strained dienophiles, trans-cyclooctene and cyclooctyne, are much more reactive than unstrained trans-2-butene and 2-butyne, because they are predistorted toward the Diels-Alder transition structures. The reactivities of substituted tetrazines correlate with the electron-withdrawing abilities of the substituents. Electron-withdrawing groups lower the LUMO+1 of tetrazines, resulting in stronger interactions with the HOMO of dienophiles. Moreover, electron-withdrawing substituents destabilize the tetrazines, and this leads to smaller distortion energies in the Diels-Alder transition states.
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  34. 34
    (a) Agard, N. J.; Prescher, J. A.; Bertozzi, C. R. A Strain-Promoted [3 + 2] Azide–Alkyne Cycloaddition for Covalent Modification of Biomolecules in Living Systems. J. Am. Chem. Soc. 2004, 126, 15046– 15047,  DOI: 10.1021/ja044996f
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    34a
    A strain-promoted [3+2] azide-alkyne cycloaddition for covalent modification of biomolecules in living systems
    Agard, Nicholas J.; Prescher, Jennifer A.; Bertozzi, Carolyn R.
    Journal of the American Chemical Society (2004), 126 (46), 15046-15047CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
    Selective chem. reactions that are orthogonal to the diverse functionality of biol. systems have become important tools in the field of chem. biol. Two notable examples are the Staudinger ligation of azides and phosphines and the Cu(I)-catalyzed [3+2] cycloaddn. of azides and alkynes ("click chem."). The Staudinger ligation has sufficient biocompatibility for performance in living animals but suffers from phosphine oxidn. and synthetic challenges. Click chem. obviates the requirement of phosphines, but the Cu(I) catalyst is toxic to cells, thereby precluding in vivo applications. Here we present a strain-promoted [3+2] cycloaddn. between cyclooctynes and azides that proceeds under physiol. conditions without the need for a catalyst. The utility of the reaction was demonstrated by selective modification of biomols. in vitro and on living cells, with no apparent toxicity.
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    (b) Lutz, J.-F. Copper-Free Azide–Alkyne Cycloadditions: New Insights and Perspectives. Angew. Chem., Int. Ed. 2008, 47, 2182– 2184,  DOI: 10.1002/anie.200705365
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    34b
    Copper-free azide-alkyne cycloadditions: new insights and perspectives
    Lutz, Jean-Francois
    Angewandte Chemie, International Edition (2008), 47 (12), 2182-2184CODEN: ACIEF5; ISSN:1433-7851. (Wiley-VCH Verlag GmbH & Co. KGaA)
    A review. Copper-mediated azide-alkyne "click" cycloaddns. (CuAAC) play a central role in contemporary synthetic chem. but rely on transition-metal catalysts, which hamper their adoption in some biol. applications. Recently, the strain-promoted and fluorine-activated cycloaddn. of cyclooctynes and org. azides was proposed as an interesting metal-free alternative to CuAAC.
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    (c) Ning, X.; Guo, J.; Wolfert, M. A.; Boons, G.-J. Visualizing Metabolically Labeled Glycoconjugates of Living Cells by Copper-Free and Fast Huisgen Cycloadditions. Angew. Chem., Int. Ed. 2008, 47, 2253– 2255,  DOI: 10.1002/anie.200705456
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    34c
    Visualizing metabolically labeled glycoconjugates of living cells by copper-free and fast huisgen cycloadditions
    Ning, Xinghai; Guo, Jun; Wolfert, Margreet A.; Boons, Geert-Jan
    Angewandte Chemie, International Edition (2008), 47 (12), 2253-2255CODEN: ACIEF5; ISSN:1433-7851. (Wiley-VCH Verlag GmbH & Co. KGaA)
    4-Dibenzocyclooctynol reacts, in the absence of a CuI catalyst, exceptionally fast with azido-contg. saccharides and amino acids to give stable triazoles. A biotin-modified deriv. is ideally suited for visualizing and tracking glycoconjugates of living cells that are metabolically labeled with azido-contg. monosaccharides.
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    (d) Patterson, D. M.; Nazarova, L. A.; Xie, B.; Kamber, D. N.; Prescher, J. A. Functionalized Cyclopropenes as Bioorthogonal Chemical Reporters. J. Am. Chem. Soc. 2012, 134, 18638– 18643,  DOI: 10.1021/ja3060436
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    34d
    Functionalized Cyclopropenes as Bioorthogonal Chemical Reporters
    Patterson, David M.; Nazarova, Lidia A.; Xie, Bryan; Kamber, David N.; Prescher, Jennifer A.
    Journal of the American Chemical Society (2012), 134 (45), 18638-18643CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
    Chem. reporters are unique functional groups that can be used to label biomols. in living systems. Only a handful of broadly applicable reporters have been identified to date, owing to the rigorous demands placed on these functional groups in biol. settings. We describe here a new chem. reporter-cyclopropene-that can be used to target biomols. in vitro and in live cells. A variety of substituted cyclopropene scaffolds were synthesized and found to be stable in aq. soln. and in the presence of biol. nucleophiles. Furthermore, some of the cyclopropene units were metabolically introduced into cell surface glycans and subsequently detected with covalent probes. The small size and selective reactivity of cyclopropenes will facilitate efforts to tag diverse collections of biomols. in vivo.
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    (e) Yang, J.; Šečkutė, J.; Cole, C. M.; Devaraj, N. K. Live-Cell Imaging of Cyclopropene Tags with Fluorogenic Tetrazine Cycloadditions. Angew. Chem., Int. Ed. 2012, 51, 7476– 7479,  DOI: 10.1002/anie.201202122
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    34e
    Live-Cell Imaging of Cyclopropene Tags with Fluorogenic Tetrazine Cycloadditions
    Yang, Jun; Seckute, Jolita; Cole, Christian M.; Devaraj, Neal K.
    Angewandte Chemie, International Edition (2012), 51 (30), 7476-7479, S7476/1-S7476/26CODEN: ACIEF5; ISSN:1433-7851. (Wiley-VCH Verlag GmbH & Co. KGaA)
    The authors demonstrated the applicability of methylcyclopropene tags as dienophiles for reaction with fluorogenic tetrazines. Through systematic synthetic modifications, the stability, size, and reactivity of the cyclopropene scaffold were optimized. Methylcyclopropene derivs. were developed that react rapidly with tetrazines while retaining their aq. stability and small size. These cyclopropene handles elicited fluorescent responses from quenched tetrazine dyes and were suitable for cellular imaging applications, which was demonstrated by imaging cyclopropene phospholipids distributed in live human breast cancer cells.
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    (f) Liu, F.; Liang, Y.; Houk, K. N. Bioorthogonal Cycloadditions: Computational Analysis with the Distortion/Interaction Model and Prediction of Reactivities. Acc. Chem. Res. 2017, 50, 2297– 2308,  DOI: 10.1021/acs.accounts.7b00265
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    34f
    Bioorthogonal Cycloadditions: Computational Analysis with the Distortion/Interaction Model and Predictions of Reactivities
    Liu, Fang; Liang, Yong; Houk, K. N.
    Accounts of Chemical Research (2017), 50 (9), 2297-2308CODEN: ACHRE4; ISSN:0001-4842. (American Chemical Society)
    A review. Bioorthogonal chem. has had a major impact on the study of biol. processes in vivo. Biomols. of interest can be tracked by using probes and reporters that do not react with cellular components and do not interfere with metabolic processes in living cells. Much time and effort has been devoted to the screening of potential bioorthogonal reagents exptl. This Account describes how the groups have performed computational screening of reactivity, bioorthogonality, and mutual orthogonality. The collaborations with experimentalists have led to developments of new and useful reactions. Dozens of bioorthogonal cycloaddns. have been reported in the literature in the past few years, but as interest in tracking multiple targets arises, the computational screening has gained importance for the discovery of new mutually orthogonal bioorthogonal cycloaddn. pairs. The reactivities of strained alkenes and alkynes with common 1,3-dipoles such as azides, along with mesoionic sydnones and other novel 1,3-dipoles, have been explored. Studies of "inverse-electron-demand" dienes such as triazines and tetrazines that have been used in bioorthogonal Diels-Alder cycloaddns. are described. The color graphics the authors have developed gives a snapshot of whether reactions are fast enough for cellular applications (green), are adequately reactive for labeling (yellow), or are only useful for synthesis or do not occur at all (red). The colors of each box give an instant view of rates, while bar graphs provide an anal. of the factors that control reactivity. This anal. uses the Distortion/Interaction or Activation Strain model of cycloaddn. reactivity developed independently by the group and that of F. Matthias Bickelhaupt in The Netherlands. The model analyzes activation barriers in terms of the energy required to distort the reactants to the transition state geometry. This energy, called the distortion energy or activation strain, constitutes the major component of the activation energy. This distortion energy is overcome when the strong bonding interactions between the termini of the two reactants, which the authors call the interaction energy, overcomes the distortion energy, and leads to the new bonds in the products. This Account describes how the authors have analyzed and predicted bioorthogonal cycloaddn. reactivity using the Distortion/Interaction Model, and how the exptl. collaborators have employed these insights to create new bioorthogonal cycloaddns. The graphics the authors use document and predict which combinations of cycloaddns. will be useful in bioorthogonal chem. and which pairs of reactions are mutually orthogonal. For example, the fast reaction of 5-phenyl-1,2,4-triazine and a thiacycloheptyne will not interfere with the other fast reaction of 3,6-diphenyl-1,2,4,5-tetrazine and a cyclopropene. No cross reactions will occur as these are very slow reactions.
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    Wang, J.; Yang, B.; Cool, T. A.; Hansen, N.; Kasper, T. Near-Threshold Absolute Photoionization Cross-Sections of Some Reaction Intermediates in Combustion. Int. J. Mass Spectrom. 2008, 269, 210– 220,  DOI: 10.1016/j.ijms.2007.10.013
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    Near-threshold absolute photoionization cross-sections of some reaction intermediates in combustion
    Wang, Juan; Yang, Bin; Cool, Terrill A.; Hansen, Nils; Kasper, Tina
    International Journal of Mass Spectrometry (2008), 269 (3), 210-220CODEN: IMSPF8; ISSN:1387-3806. (Elsevier B.V.)
    The use of photoionization mass spectrometry for the development of quant. kinetic models for the complex combustion chem. of both conventional hydrocarbon fuels and oxygenated biofuels requires near-threshold measurements of abs. photoionization cross-sections for numerous reaction intermediates. Near-threshold abs. cross-sections for mol. and dissociative photoionization for 20 stable reaction intermediates (methane, ethane, propane, n-butane, cyclopropane, methylcyclopentane, 1-butene, cis-2-butene, isobutene, 1-pentene, cyclohexene, 3,3-dimethyl-1-butene, 1,3-hexadiene, 1,3-cyclohexadiene, Me acetate, Et acetate, THF, propanal, 1-butyne, 2-butyne) are presented. Previously measured total photoionization cross-sections for 9 of these mols. are in good agreement with the present results. The measurements are performed with photoionization mass spectrometry (PIMS) using a monochromated VUV synchrotron light source with an energy resoln. of 40 meV (fwhm) comparable to that used for flame-sampling mol. beam PIMS studies of flame chem. and reaction kinetics.
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    Liang, Y.; Mackey, J. L.; Lopez, S. A.; Liu, F.; Houk, K. N. Control and Design of Mutual Orthogonality in Bioorthogonal Cycloadditions. J. Am. Chem. Soc. 2012, 134, 17904– 17907,  DOI: 10.1021/ja309241e
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    Control and Design of Mutual Orthogonality in Bioorthogonal Cycloadditions
    Liang, Yong; Mackey, Joel L.; Lopez, Steven A.; Liu, Fang; Houk, K. N.
    Journal of the American Chemical Society (2012), 134 (43), 17904-17907CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
    The azide-dibenzocyclooctyne and trans-cyclooctene-tetrazine cycloaddns. are both bioorthogonal and mutually orthogonal: trans-cyclooctene derivs. greatly prefer to react with tetrazines rather than azides, while dibenzocyclooctyne derivs. react with azides but not with tetrazines under physiol. conditions. DFT calcns. used to identify the origins of this extraordinary selectivity are reported, and design principles to guide discovery of new orthogonal cycloaddns. are proposed. Two new bioorthogonal reagents, methylcyclopropene and 3,3,6,6-tetramethylthiacycloheptyne, are predicted to be mutually orthogonal in azide and tetrazine cycloaddns.
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  37. 37
    Himo, F.; Lovell, T.; Hilgraf, R.; Rostovtsev, V. V.; Noodleman, L.; Sharpless, K. B.; Fokin, V. V. Copper(I)-Catalyzed Synthesis of Azoles. DFT Study Predicts Unprecedented Reactivity and Intermediates. J. Am. Chem. Soc. 2005, 127, 210– 216,  DOI: 10.1021/ja0471525
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    Copper(I)-Catalyzed Synthesis of Azoles. DFT Study Predicts Unprecedented Reactivity and Intermediates
    Himo, Fahmi; Lovell, Timothy; Hilgraf, Robert; Rostovtsev, Vsevolod V.; Noodleman, Louis; Sharpless, K. Barry; Fokin, Valery V.
    Journal of the American Chemical Society (2005), 127 (1), 210-216CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
    Huisgen's 1,3-dipolar cycloaddns. become nonconcerted when copper(I) acetylides react with azides and nitrile oxides, providing ready access to 1,4-disubstituted 1,2,3-triazoles and 3,4-disubstituted isoxazoles, resp. The process is highly reliable and exhibits an unusually wide scope with respect to both components. Computational studies revealed a stepwise mechanism involving unprecedented metallacycle intermediates, which appear to be common for a variety of dipoles.
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  38. 38
    (a) Bader, R. F. W. An Interpretation of Potential Interaction Constants in Terms of Low-Lying Excited States. Molecular Physics. 1960, 3, 137– 151,  DOI: 10.1080/00268976000100161
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    Interpretation of potential interaction constants in terms of low-lying excited states
    Bader, R. F. W.
    Molecular Physics (1960), 3 (), 137-51CODEN: MOPHAM; ISSN:0026-8976.
    Theoretical.
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    (b) Pearson, R. G. Concerning Jahn-Teller Effects. Proc. Nat. Acad. Sci. USA. 1975, 72, 2104– 2106,  DOI: 10.1073/pnas.72.6.2104
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    Jahn-Teller effects
    Pearson, Ralph G.
    Proceedings of the National Academy of Sciences of the United States of America (1975), 72 (6), 2104-6CODEN: PNASA6; ISSN:0027-8424.
    Jahn-Teller effects are grouped into 2 categories. The 1st arises from incomplete shells of degenerate orbitals. It includes the 1st-order Jahn-Teller effect, and the pseudo Jahn-Teller effect. The 2nd arises from filled and empty mol. orbitals that are close in energy, and is the 2nd-order Jahn-Teller effect. The 2 categories have quite different phys. bases. As a result, geometric distortions produced by the 1st are quite small and normally lead to dynamic effects only. In favorable cases, the 2nd-order Jahn-Teller effect produces very large distortions, including complete dissocn. of a mol. This can occur even when the relevant mol. orbitals are sepd. in energy by as much as 4 eV.
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    (a) Fukui, K.; Yonezawa, T.; Shingu, H. A Molecular Orbital Theory of Reactivity in Aromatic Hydrocarbons. J. Chem. Phys. 1952, 20, 722– 725,  DOI: 10.1063/1.1700523
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    A molecular-orbital theory of reactivity in aromatic hydrocarbons
    Fukui, Kenichi; Yonezawa, Teijiro; Shingu, Haruo
    Journal of Chemical Physics (1952), 20 (), 722-5CODEN: JCPSA6; ISSN:0021-9606.
    cf. Coulsen and Longuet-Higgins, C.A. 42, 1489i. In the search for a quant. correlation between reactivity and electronic configuration of aromatic hydrocarbons, the electron d., at each C atom, of the highest occupied π-orbital in the ground state of the mol. is calcd. by means of the linear-combination-of-at.-orbitals method. By comparing the result of such a calcn. on 15 condensed aromatic hydrocarbons with their chem. reactivities, the position at which the electron d. is largest is most readily attacked by electrophilic or oxidizing reagents. It is, therefore, concluded that, distinct from other π-electrons, the pair of π-electrons occupying the highest orbital, which is referred to as frontier electrons, plays a decisive role in chem. activation of these hydrocarbon mols. The theoretical significance of this discrimination of the frontier electrons in relation to the chem. activation is discussed.
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    (b) Fukui, K. Recognition of Stereochemical Paths by Orbital Interaction. Acc. Chem. Res. 1971, 4, 57– 64,  DOI: 10.1021/ar50038a003
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    39b
    Recognition of stereochemical paths by orbital interaction
    Fukui, Kenichi
    Accounts of Chemical Research (1971), 4 (2), 57-64CODEN: ACHRE4; ISSN:0001-4842.
    The favorable steric path in stereospecific processes can be interpreted based on particular orbital interaction. The subsidiary effects in stereoselection, the selectivity due to multiplicity, and the path of multicyclization are also discussed. The superiority of the orbital interaction scheme relative to comprehension of the nature of chem. interaction is pointed out.
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    (c) Fleming, I. Frontier Orbitals and Organic Chemical Reactions. London: Wiley. 1978, 24– 109
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    We have quantum chem. analyzed the catalytic effect of dihalogen mols. (X2=F2, Cl2, Br2, and I2) on the aza-Michael addn. of pyrrolidine and Me acrylate using relativistic d. functional theory and coupled-cluster theory. Our state-of-the-art computations reveal that activation barriers systematically decrease as one goes to heavier dihalogens, from 9.4 kcal mol-1 for F2 to 5.7 kcal mol-1 for I2. Activation strain and bonding analyses identify an unexpected phys. factor that controls the computed reactivity trends, namely, Pauli repulsion between the nucleophile and Michael acceptor. Thus, dihalogens do not accelerate Michael addns. by the commonly accepted mechanism of an enhanced donor-acceptor [HOMO(nucleophile)-LUMO(Michael acceptor)] interaction, but instead through a diminished Pauli repulsion between the lone-pair of the nucleophile and the Michael acceptor's π-electron system.
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    Chemistry - An Asian Journal (2020), 15 (7), 1167-1174CODEN: CAAJBI; ISSN:1861-4728. (Wiley-VCH Verlag GmbH & Co. KGaA)
    We have quantum chem. studied alkali cation-catalyzed arom. Diels-Alder reactions between benzene and acetylene forming barrelene using relativistic, dispersion-cor. d. functional theory. The alkali cation-catalyzed arom. Diels-Alder reactions are accelerated by up to 5 orders of magnitude relative to the uncatalyzed reaction and the reaction barrier increases along the series Li+ < Na+ < K+ < Rb+ < Cs+ < none. Our detailed activation strain and mol.-orbital bonding analyses reveal that the alkali cations lower the arom. Diels-Alder reaction barrier by reducing the Pauli repulsion between the closed-shell filled orbitals of the dienophile and the arom. diene. We argue that such Pauli mechanism behind Lewis-acid catalysis is a more general phenomenon. Also, our results may be of direct importance for a more complete understanding of the network of competing mechanisms towards the formation of polycyclic arom. hydrocarbons (PAHs) in an astrochem. context.
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    The Lewis acid(LA)-catalyzed Diels-Alder reaction between isoprene and Me acrylate was investigated quantum chem. using a combined d. functional theory and coupled-cluster theory approach. Computed activation energies systematically decrease as the strength of the LA increases along the series I2<SnCl4<TiCl4<ZnCl2<BF3<AlCl3. Emerging from our activation strain and Kohn-Sham MO bonding anal. was an unprecedented finding, namely that the LAs accelerate the Diels-Alder reaction by a diminished Pauli repulsion between the π-electron systems of the diene and dienophile. Our results oppose the widely accepted view that LAs catalyze the Diels-Alder reaction by enhancing the donor-acceptor [HOMOdiene-LUMOdienophile] interaction and constitute a novel phys. mechanism for this indispensable textbook org. reaction.
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  • Abstract

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    Figure 1

    Figure 1. (a) Plot of reactivity (lnk2) vs IP. Replotted in the same style as Sustmann’s original figure in ref (1). Copyright 1972 by Verlag Chemie GmbH, Germany. (b) Schematic of the azide HOMO and LUMO vs those of donor-substituted dipolarophiles, ethylene, and acceptor-substituted dipolarophiles.

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    Figure 2

    Figure 2. Correlation of aΔGA‡ with bΔGB‡ for the cycloadditions between phenyl azide and 21 dipolarophiles. aωB97X-D/aug-cc-pVTZ-CPCM(solvent)//ωB97X-D/6-31+G(d,p)-CPCM(solvent); bB2PLYP-D3/aug-cc-pVTZ-CPCM(solvent)//ωB97X-D/6-31+G(d,p)-CPCM(solvent).

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    Figure 3

    Figure 3. Correlation of logarithms of the experimental rate constants with the calculated rate constants (method B) for the cycloadditions between phenyl azide and 21 dipolarophiles.

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    Scheme 1

    Scheme 1. The 1,3-Dipolar Cycloaddition between Phenyl Azide and Different Dipolarophiles Studied by Sustmann and in This Paper
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    Figure 4

    Figure 4. Theoretical version of Sustmann’s plot with charge transfer (e), using B2PLYP-D3/aug-cc-pVTZ-CPCM(solvent)//ωB97X-D/6-31+G(d,p)-CPCM(solvent)-predicted rate constants and HF/6-31G(d)-calculated ionization potentials (eV). The three purple points, for which experimental rate constants have been given in Huisgen’s experimental study (30) but were not included in Sustmann’s analysis, are qualitatively in line with the parabolic trend. The three points in red are added to the original plot to show how distortion-accelerated dipolarophiles fit on the correlation, and the point in orange is added to the original plot to show the enormous acceleration that occurs with Cu catalysis. Data in blue (negative number) shows charge transfer from dipolarophiles to azide; data in green (positive number) shows charge transfer from azide to dipolarophiles; data in black shows charge transfer of 0.05 e or less between reactants, essentially zero.

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    Figure 5

    Figure 5. Plots of logarithms of the experimental rate constants versus (a) distortion and (b) interaction energies for the cycloadditions between phenyl azide and dipolarophiles. Energies are in kcal/mol.

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    Figure 6

    Figure 6. Plot of optimum FMO gaps (eV) between dipole and dipolarophiles versus calculated ionization potentials (eV) of a number of dipolarophiles.

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    Figure 7

    Figure 7. DFT-optimized transition structures for cycloadditions between phenyl azide and five representative dipolarophiles. TS1 and TS17 are for the experimentally observed regioselectivity.

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    Figure 8

    Figure 8. Orbital interaction diagrams for the cycloadditions between phenyl azide and selected dipolarophiles. In order to justify that HOMO-3 and LUMO+2 of phenyl azide are the effective orbitals involved in the orbital interactions between phenyl azide and dipolarophiles, we show the HOMO, HOMO-1, and HOMO-2 as well as the LUMO and LUMO+1 of phenyl azide in the upper left corner for comparison.

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    Figure 9

    Figure 9. Distortion/interaction-activation strain (DIAS) analysis for selected cycloaddition reactions. Reactant distortion and interaction energies were calculated at the ωB97X-D level of theory with the aug-cc-pVTZ basis set, in the gas phase. (a) Electronic energies (ΔE). (b) Distortion energies (ΔEdist). (c) Interaction energies (ΔEint).

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    Figure 10

    Figure 10. Orbital interaction diagrams for the cycloadditions between phenyl azide and selected dipolarophiles. We added orbital coefficients for the interacting orbitals. For phenyl azide, N1 is the nitrogen attached to the phenyl group, and N2 is the terminal-unsubstituted nitrogen. For dipolarophiles, C3 is the carbon attached to the substituent, and C4 is the terminal-unsubstituted carbon. In order to justify that HOMO-3 and LUMO+2 of phenyl azide are the effective orbitals involved in the orbital interactions between phenyl azide and dipolarophiles, we show the HOMO, HOMO-1, and HOMO-2 as well as the LUMO and LUMO+1 of phenyl azide in the upper left corner of Figure 10 for comparison.

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    Figure 11

    Figure 11. Distortion/interaction-activation strain (DIAS) analysis of the cycloaddition transition states to reveal the origins of regioselectivity. Free energies were calculated at the ωB97X-D/aug-cc-pVTZ-CPCM(solvent)//ωB97X-D/6-31+G(d,p)-CPCM(solvent) level of theory. Fragment distortion and interaction energies were calculated at the ωB97X-D level of theory with the aug-cc-pVTZ basis set, without the inclusion of solvation energy corrections (black, activation energies; blue, distortion energies of azide; green, distortion energies of dipolarophiles; red, interaction energies). Energies are in kcal/mol. The starred transition state is the regioisomeric transition state, which is unfavorable compared to the one without an asterisk.

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  • References

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      Rabalais, J. W.; Colton, R. I.
      Journal of Electron Spectroscopy and Related Phenomena (1972), 1 (1), 83-99CODEN: JESRAW; ISSN:0368-2048.
      The high-resoln. He I photoelectron spectra of some isoelectronic substituted benzenes with 11 valence electron substituents (styrene, PhCHO, and PhNO) and 9 valence electron substituents (PhC≡CH and PhCN) were obtained and the ionization bands in the low-binding-energy region of the spectra were identified and assigned. The spectra of CH2:CHCH2Ph and PhCH2CHO were also obtained to illustrate the effect of an "insulating" group between the 2 interacting components of the mol. The photoelectron bands were identified by using a "composite mol." approach in which the known levels of C6H6 and the various substituents are correlated with those of the mol. The assignment of the photoelectron bands was also assisted by information supplied from vibrational anal. of the spectra and by ref. to the results of CNDO (complete neglect of differential overlap)/2 and INDO (intermediate neglect of differential overlap) calcns. performed in these labs. The CNDO/2 and INDO calcns. predict the correct MO ordering for all mols. studied except PhCHO. The MO eigenvalues are consistently higher than the exptl. ionization energies. Of the mols. studied, the greatest amt. of conjugation and electron delocalization between the Ph group and its substituent group occurs in styrene. The nonbonding orbital of PhCHO is accidentally near-degenerate with the Ph π-orbitals. The outermost orbital of PhNO is the nonbonding orbital which is highly localized on the NO group. The degeneracy of the substituent π-orbitals in PhC≡CH and PhCN is lifted by conjugation with the Ph ring. The outermost σ-orbital of the Ph group exhibits a marked sensitivity to the electronegativity of the substituent group. Substitution of a methylene group between the 2 interacting components of a composite mol. is very effective in decoupling the electronic interaction between these 2 components.
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    8. 8
      Baker, A. D.; Betteridge, D. Photoelectron Spectroscopy. Chemical and Analytical Aspects; Pergamon Press: Oxford, 1972.
      There is no corresponding record for this reference.
    9. 9
      (a) Houk, K. N. Regioselectivity and Reactivity in the 1,3-Dipolar Cycloadditions of Diazonium Betaines (Diazoalkanes, Azides, and Nitrous Oxide). J. Am. Chem. Soc. 1972, 94, 8953– 8955,  DOI: 10.1021/ja00780a077
      9a
      Regioselectivity and reactivity in the 1,3-dipolar cycloadditions of diazonium betaines (diazoalkanes, azides, and nitrous oxide)
      Houk, K. N.
      Journal of the American Chemical Society (1972), 94 (25), 8953-5CODEN: JACSAT; ISSN:0002-7863.
      The regioselectivity and relative reactivity in 1,3-dipolar cycloaddns. of diazonium betaines with unsym. dipolarophiles was rationalized by consideration of frontier orbital interactions in concerted transition states. The results of R. Sustmann (1971, 1972) on azide reactivity, combined with these results on regioselectivity, provided a complete rationalization of the exptl. facts about reactivity and regioselectivity in diazonium betaine cycloaddns.
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      (b) Houk, K. N.; Sims, J.; Duke, R. E.; Strozier, R. W.; George, J. K. Frontier Molecular Orbitals of 1,3 Dipoles and Dipolarophiles. J. Am. Chem. Soc. 1973, 95, 7287– 7301,  DOI: 10.1021/ja00803a017
      9b
      Frontier molecular orbitals of 1,3 dipoles and dipolarophiles
      Houk, K. N.; Sims, Joyner; Duke, R. E., Jr.; Strozier, R. W.; George, John K.
      Journal of the American Chemical Society (1973), 95 (22), 7287-301CODEN: JACSAT; ISSN:0002-7863.
      MO calcns. were performed by CNDO/2 and extended Hueckel methods for parent and some substituted nitrilium betaines, diazonium betaines, azomethinium betaines, and carbonyl betaines and for a series of substituted alkenes. Exptl. values for ionization potentials and electron affinities, calcns. performed here, and calcns. in the literature were used to generate a set of frontier orbital energies and coeffs. for 1,3 dipoles and dipolarophiles. The effects of substituents on orbital energies and coeffs. are deduced. These frontier orbitals are of general utility in the rationalization and prediction of relative rates and regioselectivity of 1,3-dipolar cycloaddns., as well as other cycloaddns. and frontier-controlled org. reactions.
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      (c) Houk, K. N.; Sims, J.; Watts, C. R.; Luskus, L. J. Origin of Reactivity, Regioselectivity, and Periselectivity in 1,3-Dipolar Cycloadditions. J. Am. Chem. Soc. 1973, 95, 7301– 7315,  DOI: 10.1021/ja00803a018
      9c
      Origin of reactivity, regioselectivity, and periselectivity in 1,3-dipolar cycloadditions
      Houk, K. N.; Sims, Joyner; Watts, Charles R.; Luskus, L. J.
      Journal of the American Chemical Society (1973), 95 (22), 7301-15CODEN: JACSAT; ISSN:0002-7863.
      Perturbation theory is applied to 1,3-dipolar cycloaddn. phenomena. The generalizations made previously (1973) concerning 1,3 dipole and dipolarophile frontier orbital energies and coeffs. allow a specific qual. treatment of reactivity of individual 1,3 dipoles. The explanation of regioselectivity and periselectivity phenomena also follows from this treatment. Extensions of the frontier orbital method to other cycloaddn. reactions are outlined.
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    10. 10
      (a) Ess, D. H.; Houk, K. N. Distortion/Interaction Energy Control of 1,3-Dipolar Cycloaddition Reactivity. J. Am. Chem. Soc. 2007, 129, 10646– 10647,  DOI: 10.1021/ja0734086
      10a
      Distortion/Interaction Energy Control of 1,3-Dipolar Cycloaddition Reactivity
      Ess, Daniel H.; Houk, K. N.
      Journal of the American Chemical Society (2007), 129 (35), 10646-10647CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
      Computations of activation barriers and reaction energies for 1,3-dipolar cycloaddns. by a high-accuracy quantum mech. method (CBS-QB3) now reveal previously unrecognized quant. trends in activation barriers. The distortion/interaction theory explains why (1) there is a monotonic decrease of ∼6 kcal/mol in the barrier height along the series oxides, imine, and ylide, for each class of 1,3-dipoles; (2) the corresponding nitrilium and azomethine betaines have almost identical cycloaddn. barrier heights; (3) cycloaddns. of a given 1,3-dipole with ethylene and acetylene have the same activation energies, in spite of very different reaction thermodn. and frontier orbital gaps. There is a linear correlation between distortion energies (ΔEd⧧) and the activation barrier (ΔE⧧ = 0.75ΔEd⧧ - 2.9 kcal/mol) that is general for substituted and unsubstituted 1,3-dipoles in these cycloaddns. The energy to distort the 1,3-dipole to the geometry favorable for interaction with the dipolarophile, i.e., the transition state geometry, rather than frontier MO (FMO) interactions or reaction thermodn., controls reactivity. Interaction energies between the 1,3-dipole and the dipolarophile differentiate dipolarophile reactivity, and FMO interactions influence this.
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      (b) Ess, D. H.; Jones, G. O.; Houk, K. N. Transition States of Strain-Promoted Metal-Free Click Chemistry: 1,3-Dipolar Cycloadditions of Phenyl Azide and Cyclooctynes. Org. Lett. 2008, 10, 1633– 1636,  DOI: 10.1021/ol8003657
      10b
      Transition States of Strain-Promoted Metal-Free Click Chemistry: 1,3-Dipolar Cycloadditions of Phenyl Azide and Cyclooctynes
      Ess, Daniel H.; Jones, Gavin O.; Houk, K. N.
      Organic Letters (2008), 10 (8), 1633-1636CODEN: ORLEF7; ISSN:1523-7060. (American Chemical Society)
      D. functional theory (B3LYP) calcns. on the transition states for the Huisgen 1,3-dipolar cycloaddns. of Ph azide with acetylene, cyclooctyne, 3-fluorocyclooctyne, and 3,3-difluorocyclooctyne are reported. The low activation energy of the cyclooctyne "strain-promoted" cycloaddn. (ΔE⧧ = 8.0) compared to the strain-free acetylene cycloaddn. (ΔE⧧ = 16.2) is due to decreased distortion energy (ΔEd⧧) of cyclooctyne (ΔΔEd⧧ = 4.6) and Ph azide (ΔΔEd⧧ = 4.5) to achieve that cycloaddn. transition state. Electroneg. fluorine substituents on cyclooctyne further increase the rate of cycloaddn. by increasing interaction energies.
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      (c) Schoenebeck, F.; Ess, D. H.; Jones, G. O.; Houk, K. N. Reactivity and Regioselectivity in 1,3-Dipolar Cycloadditions of Azides to Strained Alkynes and Alkenes: A Computational Study. J. Am. Chem. Soc. 2009, 131, 8121– 8133,  DOI: 10.1021/ja9003624
      10c
      Reactivity and Regioselectivity in 1,3-Dipolar Cycloadditions of Azides to Strained Alkynes and Alkenes: A Computational Study
      Schoenebeck, Franziska; Ess, Daniel H.; Jones, Gavin O.; Houk, K. N.
      Journal of the American Chemical Society (2009), 131 (23), 8121-8133CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
      The transition states and activation barriers of the 1,3-dipolar cycloaddns. of azides with cycloalkynes and cycloalkenes were explored using B3LYP d. functional theory (DFT) and spin component scaled SCS-MP2 methods. A survey of benzyl azide cycloaddns. to substituted cyclooctynes (OMe, Cl, F, CN) showed that fluorine substitution has the most dramatic effect on reactivity. Azide cycloaddns. to 3-substituted cyclooctynes prefer 1,5-addn. regiochem. in the gas phase, but CPCM solvation abolishes the regioselectivity preference, in accord with expts. in soln. The activation energies for Ph azide addn. to cycloalkynes decrease considerably as the ring size is decreased (cyclononyne ΔG⧧ = 29.2 kcal/mol, cyclohexyne ΔG⧧ = 14.1 kcal/mol). The origin of this trend is explained by the distortion/interaction model. Cycloalkynes are predicted to be significantly more reactive dipolarophiles than cycloalkenes. The activation barriers for the cycloaddns. of Ph azide and picryl azide (2,4,6-trinitrophenyl azide) to five- through nine-membered cycloalkenes were also studied and compared to expt. Picryl azide has considerably lower activation barriers than Ph azide. Dissection of the transition state energies into distortion and interaction energies revealed that "strain-promoted" cycloalkyne and cycloalkene cycloaddn. transition states must still pay an energetic penalty to achieve their transition state geometries, and the differences in reactivity are more closely related to differences in distortion energies than the amt. of strain released in the product. Trans-cycloalkene dipolarophiles have much lower barriers than cis-cycloalkenes.
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      (d) Gordon, C. G.; Mackey, J. L.; Jewett, J. C.; Sletten, E. M.; Houk, K. N.; Bertozzi, C. R. Reactivity of Biarylazacyclooctynones in Copper-Free Click Chemistry. J. Am. Chem. Soc. 2012, 134, 9199– 9208,  DOI: 10.1021/ja3000936
      10d
      Reactivity of Biarylazacyclooctynones in Copper-Free Click Chemistry
      Gordon, Chelsea G.; Mackey, Joel L.; Jewett, John C.; Sletten, Ellen M.; Houk, K. N.; Bertozzi, Carolyn R.
      Journal of the American Chemical Society (2012), 134 (22), 9199-9208CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
      The 1,3-dipolar cycloaddn. of cyclooctynes with azides, also called "copper-free click chem.", is a bioorthogonal reaction with widespread applications in biol. discovery. The kinetics of this reaction are of paramount importance for studies of dynamic processes, particularly in living subjects. Here we performed a systematic anal. of the effects of strain and electronics on the reactivity of cyclooctynes with azides through both exptl. measurements and computational studies using a d. functional theory (DFT) distortion/interaction transition state model. In particular, we focused on biarylazacyclooctynone (BARAC) because it reacts with azides faster than any other reported cyclooctyne and its modular synthesis facilitated rapid access to analogs. We found that substituents on BARAC's aryl rings can alter the calcd. transition state interaction energy of the cycloaddn. through electronic effects or the calcd. distortion energy through steric effects. Exptl. data confirmed that electronic perturbation of BARAC's aryl rings has a modest effect on reaction rate, whereas steric hindrance in the transition state can significantly retard the reaction. Drawing on these results, we analyzed the relationship between alkyne bond angles, which we detd. using X-ray crystallog., and reactivity, quantified by exptl. second-order rate consts., for a range of cyclooctynes. Our results suggest a correlation between decreased alkyne bond angle and increased cyclooctyne reactivity. Finally, we obtained structural and computational data that revealed the relationship between the conformation of BARAC's central lactam and compd. reactivity. Collectively, these results indicate that the distortion/interaction model combined with bond angle anal. will enable predictions of cyclooctyne reactivity and the rational design of new reagents for copper-free click chem.
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      (e) Bickelhaupt, F. M.; Houk, K. N. Analyzing Reaction Rates with the Distortion/Interaction-Activation Strain Model. Angew. Chem. Int. Ed. 2017, 56, 10070– 10086,  DOI: 10.1002/anie.201701486
      10e
      Analyzing Reaction Rates with the Distortion/Interaction-Activation Strain Model
      Bickelhaupt, F. Matthias; Houk, Kendall N.
      Angewandte Chemie, International Edition (2017), 56 (34), 10070-10086CODEN: ACIEF5; ISSN:1433-7851. (Wiley-VCH Verlag GmbH & Co. KGaA)
      The activation strain or distortion/interaction model is a tool to analyze activation barriers that det. reaction rates. For bimol. reactions, the activation energies are the sum of the energies to distort the reactants into geometries they have in transition states plus the interaction energies between the two distorted mols. The energy required to distort the mols. is called the activation strain or distortion energy. This energy is the principal contributor to the activation barrier. The transition state occurs when this activation strain is overcome by the stabilizing interaction energy. Following the changes in these energies along the reaction coordinate gives insights into the factors controlling reactivity. This model has been applied to reactions of all types in both org. and inorg. chem., including substitutions and eliminations, cycloaddns., and several types of organometallic reactions.
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      (f) Hamlin, T. A.; Svatunek, D.; Yu, S.; Ridder, L.; Infante, I.; Visscher, L.; Bickelhaupt, F. M. Elucidating the Trends in Reactivity of Aza-1,3-Dipolar Cycloadditions. Eur. J. Org. Chem. 2019, 378– 386,  DOI: 10.1002/ejoc.201800572
      10f
      Elucidating the Trends in Reactivity of Aza-1,3-Dipolar Cycloadditions
      Hamlin, Trevor A.; Svatunek, Dennis; Yu, Song; Ridder, Lars; Infante, Ivan; Visscher, Lucas; Bickelhaupt, F. Matthias
      European Journal of Organic Chemistry (2019), 2019 (2-3), 378-386CODEN: EJOCFK; ISSN:1099-0690. (Wiley-VCH Verlag GmbH & Co. KGaA)
      This report describes a d. functional theory investigation into the reactivities of a series of aza-1,3-dipoles with ethylene at the BP86/TZ2P level. A benchmark study was carried out using QMflows, a newly developed program for automated workflows of quantum chem. calcns. In total, 24 1,3-dipolar cycloaddn. (1,3-DCA) reactions were benchmarked using the highly accurate G3B3 method as a ref. We screened a no. of exchange and correlation functionals, including PBE, OLYP, BP86, BLYP, both with and without explicit dispersion corrections, to assess their accuracies and to det. which of these computationally efficient functionals performed the best for calcg. the energetics for cycloaddn. reactions. The BP86/TZ2P method produced the smallest errors for the activation and reaction enthalpies. Then, to understand the factors controlling the reactivity in these reactions, seven archetypal aza-1,3-dipolar cycloaddns. were investigated using the activation strain model and energy decompn. anal. Our investigations highlight the fact that differences in activation barrier for these 1,3-DCA reactions do not arise from differences in strain energy of the dipole, as previously proposed. Instead, relative reactivities originate from differences in interaction energy. Anal. of the 1,3-dipole-dipolarophile interactions reveals the reactivity trends primarily result from differences in the extent of the primary orbital interactions.
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    11. 11
      (a) Domingo, L. R. Molecular Electron Density Theory: A Modern View of Reactivity in Organic Chemistry. Molecules 2016, 21, 1319,  DOI: 10.3390/molecules21101319
      11a
      Molecular electron density theory: a modern view of reactivity in organic chemistry
      Domingo, Luis R.
      Molecules (2016), 21 (10), 1319/1-1319/15CODEN: MOLEFW; ISSN:1420-3049. (MDPI AG)
      A review. A new theory for the study of the reactivity in Org. Chem., named Mol. Electron D. Theory (MEDT), is proposed herein. MEDT is based on the idea that while the electron d. distribution at the ground state is responsible for phys. and chem. mol. properties, as proposed by the D. Functional Theory (DFT), the capability for changes in electron d. is responsible for mol. reactivity. Within MEDT, the reactivity in Org. Chem. is studied through a rigorous quantum chem. anal. of the changes of the electron d. as well as the energies assocd. with these changes along the reaction path in order to understand exptl. outcomes. Studies performed using MEDT allow establishing a modern rationalisation and to gain insight into mol. mechanisms and reactivity in Org. Chem.
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      Applications to azide cycloadditions:

      (b) Ben El Ayouchia, H.; Lahoucine, B.; Anane, H.; Ríos-Gutiérrez, M.; Domingo, L. R.; Stiriba, S.-E. Experimental and Theoretical MEDT Study of the Thermal [3+2] Cycloaddition Reactions of Aryl Azides with Alkyne Derivatives. ChemistrySelect 2018, 3, 1215– 1223,  DOI: 10.1002/slct.201702588
      11b
      Experimental and Theoretical MEDT Study of the Thermal [3+2] Cycloaddition Reactions of Aryl Azides with Alkyne Derivatives
      Ben El Ayouchia, Hicham; Lahoucine, Bahsis; Anane, Hafid; Rios-Gutierrez, Mar; Domingo, Luis R.; Stiriba, Salah-Eddine
      ChemistrySelect (2018), 3 (4), 1215-1223CODEN: CHEMUD; ISSN:2365-6549. (Wiley-VCH Verlag GmbH & Co. KGaA)
      The reactivity and regioselectivity of the [3+2] cycloaddn. (32CA) reactions of a series of 4-substituted-aryl azides/alkynes in toluene have been explored exptl. These 32CA reactions have been also studied within the Mol. Electron D. Theory (MEDT) using D. Functional Theory (DFT) calcns. at the B3LYP/6-31G(d) computational level. The computed activation energies, in gas phase and in toluene, show that the 1,5-regioisomeric channels are slightly favored kinetically as found exptl. The topol. anal. of the electron localization function (ELF) of some relevant points of the regioisomeric reaction paths shows that while the formation of the 1,4-diaryl triazoles takes place via a low asynchronous C-N bond formation process, the formation of the favored 1,5-diaryl triazoles takes place via a two-stage one-step mechanism, as the result of the attack of the most nucleophilic center of the aryl alkyne on the most electrocyclic center of aryl azide.
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      Domingo, L. R.; Acharjee, N. Unravelling the Strain-Promoted [3+2] Cycloadditi on Reactions of Phenyl Azide with Cycloalkynes from the Molecular Electron Density Theory Perspective. New J. Chem. 2020, 44, 13633-13643.

    12. 12
      Freindorf, M.; Sexton, T.; Kraka, E.; Cremer, D. The Mechanism of the Cycloaddition Reaction of 1,3-Dipole Molecules with Acetylene: An Investigation with the Unified Reaction Valley Approach. Theoret. Chem. Acc. 2014, 133, 1423,  DOI: 10.1007/s00214-013-1423-z
      There is no corresponding record for this reference.
    13. 13
      (a) Riplinger, C.; Neese, F. An Efficient and Near Linear Scaling Pair Natural Orbital Based Local Coupled Cluster Method. J. Chem. Phys. 2013, 138, 034106  DOI: 10.1063/1.4773581
      13a
      An efficient and near linear scaling pair natural orbital based local coupled cluster method
      Riplinger, Christoph; Neese, Frank
      Journal of Chemical Physics (2013), 138 (3), 034106/1-034106/18CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
      In previous publications, it was shown that an efficient local coupled cluster method with single- and double excitations can be based on the concept of pair natural orbitals (PNOs) . The resulting local pair natural orbital-coupled-cluster single double (LPNO-CCSD) method has since been proven to be highly reliable and efficient. For large mols., the no. of amplitudes to be detd. is reduced by a factor of 105-106 relative to a canonical CCSD calcn. on the same system with the same basis set. In the original method, the PNOs were expanded in the set of canonical virtual orbitals and single excitations were not truncated. This led to a no. of fifth order scaling steps that eventually rendered the method computationally expensive for large mols. (e.g., >100 atoms). In the present work, these limitations are overcome by a complete redesign of the LPNO-CCSD method. The new method is based on the combination of the concepts of PNOs and projected AOs (PAOs). Thus, each PNO is expanded in a set of PAOs that in turn belong to a given electron pair specific domain. In this way, it is possible to fully exploit locality while maintaining the extremely high compactness of the original LPNO-CCSD wavefunction. No terms are dropped from the CCSD equations and domains are chosen conservatively. The correlation energy loss due to the domains remains below <0.05%, which implies typically 15-20 but occasionally up to 30 atoms per domain on av. The new method has been given the acronym DLPNO-CCSD ("domain based LPNO-CCSD"). The method is nearly linear scaling with respect to system size. The original LPNO-CCSD method had three adjustable truncation thresholds that were chosen conservatively and do not need to be changed for actual applications. In the present treatment, no addnl. truncation parameters have been introduced. Any addnl. truncation is performed on the basis of the three original thresholds. There are no real-space cutoffs. Single excitations are truncated using singles-specific natural orbitals. Pairs are prescreened according to a multipole expansion of a pair correlation energy est. based on local orbital specific virtual orbitals (LOSVs). Like its LPNO-CCSD predecessor, the method is completely of black box character and does not require any user adjustments. It is shown here that DLPNO-CCSD is as accurate as LPNO-CCSD while leading to computational savings exceeding one order of magnitude for larger systems. The largest calcns. reported here featured >8800 basis functions and >450 atoms. In all larger test calcns. done so far, the LPNO-CCSD step took less time than the preceding Hartree-Fock calcn., provided no approxns. have been introduced in the latter. Thus, based on the present development reliable CCSD calcns. on large mols. with unprecedented efficiency and accuracy are realized. (c) 2013 American Institute of Physics.
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      (b) Riplinger, C.; Sandhoefer, B.; Hansen, A.; Neese, F. Natural Triple Excitations in Local Coupled Cluster Calculations with Pair Natural Orbitals. J. Chem. Phys. 2013, 139, 134101,  DOI: 10.1063/1.4821834
      13b
      Natural triple excitations in local coupled cluster calculations with pair natural orbitals
      Riplinger, Christoph; Sandhoefer, Barbara; Hansen, Andreas; Neese, Frank
      Journal of Chemical Physics (2013), 139 (13), 134101/1-134101/13CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
      In this work, the extension of the previously developed domain based local pair-natural orbital (DLPNO) based singles- and doubles coupled cluster (DLPNO-CCSD) method to perturbatively include connected triple excitations is reported. The development is based on the concept of triples-natural orbitals that span the joint space of the three pair natural orbital (PNO) spaces of the three electron pairs that are involved in the calcn. of a given triple-excitation contribution. The truncation error is very smooth and can be significantly reduced through extrapolation to the zero threshold. However, the extrapolation procedure does not improve relative energies. The overall computational effort of the method is asymptotically linear with the system size O(N). Actual linear scaling has been confirmed in test calcns. on alkane chains. The accuracy of the DLPNO-CCSD(T) approxn. relative to semicanonical CCSD(T0) is comparable to the previously developed DLPNO-CCSD method relative to canonical CCSD. Relative energies are predicted with an av. error of approx. 0.5 kcal/mol for a challenging test set of medium sized org. mols. The triples correction typically adds 30%-50% to the overall computation time. Thus, very large systems can be treated on the basis of the current implementation. In addn. to the linear C150H302 (452 atoms, >8800 basis functions) we demonstrate the first CCSD(T) level calcn. on an entire protein, Crambin with 644 atoms, and more than 6400 basis functions.
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      (c) Liakos, D. G.; Neese, F. Is It Possible To Obtain Coupled Cluster Quality Energies at near Density Functional Theory Cost? Domain-Based Local Pair Natural Orbital Coupled Cluster vs. Modern Density Functional Theory. J. Chem. Theory Comput. 2015, 11, 4054– 4063,  DOI: 10.1021/acs.jctc.5b00359
      13c
      Is It Possible To Obtain Coupled Cluster Quality Energies at near Density Functional Theory Cost? Domain-Based Local Pair Natural Orbital Coupled Cluster vs Modern Density Functional Theory
      Liakos, Dimitrios G.; Neese, Frank
      Journal of Chemical Theory and Computation (2015), 11 (9), 4054-4063CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
      The recently developed domain-based local pair natural orbital coupled cluster theory with single, double, and perturbative triple excitations (DLPNO-CCSD(T)) delivers results that are closely approaching those of the parent canonical coupled cluster method at a small fraction of the computational cost. A recent extended benchmark study established that, depending on the three main truncation thresholds, it is possible to approach the canonical CCSD(T) results within 1 kJ (default setting, TightPNO), 1 kcal/mol (default setting, NormalPNO), and 2-3 kcal (default setting, LoosePNO). Although thresholds for calcns. with TightPNO are 2-4 times slower than those based on NormalPNO thresholds, they are still many orders of magnitude faster than canonical CCSD(T) calcns., even for small and medium sized mols. where there is little locality. The computational effort for the coupled cluster step scales nearly linearly with system size. Since, in many instances, the coupled cluster step in DLPNO-CCSD(T) is cheaper or at least not much more expensive than the preceding Hartree-Fock calcn., it is useful to compare the method against modern d. functional theory (DFT), which requires an effort comparable to that of Hartree-Fock theory (at least if Hartree-Fock exchange is part of the functional definition). Double hybrid d. functionals (DHDF's) even require a MP2-like step. The purpose of this article is to evaluate the cost vs accuracy ratio of DLPNO-CCSD(T) against modern DFT (including the PBE, B3LYP, M06-2X, B2PLYP, and B2GP-PLYP functionals and, where applicable, their van der Waals cor. counterparts). To eliminate any possible bias in favor of DLPNO-CCSD(T), we have chosen established benchmark sets that were specifically proposed for evaluating DFT functionals. It is demonstrated that DLPNO-CCSD(T) with any of the three default thresholds is more accurate than any of the DFT functionals. Furthermore, using the aug-cc-pVTZ basis set and the LoosePNO default settings, DLPNO-CCSD(T) is only about 1.2 times slower than B3LYP. With NormalPNO thresholds, DLPNO-CCSD(T) is about a factor of 2 slower than B3LYP and shows a mean abs. deviation of less than 1 kcal/mol to the ref. values for the four different data sets used. Our conclusion is that coupled cluster energies can indeed be obtained at near DFT cost.
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    14. 14
      (a) Breugst, M.; Huisgen, R.; Reissig, H.-U. Regioselective 1,3-Dipolar Cycloadditions of Diazoalkanes with Heteroatom-Substituted Alkynes: Theory and Experiment. Eur. J. Org. Chem. 2018, 2477– 2485,  DOI: 10.1002/ejoc.201800100
      14a
      Regioselective 1,3-Dipolar Cycloadditions of Diazoalkanes with Heteroatom-Substituted Alkynes: Theory and Experiment
      Breugst, Martin; Huisgen, Rolf; Reissig, Hans-Ulrich
      European Journal of Organic Chemistry (2018), 2018 (20-21), 2477-2485CODEN: EJOCFK; ISSN:1099-0690. (Wiley-VCH Verlag GmbH & Co. KGaA)
      The 1,3-dipolar cycloaddns. of diazomethane and diazoethane with Me 3-(diethylamino)propiolate were investigated exptl. and computationally by employing d. functional theory (DFT). The expts. provided Me 3-(diethylamino)-pyrazole-4-carboxylates as the only isolated regioisomers. The constitution of these cycloadducts was secured by independent synthesis and decarboxylation to 3-(diethylamino)pyrazoles. The calcns. fully support the exptl. findings. For the preferred pathway of the diazomethane cycloaddn. with the alkyne, a kinetic preference of 9.6 kJ mol-1 was calcd. in Et2O soln. The computational anal. was extended to other alkynes, for instance to heteroatom-substituted alkynes such as ethoxyethyne and (ethylthio)ethyne. Again, the calcns. nicely explain the switch in regioselectivity of the 1,3-dipolar cycloaddns. of diazomethane with these two alkynes, which has been reported earlier by the group of Arens.
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      (b) Breugst, M.; Reissig, H.-U. The Huisgen Reaction: Milestones of the 1,3-Dipolar Cycloaddition. Angew. Chem. Int. Ed. 2020, 59, 12293– 12307,  DOI: 10.1002/anie.202003115
      14b
      The Huisgen Reaction: Milestones of the 1,3-Dipolar Cycloaddition
      Breugst, Martin; Reissig, Hans-Ulrich
      Angewandte Chemie, International Edition (2020), 59 (30), 12293-12307CODEN: ACIEF5; ISSN:1433-7851. (Wiley-VCH Verlag GmbH & Co. KGaA)
      A review. The concept of 1,3-dipolar cycloaddns. was presented by Rolf Huisgen 60 years ago. Previously unknown reactive intermediates, for example azomethine ylides, were introduced to org. chem. and the (3+2) cycloaddns. of 1,3-dipoles to multiple-bond systems (Huisgen reaction) developed into one of the most versatile synthetic methods in heterocyclic chem. In this Review, the authors present the history of this research area, highlight important older reports, and describe the evolution and further development of the concept. The most important mechanistic and synthetic results are discussed. Quantum-mech. calcns. support the concerted mechanism always favored by R. Huisgen; however, in extreme cases intermediates may be involved. The impact of 1,3-dipolar cycloaddns. on the click chem. concept of K. B. Sharpless will also be discussed.
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    15. 15

      For some selected computational studies on the reactivity of azides in 1,3-dipolar cycloadditions, see:

      (a) Hamlin, T. A.; Levandowski, B. J.; Narsaria, A. K.; Houk, K. N.; Bickelhaupt, F. M. Structural Distortion of Cycloalkynes Influences Cycloaddition Rates both by Strain and Interaction Energies. Chem. Eur. J. 2019, 25, 6342– 6348,  DOI: 10.1002/chem.201900295
      15a
      Structural Distortion of Cycloalkynes Influences Cycloaddition Rates both by Strain and Interaction Energies
      Hamlin, Trevor A.; Levandowski, Brian J.; Narsaria, Ayush K.; Houk, Kendall N.; Bickelhaupt, F. Matthias
      Chemistry - A European Journal (2019), 25 (25), 6342-6348CODEN: CEUJED; ISSN:0947-6539. (Wiley-VCH Verlag GmbH & Co. KGaA)
      The reactivities of 2-butyne, cycloheptyne, cyclooctyne, and cyclononyne in the 1,3-dipolar cycloaddn. reaction with Me azide were evaluated through DFT calcns. at the M06-2X/6-311++G(d)//M06-2X/6-31+G(d) level of theory. Computed activation free energies for the cycloaddns. of cycloalkynes are 16.5-22.0 kcal mol-1 lower in energy than that of the acyclic 2-butyne. The strained or predistorted nature of cycloalkynes is often solely used to rationalize this significant rate enhancement. Our distortion/interaction-activation strain anal. has been revealed that the degree of geometrical predistortion of the cycloalkyne ground-state geometries acts to enhance reactivity compared with that of acyclic alkynes through three distinct mechanisms, not only due to (i) a reduced strain or distortion energy, but also to (ii) a smaller HOMO-LUMO gap, and (iii) an enhanced orbital overlap, which both contribute to more stabilizing orbital interactions.
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      (b) Dommerholt, J.; van Rooijen, O.; Borrmann, A.; Fonseca Guerra, C.; Bickelhaupt, F. M.; van Delft, F. L. Highly Accelerated Inverse Electron-Demand Cycloaddition of Electron-Deficient Azides with Aliphatic Cyclooctynes. Nat. Commun. 2014, 5, 5378,  DOI: 10.1038/ncomms6378
      15b
      Highly accelerated inverse electron-demand cycloaddition of electron-deficient azides with aliphatic cyclooctynes
      Dommerholt, Jan; van Rooijen, Olivia; Borrmann, Annika; Guerra, Celia Fonseca; Bickelhaupt, F. Matthias; van Delft, Floris L.
      Nature Communications (2014), 5 (), 5378CODEN: NCAOBW; ISSN:2041-1723. (Nature Publishing Group)
      Strain-promoted azide-alkyne cycloaddn. (SPAAC) as a conjugation tool has found broad application in material sciences, chem. biol. and even in vivo use. However, despite tremendous effort, SPAAC remains fairly slow (0.2-0.5 M-1 s-1) and efforts to increase reaction rates by tailoring of cyclooctyne structure have suffered from a poor trade-off between cyclooctyne reactivity and stability. We here wish to report tremendous acceleration of strain-promoted cycloaddn. of an aliph. cyclooctyne (bicyclo[6.1.0]non-4-yne, BCN) with electron-deficient aryl azides, with reaction rate consts. reaching 2.0-2.9 M-1 s-1. A remarkable difference in rate consts. of aliph. cyclooctynes vs. benzoannulated cyclooctynes is noted, enabling a next level of orthogonality by a judicious choice of azide-cyclooctyne combinations, which is inter alia applied in one-pot three-component protein labeling. The pivotal role of azide electronegativity is explained by d.-functional theory calcns. and electronic-structure analyses, which indicates an inverse electron-demand mechanism is operative with an aliph. cyclooctyne.
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      (c) Lopez, S. A.; Munk, M. E.; Houk, K. N. Mechanisms and Transition States of 1,3-Dipolar Cycloadditions of Phenyl Azide with Enamines: A Computational Analysis. J. Org. Chem. 2013, 78, 1576– 1582,  DOI: 10.1021/jo302695n
      15c
      Mechanisms and Transition States of 1,3-Dipolar Cycloadditions of Phenyl Azide with Enamines: A Computational Analysis
      Lopez, Steven A.; Munk, Morton E.; Houk, K. N.
      Journal of Organic Chemistry (2013), 78 (4), 1576-1582CODEN: JOCEAH; ISSN:0022-3263. (American Chemical Society)
      The transition structures for the 1,3-dipolar cycloaddns. of Ph azide to enamines derived from acetophenone or phenylacetaldehyde and piperidine, morpholine, or pyrrolidine were located using quantum mech. methods. These cycloaddns. were studied exptl. in 1975 by Meilahn, Cox, and Munk (J. Org. Chem.1975, 40, 819-823). Calcns. were carried out with M06-2X/6-311+G(d,p), SCS-MP2/6-311+G(d,p)//M06-2X/6-311+G(d,p), and B97D/6-311+G(d,p) methods with the IEF-PCM solvation model for chloroform and ethanol. The distortion/interaction model was utilized to understand mechanisms, reactivities, and selectivities.
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      (d) Lopez, S. A.; Houk, K. N. Alkene Distortion Energies and Torsional Effects Control Reactivities, and Stereoselectivities of Azide Cycloadditions to Norbornene and Substituted Norbornenes. J. Org. Chem. 2013, 78, 1778– 1783,  DOI: 10.1021/jo301267b
      15d
      Alkene Distortion Energies and Torsional Effects Control Reactivities, and Stereoselectivities of Azide Cycloadditions to Norbornene and Substituted Norbornenes
      Lopez, Steven A.; Houk, K. N.
      Journal of Organic Chemistry (2013), 78 (5), 1778-1783CODEN: JOCEAH; ISSN:0022-3263. (American Chemical Society)
      The transition structures for 1,3-dipolar cycloaddns. of Ph azide to norbornene derivs. were located with quantum mech. methods. Calcns. were carried out with M06-2X/6-311G(d,p) and SCS-MP2/6-311G(d,p)//M06-2X/6-311G(d,p) methods. The calcd. activation barriers strongly correlate with transition state distortion energies (ΔEd‡) but not with the reaction energies. Strain-promoted reactions are accelerated because it is easy to distort the strained reactants to a pyramidalized transition state geometry; a correlation of cycloaddn. rates with substrate distortion was found for the bicyclic and tricyclic alkenes studied here. The stereoselectivities of reactions of norbornene derivs. are controlled primarily by torsional effects that also influence alkene pyramidalization. These reactions are distortion-accelerated.
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    16. 16
      Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Petersson, G. A.; Nakatsuji, H.; Li, X.; Caricato, M.; Marenich, A. V.; Bloino, J.; Janesko, B. G.; Gomperts, R.; Mennucci, B.; Hratchian, H. P.; Ortiz, J. V.; Izmaylov, A. F.; Sonnenberg, J. L.; Williams; ; Ding, F.; Lipparini, F.; Egidi, F.; Goings, J.; Peng, B.; Petrone, A.; Henderson, T.; Ranasinghe, D.; Zakrzewski, V. G.; Gao, J.; Rega, N.; Zheng, G.; Liang, W.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Vreven, T.; Throssell, K.; Montgomery, J. A., Jr.; Peralta, J. E.; Ogliaro, F.; Bearpark, M. J.; Heyd, J. J.; Brothers, E. N.; Kudin, K. N.; Staroverov, V. N.; Keith, T. A.; Kobayashi, R.; Normand, J.; Raghavachari, K.; Rendell, A. P.; Burant, J. C.; Iyengar, S. S.; Tomasi, J.; Cossi, M.; Millam, J. M.; Klene, M.; Adamo, C.; Cammi, R.; Ochterski, J. W.; Martin, R. L.; Morokuma, K.; Farkas, O.; Foresman, J. B.; Fox, D. J. Gaussian 16, Rev. A.03, Wallingford, CT, 2016.
      There is no corresponding record for this reference.
    17. 17
      Chai, J.-D.; Head-Gordon, M. Long-Range Corrected Hybrid Density Functionals with Damped Atom–Atom Dispersion Corrections. Phys. Chem. Chem. Phys. 2008, 10, 6615– 6620,  DOI: 10.1039/b810189b
      17
      Long-range corrected hybrid density functionals with damped atom-atom dispersion corrections
      Chai, Jeng-Da; Head-Gordon, Martin
      Physical Chemistry Chemical Physics (2008), 10 (44), 6615-6620CODEN: PPCPFQ; ISSN:1463-9076. (Royal Society of Chemistry)
      We report re-optimization of a recently proposed long-range cor. (LC) hybrid d. functional [J.-D. Chai and M. Head-Gordon, J. Chem. Phys., 2008, 128, 084106] to include empirical atom-atom dispersion corrections. The resulting functional, ωB97X-D yields satisfactory accuracy for thermochem., kinetics, and non-covalent interactions. Tests show that for non-covalent systems, ωB97X-D shows slight improvement over other empirical dispersion-cor. d. functionals, while for covalent systems and kinetics it performs noticeably better. Relative to our previous functionals, such as ωB97X, the new functional is significantly superior for non-bonded interactions, and very similar in performance for bonded interactions.
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    18. 18
      (a) Grimme, S. Semiempirical Hybrid Density Functional with Perturbative Second-order Correlation. J. Chem. Phys. 2006, 124, 034108  DOI: 10.1063/1.2148954
      18a
      Semiempirical hybrid density functional with perturbative second-order correlation
      Grimme, Stefan
      Journal of Chemical Physics (2006), 124 (3), 034108/1-034108/16CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
      A new hybrid d. functional for general chem. applications is proposed. It is based on a mixing of std. generalized gradient approxns. (GGAs) for exchange by Becke (B) and for correlation by Lee, Yang, and Parr (LYP) with Hartree-Fock (HF) exchange and a perturbative second-order correlation part (PT2) that is obtained from the Kohn-Sham (GGA) orbitals and eigenvalues. This virtual orbital-dependent functional contains only two global parameters that describe the mixt. of HF and GGA exchange (ax) and of the PT2 and GGA correlation (c), resp. The parameters are obtained in a least-squares-fit procedure to the G2/97 set of heat of formations. Opposed to conventional hybrid functionals, the optimum ax is found to be quite large (53% with c = 27%) which at least in part explains the success for many problematic mol. systems compared to conventional approaches. The performance of the new functional termed B2-PLYP is assessed by the G2/97 std. benchmark set, a second test suite of atoms, mols., and reactions that are considered as electronically very difficult (including transition-metal compds., weakly bonded complexes, and reaction barriers) and comparisons with other hybrid functionals of GGA and meta-GGA types. According to many realistic tests, B2-PLYP can be regarded as the best general purpose d. functional for mols. (e.g., a mean abs. deviation for the two test sets of only 1.8 and 3.2 kcal/mol compared to about 3 and 5 kcal/mol, resp., for the best other d. functionals). Very importantly, also the max. and minium errors (outliers) are strongly reduced (by about 10-20 kcal/mol). Furthermore, very good results are obtained for transition state barriers but unlike previous attempts at such a good description, this definitely comes not at the expense of equil. properties. Preliminary calcns. of the equil. bond lengths and harmonic vibrational frequencies for diat. mols. and transition-metal complexes also show very promising results. The uniformity with which B2-PLYP improves for a wide range of chem. systems emphasizes the need of (virtual) orbital-dependent terms that describe nonlocal electron correlation in accurate exchange-correlation functionals. From a practical point of view, the new functional seems to be very robust and it is thus suggested as an efficient quantum chem. method of general purpose.
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      (b) Grimme, S. Semiempirical GGA-Type Density Functional Constructed with A Long-Range Dispersion Correction. J. Comput. Chem. 2006, 27, 1787– 1799,  DOI: 10.1002/jcc.20495
      18b
      Semiempirical GGA-type density functional constructed with a long-range dispersion correction
      Grimme, Stefan
      Journal of Computational Chemistry (2006), 27 (15), 1787-1799CODEN: JCCHDD; ISSN:0192-8651. (John Wiley & Sons, Inc.)
      A new d. functional (DF) of the generalized gradient approxn. (GGA) type for general chem. applications termed B97-D is proposed. It is based on Becke's power-series ansatz from 1997 and is explicitly parameterized by including damped atom-pairwise dispersion corrections of the form C6·R-6. A general computational scheme for the parameters used in this correction has been established and parameters for elements up to xenon and a scaling factor for the dispersion part for several common d. functionals (BLYP, PBE, TPSS, B3LYP) are reported. The new functional is tested in comparison with other GGAs and the B3LYP hybrid functional on std. thermochem. benchmark sets, for 40 noncovalently bound complexes, including large stacked arom. mols. and group II element clusters, and for the computation of mol. geometries. Further cross-validation tests were performed for organometallic reactions and other difficult problems for std. functionals. In summary, it is found that B97-D belongs to one of the most accurate general purpose GGAs, reaching, for example for the G97/2 set of heat of formations, a mean abs. deviation of only 3.8 kcal mol-1. The performance for noncovalently bound systems including many pure van der Waals complexes is exceptionally good, reaching on the av. CCSD(T) accuracy. The basic strategy in the development to restrict the d. functional description to shorter electron correlation lengths scales and to describe situations with medium to large interat. distances by damped C6·R-6 terms seems to be very successful, as demonstrated for some notoriously difficult reactions. As an example, for the isomerization of larger branched to linear alkanes, B97-D is the only DF available that yields the right sign for the energy difference. From a practical point of view, the new functional seems to be quite robust and it is thus suggested as an efficient and accurate quantum chem. method for large systems where dispersion forces are of general importance.
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    19. 19
      (a) Dunning, T. H. Gaussian-Basis Sets for Use in Correlated Molecular Calculations. I. The Atoms Boron through Neon and Hydrogen. J. Chem. Phys. 1989, 90, 1007– 1023,  DOI: 10.1063/1.456153
      19a
      Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogen
      Dunning, Thom H., Jr.
      Journal of Chemical Physics (1989), 90 (2), 1007-23CODEN: JCPSA6; ISSN:0021-9606.
      Guided by the calcns. on oxygen in the literature, basis sets for use in correlated at. and mol. calcns. were developed for all of the first row atoms from boron through neon, and for hydrogen. As in the oxygen atom calcns., the incremental energy lowerings, due to the addn. of correlating functions, fall into distinct groups. This leads to the concept of correlation-consistent basis sets, i.e., sets which include all functions in a given group as well as all functions in any higher groups. Correlation-consistent sets are given for all of the atoms considered. The most accurate sets detd. in this way, [5s4p3d2f1g], consistently yield 99% of the correlation energy obtained with the corresponding at.-natural-orbital sets, even though the latter contains 50% more primitive functions and twice as many primitive polarization functions. It is estd. that this set yields 94-97% of the total (HF + 1 + 2) correlation energy for the atoms neon through boron.
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      (b) Kendall, R. A.; Dunning Jr, T. H.; Harrison, R. J. Electron Affinities of the First-Row Atoms Revisited. Systematic Basis Sets and Wave Functions. J. Chem. Phys. 1992, 96, 6796– 6806,  DOI: 10.1063/1.462569
      19b
      Electron affinities of the first-row atoms revisited. Systematic basis sets and wave functions
      Kendall, Rick A.; Dunning, Thom H., Jr.; Harrison, Robert J.
      Journal of Chemical Physics (1992), 96 (9), 6796-806CODEN: JCPSA6; ISSN:0021-9606.
      The authors describe a reliable procedure for calcg. the electron affinity of an atom and present results for H, B, C, O, and F (H is included for completeness). This procedure involves the use of the recently proposed correlation-consistent basis sets augmented with functions to describe the more diffuse character of the at. anion coupled with a straightforward, uniform expansion of the ref. space for multireference singles and doubles configuration-interaction (MRSD-CI) calcns. A comparison is given with previous results and with corresponding full CI calcns. The most accurate EAs obtained from the MRSD-CI calcns. are (with exptl. values in parentheses): H 0.740 eV (0.754), B 0.258 (0.277), C 1.245 (1.263), O 1.384 (1.461), and F 3.337 (3.401). The EAs obtained from the MR-SDCI calcns. differ by less than 0.03 eV from those predicted by the full CI calcns.
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    20. 20
      Cossi, M.; Rega, N.; Scalmani, G.; Barone, V. Energies, Structures, and Electronic Properties of Molecules in Solution with the C-PCM Solvation Model. J. Comput. Chem. 2003, 24, 669– 681,  DOI: 10.1002/jcc.10189
      20
      Energies, structures, and electronic properties of molecules in solution with the C-PCM solvation model
      Cossi, Maurizio; Rega, Nadia; Scalmani, Giovanni; Barone, Vincenzo
      Journal of Computational Chemistry (2003), 24 (6), 669-681CODEN: JCCHDD; ISSN:0192-8651. (John Wiley & Sons, Inc.)
      The conductor-like solvation model, as developed in the framework of the polarizable continuum model (PCM), has been reformulated and newly implemented in order to compute energies, geometric structures, harmonic frequencies, and electronic properties in soln. for any chem. system that can be studied in vacuo. Particular attention is devoted to large systems requiring suitable iterative algorithms to compute the solvation charges: the fast multipole method (FMM) has been extensively used to ensure a linear scaling of the computational times with the size of the solute. A no. of test applications are presented to evaluate the performances of the method.
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    21. 21
      (a) Lu, T.; Chen, F. Multiwfn: A Multifunctional Wavefunction Analyzer. J. Comput. Chem. 2012, 33, 580– 592,  DOI: 10.1002/jcc.22885
      21a
      Multiwfn: A multifunctional wavefunction analyzer
      Lu, Tian; Chen, Feiwu
      Journal of Computational Chemistry (2012), 33 (5), 580-592CODEN: JCCHDD; ISSN:0192-8651. (John Wiley & Sons, Inc.)
      Multiwfn is a multifunctional program for wavefunction anal. Its main functions are: (1) Calcg. and visualizing real space function, such as electrostatic potential and electron localization function at point, in a line, in a plane or in a spatial scope. (2) Population anal. (3) Bond order anal. (4) Orbital compn. anal. (5) Plot d.-of-states and spectrum. (6) Topol. anal. for electron d. Some other useful utilities involved in quantum chem. studies are also provided. The built-in graph module enables the results of wavefunction anal. to be plotted directly or exported to high-quality graphic file. The program interface is very user-friendly and suitable for both research and teaching purpose. The code of Multiwfn is substantially optimized and parallelized. Its efficiency is demonstrated to be significantly higher than related programs with the same functions. Five practical examples involving a wide variety of systems and anal. methods are given to illustrate the usefulness of Multiwfn. The program is free of charge and open-source. Its precompiled file and source codes are available from http://multiwfn.codeplex.com. © 2011 Wiley Periodicals, Inc. J Comput Chem, 2011.
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      (b) Lu, T.; Chen, F. Quantitative Analysis of Molecular Surface Based on Improved Marching Tetrahedra Algorithm. J. Mol. Graphics Model. 2012, 38, 314– 323,  DOI: 10.1016/j.jmgm.2012.07.004
      21b
      Quantitative analysis of molecular surface based on improved Marching Tetrahedra algorithm
      Lu, Tian; Chen, Feiwu
      Journal of Molecular Graphics & Modelling (2012), 38 (), 314-323CODEN: JMGMFI; ISSN:1093-3263. (Elsevier Ltd.)
      Quant. anal. of mol. surface is a valuable technique for analyzing non-covalent interaction, studying mol. recognition mode, predicting reactive site and reactivity. An efficient way to realize the anal. was first proposed by Bulat et al. (J. Mol. Model., 16, 1679), in which Marching Tetrahedra (MT) approach commonly used in computer graphics is employed to generate vertices on mol. surface. However, it has been found that the computations of the electrostatic potential in the MT vertices are very expensive and some artificial surface extremes will be presented due to the uneven distribution of MT vertices. In this article, we propose a simple and reliable method to eliminate these unreasonably distributed surface vertices generated in the original MT. This treatment can save more than 60% of total anal. time of electrostatic potential, yet the loss in accuracy is almost negligible. The artificial surface extremes are also largely avoided as a byproduct of this algorithm. In addn., the bisection iteration procedure has been exploited to improve accuracy of linear interpolation in MT. The most appropriate grid spacing for surface anal. has also been investigated. 0.25 and 0.20 bohr are recommended to be used for surface anal. of electrostatic potential and av. local ionization energy, resp.
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    22. 22
      Humphrey, W.; Dalke, A.; Schulten, K. VMD: Visual Molecular Dynamics. J. Mol. Graphics. 1996, 14, 33– 38,  DOI: 10.1016/0263-7855(96)00018-5
      22
      VDM: visual molecular dynamics
      Humphrey, William; Dalke, Andrew; Schulten, Klaus
      Journal of Molecular Graphics (1996), 14 (1), 33-8, plates, 27-28CODEN: JMGRDV; ISSN:0263-7855. (Elsevier)
      VMD is a mol. graphics program designed for the display and anal. of mol. assemblies, in particular, biopolymers such as proteins and nucleic acids. VMD can simultaneously display any no. of structures using a wide variety of rendering styles and coloring methods. Mols. are displayed as one or more "representations," in which each representation embodies a particular rendering method and coloring scheme for a selected subset of atoms. The atoms displayed in each representation are chosen using an extensive atom selection syntax, which includes Boolean operators and regular expressions. VMD provides a complete graphical user interface for program control, as well as a text interface using the Tcl embeddable parser to allow for complex scripts with variable substitution, control loops, and function calls. Full session logging is supported, which produces a VMD command script for later playback. High-resoln. raster images of displayed mols. may be produced by generating input scripts for use by a no. of photorealistic image-rendering applications. VMD has also been expressly designed with the ability to animate mol. dynamics (MD) simulation trajectories, imported either from files or from a direct connection to a running MD simulation. VMD is the visualization component of MDScope, a set of tools for interactive problem solving in structural biol., which also includes the parallel MD program NAMD, and the MDCOMM software used to connect the visualization and simulation programs, VMD is written in C++, using an object-oriented design; the program, including source code and extensive documentation, is freely available via anonymous ftp and through the World Wide Web.
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      VMD Official website. http://www.ks.uiuc.edu/Research/ vmd/.

    23. 23
      Svatunek, D.; Houk, K. N. autoDIAS: A Python Tool for an Automated Distortion/Interaction Activation Strain Analysis. J. Comput. Chem. 2019, 40, 2509– 2515,  DOI: 10.1002/jcc.26023
      23
      autoDIAS: a python tool for an automated distortion/interaction activation strain analysis
      Svatunek, Dennis; Houk, Kendall N.
      Journal of Computational Chemistry (2019), 40 (28), 2509-2515CODEN: JCCHDD; ISSN:0192-8651. (John Wiley & Sons, Inc.)
      The distortion/interaction activation strain (DIAS) anal. is a powerful tool for the investigation of energy barriers. However, setup and data anal. of such a calcn. can be cumbersome and requires lengthy intervention of the user. We present autoDIAS, a python tool for the automated setup, performance, and data extn. of the DIAS anal., including automated detection of fragments and relevant geometric parameters. © 2019 Wiley Periodicals, Inc.
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    24. 24
      te Velde, G.; Bickelhaupt, F. M.; Baerends, E. J.; Fonseca Guerra, C.; van Gisbergen, S. J. A.; Snijders, J. G.; Ziegler, T. Chemistry with ADF. J. Comput. Chem. 2001, 22, 931– 967,  DOI: 10.1002/jcc.1056
      24
      Chemistry with ADF
      Te Velde, G.; Bickelhaupt, F. M.; Baerends, E. J.; Fonseca Guerra, C.; Van Gisbergen, S. J. A.; Snijders, J. G.; Ziegler, T.
      Journal of Computational Chemistry (2001), 22 (9), 931-967CODEN: JCCHDD; ISSN:0192-8651. (John Wiley & Sons, Inc.)
      A review with 241 refs. We present the theor. and tech. foundations of the Amsterdam D. Functional (ADF) program with a survey of the characteristics of the code (numerical integration, d. fitting for the Coulomb potential, and STO basis functions). Recent developments enhance the efficiency of ADF (e.g., parallelization, near order-N scaling, QM/MM) and its functionality (e.g., NMR chem. shifts, COSMO solvent effects, ZORA relativistic method, excitation energies, frequency-dependent (hyper)polarizabilities, at. VDD charges). In the Applications section we discuss the phys. model of the electronic structure and the chem. bond, i.e., the Kohn-Sham MO (MO) theory, and illustrate the power of the Kohn-Sham MO model in conjunction with the ADF-typical fragment approach to quant. understand and predict chem. phenomena. We review the "Activation-strain TS interaction" (ATS) model of chem. reactivity as a conceptual framework for understanding how activation barriers of various types of (competing) reaction mechanisms arise and how they may be controlled, for example, in org. chem. or homogeneous catalysis. Finally, we include a brief discussion of exemplary applications in the field of biochem. (structure and bonding of DNA) and of time-dependent d. functional theory (TDDFT) to indicate how this development further reinforces the ADF tools for the anal. of chem. phenomena.
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    25. 25
      Baerends, E. J.; Ellis, D. E.; Ros, P. Self-Consistent Molecular Hartree-Fock-Slater Calculations I. The Computational Procedure. Chem. Phys. 1973, 2, 41– 51,  DOI: 10.1016/0301-0104(73)80059-X
      25
      Self-consistent molecular Hartree-Fock-Slater calculations. I. Computational procedure
      Baerends, E. J.; Ellis, D. E.; Ros, P.
      Chemical Physics (1973), 2 (1), 41-51CODEN: CMPHC2; ISSN:0301-0104.
      A numerical-variational computational scheme is presented for making SCF-LCAO-MO calcns. with the Hartree-Fock-Slater model (e.g., J. C. Slater and K. H. Johnson, 1972). The local exchange approxn. is used, but the usual muffin-tin approxn. for the potentials or ds. (e.g., J. and F. C. Smith Jr., 1972) is avoided. Procedures are given that are specifically optimized for treating large systems such as transition-metal complexes. Illustrative calcns. are given of the electronic structure of mol. CO, and the bond lengths of LiF, NO, N2, O2, and C2H4. The 1-electron energies and the charge distributions can be calcd. rapidly, whereas the total energies, and therefore the optimized mol. geometries, require more computation time.
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    26. 26
      Sun, X.; Soini, T. M.; Poater, J.; Hamlin, T. A.; Bickelhaupt, F. M. PyFrag 2019-Automating the Exploration and Analysis of Reaction Mechanisms. J. Comput. Chem. 2019, 40, 2227– 2233,  DOI: 10.1002/jcc.25871
      26
      PyFrag 2019-Automating the exploration and analysis of reaction mechanisms
      Sun, Xiaobo; Soini, Thomas M.; Poater, Jordi; Hamlin, Trevor A.; Bickelhaupt, F. Matthias
      Journal of Computational Chemistry (2019), 40 (25), 2227-2233CODEN: JCCHDD; ISSN:0192-8651. (John Wiley & Sons, Inc.)
      We present a substantial update to the PyFrag 2008 program, which was originally designed to perform a fragment-based activation strain anal. along a provided potential energy surface. The original PyFrag 2008 workflow facilitated the characterization of reaction mechanisms in terms of the intrinsic properties, such as strain and interaction, of the reactants. The new PyFrag 2019 program has automated and reduced the time-consuming and laborious task of setting up, running, analyzing, and visualizing computational data from reaction mechanism studies to a single job. PyFrag 2019 resolves three main challenges assocd. with the automated computational exploration of reaction mechanisms: it (1) computes the reaction path by carrying out multiple parallel calcns. using initial coordinates provided by the user; (2) monitors the entire workflow process; and (3) tabulates and visualizes the final data in a clear way. The activation strain and canonical energy decompn. results that are generated relate the characteristics of the reaction profile in terms of intrinsic properties (strain, interaction, orbital overlaps, orbital energies, populations) of the reactant species.
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    27. 27
      (a) Foster, J. P.; Weinhold, F. Natural Hybrid Orbitals. J. Am. Chem. Soc. 1980, 102, 7211– 7218,  DOI: 10.1021/ja00544a007
      27a
      Natural hybrid orbitals
      Foster, J. P.; Weinhold, F.
      Journal of the American Chemical Society (1980), 102 (24), 7211-18CODEN: JACSAT; ISSN:0002-7863.
      From the information contained in the (exact or approx.) 1st-order d. matrix, a method is described for extg. a unique set of at. hybrids and bond orbitals for a given mol., thereby constructing its Lewis structure in an a priori manner. The natural hybrids are optimal in a certain sense, they are efficiently computed, and agree with chem. intuition (as summarized, for example, in H. A. Bent's Rule (1961) and with hybrids obtained by other procedures). By using simple INDO-SCF-MO wave functions, applications are given of the natural hybrid orbital anal. to mols. exhibiting a variety of bonding features, including lone pairs, multiple bonds, strained rings and bent bonds, multiple resonance structures, H-bonds, and 3-center bonds. Three examples are given: (1) orbital following during NH3 umbrella inversion, (2) dimerization of water mols., and (3) the H-bridged bonds of diborane.
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      (b) Reed, A. E.; Weinstock, R. B.; Weinhold, F. Natural Population Analysis. J. Chem. Phys. 1985, 83, 735– 746,  DOI: 10.1063/1.449486
      27b
      Natural population analysis
      Reed, Alan E.; Weinstock, Robert B.; Weinhold, Frank
      Journal of Chemical Physics (1985), 83 (2), 735-46CODEN: JCPSA6; ISSN:0021-9606.
      A method of "natural population anal." was developed to calc. at. charges and orbital populations of mol. wave functions in general AO basis sets. The natural anal. is an alternative to the conventional Mulliken population anal., and seems to exhibit improved numerical stability, and to describe better the electron distribution in compds. of high ionic character, such as those contg. metal atoms. Ab-initio SCF-MO wave functions were calcd. for compds. of type CH3X and LiX (X = F, OH, NH2, CH3, BH2, BeH, Li, H) in a variety of basis sets to illustrate the generality of the method, and to compare the natural populations with results of Mulliken anal., d. integration, and empirical measures of ionic character. Natural populations gave a satisfactory description of these mols., and provided a unified treatment of covalent and extreme ionic limits at modest computational cost.
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    28. 28
      Legault, C. Y. CYLview; version 1.0b; Université de Sherbrooke: 2009 (http://www.cylview.org).
      There is no corresponding record for this reference.
    29. 29
      We calculated the rate constants from the activation barriers based on Eyring Equation, which follows from the transition state theory, also known as activated-complex theory.
      There is no corresponding record for this reference.
    30. 30
      Huisgen, R.; Szeimie, G.; Möbius, L. 1.3-Dipolare Cycloadditionen, XXXII. Kinetik der Additionen organischer Azide an CC-Mehrfachbindungen. Chem. Ber. 1967, 100, 2494– 2507,  DOI: 10.1002/cber.19671000806
      30
      1,3-Dipolar cycloadditions. XXXII. Kinetics of the addition of organic azides to carbon-carbon multiple bonds
      Huisgen, Rolf; Szeimies, Guenter; Moebius, Leander
      Chemische Berichte (1967), 100 (8), 2494-507CODEN: CHBEAM; ISSN:0009-2940.
      cf. preceding abstr. The ir spectrophotometrically-detd. addn. consts. of phenyl azide to 27 olefinic and 4 acetylenic dipolarophiles at 25° are of the 107 order of magnitude. The interaction between electronic and steric substitution effects on the dipolarophiles is discussed. The addn. rates of the ring-substituted phenyl azides obeyed the Hammett equation; the ρ values depended on the dipolarophile, and are as follows: maleic anhydride -1.1, N-phenylmaleimide -0.8, norbornene 0.88, cyclopentene 0.9, 1-pyrrolidinocyclohexene 2.5. The activation entropies for cycloaddn. of the 4 azides are -26 to -36 cal./mole degree. The addn. const. of phenyl azide to pyrrolidinocyclopentane depends only slightly on the polarity of the solvent. The cycloaddn. of azides seems to be a multicenter reaction.
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    31. 31
      Koopmans, T. Über die Zuordnung von Wellenfunktionen und Eigenwerten zu den einzelnen Elektronen eines Atoms. Physica. 1934, 1, 104– 113,  DOI: 10.1016/S0031-8914(34)90011-2
      There is no corresponding record for this reference.
    32. 32

      The exact dipolarophile used in the experiment is 1-ethoxycyclopentene. (30) In the calculation, 1-methoxycyclopentene is substituted for 1-ethoxycyclopentene in order to simplify the calculation model.

      There is no corresponding record for this reference.
    33. 33
      Liu, F.; Liang, Y.; Houk, K. N. Theoretical Elucidation of the Origins of Substituent and Strain Effects on the Rates of Diels–Alder Reactions of 1,2,4,5-Tetrazines. J. Am. Chem. Soc. 2014, 136, 11483– 11493,  DOI: 10.1021/ja505569a
      33
      Theoretical Elucidation of the Origins of Substituent and Strain Effects on the Rates of Diels-Alder Reactions of 1,2,4,5-Tetrazines
      Liu, Fang; Liang, Yong; Houk, K. N.
      Journal of the American Chemical Society (2014), 136 (32), 11483-11493CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
      The Diels-Alder reactions of seven 1,2,4,5-tetrazines with unstrained and strained alkenes and alkynes were studied with quantum mech. calcns. (M06-2X d. functional theory) and analyzed with the distortion/interaction model. The higher reactivities of alkenes compared to alkynes in the Diels-Alder reactions with tetrazines arise from the differences in both interaction and distortion energies. Alkenes have HOMO energies higher than those of alkynes and therefore stronger interaction energies in inverse-electron-demand Diels-Alder reactions with tetrazines. We have also found that the energies to distort alkenes into the Diels-Alder transition-state geometries are smaller than for alkynes in these reactions. The strained dienophiles, trans-cyclooctene and cyclooctyne, are much more reactive than unstrained trans-2-butene and 2-butyne, because they are predistorted toward the Diels-Alder transition structures. The reactivities of substituted tetrazines correlate with the electron-withdrawing abilities of the substituents. Electron-withdrawing groups lower the LUMO+1 of tetrazines, resulting in stronger interactions with the HOMO of dienophiles. Moreover, electron-withdrawing substituents destabilize the tetrazines, and this leads to smaller distortion energies in the Diels-Alder transition states.
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    34. 34
      (a) Agard, N. J.; Prescher, J. A.; Bertozzi, C. R. A Strain-Promoted [3 + 2] Azide–Alkyne Cycloaddition for Covalent Modification of Biomolecules in Living Systems. J. Am. Chem. Soc. 2004, 126, 15046– 15047,  DOI: 10.1021/ja044996f
      34a
      A strain-promoted [3+2] azide-alkyne cycloaddition for covalent modification of biomolecules in living systems
      Agard, Nicholas J.; Prescher, Jennifer A.; Bertozzi, Carolyn R.
      Journal of the American Chemical Society (2004), 126 (46), 15046-15047CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
      Selective chem. reactions that are orthogonal to the diverse functionality of biol. systems have become important tools in the field of chem. biol. Two notable examples are the Staudinger ligation of azides and phosphines and the Cu(I)-catalyzed [3+2] cycloaddn. of azides and alkynes ("click chem."). The Staudinger ligation has sufficient biocompatibility for performance in living animals but suffers from phosphine oxidn. and synthetic challenges. Click chem. obviates the requirement of phosphines, but the Cu(I) catalyst is toxic to cells, thereby precluding in vivo applications. Here we present a strain-promoted [3+2] cycloaddn. between cyclooctynes and azides that proceeds under physiol. conditions without the need for a catalyst. The utility of the reaction was demonstrated by selective modification of biomols. in vitro and on living cells, with no apparent toxicity.
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      (b) Lutz, J.-F. Copper-Free Azide–Alkyne Cycloadditions: New Insights and Perspectives. Angew. Chem., Int. Ed. 2008, 47, 2182– 2184,  DOI: 10.1002/anie.200705365
      34b
      Copper-free azide-alkyne cycloadditions: new insights and perspectives
      Lutz, Jean-Francois
      Angewandte Chemie, International Edition (2008), 47 (12), 2182-2184CODEN: ACIEF5; ISSN:1433-7851. (Wiley-VCH Verlag GmbH & Co. KGaA)
      A review. Copper-mediated azide-alkyne "click" cycloaddns. (CuAAC) play a central role in contemporary synthetic chem. but rely on transition-metal catalysts, which hamper their adoption in some biol. applications. Recently, the strain-promoted and fluorine-activated cycloaddn. of cyclooctynes and org. azides was proposed as an interesting metal-free alternative to CuAAC.
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      (c) Ning, X.; Guo, J.; Wolfert, M. A.; Boons, G.-J. Visualizing Metabolically Labeled Glycoconjugates of Living Cells by Copper-Free and Fast Huisgen Cycloadditions. Angew. Chem., Int. Ed. 2008, 47, 2253– 2255,  DOI: 10.1002/anie.200705456
      34c
      Visualizing metabolically labeled glycoconjugates of living cells by copper-free and fast huisgen cycloadditions
      Ning, Xinghai; Guo, Jun; Wolfert, Margreet A.; Boons, Geert-Jan
      Angewandte Chemie, International Edition (2008), 47 (12), 2253-2255CODEN: ACIEF5; ISSN:1433-7851. (Wiley-VCH Verlag GmbH & Co. KGaA)
      4-Dibenzocyclooctynol reacts, in the absence of a CuI catalyst, exceptionally fast with azido-contg. saccharides and amino acids to give stable triazoles. A biotin-modified deriv. is ideally suited for visualizing and tracking glycoconjugates of living cells that are metabolically labeled with azido-contg. monosaccharides.
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      (d) Patterson, D. M.; Nazarova, L. A.; Xie, B.; Kamber, D. N.; Prescher, J. A. Functionalized Cyclopropenes as Bioorthogonal Chemical Reporters. J. Am. Chem. Soc. 2012, 134, 18638– 18643,  DOI: 10.1021/ja3060436
      34d
      Functionalized Cyclopropenes as Bioorthogonal Chemical Reporters
      Patterson, David M.; Nazarova, Lidia A.; Xie, Bryan; Kamber, David N.; Prescher, Jennifer A.
      Journal of the American Chemical Society (2012), 134 (45), 18638-18643CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
      Chem. reporters are unique functional groups that can be used to label biomols. in living systems. Only a handful of broadly applicable reporters have been identified to date, owing to the rigorous demands placed on these functional groups in biol. settings. We describe here a new chem. reporter-cyclopropene-that can be used to target biomols. in vitro and in live cells. A variety of substituted cyclopropene scaffolds were synthesized and found to be stable in aq. soln. and in the presence of biol. nucleophiles. Furthermore, some of the cyclopropene units were metabolically introduced into cell surface glycans and subsequently detected with covalent probes. The small size and selective reactivity of cyclopropenes will facilitate efforts to tag diverse collections of biomols. in vivo.
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      (e) Yang, J.; Šečkutė, J.; Cole, C. M.; Devaraj, N. K. Live-Cell Imaging of Cyclopropene Tags with Fluorogenic Tetrazine Cycloadditions. Angew. Chem., Int. Ed. 2012, 51, 7476– 7479,  DOI: 10.1002/anie.201202122
      34e
      Live-Cell Imaging of Cyclopropene Tags with Fluorogenic Tetrazine Cycloadditions
      Yang, Jun; Seckute, Jolita; Cole, Christian M.; Devaraj, Neal K.
      Angewandte Chemie, International Edition (2012), 51 (30), 7476-7479, S7476/1-S7476/26CODEN: ACIEF5; ISSN:1433-7851. (Wiley-VCH Verlag GmbH & Co. KGaA)
      The authors demonstrated the applicability of methylcyclopropene tags as dienophiles for reaction with fluorogenic tetrazines. Through systematic synthetic modifications, the stability, size, and reactivity of the cyclopropene scaffold were optimized. Methylcyclopropene derivs. were developed that react rapidly with tetrazines while retaining their aq. stability and small size. These cyclopropene handles elicited fluorescent responses from quenched tetrazine dyes and were suitable for cellular imaging applications, which was demonstrated by imaging cyclopropene phospholipids distributed in live human breast cancer cells.
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      (f) Liu, F.; Liang, Y.; Houk, K. N. Bioorthogonal Cycloadditions: Computational Analysis with the Distortion/Interaction Model and Prediction of Reactivities. Acc. Chem. Res. 2017, 50, 2297– 2308,  DOI: 10.1021/acs.accounts.7b00265
      34f
      Bioorthogonal Cycloadditions: Computational Analysis with the Distortion/Interaction Model and Predictions of Reactivities
      Liu, Fang; Liang, Yong; Houk, K. N.
      Accounts of Chemical Research (2017), 50 (9), 2297-2308CODEN: ACHRE4; ISSN:0001-4842. (American Chemical Society)
      A review. Bioorthogonal chem. has had a major impact on the study of biol. processes in vivo. Biomols. of interest can be tracked by using probes and reporters that do not react with cellular components and do not interfere with metabolic processes in living cells. Much time and effort has been devoted to the screening of potential bioorthogonal reagents exptl. This Account describes how the groups have performed computational screening of reactivity, bioorthogonality, and mutual orthogonality. The collaborations with experimentalists have led to developments of new and useful reactions. Dozens of bioorthogonal cycloaddns. have been reported in the literature in the past few years, but as interest in tracking multiple targets arises, the computational screening has gained importance for the discovery of new mutually orthogonal bioorthogonal cycloaddn. pairs. The reactivities of strained alkenes and alkynes with common 1,3-dipoles such as azides, along with mesoionic sydnones and other novel 1,3-dipoles, have been explored. Studies of "inverse-electron-demand" dienes such as triazines and tetrazines that have been used in bioorthogonal Diels-Alder cycloaddns. are described. The color graphics the authors have developed gives a snapshot of whether reactions are fast enough for cellular applications (green), are adequately reactive for labeling (yellow), or are only useful for synthesis or do not occur at all (red). The colors of each box give an instant view of rates, while bar graphs provide an anal. of the factors that control reactivity. This anal. uses the Distortion/Interaction or Activation Strain model of cycloaddn. reactivity developed independently by the group and that of F. Matthias Bickelhaupt in The Netherlands. The model analyzes activation barriers in terms of the energy required to distort the reactants to the transition state geometry. This energy, called the distortion energy or activation strain, constitutes the major component of the activation energy. This distortion energy is overcome when the strong bonding interactions between the termini of the two reactants, which the authors call the interaction energy, overcomes the distortion energy, and leads to the new bonds in the products. This Account describes how the authors have analyzed and predicted bioorthogonal cycloaddn. reactivity using the Distortion/Interaction Model, and how the exptl. collaborators have employed these insights to create new bioorthogonal cycloaddns. The graphics the authors use document and predict which combinations of cycloaddns. will be useful in bioorthogonal chem. and which pairs of reactions are mutually orthogonal. For example, the fast reaction of 5-phenyl-1,2,4-triazine and a thiacycloheptyne will not interfere with the other fast reaction of 3,6-diphenyl-1,2,4,5-tetrazine and a cyclopropene. No cross reactions will occur as these are very slow reactions.
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    35. 35
      Wang, J.; Yang, B.; Cool, T. A.; Hansen, N.; Kasper, T. Near-Threshold Absolute Photoionization Cross-Sections of Some Reaction Intermediates in Combustion. Int. J. Mass Spectrom. 2008, 269, 210– 220,  DOI: 10.1016/j.ijms.2007.10.013
      35
      Near-threshold absolute photoionization cross-sections of some reaction intermediates in combustion
      Wang, Juan; Yang, Bin; Cool, Terrill A.; Hansen, Nils; Kasper, Tina
      International Journal of Mass Spectrometry (2008), 269 (3), 210-220CODEN: IMSPF8; ISSN:1387-3806. (Elsevier B.V.)
      The use of photoionization mass spectrometry for the development of quant. kinetic models for the complex combustion chem. of both conventional hydrocarbon fuels and oxygenated biofuels requires near-threshold measurements of abs. photoionization cross-sections for numerous reaction intermediates. Near-threshold abs. cross-sections for mol. and dissociative photoionization for 20 stable reaction intermediates (methane, ethane, propane, n-butane, cyclopropane, methylcyclopentane, 1-butene, cis-2-butene, isobutene, 1-pentene, cyclohexene, 3,3-dimethyl-1-butene, 1,3-hexadiene, 1,3-cyclohexadiene, Me acetate, Et acetate, THF, propanal, 1-butyne, 2-butyne) are presented. Previously measured total photoionization cross-sections for 9 of these mols. are in good agreement with the present results. The measurements are performed with photoionization mass spectrometry (PIMS) using a monochromated VUV synchrotron light source with an energy resoln. of 40 meV (fwhm) comparable to that used for flame-sampling mol. beam PIMS studies of flame chem. and reaction kinetics.
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    36. 36
      Liang, Y.; Mackey, J. L.; Lopez, S. A.; Liu, F.; Houk, K. N. Control and Design of Mutual Orthogonality in Bioorthogonal Cycloadditions. J. Am. Chem. Soc. 2012, 134, 17904– 17907,  DOI: 10.1021/ja309241e
      36
      Control and Design of Mutual Orthogonality in Bioorthogonal Cycloadditions
      Liang, Yong; Mackey, Joel L.; Lopez, Steven A.; Liu, Fang; Houk, K. N.
      Journal of the American Chemical Society (2012), 134 (43), 17904-17907CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
      The azide-dibenzocyclooctyne and trans-cyclooctene-tetrazine cycloaddns. are both bioorthogonal and mutually orthogonal: trans-cyclooctene derivs. greatly prefer to react with tetrazines rather than azides, while dibenzocyclooctyne derivs. react with azides but not with tetrazines under physiol. conditions. DFT calcns. used to identify the origins of this extraordinary selectivity are reported, and design principles to guide discovery of new orthogonal cycloaddns. are proposed. Two new bioorthogonal reagents, methylcyclopropene and 3,3,6,6-tetramethylthiacycloheptyne, are predicted to be mutually orthogonal in azide and tetrazine cycloaddns.
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    37. 37
      Himo, F.; Lovell, T.; Hilgraf, R.; Rostovtsev, V. V.; Noodleman, L.; Sharpless, K. B.; Fokin, V. V. Copper(I)-Catalyzed Synthesis of Azoles. DFT Study Predicts Unprecedented Reactivity and Intermediates. J. Am. Chem. Soc. 2005, 127, 210– 216,  DOI: 10.1021/ja0471525
      37
      Copper(I)-Catalyzed Synthesis of Azoles. DFT Study Predicts Unprecedented Reactivity and Intermediates
      Himo, Fahmi; Lovell, Timothy; Hilgraf, Robert; Rostovtsev, Vsevolod V.; Noodleman, Louis; Sharpless, K. Barry; Fokin, Valery V.
      Journal of the American Chemical Society (2005), 127 (1), 210-216CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
      Huisgen's 1,3-dipolar cycloaddns. become nonconcerted when copper(I) acetylides react with azides and nitrile oxides, providing ready access to 1,4-disubstituted 1,2,3-triazoles and 3,4-disubstituted isoxazoles, resp. The process is highly reliable and exhibits an unusually wide scope with respect to both components. Computational studies revealed a stepwise mechanism involving unprecedented metallacycle intermediates, which appear to be common for a variety of dipoles.
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    38. 38
      (a) Bader, R. F. W. An Interpretation of Potential Interaction Constants in Terms of Low-Lying Excited States. Molecular Physics. 1960, 3, 137– 151,  DOI: 10.1080/00268976000100161
      38a
      Interpretation of potential interaction constants in terms of low-lying excited states
      Bader, R. F. W.
      Molecular Physics (1960), 3 (), 137-51CODEN: MOPHAM; ISSN:0026-8976.
      Theoretical.
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      (b) Pearson, R. G. Concerning Jahn-Teller Effects. Proc. Nat. Acad. Sci. USA. 1975, 72, 2104– 2106,  DOI: 10.1073/pnas.72.6.2104
      38b
      Jahn-Teller effects
      Pearson, Ralph G.
      Proceedings of the National Academy of Sciences of the United States of America (1975), 72 (6), 2104-6CODEN: PNASA6; ISSN:0027-8424.
      Jahn-Teller effects are grouped into 2 categories. The 1st arises from incomplete shells of degenerate orbitals. It includes the 1st-order Jahn-Teller effect, and the pseudo Jahn-Teller effect. The 2nd arises from filled and empty mol. orbitals that are close in energy, and is the 2nd-order Jahn-Teller effect. The 2 categories have quite different phys. bases. As a result, geometric distortions produced by the 1st are quite small and normally lead to dynamic effects only. In favorable cases, the 2nd-order Jahn-Teller effect produces very large distortions, including complete dissocn. of a mol. This can occur even when the relevant mol. orbitals are sepd. in energy by as much as 4 eV.
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    39. 39
      (a) Fukui, K.; Yonezawa, T.; Shingu, H. A Molecular Orbital Theory of Reactivity in Aromatic Hydrocarbons. J. Chem. Phys. 1952, 20, 722– 725,  DOI: 10.1063/1.1700523
      39a
      A molecular-orbital theory of reactivity in aromatic hydrocarbons
      Fukui, Kenichi; Yonezawa, Teijiro; Shingu, Haruo
      Journal of Chemical Physics (1952), 20 (), 722-5CODEN: JCPSA6; ISSN:0021-9606.
      cf. Coulsen and Longuet-Higgins, C.A. 42, 1489i. In the search for a quant. correlation between reactivity and electronic configuration of aromatic hydrocarbons, the electron d., at each C atom, of the highest occupied π-orbital in the ground state of the mol. is calcd. by means of the linear-combination-of-at.-orbitals method. By comparing the result of such a calcn. on 15 condensed aromatic hydrocarbons with their chem. reactivities, the position at which the electron d. is largest is most readily attacked by electrophilic or oxidizing reagents. It is, therefore, concluded that, distinct from other π-electrons, the pair of π-electrons occupying the highest orbital, which is referred to as frontier electrons, plays a decisive role in chem. activation of these hydrocarbon mols. The theoretical significance of this discrimination of the frontier electrons in relation to the chem. activation is discussed.
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      (b) Fukui, K. Recognition of Stereochemical Paths by Orbital Interaction. Acc. Chem. Res. 1971, 4, 57– 64,  DOI: 10.1021/ar50038a003
      39b
      Recognition of stereochemical paths by orbital interaction
      Fukui, Kenichi
      Accounts of Chemical Research (1971), 4 (2), 57-64CODEN: ACHRE4; ISSN:0001-4842.
      The favorable steric path in stereospecific processes can be interpreted based on particular orbital interaction. The subsidiary effects in stereoselection, the selectivity due to multiplicity, and the path of multicyclization are also discussed. The superiority of the orbital interaction scheme relative to comprehension of the nature of chem. interaction is pointed out.
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      (c) Fleming, I. Frontier Orbitals and Organic Chemical Reactions. London: Wiley. 1978, 24– 109
      There is no corresponding record for this reference.

      ISBN 0-471-01819-8.

    40. 40
      (a) Hamlin, T. A.; Fernández, I.; Bickelhaupt, F. M. How Dihalogens Catalyze Michael Addition Reactions. Angew. Chem. Int. Ed. 2019, 58, 8922– 8926,  DOI: 10.1002/anie.201903196
      40a
      How Dihalogens Catalyze Michael Addition Reactions
      Hamlin, Trevor A.; Fernandez, Israel; Bickelhaupt, F. Matthias
      Angewandte Chemie, International Edition (2019), 58 (26), 8922-8926CODEN: ACIEF5; ISSN:1433-7851. (Wiley-VCH Verlag GmbH & Co. KGaA)
      We have quantum chem. analyzed the catalytic effect of dihalogen mols. (X2=F2, Cl2, Br2, and I2) on the aza-Michael addn. of pyrrolidine and Me acrylate using relativistic d. functional theory and coupled-cluster theory. Our state-of-the-art computations reveal that activation barriers systematically decrease as one goes to heavier dihalogens, from 9.4 kcal mol-1 for F2 to 5.7 kcal mol-1 for I2. Activation strain and bonding analyses identify an unexpected phys. factor that controls the computed reactivity trends, namely, Pauli repulsion between the nucleophile and Michael acceptor. Thus, dihalogens do not accelerate Michael addns. by the commonly accepted mechanism of an enhanced donor-acceptor [HOMO(nucleophile)-LUMO(Michael acceptor)] interaction, but instead through a diminished Pauli repulsion between the lone-pair of the nucleophile and the Michael acceptor's π-electron system.
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      (b) Vermeeren, P.; Brinkhuis, F.; Hamlin, T. A.; Bickelhaupt, F. M. How Alkali Cations Catalyze Aromatic Diels-Alder Reactions. Chem Asian J. 2020, 15, 1167– 1174,  DOI: 10.1002/asia.202000009
      40b
      How Alkali Cations Catalyze Aromatic Diels-Alder Reactions
      Vermeeren, Pascal; Brinkhuis, Francine; Hamlin, Trevor A.; Bickelhaupt, F. Matthias
      Chemistry - An Asian Journal (2020), 15 (7), 1167-1174CODEN: CAAJBI; ISSN:1861-4728. (Wiley-VCH Verlag GmbH & Co. KGaA)
      We have quantum chem. studied alkali cation-catalyzed arom. Diels-Alder reactions between benzene and acetylene forming barrelene using relativistic, dispersion-cor. d. functional theory. The alkali cation-catalyzed arom. Diels-Alder reactions are accelerated by up to 5 orders of magnitude relative to the uncatalyzed reaction and the reaction barrier increases along the series Li+ < Na+ < K+ < Rb+ < Cs+ < none. Our detailed activation strain and mol.-orbital bonding analyses reveal that the alkali cations lower the arom. Diels-Alder reaction barrier by reducing the Pauli repulsion between the closed-shell filled orbitals of the dienophile and the arom. diene. We argue that such Pauli mechanism behind Lewis-acid catalysis is a more general phenomenon. Also, our results may be of direct importance for a more complete understanding of the network of competing mechanisms towards the formation of polycyclic arom. hydrocarbons (PAHs) in an astrochem. context.
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      (c) Vermeeren, P.; Hamlin, T. A.; Fernández, I.; Bickelhaupt, F. M. How Lewis Acids Catalyze Diels–Alder Reactions. Angew. Chem. Int. Ed. 2020, 59, 6201– 6206,  DOI: 10.1002/anie.201914582
      40c
      How Lewis Acids Catalyze Diels-Alder Reactions
      Vermeeren, Pascal; Hamlin, Trevor A.; Fernandez, Israel; Bickelhaupt, F. Matthias
      Angewandte Chemie, International Edition (2020), 59 (15), 6201-6206CODEN: ACIEF5; ISSN:1433-7851. (Wiley-VCH Verlag GmbH & Co. KGaA)
      The Lewis acid(LA)-catalyzed Diels-Alder reaction between isoprene and Me acrylate was investigated quantum chem. using a combined d. functional theory and coupled-cluster theory approach. Computed activation energies systematically decrease as the strength of the LA increases along the series I2<SnCl4<TiCl4<ZnCl2<BF3<AlCl3. Emerging from our activation strain and Kohn-Sham MO bonding anal. was an unprecedented finding, namely that the LAs accelerate the Diels-Alder reaction by a diminished Pauli repulsion between the π-electron systems of the diene and dienophile. Our results oppose the widely accepted view that LAs catalyze the Diels-Alder reaction by enhancing the donor-acceptor [HOMOdiene-LUMOdienophile] interaction and constitute a novel phys. mechanism for this indispensable textbook org. reaction.
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