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Reaction Mechanisms

Unraveling the Bürgi-Dunitz Angle with Precision: The Power of a Two-Dimensional Energy Decomposition Analysis
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  • Israel Fernández
    Israel Fernández
    Departamento de Química Orgánica and Centro de Innovación en Química Avanzada (ORFEO−CINQA), Facultad de Ciencias Químicas, Universidad Complutense de Madrid, 28040-Madrid, Spain
    More by Israel Fernández
    Orcidhttps://orcid.org/0000-0002-0186-9774
  • F. Matthias Bickelhaupt
    F. Matthias Bickelhaupt
    Department of Chemistry and Pharmaceutical Sciences, AIMMS, Vrije Universiteit Amsterdam, De Boelelaan 1108, 1081 HZ Amsterdam, The Netherlands
    Institute for Molecules and Materials (IMM), Radboud University, Nijmegen 6500 GL, The Netherlands
    Department of Chemical Sciences, University of Johannesburg, Johannesburg 2006, South Africa
    More by F. Matthias Bickelhaupt
    Orcidhttps://orcid.org/0000-0003-4655-7747
  • Dennis Svatunek*
    Dennis Svatunek
    Institute of Applied Synthetic Chemistry, TU Wien, Getreidemarkt 9, 1060 Vienna, Austria
    *[email protected]
    More by Dennis Svatunek
    Orcidhttps://orcid.org/0000-0003-1101-2376
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Journal of Chemical Theory and Computation

Cite this: J. Chem. Theory Comput. 2023, 19, 20, 7300–7306
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https://doi.org/10.1021/acs.jctc.3c00907
Published October 4, 2023

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Abstract

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Understanding the geometrical preferences in chemical reactions is crucial for advancing the field of organic chemistry and improving synthetic strategies. One such preference, the Bürgi-Dunitz angle, is central to nucleophilic addition reactions involving carbonyl groups. This study successfully employs a novel two-dimensional Distortion-Interaction/Activation-Strain Model in combination with a two-dimensional Energy Decomposition Analysis to investigate the origins of the Bürgi-Dunitz angle in the addition reaction of CN– to (CH3)2C═O. We constructed a 2D potential energy surface defined by the distance between the nucleophile and carbonylic carbon atom and by the attack angle, followed by an in-depth exploration of energy components, including strain and interaction energy. Our analysis reveals that the Bürgi-Dunitz angle emerges from a delicate balance between two key factors: strain energy and interaction energy. High strain energy, as a result of the carbonyl compound distorting to avoid Pauli repulsion, is encountered at high angles, thus setting the upper bound. On the other hand, interaction energy is shaped by a dominant Pauli repulsion when the angles are lower. This work emphasizes the value of the 2D Energy Decomposition Analysis as a refined tool, offering both quantitative and qualitative insights into chemical reactivity and selectivity.

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Introduction

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Computational chemistry has been beneficial in providing insight into chemical reactions and offering valuable information for experimental work. Among the tools utilized in computational organic chemistry, the Distortion-Interaction/Activation-Strain Model (DI/ASM) (1) coupled with Energy Decomposition Analysis (EDA) (2) stands out. These methods are known for delivering both quantitative and qualitative insights into reactivity and selectivity. With a practical and adaptable approach, they have been employed in a variety of chemical contexts, ranging from refining textbook explanations (3−5) to contributing to applied research in organic (6−9) or main group (10) chemistry and catalysis. (11−13)
The DI/ASM was pioneered by the groups of F. M. Bickelhaupt, who introduced the activation-strain model, and K. N. Houk, who contributed the distortion-interaction model. (1) These two models within DI/ASM are equivalent and serve to dissect the change in energy ΔE of a chemical system composed of two distinct species, often termed fragments (e.g., reactants during a reaction), into two contributing factors:
ΔE=ΔEstrain+ΔEint
First, the strain energy, ΔEstrain (also known as distortion energy), quantifies the energy required to alter the fragments from their isolated relaxed geometry to the geometry adopted during interaction with the other species. Second, the interaction energy, ΔEint, accounts for the energy released upon bringing the two distorted fragments together.
Energy Decomposition Analysis can be used to further dissect the interaction energy into physically meaningful components. In this context, we employed the canonical EDA as implemented in the ADF software package. This method, which is based on the Ziegler-Rauk energy decomposition analysis, (14) subdivides the interaction energy ΔEint into three components:
ΔEint=ΔVelstat+ΔEPauli+ΔEoi
ΔVelstat represents the electrostatic attraction of the charge distribution of one reactant with that of the other reactant. ΔEPauli characterizes the destabilization resulting from intermolecular filled-orbital/filled-orbital interactions and is responsible for steric repulsion. ΔEoi accounts for the stabilization due to intermolecular filled-orbital/empty-orbital interactions and intrafragment polarization. For details, see ref (2).
Traditionally, these methods have been deployed to contrast the energetics between critical points, such as transition states, across different systems. However, it has been observed that this approach can sometimes yield data that is challenging to interpret or even lead to incorrect conclusions. (1,15,16) One reason is that transition states can vary in terms of their progression, and a later transition state typically exhibits higher strain and interaction energies due to the closer proximity of the fragments. This proximity also significantly affects the EDA components, which generally intensify as the fragments draw nearer.
As a result, contemporary applications of DI/ASM and EDA often employ a “consistent geometry” approach, where specific geometric parameters are maintained consistently across systems, or they are conducted along a trajectory, such as a reaction coordinate. (1,15,16) These refinements have markedly enhanced the clarity and reliability of insights garnered from such analyses. (7,17)
In a recent study, two of us (IF and FMB) explored the origin of the Bürgi-Dunitz (BD) angle in various nucleophilic addition reactions at carbonyl groups using quantitative Kohn–Sham molecular orbital (MO) theory and the Energy Decomposition Analysis. (18) The Bürgi-Dunitz angle, typically around 107°, refers to the geometric angle at which a nucleophile approaches a carbonyl carbon during an addition reaction. (19−21) This angle is considered stereochemically favorable for facilitating bond formation. Our research examined the energy differences between the optimal attack angle and the perpendicular (90°) attack using the interaction of cyanide with acetone as a model system. We compared an artificially created transition state with an attack angle constrained to 90° (TS90) to an unconstrained transition state (TS) at approximately 111°. Given the significant differences in bond length formation between these two transition states, the analysis was carried out along the two trajectories of 111° and 90°, comparing values at the same distance. Decreased Pauli repulsion, more favorable electrostatic interactions, and stronger orbital interactions were identified as the deciding factors. An EDA-NOCV (natural orbitals for chemical valence) analysis of the orbital interaction revealed a more favorable HOMO(nucleophile)-π*(C═O) LUMO interaction at 111°. Therefore, this study provided a comprehensive understanding and detailed analysis of why the 111° angle is preferred over 90° for this system.
Building on this foundation, we now propose extending this analysis to a 2D potential energy surface to gain a complete picture of the origin of the Bürgi-Dunitz angle. We are interested in not only what pushes the angle from 90° to higher values but also what limits the angle to even higher values. We introduce an enhanced method of employing DI/ASM and EDA─by applying them across multidimensional surfaces, with our focus on the 2D potential energy surface. Theoretically, this approach can be adapted to higher dimensions, providing a broader perspective of complex chemical interactions. With regard to the Bürgi-Dunitz angle, this methodology shines a spotlight on the nuanced factors that shape the potential energy surface. A clear advantage of this technique is its simplification of analysis. The intuitive graphical representation bypasses the need to trace numerous lines on a graph, which is a common challenge when analysis is restricted to a single reaction coordinate. Moreover, this approach allows the extraction of various 1D slices from the 2D surface, paving the way for a detailed quantitative inspection of key influences.
We demonstrate that an Energy Decomposition Analysis on a 2D plane offers a comprehensive, quantitative, and qualitative understanding of a range of potential attack trajectories. This approach serves as an effective tool for enhancing our understanding of intricate chemical interactions.

Results and Discussion

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In our study, we employ the cyanide/acetone model system as a representative framework for the analysis. To investigate the potential energy surface associated with the attack of cyanide on acetone, we devised a grid encompassing 324 structures. This grid was laid out on a 2D surface, characterized by two principal geometric descriptors: the C–C distance spanning between the carbon of the cyanide and the carbonyl carbon in acetone (ranging from 1.25 to 2.95 Å) and the C–C–O angle formed by the alignment of the carbon in CN, the carbonyl carbon, and the oxygen in acetone (varying from 70° to 155°, Figure 1).

Figure 1

Figure 1. Transition state of the investigated reaction and schematic representation of the 2D energy surface grid composed of 324 structures, parametrized by the C–C distance (between cyanide and the carbonyl carbon) and the C–C–O angle (between the cyanide carbon, carbonyl carbon, and oxygen) for the cyanide/acetone model system. The carbonyl bond is aligned along the x-axis with carbon (gray sphere) at the origin and oxygen (red sphere) at 1.2 Å.

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This comprehensive grid allowed us to meticulously examine the energy landscape as the geometrical parameters evolved, offering valuable insights into the interplay between distance and angular configurations during nucleophilic attack.
The Potential Energy Surface (PES) spanning the aforementioned region is illustrated in Figure 2. Upon analysis, the PES can be divided into six discrete regions. Region 1 encompasses the reactant complex area. Region 2 denotes the transition state, with the saddle point distinctly marked by a white dot. Region 3 represents the product zone. Regions 4 and 5 are peripheral zones with elevated energy levels. These “flanking” zones are instrumental in shaping the product valley and also in establishing the energy barrier or saddle point that separates the reactants from the product. Lastly, Region 6 signifies the high-energy sector corresponding to short C–C distances and is predominantly influenced by direct interatomic repulsion.

Figure 2

Figure 2. Potential energy surface (PES) for the cyanide/acetone interaction. The PES is divided into six distinct regions, with regions labeled 1–6 for reactant complex, transition state (saddle point marked with a white dot), product, high energy flanking regions, and atomic repulsion region, respectively. The light blue line shows the optimal attack angle of 111°.

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Subsequently, we carried out the Distortion-Interaction/Activation-Strain Analysis on this PES. This analysis yielded four additional energy surfaces, namely, the surfaces corresponding to the strain of each reactant, the cumulative strain energy, and the interaction energy. It is worth noting that the strain energy for the cyanide anion remains marginal, below 1 kcal/mol, throughout the evaluated surface. As a consequence, total strain energy is almost completely governed by the strain of acetone and will be investigated instead of analyzing strain for each reactant separately (Figure 3).

Figure 3

Figure 3. Strain energy surface for the cyanide/acetone interaction depicting the dependency of strain energy on the C–C distance and the C–C–O angle. The figure shows how the strain energy increases with decreasing intramolecular distance and also reveals angle-dependent components.

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As expected, the strain energy increases significantly at shorter intramolecular distances. Additionally, we observed an angle-dependent characteristic; strain energy tends to be higher at larger angles for equivalent distances. This observation can be rationalized in terms of steric hindrances; at large angles, unfavorable Pauli repulsion arises between the incoming nucleophile and the methyl groups of acetone, leading to unfavorable interactions. However, the nucleophile can moderate some of this repulsion by adjusting its own distortion to minimize the total energy. The flexibility of the carbonyl compound thus becomes crucial, enabling the system to adapt to this Pauli repulsion, and hence, the resulting high-strain energy region emerges as a product of this Pauli-induced distortion. As such, the distinctive shape of the energy landscape is derived from the interplay between the adaptability of the carbonyl compound and Pauli repulsion.
Figure 4 shows the energy surface for the interaction energy. Interestingly, there is an energy minimum at an angle of 125°, which is quite different from the angles at the product and transition state in the full PES. This suggests that the attack angle does not adopt higher bond angles mainly because of strain, as it is the main factor contributing to the high energy in Region 4 in Figure 2, while interaction energy alone would favor a larger angle than observed.

Figure 4

Figure 4. Interaction energy surface obtained from the Distortion-Interaction/Activation-Strain Analysis. The figure displays a minimum in energy at an angle of 125°, illustrating the influence of distortion energy on the angle of attack.

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Additionally, there is a high-energy region in the interaction energy at lower angles and distances of about 2 Å. This region roughly corresponds to high energy Region 5 in the complete PES (Figure 2) and is responsible for diverting the 90° attack trajectory to higher angles. To delve into the intricacies of the interaction energy surface, it is imperative to conduct an Energy Decomposition Analysis that leaves us with three additional energy surfaces: electrostatic potential, orbital interactions, and Pauli repulsion (Figure 5).

Figure 5

Figure 5. Energy Decomposition Analysis energy surfaces depicting electrostatic potential, orbital interactions, and Pauli repulsion. The plots illustrate the interplay between these energy components as a function of the C–C distance and C/C/O angle.

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All three EDA energy components exhibit a strong dependence on interfragment distance. The electrostatic potential and orbital interactions become increasingly favorable as the distance decreases, while the Pauli repulsion correspondingly becomes more repulsive. At first glance, the energy components appear to exhibit a minimal angular dependence. However, upon closer inspection, it is evident that they deviate from a perfectly circular pattern, particularly at smaller angles. This deviation suggests that there is a subtle angular dependence in the energy components in addition to the pronounced radial dependence.
One of the challenges here is the choice of a coordinate system. Employing a plot with radial distance versus angle offers better clarity regarding the angular dependence (Figure 6).

Figure 6

Figure 6. Radial distance vs angle plot for interaction energy and the EDA energy components, demonstrating the angular dependence of electrostatic potential, orbital interactions, and Pauli repulsion.

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This plot illustrates that the angular dependence is considerably prominent at smaller angles. The greater interaction at lower angles and longer distances signifies that the electrostatic potential, orbital interactions, and Pauli repulsions have a relatively stronger effect at these positions. This implies that as the interacting fragments are farther apart, they experience stronger interactions at lower angles compared to higher angles. All three components, electrostatic potential, Pauli repulsion, and orbital interactions, showcase this behavior.
However, discerning how the interplay of these components shapes the interaction energy surface is still challenging, particularly since the change in energies with the radial distance is much higher than the angular differences. This underscores the limitations of 2D EDA for visual analysis. Nonetheless, with the energy surfaces at hand, it is feasible to create cross sections of these surfaces in various orientations for quantitative investigations.
We now turn our focus to discern what gives rise to the high-energy region in the interaction PES at around a 2 Å distance and lower angles (70–90°), which consequently nudges the attack trajectory toward higher angles (Figure 6a). We dissect the interaction energy, electrostatic potential, orbital interaction, and Pauli repulsion surfaces along a fixed distance of 1.95 Å for angles ranging from 70 to 155 degrees. We opted for 1.95 Å since it is marginally shorter than the TS distance and is in proximity to where the interaction energy reaches its maximum (Figure 7).

Figure 7

Figure 7. Cross-sectional data of interaction energy, electrostatic potential, orbital interaction, and Pauli repulsion surfaces at a fixed distance of 1.95 Å across angles ranging from 70 to 155 degrees. The figure highlights the dominance of the Pauli repulsion in shaping the overall interaction energy.

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Pauli repulsion appears relatively flat in the range between 130° and 100° but exhibits a sharp uptick between 100° and 70°. As for the electrostatic potential, we observe a slight, nearly linear decrease in stabilization from 155° to 90°, transitioning to a stronger stabilization trend as the angle approaches 70°. However, this increased stabilization is insufficient to counterbalance the growth in the Pauli repulsion.
For the orbital interactions, a modest decrease in the strength of attraction occurs as the angle draws near 80°. As the angle diminishes further beyond 80° toward 70°, the strength of the orbital interaction reestablishes, becoming more attractive. It is important to note that these variations in the orbital interaction strength are relatively minor when compared to the changes in Pauli repulsion.
By analyzing the data, we discern three segments in the Pauli repulsion curve that stand out. Below 90° and above approximately 125°, it is the Pauli repulsion that exerts control over the interaction energy. However, within the middle segment from 90° to 125°, the interaction energy seems more governed by the curves of the electrostatic potential and orbital interaction, which gradually become less favorable upon transitioning from 125° to 90°.
To comprehend the nuanced behavior of the orbital interaction curve, we analyzed the overlap between the HOMO of nitrile and the LUMO of acetone (Figure 8). The maximum overlap occurs at around 120° with a slight decrease toward higher angles and a more pronounced decrease toward lower angles. This aligns with the analysis in the previous paper (13) and offers further understanding of the preference for the Bürgi-Dunitz angle over a 90° approach.

Figure 8

Figure 8. HOMOcyanide/LUMOacetone orbital overlap at a fixed distance of 1.95 Å across angles ranging from 70 to 155 degrees.

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Our findings reveal that the Bürgi-Dunitz angle is a result of a balance between the strain energy and the interaction energy. Notably, we observed that the strain energy limits the Bürgi-Dunitz angle from reaching higher values, which would have otherwise been favored by the interaction energy (Figure 9). This higher strain at a larger angle is the manifestation of steric Pauli repulsion between the nucleophile and the methyl substituents that is absorbed into a geometrical deformation of the acetone reactant.

Figure 9

Figure 9. Illustration of the main factors locking the attack angle to 111° in the cyanide/acetone system.

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The angular dependence of the interaction energy was further analyzed, and it was found that the Pauli repulsion dominates in shaping the overall interaction energy at the relevant distances. Specifically, an increase in Pauli repulsion at lower angles and interfragment distances around 2 Å forces the attack trajectory to higher angles. Note that, at these lower angles, Pauli repulsion is not converted into acetone deformation because, besides carbon, the carbonyl oxygen has no substituents to be involved in steric repulsion that could bend away from the nucleophile.

Conclusion

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We have explored the origin of the Bürgi-Dunitz angle through an insightful and comprehensive two-dimensional Energy Decomposition Analysis using the cyanide/acetone model system. The potential energy surface and the accompanying energy components, such as strain energy and interaction energy, were visualized across a wide range of possible attack trajectories. The graphical analysis provides an intuitive understanding of the various factors that influence the geometry of nucleophilic attack on carbonyl groups.
A remarkable aspect of this study is the successful application, for the first time, of the 2D distortion-interaction-activation-strain model and EDA, which proved to be invaluable in yielding both quantitative and qualitative insights into reactivity and selectivity. This two-dimensional approach extends the depth of analysis beyond traditional methods, allowing for more nuanced explorations of energy surfaces and offering a clearer understanding of the underlying energetic contributions. As demonstrated through analysis of the Bürgi-Dunitz angle, reactivity arises from a complex interplay of competing factors that achieve a balanced state. A multidimensional analysis is essential for accurately capturing the influences of different factors on a hyperdimensional energy surface.
We anticipate that this two-dimensional methodology will be especially useful in scenarios where it is difficult to define a common point for comparative analysis such as cycloaddition reactions with varying asynchronicities. It enables an unbiased examination of the potential energy surface, circumventing the bias that might be introduced by selecting specific reaction coordinates.

Computational Methods

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Geometry optimizations for the 2D potential energy surface scan were conducted using the Gaussian 16 software package, (22) employing the M06-2X functional (23) with the 6-311+G(d,p) basis set. (24) For these calculations, relaxed scans were utilized, treating the C–C distance (between the cyanide and carbonyl carbons) and the C–C–O angle (between the cyanide carbon, carbonyl carbon, and oxygen) as constrained parameters. Following the geometry optimization, the Distortion-Interaction/Activation-Strain Model and Energy Decomposition Analysis were implemented using single-point calculations in the Amsterdam Density Functional (ADF) software. (25−27) These calculations utilized the M06-2X functional with the TZ2P basis set, (28,29) without frozen core approximation. The numerical quality was set to “very good”, and the scalar relativistic effects were accounted for using the Zeroth-Order Regular Approximation (ZORA). (30)
All scripts employed for the analysis are publicly accessible on GitHub at https://github.com/dsvatunek/2D_EDA/releases/tag/v1.0.0 and will be incorporated in the forthcoming release of our autoDIAS software package. (31) All used geometries and obtained energies are provided as Supporting Information.
The computations were executed on a Windows workstation equipped with a 32-core AMD Ryzen ThreadripperTM 3970X CPU, with the entire computational process taking under 16 h. Notably, the 2D EDA proved to be computationally efficient, underscoring its practicality for similar investigations, even without the need for high-performance computing resources.

Supporting Information

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The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.jctc.3c00907.

  • jmol file (XYZ)

  • Orbital overlaps (XLSX)

  • jmol file (XYZ)

  • jmol file (XYZ)

  • EDA energies (XLSX)

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Author Information

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  • Corresponding Author
  • Authors
    • Israel Fernández - Departamento de Química Orgánica and Centro de Innovación en Química Avanzada (ORFEO−CINQA), Facultad de Ciencias Químicas, Universidad Complutense de Madrid, 28040-Madrid, Spain;  Orcidhttps://orcid.org/0000-0002-0186-9774
    • F. Matthias Bickelhaupt - Department of Chemistry and Pharmaceutical Sciences, AIMMS, Vrije Universiteit Amsterdam, De Boelelaan 1108, 1081 HZ Amsterdam, The Netherlands;  Institute for Molecules and Materials (IMM), Radboud University, Nijmegen 6500 GL, The Netherlands;  Department of Chemical Sciences, University of Johannesburg, Johannesburg 2006, South Africa;  Orcidhttps://orcid.org/0000-0003-4655-7747
  • Funding

    Open Access is funded by the Austrian Science Fund (FWF).

  • Notes
    The authors declare no competing financial interest.

Acknowledgments

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This work was supported by the Austrian Science Funds (FWF) project ESP-2. FMB thanks The Netherlands Organization for Scientific Research for support. This work was also supported by the Spanish MCIN/AEI/10.13039/501100011033 (Grants PID2019-106184GB-I00 and RED2018-102387-T to I.F.).

References

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This article references 31 other publications.

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    Blokker, Eva; Sun, Xiaobo; Poater, Jordi; van der Schuur, J. Martijn; Hamlin, Trevor A.; Bickelhaupt, F. Matthias
    Chemistry - A European Journal (2021), 27 (63), 15616-15622CODEN: CEUJED; ISSN:0947-6539. (Wiley-VCH Verlag GmbH & Co. KGaA)
    We have quantum chem. analyzed element-element bonds of archetypal HnX-YHn mols. (X, Y = C, N, O, F, Si, P, S, Cl, Br, I), using d. functional theory. One purpose is to obtain a set of consistent homolytic bond dissocn. energies (BDE) for establishing accurate trends across the periodic table. The main objective is to elucidate the underlying phys. factors behind these chem. bonding trends. On one hand, we confirm that, along a period (e. g., from C-C to C-F), bonds strengthen because the electronegativity difference across the bond increases. But, down a period, our findings constitute a paradigm shift. From C-F to C-I, for example, bonds do become weaker, however, not because of the decreasing electronegativity difference. Instead, we show that the effective atom size (via steric Pauli repulsion) is the causal factor behind bond weakening in this series, and behind the weakening in orbital interactions at the equil. distance. We discuss the actual bonding mechanism and the importance of analyzing this mechanism as a function of the bond distance.
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  6. 6
    Svatunek, D.; Wilkovitsch, M.; Hartmann, L.; Houk, K. N.; Mikula, H. Uncovering the Key Role of Distortion in Bioorthogonal Tetrazine Tools That Defy the Reactivity/Stability Trade-Off. J. Am. Chem. Soc. 2022, 144 (18), 8171– 8177,  DOI: 10.1021/jacs.2c01056
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    6
    Uncovering the Key Role of Distortion in Bioorthogonal Tetrazine Tools That Defy the Reactivity/Stability Trade-Off
    Svatunek, Dennis; Wilkovitsch, Martin; Hartmann, Lea; Houk, K. N.; Mikula, Hannes
    Journal of the American Chemical Society (2022), 144 (18), 8171-8177CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
    The tetrazine/trans-cyclooctene ligation stands out from the bioorthogonal toolbox due to its exceptional reaction kinetics, enabling multiple mol. technologies in vitro and in living systems. Highly reactive 2-pyridyl-substituted tetrazines have become state of the art for time-crit. processes and selective reactions at very low concns. It is widely accepted that the enhanced reactivity of these chem. tools is attributed to the electron-withdrawing effect of the heteroaryl substituent. In contrast, we show that the obsd. reaction rates are way too high to be explained on this basis. Computational investigation of this phenomenon revealed that distortion of the tetrazine caused by intramol. repulsive N-N interaction plays a key role in accelerating the cycloaddn. step. We show that the limited stability of tetrazines in biol. media strongly correlates with the electron-withdrawing effect of the substituent, while intramol. repulsion increases the reactivity without reducing the stability. These fundamental insights reveal thus far overlooked mechanistic aspects that govern the reactivity/stability trade-off for tetrazines in physiol. relevant environments, thereby providing a new strategy that may facilitate the rational design of these bioorthogonal tools.
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  7. 7
    Svatunek, D.; Houszka, N.; Hamlin, T. A.; Bickelhaupt, F. M.; Mikula, H. Chemoselectivity of Tertiary Azides in Strain-Promoted Alkyne-Azide Cycloadditions. Chem.─Eur. J. 2019, 25 (3), 754– 758,  DOI: 10.1002/chem.201805215
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    7
    Chemoselectivity of Tertiary Azides in Strain-Promoted Alkyne-Azide Cycloadditions
    Svatunek, Dennis; Houszka, Nicole; Hamlin, Trevor A.; Bickelhaupt, F. Matthias; Mikula, Hannes
    Chemistry - A European Journal (2019), 25 (3), 754-758CODEN: CEUJED; ISSN:0947-6539. (Wiley-VCH Verlag GmbH & Co. KGaA)
    The strain-promoted alkyne-azide cycloaddn. (SPAAC) is the most commonly employed bioorthogonal reaction with applications in a broad range of fields. Over the years, several different cyclooctyne derivs. have been developed and investigated in regard to their reactivity in SPAAC reactions with azides. However, only a few studies examd. the influence of structurally diverse azides on reaction kinetics. Herein, we report our investigations of the reactivity of primary, secondary, and tertiary azides with the cyclooctynes BCN and ADIBO applying exptl. and computational methods. All azides show similar reaction rates with the sterically non-demanding cyclooctyne BCN. However, due to the increased steric demand of the dibenzocyclooctyne ADIBO, the reactivity of tertiary azides drops by several orders of magnitude in comparison to primary and secondary azides. We show that this chemoselective behavior of tertiary azides can be exploited to achieve semiorthogonal dual-labeling without the need for any catalyst using SPAAC exclusively.
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  8. 8
    Fernández, I. Understanding the Reactivity of Fullerenes Through the Activation Strain Model. Eur. J. Org. Chem. 2018, 2018 (12), 1394– 1402,  DOI: 10.1002/ejoc.201701626
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    Understanding the Reactivity of Fullerenes Through the Activation Strain Model
    Fernandez, Israel
    European Journal of Organic Chemistry (2018), 2018 (12), 1394-1402CODEN: EJOCFK; ISSN:1099-0690. (Wiley-VCH Verlag GmbH & Co. KGaA)
    The Activation Strain Model of reactivity nowadays constitutes a powerful tool to aid quant. understanding of chem. reactions, and also their design. This approach, combined with the Energy Decompn. Anal. method, has been really helpful for our current understanding of different fundamental transformations in chem. This Microreview illustrates the usefulness of this methodol. in providing more insight into the chem. of fullerenes. To this end, representative recent applications, ranging from the regioselectivity in Diels-Alder cycloaddn. to the reactivity of endohedral fullerenes, are presented.
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  9. 9
    Fernandez, I. Understanding the reactivity of polycyclic aromatic hydrocarbons and related compounds. Chem. Sci. 2020, 11 (15), 3769– 3779,  DOI: 10.1039/D0SC00222D
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    9
    Understanding the reactivity of polycyclic aromatic hydrocarbons and related compounds
    Fernandez, Israel
    Chemical Science (2020), 11 (15), 3769-3779CODEN: CSHCCN; ISSN:2041-6520. (Royal Society of Chemistry)
    A review. This perspective article summarizes recent applications of the combination of the activation strain model of reactivity and the energy decompn. anal. methods to the study of the reactivity of polycyclic arom. hydrocarbons and related compds. such as cycloparaphenylenes, fullerenes and doped systems. To this end, we have selected representative examples to highlight the usefulness of this relatively novel computational approach to gain quant. insight into the factors controlling the so far not fully understood reactivity of these species. Issues such as the influence of the size and curvature of the system on the reactivity are covered herein, which is crucial for the rational design of novel compds. with tuneable applications in different fields such as materials science or medicinal chem.
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  10. 10
    Fernandez, I. Understanding the reactivity of frustrated Lewis pairs with the help of the activation strain model-energy decomposition analysis method. Chem. Commun. 2022, 58 (32), 4931– 4940,  DOI: 10.1039/D2CC00233G
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    10
    Understanding the reactivity of frustrated Lewis pairs with the help of the activation strain model-energy decomposition analysis method
    Fernandez, Israel
    Chemical Communications (Cambridge, United Kingdom) (2022), 58 (32), 4931-4940CODEN: CHCOFS; ISSN:1359-7345. (Royal Society of Chemistry)
    This Feature article presents recent representative applications of the combination of the Activation Strain Model of reactivity and the Energy Decompn. Anal. methods to understand the reactivity of Frustrated Lewis Pairs (FLPs). This approach has been helpful to not only gain a deeper quant. insight into the factors controlling the cooperative action between the Lewis acid/base partners but also to rationally design highly active systems for different bond activation reactions. Issues such as the influence of the nature of the FLP antagonists or the substituents directly attached to them on the reactivity are covered herein, which are crucial for the future development of this fascinating family of compds.
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  11. 11
    Qi, X.; Kohler, D. G.; Hull, K. L.; Liu, P. Energy Decomposition Analyses Reveal the Origins of Catalyst and Nucleophile Effects on Regioselectivity in Nucleopalladation of Alkenes. J. Am. Chem. Soc. 2019, 141 (30), 11892– 11904,  DOI: 10.1021/jacs.9b02893
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    11
    Energy Decomposition Analyses Reveal the Origins of Catalyst and Nucleophile Effects on Regioselectivity in Nucleopalladation of Alkenes
    Qi, Xiaotian; Kohler, Daniel G.; Hull, Kami L.; Liu, Peng
    Journal of the American Chemical Society (2019), 141 (30), 11892-11904CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
    Nucleopalladation is one of the most common mechanisms for Pd-catalyzed hydro- and oxidative functionalization of alkenes. Due to the electronic bias of the π-alkene-palladium complexes, nucleopalladations with terminal aliph. alkenes typically deliver the nucleophile to the more substituted sp2 carbon to form the Markovnikov-selective products. The selective formation of the anti-Markovnikov nucleopalladation products requires the inherent electronic effects to be overridden, which is still a significant challenge for reactions with simple aliph. alkenes. Because the interactions between the nucleophile and the alkene substrate are influenced by a complex combination of multiple types of steric and electronic effects, a thorough understanding of the interplay of these underlying interactions is needed to rationalize and predict the regioselectivity. Here, we employ an energy decompn. approach to quant. sep. the different types of nucleophile-substrate interactions, including steric, electrostatic, orbital interactions, and dispersion effects, and to predict the impacts of each factor on regioselectivity. We demonstrate the use of this approach on the origins of catalyst-controlled anti-Markovnikov-selectivity in Hull's Pd-catalyzed oxidative amination reactions. In addn., we evaluated the regioselectivity in a series of nucleopalladation reactions with different neutral and anionic Pd catalysts and N- and O-nucleophiles with different steric and electronic properties. Based on these computational analyses, a generalized scheme is established to identify the dominant nucleophile-substrate interaction affecting the regioselectivity of nucleopalladations with different Pd catalysts and nucleophiles.
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  12. 12
    Miller, E.; Mai, B. K.; Read, J. A.; Bell, W. C.; Derrick, J. S.; Liu, P.; Toste, F. D. A Combined DFT, Energy Decomposition, and Data Analysis Approach to Investigate the Relationship Between Noncovalent Interactions and Selectivity in a Flexible DABCOnium/Chiral Anion Catalyst System. ACS Catal. 2022, 12 (19), 12369– 12385,  DOI: 10.1021/acscatal.2c03077
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    12
    A Combined DFT, Energy Decomposition, and Data Analysis Approach to Investigate the Relationship Between Noncovalent Interactions and Selectivity in a Flexible DABCOnium/Chiral Anion Catalyst System
    Miller, Edward; Mai, Binh Khanh; Read, Jacquelyne A.; Bell, William C.; Derrick, Jeffrey S.; Liu, Peng; Toste, F. Dean
    ACS Catalysis (2022), 12 (19), 12369-12385CODEN: ACCACS; ISSN:2155-5435. (American Chemical Society)
    Developing strategies to study reactivity and selectivity in flexible catalyst systems has become an important topic of research. Herein, we report a combined exptl. and computational study aimed at understanding the mechanistic role of an achiral DABCOnium cofactor in a regio- and enantiodivergent bromocyclization reaction. It was found that electron-deficient aryl substituents enable rigidified transition states via an anion-π interaction with the catalyst, which drives the selectivity of the reaction. In contrast, electron-rich aryl groups on the DABCOnium result in significantly more flexible transition states, where interactions between the catalyst and substrate are more important. An anal. of not only the lowest-energy transition state structures but also an ensemble of low-energy transition state conformers via energy decompn. anal. and machine learning was crucial to revealing the dominant noncovalent interactions responsible for obsd. changes in selectivity in this flexible system.
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    Portela, S.; Cabrera-Trujillo, J. J.; Fernandez, I. Catalysis by Bidentate Iodine(III)-Based Halogen Donors: Surpassing the Activity of Strong Lewis Acids. J. Org. Chem. 2021, 86 (7), 5317– 5326,  DOI: 10.1021/acs.joc.1c00534
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    Catalysis by Bidentate Iodine(III)-Based Halogen Donors: Surpassing the Activity of Strong Lewis Acids
    Portela, Susana; Cabrera-Trujillo, Jorge J.; Fernandez, Israel
    Journal of Organic Chemistry (2021), 86 (7), 5317-5326CODEN: JOCEAH; ISSN:0022-3263. (American Chemical Society)
    The poorly understood mode of activation and catalysis of bidentate iodine(III)-based halogen donors have been quant. explored in detail by means of state-of-the-art computational methods. To this end, the uncatalyzed Diels-Alder cycloaddn. reaction between cyclohexadiene and Me vinyl ketone is compared to the analogous process mediated by a bidentate iodine(III)-organocatalyst and by related, highly active iodine(I) species. It is found that the bidentate iodine(III)-catalyst accelerates the cycloaddn. by lowering the reaction barrier up to 10 kcal mol-1 compared to the parent uncatalyzed reaction. Our quant. analyses reveal that the origin of the catalysis is found in a significant redn. of the steric (Pauli) repulsion between the diene and dienophile, which originates from both a more asynchronous reaction mode and a significant polarization of the π-system of the dienophile away from the incoming diene. Notably, the activity of the iodine(III)-catalyst can be further enhanced by increasing the electrophilic nature of the system. Thus, novel systems are designed whose activity actually surpasses that of strong Lewis acids such as BF3.
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  14. 14
    Ziegler, T.; Rauk, A. A theoretical study of the ethylene-metal bond in complexes between copper(1+), silver(1+), gold(1+), platinum(0) or platinum(2+) and ethylene, based on the Hartree-Fock-Slater transition-state method. Inorg. Chem. 1979, 18 (6), 1558– 1565,  DOI: 10.1021/ic50196a034
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    A theoretical study of the ethylene-metal bond in complexes between copper(1+), silver(1+), gold(1+), platinum(0) or platinum(2+) and ethylene, based on the Hartree-Fock-Slater transition-state method
    Ziegler, Tom; Rauk, Arvi
    Inorganic Chemistry (1979), 18 (6), 1558-65CODEN: INOCAJ; ISSN:0020-1669.
    An anal. based on the Hartree-Fock-Slater (HFS) transition-state method is given of the metal-ethylene bond in the ion-ethylene complexes Cu+-C2H4, Ag+-C2H4, and Au+-C2H4 as well as in complexes with PtCl3- and Pt(PH3)2. The contribution from σ-donation to the bonding energy was equally important for all three complexes with the ions, whereas the contribution from the π back-donation was important only for the Cu complex. A similar anal. of Pt(Cl)3--C2H4 and Pt(PH3)2-C2H4 showed that the position of ethylene perpendicular to the coordination plane of Pt(Cl)3- in Zeise's salt is caused by steric factors, whereas the position of ethylene in Pt(PH3)2-C2H4 is due to electronic factors, specifically π back-donations.
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    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, 2019 (2–3), 378– 386,  DOI: 10.1002/ejoc.201800572
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    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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    Vermeeren, P.; van der Lubbe, S. C. C.; Fonseca Guerra, C.; Bickelhaupt, F. M.; Hamlin, T. A. Understanding chemical reactivity using the activation strain model. Nat. Protoc. 2020, 15 (2), 649– 667,  DOI: 10.1038/s41596-019-0265-0
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    Understanding chemical reactivity using the activation strain model
    Vermeeren, Pascal; van der Lubbe, Stephanie C. C.; Fonseca Guerra, Celia; Bickelhaupt, F. Matthias; Hamlin, Trevor A.
    Nature Protocols (2020), 15 (2), 649-667CODEN: NPARDW; ISSN:1750-2799. (Nature Research)
    Understanding chem. reactivity through the use of state-of-the-art computational techniques enables chemists to both predict reactivity and rationally design novel reactions. This protocol aims to provide chemists with the tools to implement a powerful and robust method for analyzing and understanding any chem. reaction using PyFrag 2019. The approach is based on the so-called activation strain model (ASM) of reactivity, which relates the relative energy of a mol. system to the sum of the energies required to distort the reactants into the geometries required to react plus the strength of their mutual interactions. Other available methods analyze only a stationary point on the potential energy surface, but our methodol. analyzes the change in energy along a reaction coordinate. The use of this methodol. has been proven to be crit. to the understanding of reactions, spanning the realms of the inorg. and org., as well as the supramol. and biochem., fields. This protocol provides step-by-step instructions-starting from the optimization of the stationary points and extending through calcn. of the potential energy surface and anal. of the trend-decisive energy terms-that can serve as a guide for carrying out the anal. of any given reaction of interest within hours to days, depending on the size of the mol. system.
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    Houszka, N.; Mikula, H.; Svatunek, D. Substituent Effects in Bioorthogonal Diels-Alder Reactions of 1,2,4,5-Tetrazines. Chem.─Eur. J. 2023, 29 (29), e202300345,  DOI: 10.1002/chem.202300345
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    Substituent Effects in Bioorthogonal Diels-Alder Reactions of 1,2,4,5-Tetrazines
    Houszka, Nicole; Mikula, Hannes; Svatunek, Dennis
    Chemistry - A European Journal (2023), 29 (29), e202300345CODEN: CEUJED; ISSN:0947-6539. (Wiley-VCH Verlag GmbH & Co. KGaA)
    1,2,4,5-Tetrazines are increasingly used as reactants in bioorthogonal chem. due to their high reactivity in Diels-Alder reactions with various dienophiles. Substituents in the 3- and 6-positions of the tetrazine scaffold are known to have a significant impact on the rate of cycloaddns.; this is commonly explained on the basis of frontier MO theory. In contrast, we show that reactivity differences between commonly used classes of tetrazines are not controlled by frontier MO interactions. In particular, we demonstrate that mono-substituted tetrazines show high reactivity due to decreased Pauli repulsion, which leads to a more asynchronous approach assocd. with reduced distortion energy. This follows the recent Vermeeren-Hamlin-Bickelhaupt model of reactivity increase in asym. Diels-Alder reactions. In addn., we reveal that ethylene is not a good model compd. for other alkenes in Diels-Alder reactions.
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    Rodriguez, H. A.; Bickelhaupt, F. M.; Fernandez, I. Origin of the Bürgi-Dunitz Angle. ChemPhysChem 2023, 24, e202300379,  DOI: 10.1002/cphc.202300379
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    Origin of the Buergi-Dunitz Angle
    Rodriguez, Humberto A.; Bickelhaupt, F. Matthias; Fernandez, Israel
    ChemPhysChem (2023), 24 (17), e202300379CODEN: CPCHFT; ISSN:1439-4235. (Wiley-VCH Verlag GmbH & Co. KGaA)
    The Buergi-Dunitz (BD) angle plays a pivotal role in org. chem. to rationalize the nucleophilic addn. to carbonyl groups. Yet, the origin of the obtuse trajectory of the nucleophile remains incompletely understood. Herein, we quantify the importance of the underlying phys. factors quantum chem. The obtuse BD angle appears to originate from the concerted action of a reduced Pauli repulsion between the nucleophile HOMO and carbonyl π bond, a more stabilizing HOMO-π*-LUMO(C=O) interaction, as well as a more favorable electrostatic attraction.
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    Bürgi, H. B.; Dunitz, J. D.; Shefter, E. Geometrical reaction coordinates. II. Nucleophilic addition to a carbonyl group. J. Am. Chem. Soc. 1973, 95 (15), 5065– 5067,  DOI: 10.1021/ja00796a058
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    Geometrical reaction coordinates. II. Nucleophilic addition to a carbonyl group
    Burgi, H. B.; Dunitz, J. D.; Shefter, Eli
    Journal of the American Chemical Society (1973), 95 (15), 5065-7CODEN: JACSAT; ISSN:0002-7863.
    Analysis of intramol. N...C:O interactions obsd. in six crystal structures provides an exptl. basis for mapping the reaction coordinate (min. energy pathway) for the addn. reaction of a nucleophile to a carbonyl group. The line of approach of the nucleophile is not perpendicular to the C-O bond but is inclined at about 107° to it.
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    Bürgi, H. B.; Lehn, J. M.; Wipff, G. Ab initio study of nucleophilic addition to a carbonyl group. J. Am. Chem. Soc. 1974, 96 (6), 1956– 1957,  DOI: 10.1021/ja00813a062
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    Ab initio study of nucleophilic addition to a carbonyl group
    Buergi, H. B.; Lehn, J. M.; Wipff, G.
    Journal of the American Chemical Society (1974), 96 (6), 1956-7CODEN: JACSAT; ISSN:0002-7863.
    Ab initio SCF-LCGO (linear combination of Gaussian orbitals)-MO computations were performed on the reaction of hydride ion with HCHO, considered as model for nucleophilic addns. to the carbonyl group. Geometrical changes and electronic rearrangements were obtained as a function of the reaction coordinate. Orientational constraints in the course of the reaction bear relation to orbital steering, togetherness, and proximity effects considered in the literature. The calcd. geometrical changes correlate with the changes obsd. in crystal structures for the approach of an amino site toward a carbonyl group. A computation of the NH3-HCHO system at one fixed sepn. was also performed for comparison purposes.
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    Bürgi, H. B.; Dunitz, J. D.; Lehn, J. M.; Wipff, G. Stereochemistry of reaction paths at carbonyl centres. Tetrahedron 1974, 30 (12), 1563– 1572,  DOI: 10.1016/S0040-4020(01)90678-7
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    Stereochemistry of reaction paths at carbonyl centers
    Buergi, H. B.; Dunitz, J. D.; Lehn, J. M.; Wipff, G.
    Tetrahedron (1974), 30 (12), 1563-72CODEN: TETRAB; ISSN:0040-4020.
    Ab initio MO calcns. and crystal structure structure data were used to infer the reaction paths of nucleophilic addn. to carbonyl compds.
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  • Abstract

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    Figure 1

    Figure 1. Transition state of the investigated reaction and schematic representation of the 2D energy surface grid composed of 324 structures, parametrized by the C–C distance (between cyanide and the carbonyl carbon) and the C–C–O angle (between the cyanide carbon, carbonyl carbon, and oxygen) for the cyanide/acetone model system. The carbonyl bond is aligned along the x-axis with carbon (gray sphere) at the origin and oxygen (red sphere) at 1.2 Å.

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    Figure 2

    Figure 2. Potential energy surface (PES) for the cyanide/acetone interaction. The PES is divided into six distinct regions, with regions labeled 1–6 for reactant complex, transition state (saddle point marked with a white dot), product, high energy flanking regions, and atomic repulsion region, respectively. The light blue line shows the optimal attack angle of 111°.

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    Figure 3

    Figure 3. Strain energy surface for the cyanide/acetone interaction depicting the dependency of strain energy on the C–C distance and the C–C–O angle. The figure shows how the strain energy increases with decreasing intramolecular distance and also reveals angle-dependent components.

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    Figure 4

    Figure 4. Interaction energy surface obtained from the Distortion-Interaction/Activation-Strain Analysis. The figure displays a minimum in energy at an angle of 125°, illustrating the influence of distortion energy on the angle of attack.

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    Figure 5

    Figure 5. Energy Decomposition Analysis energy surfaces depicting electrostatic potential, orbital interactions, and Pauli repulsion. The plots illustrate the interplay between these energy components as a function of the C–C distance and C/C/O angle.

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    Figure 6

    Figure 6. Radial distance vs angle plot for interaction energy and the EDA energy components, demonstrating the angular dependence of electrostatic potential, orbital interactions, and Pauli repulsion.

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    Figure 7

    Figure 7. Cross-sectional data of interaction energy, electrostatic potential, orbital interaction, and Pauli repulsion surfaces at a fixed distance of 1.95 Å across angles ranging from 70 to 155 degrees. The figure highlights the dominance of the Pauli repulsion in shaping the overall interaction energy.

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    Figure 8

    Figure 8. HOMOcyanide/LUMOacetone orbital overlap at a fixed distance of 1.95 Å across angles ranging from 70 to 155 degrees.

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    Figure 9

    Figure 9. Illustration of the main factors locking the attack angle to 111° in the cyanide/acetone system.

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  • References

    This article references 31 other publications.

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      Analyzing Reaction Rates with the Distortion/Interaction-Activation Strain Model
      Bickelhaupt, F. Matthias; Houk, Kendall N.
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      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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      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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      The Pauli Repulsion-Lowering Concept in Catalysis
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      Accounts of Chemical Research (2021), 54 (8), 1972-1981CODEN: ACHRE4; ISSN:0001-4842. (American Chemical Society)
      A review. Org. chem. has undoubtedly had a profound impact on humanity. Day in and day out, we find ourselves constantly surrounded by org. compds. Pharmaceuticals, plastics, fuels, cosmetics, detergents, and agrochems., to name a few, are all synthesized by org. reactions. Very often, these reactions require a catalyst in order to proceed in a timely and selective manner. Lewis acids and organocatalysts are commonly employed to catalyze org. reactions and are considered to enhance the frontier MO (FMO) interactions. A vast no. of textbooks and primary literature sources suggest that the binding of a Lewis acid or an iminium catalyst to a reactant (R1) stabilizes its LUMO and leads to a smaller HOMO(R2)-LUMO(R1) energy gap with the other reactant (R2), thus resulting in a faster reaction. This forms the basis for the so-called LUMO-lowering catalysis concept. Despite the simplicity and popularity of FMO theory, a no. of deficiencies have emerged over the years, as a consequence of these FMOs not being the operative factor in the catalysis. LUMO-lowering catalysis is ultimately incomplete and is not always operative in catalyzed org. reactions. Our groups have recently undertaken a concerted effort to generate a unified framework to rationalize and predict chem. reactivity using a causal model that is rooted in quantum mechanics. In this Account, we propose the concept of Pauli repulsion-lowering catalysis to understand the catalysis in fundamental processes in org. chem. Our findings emerge from state-of-the-art computational methods, namely, the activation strain model (ASM) of reactivity in conjunction with quant. Kohn-Sham MO theory (KS-MO) and a matching energy decompn. anal. (EDA). The binding of the catalyst to the substrate not only leads to a stabilization of its LUMO but also induces a significant redn. of the two-orbital, four-electron Pauli repulsion involving the key MOs of both reactants. This repulsion-lowering originates, for the textbook Lewis acid-catalyzed Diels-Alder reaction, from the catalyst polarizing the occupied π orbital of the dienophile away from the carbon atoms that form new bonds with the diene. This polarization of the occupied dienophile π orbital reduces the occupied orbital overlap with the diene and constitutes the ultimate phys. factor responsible for the acceleration of the catalyzed process as compared to the analogous uncatalyzed reaction. We show that this phys. mechanism is generally applicable regardless of the type of reaction (Diels-Alder and Michael addn. reactions) and the way the catalyst is bonded to the reactants (i.e., from pure covalent or dative bonds to weaker hydrogen or halogen bonds). We envisage that the insights emerging from our anal. will guide future exptl. developments toward the design of more efficient catalytic transformations.
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      Blokker, E.; Sun, X.; Poater, J.; van der Schuur, J. M.; Hamlin, T. A.; Bickelhaupt, F. M. The Chemical Bond: When Atom Size Instead of Electronegativity Difference Determines Trend in Bond Strength. Chem.─Eur. J. 2021, 27 (63), 15616– 15622,  DOI: 10.1002/chem.202103544
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      The Chemical Bond: When Atom Size Instead of Electronegativity Difference Determines Trend in Bond Strength
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      We have quantum chem. analyzed element-element bonds of archetypal HnX-YHn mols. (X, Y = C, N, O, F, Si, P, S, Cl, Br, I), using d. functional theory. One purpose is to obtain a set of consistent homolytic bond dissocn. energies (BDE) for establishing accurate trends across the periodic table. The main objective is to elucidate the underlying phys. factors behind these chem. bonding trends. On one hand, we confirm that, along a period (e. g., from C-C to C-F), bonds strengthen because the electronegativity difference across the bond increases. But, down a period, our findings constitute a paradigm shift. From C-F to C-I, for example, bonds do become weaker, however, not because of the decreasing electronegativity difference. Instead, we show that the effective atom size (via steric Pauli repulsion) is the causal factor behind bond weakening in this series, and behind the weakening in orbital interactions at the equil. distance. We discuss the actual bonding mechanism and the importance of analyzing this mechanism as a function of the bond distance.
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    6. 6
      Svatunek, D.; Wilkovitsch, M.; Hartmann, L.; Houk, K. N.; Mikula, H. Uncovering the Key Role of Distortion in Bioorthogonal Tetrazine Tools That Defy the Reactivity/Stability Trade-Off. J. Am. Chem. Soc. 2022, 144 (18), 8171– 8177,  DOI: 10.1021/jacs.2c01056
      6
      Uncovering the Key Role of Distortion in Bioorthogonal Tetrazine Tools That Defy the Reactivity/Stability Trade-Off
      Svatunek, Dennis; Wilkovitsch, Martin; Hartmann, Lea; Houk, K. N.; Mikula, Hannes
      Journal of the American Chemical Society (2022), 144 (18), 8171-8177CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
      The tetrazine/trans-cyclooctene ligation stands out from the bioorthogonal toolbox due to its exceptional reaction kinetics, enabling multiple mol. technologies in vitro and in living systems. Highly reactive 2-pyridyl-substituted tetrazines have become state of the art for time-crit. processes and selective reactions at very low concns. It is widely accepted that the enhanced reactivity of these chem. tools is attributed to the electron-withdrawing effect of the heteroaryl substituent. In contrast, we show that the obsd. reaction rates are way too high to be explained on this basis. Computational investigation of this phenomenon revealed that distortion of the tetrazine caused by intramol. repulsive N-N interaction plays a key role in accelerating the cycloaddn. step. We show that the limited stability of tetrazines in biol. media strongly correlates with the electron-withdrawing effect of the substituent, while intramol. repulsion increases the reactivity without reducing the stability. These fundamental insights reveal thus far overlooked mechanistic aspects that govern the reactivity/stability trade-off for tetrazines in physiol. relevant environments, thereby providing a new strategy that may facilitate the rational design of these bioorthogonal tools.
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    7. 7
      Svatunek, D.; Houszka, N.; Hamlin, T. A.; Bickelhaupt, F. M.; Mikula, H. Chemoselectivity of Tertiary Azides in Strain-Promoted Alkyne-Azide Cycloadditions. Chem.─Eur. J. 2019, 25 (3), 754– 758,  DOI: 10.1002/chem.201805215
      7
      Chemoselectivity of Tertiary Azides in Strain-Promoted Alkyne-Azide Cycloadditions
      Svatunek, Dennis; Houszka, Nicole; Hamlin, Trevor A.; Bickelhaupt, F. Matthias; Mikula, Hannes
      Chemistry - A European Journal (2019), 25 (3), 754-758CODEN: CEUJED; ISSN:0947-6539. (Wiley-VCH Verlag GmbH & Co. KGaA)
      The strain-promoted alkyne-azide cycloaddn. (SPAAC) is the most commonly employed bioorthogonal reaction with applications in a broad range of fields. Over the years, several different cyclooctyne derivs. have been developed and investigated in regard to their reactivity in SPAAC reactions with azides. However, only a few studies examd. the influence of structurally diverse azides on reaction kinetics. Herein, we report our investigations of the reactivity of primary, secondary, and tertiary azides with the cyclooctynes BCN and ADIBO applying exptl. and computational methods. All azides show similar reaction rates with the sterically non-demanding cyclooctyne BCN. However, due to the increased steric demand of the dibenzocyclooctyne ADIBO, the reactivity of tertiary azides drops by several orders of magnitude in comparison to primary and secondary azides. We show that this chemoselective behavior of tertiary azides can be exploited to achieve semiorthogonal dual-labeling without the need for any catalyst using SPAAC exclusively.
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    8. 8
      Fernández, I. Understanding the Reactivity of Fullerenes Through the Activation Strain Model. Eur. J. Org. Chem. 2018, 2018 (12), 1394– 1402,  DOI: 10.1002/ejoc.201701626
      8
      Understanding the Reactivity of Fullerenes Through the Activation Strain Model
      Fernandez, Israel
      European Journal of Organic Chemistry (2018), 2018 (12), 1394-1402CODEN: EJOCFK; ISSN:1099-0690. (Wiley-VCH Verlag GmbH & Co. KGaA)
      The Activation Strain Model of reactivity nowadays constitutes a powerful tool to aid quant. understanding of chem. reactions, and also their design. This approach, combined with the Energy Decompn. Anal. method, has been really helpful for our current understanding of different fundamental transformations in chem. This Microreview illustrates the usefulness of this methodol. in providing more insight into the chem. of fullerenes. To this end, representative recent applications, ranging from the regioselectivity in Diels-Alder cycloaddn. to the reactivity of endohedral fullerenes, are presented.
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    9. 9
      Fernandez, I. Understanding the reactivity of polycyclic aromatic hydrocarbons and related compounds. Chem. Sci. 2020, 11 (15), 3769– 3779,  DOI: 10.1039/D0SC00222D
      9
      Understanding the reactivity of polycyclic aromatic hydrocarbons and related compounds
      Fernandez, Israel
      Chemical Science (2020), 11 (15), 3769-3779CODEN: CSHCCN; ISSN:2041-6520. (Royal Society of Chemistry)
      A review. This perspective article summarizes recent applications of the combination of the activation strain model of reactivity and the energy decompn. anal. methods to the study of the reactivity of polycyclic arom. hydrocarbons and related compds. such as cycloparaphenylenes, fullerenes and doped systems. To this end, we have selected representative examples to highlight the usefulness of this relatively novel computational approach to gain quant. insight into the factors controlling the so far not fully understood reactivity of these species. Issues such as the influence of the size and curvature of the system on the reactivity are covered herein, which is crucial for the rational design of novel compds. with tuneable applications in different fields such as materials science or medicinal chem.
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    10. 10
      Fernandez, I. Understanding the reactivity of frustrated Lewis pairs with the help of the activation strain model-energy decomposition analysis method. Chem. Commun. 2022, 58 (32), 4931– 4940,  DOI: 10.1039/D2CC00233G
      10
      Understanding the reactivity of frustrated Lewis pairs with the help of the activation strain model-energy decomposition analysis method
      Fernandez, Israel
      Chemical Communications (Cambridge, United Kingdom) (2022), 58 (32), 4931-4940CODEN: CHCOFS; ISSN:1359-7345. (Royal Society of Chemistry)
      This Feature article presents recent representative applications of the combination of the Activation Strain Model of reactivity and the Energy Decompn. Anal. methods to understand the reactivity of Frustrated Lewis Pairs (FLPs). This approach has been helpful to not only gain a deeper quant. insight into the factors controlling the cooperative action between the Lewis acid/base partners but also to rationally design highly active systems for different bond activation reactions. Issues such as the influence of the nature of the FLP antagonists or the substituents directly attached to them on the reactivity are covered herein, which are crucial for the future development of this fascinating family of compds.
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    11. 11
      Qi, X.; Kohler, D. G.; Hull, K. L.; Liu, P. Energy Decomposition Analyses Reveal the Origins of Catalyst and Nucleophile Effects on Regioselectivity in Nucleopalladation of Alkenes. J. Am. Chem. Soc. 2019, 141 (30), 11892– 11904,  DOI: 10.1021/jacs.9b02893
      11
      Energy Decomposition Analyses Reveal the Origins of Catalyst and Nucleophile Effects on Regioselectivity in Nucleopalladation of Alkenes
      Qi, Xiaotian; Kohler, Daniel G.; Hull, Kami L.; Liu, Peng
      Journal of the American Chemical Society (2019), 141 (30), 11892-11904CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
      Nucleopalladation is one of the most common mechanisms for Pd-catalyzed hydro- and oxidative functionalization of alkenes. Due to the electronic bias of the π-alkene-palladium complexes, nucleopalladations with terminal aliph. alkenes typically deliver the nucleophile to the more substituted sp2 carbon to form the Markovnikov-selective products. The selective formation of the anti-Markovnikov nucleopalladation products requires the inherent electronic effects to be overridden, which is still a significant challenge for reactions with simple aliph. alkenes. Because the interactions between the nucleophile and the alkene substrate are influenced by a complex combination of multiple types of steric and electronic effects, a thorough understanding of the interplay of these underlying interactions is needed to rationalize and predict the regioselectivity. Here, we employ an energy decompn. approach to quant. sep. the different types of nucleophile-substrate interactions, including steric, electrostatic, orbital interactions, and dispersion effects, and to predict the impacts of each factor on regioselectivity. We demonstrate the use of this approach on the origins of catalyst-controlled anti-Markovnikov-selectivity in Hull's Pd-catalyzed oxidative amination reactions. In addn., we evaluated the regioselectivity in a series of nucleopalladation reactions with different neutral and anionic Pd catalysts and N- and O-nucleophiles with different steric and electronic properties. Based on these computational analyses, a generalized scheme is established to identify the dominant nucleophile-substrate interaction affecting the regioselectivity of nucleopalladations with different Pd catalysts and nucleophiles.
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    12. 12
      Miller, E.; Mai, B. K.; Read, J. A.; Bell, W. C.; Derrick, J. S.; Liu, P.; Toste, F. D. A Combined DFT, Energy Decomposition, and Data Analysis Approach to Investigate the Relationship Between Noncovalent Interactions and Selectivity in a Flexible DABCOnium/Chiral Anion Catalyst System. ACS Catal. 2022, 12 (19), 12369– 12385,  DOI: 10.1021/acscatal.2c03077
      12
      A Combined DFT, Energy Decomposition, and Data Analysis Approach to Investigate the Relationship Between Noncovalent Interactions and Selectivity in a Flexible DABCOnium/Chiral Anion Catalyst System
      Miller, Edward; Mai, Binh Khanh; Read, Jacquelyne A.; Bell, William C.; Derrick, Jeffrey S.; Liu, Peng; Toste, F. Dean
      ACS Catalysis (2022), 12 (19), 12369-12385CODEN: ACCACS; ISSN:2155-5435. (American Chemical Society)
      Developing strategies to study reactivity and selectivity in flexible catalyst systems has become an important topic of research. Herein, we report a combined exptl. and computational study aimed at understanding the mechanistic role of an achiral DABCOnium cofactor in a regio- and enantiodivergent bromocyclization reaction. It was found that electron-deficient aryl substituents enable rigidified transition states via an anion-π interaction with the catalyst, which drives the selectivity of the reaction. In contrast, electron-rich aryl groups on the DABCOnium result in significantly more flexible transition states, where interactions between the catalyst and substrate are more important. An anal. of not only the lowest-energy transition state structures but also an ensemble of low-energy transition state conformers via energy decompn. anal. and machine learning was crucial to revealing the dominant noncovalent interactions responsible for obsd. changes in selectivity in this flexible system.
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    13. 13
      Portela, S.; Cabrera-Trujillo, J. J.; Fernandez, I. Catalysis by Bidentate Iodine(III)-Based Halogen Donors: Surpassing the Activity of Strong Lewis Acids. J. Org. Chem. 2021, 86 (7), 5317– 5326,  DOI: 10.1021/acs.joc.1c00534
      13
      Catalysis by Bidentate Iodine(III)-Based Halogen Donors: Surpassing the Activity of Strong Lewis Acids
      Portela, Susana; Cabrera-Trujillo, Jorge J.; Fernandez, Israel
      Journal of Organic Chemistry (2021), 86 (7), 5317-5326CODEN: JOCEAH; ISSN:0022-3263. (American Chemical Society)
      The poorly understood mode of activation and catalysis of bidentate iodine(III)-based halogen donors have been quant. explored in detail by means of state-of-the-art computational methods. To this end, the uncatalyzed Diels-Alder cycloaddn. reaction between cyclohexadiene and Me vinyl ketone is compared to the analogous process mediated by a bidentate iodine(III)-organocatalyst and by related, highly active iodine(I) species. It is found that the bidentate iodine(III)-catalyst accelerates the cycloaddn. by lowering the reaction barrier up to 10 kcal mol-1 compared to the parent uncatalyzed reaction. Our quant. analyses reveal that the origin of the catalysis is found in a significant redn. of the steric (Pauli) repulsion between the diene and dienophile, which originates from both a more asynchronous reaction mode and a significant polarization of the π-system of the dienophile away from the incoming diene. Notably, the activity of the iodine(III)-catalyst can be further enhanced by increasing the electrophilic nature of the system. Thus, novel systems are designed whose activity actually surpasses that of strong Lewis acids such as BF3.
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    14. 14
      Ziegler, T.; Rauk, A. A theoretical study of the ethylene-metal bond in complexes between copper(1+), silver(1+), gold(1+), platinum(0) or platinum(2+) and ethylene, based on the Hartree-Fock-Slater transition-state method. Inorg. Chem. 1979, 18 (6), 1558– 1565,  DOI: 10.1021/ic50196a034
      14
      A theoretical study of the ethylene-metal bond in complexes between copper(1+), silver(1+), gold(1+), platinum(0) or platinum(2+) and ethylene, based on the Hartree-Fock-Slater transition-state method
      Ziegler, Tom; Rauk, Arvi
      Inorganic Chemistry (1979), 18 (6), 1558-65CODEN: INOCAJ; ISSN:0020-1669.
      An anal. based on the Hartree-Fock-Slater (HFS) transition-state method is given of the metal-ethylene bond in the ion-ethylene complexes Cu+-C2H4, Ag+-C2H4, and Au+-C2H4 as well as in complexes with PtCl3- and Pt(PH3)2. The contribution from σ-donation to the bonding energy was equally important for all three complexes with the ions, whereas the contribution from the π back-donation was important only for the Cu complex. A similar anal. of Pt(Cl)3--C2H4 and Pt(PH3)2-C2H4 showed that the position of ethylene perpendicular to the coordination plane of Pt(Cl)3- in Zeise's salt is caused by steric factors, whereas the position of ethylene in Pt(PH3)2-C2H4 is due to electronic factors, specifically π back-donations.
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    15. 15
      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, 2019 (2–3), 378– 386,  DOI: 10.1002/ejoc.201800572
      15
      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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    16. 16
      Vermeeren, P.; van der Lubbe, S. C. C.; Fonseca Guerra, C.; Bickelhaupt, F. M.; Hamlin, T. A. Understanding chemical reactivity using the activation strain model. Nat. Protoc. 2020, 15 (2), 649– 667,  DOI: 10.1038/s41596-019-0265-0
      16
      Understanding chemical reactivity using the activation strain model
      Vermeeren, Pascal; van der Lubbe, Stephanie C. C.; Fonseca Guerra, Celia; Bickelhaupt, F. Matthias; Hamlin, Trevor A.
      Nature Protocols (2020), 15 (2), 649-667CODEN: NPARDW; ISSN:1750-2799. (Nature Research)
      Understanding chem. reactivity through the use of state-of-the-art computational techniques enables chemists to both predict reactivity and rationally design novel reactions. This protocol aims to provide chemists with the tools to implement a powerful and robust method for analyzing and understanding any chem. reaction using PyFrag 2019. The approach is based on the so-called activation strain model (ASM) of reactivity, which relates the relative energy of a mol. system to the sum of the energies required to distort the reactants into the geometries required to react plus the strength of their mutual interactions. Other available methods analyze only a stationary point on the potential energy surface, but our methodol. analyzes the change in energy along a reaction coordinate. The use of this methodol. has been proven to be crit. to the understanding of reactions, spanning the realms of the inorg. and org., as well as the supramol. and biochem., fields. This protocol provides step-by-step instructions-starting from the optimization of the stationary points and extending through calcn. of the potential energy surface and anal. of the trend-decisive energy terms-that can serve as a guide for carrying out the anal. of any given reaction of interest within hours to days, depending on the size of the mol. system.
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    17. 17
      Houszka, N.; Mikula, H.; Svatunek, D. Substituent Effects in Bioorthogonal Diels-Alder Reactions of 1,2,4,5-Tetrazines. Chem.─Eur. J. 2023, 29 (29), e202300345,  DOI: 10.1002/chem.202300345
      17
      Substituent Effects in Bioorthogonal Diels-Alder Reactions of 1,2,4,5-Tetrazines
      Houszka, Nicole; Mikula, Hannes; Svatunek, Dennis
      Chemistry - A European Journal (2023), 29 (29), e202300345CODEN: CEUJED; ISSN:0947-6539. (Wiley-VCH Verlag GmbH & Co. KGaA)
      1,2,4,5-Tetrazines are increasingly used as reactants in bioorthogonal chem. due to their high reactivity in Diels-Alder reactions with various dienophiles. Substituents in the 3- and 6-positions of the tetrazine scaffold are known to have a significant impact on the rate of cycloaddns.; this is commonly explained on the basis of frontier MO theory. In contrast, we show that reactivity differences between commonly used classes of tetrazines are not controlled by frontier MO interactions. In particular, we demonstrate that mono-substituted tetrazines show high reactivity due to decreased Pauli repulsion, which leads to a more asynchronous approach assocd. with reduced distortion energy. This follows the recent Vermeeren-Hamlin-Bickelhaupt model of reactivity increase in asym. Diels-Alder reactions. In addn., we reveal that ethylene is not a good model compd. for other alkenes in Diels-Alder reactions.
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    18. 18
      Rodriguez, H. A.; Bickelhaupt, F. M.; Fernandez, I. Origin of the Bürgi-Dunitz Angle. ChemPhysChem 2023, 24, e202300379,  DOI: 10.1002/cphc.202300379
      18
      Origin of the Buergi-Dunitz Angle
      Rodriguez, Humberto A.; Bickelhaupt, F. Matthias; Fernandez, Israel
      ChemPhysChem (2023), 24 (17), e202300379CODEN: CPCHFT; ISSN:1439-4235. (Wiley-VCH Verlag GmbH & Co. KGaA)
      The Buergi-Dunitz (BD) angle plays a pivotal role in org. chem. to rationalize the nucleophilic addn. to carbonyl groups. Yet, the origin of the obtuse trajectory of the nucleophile remains incompletely understood. Herein, we quantify the importance of the underlying phys. factors quantum chem. The obtuse BD angle appears to originate from the concerted action of a reduced Pauli repulsion between the nucleophile HOMO and carbonyl π bond, a more stabilizing HOMO-π*-LUMO(C=O) interaction, as well as a more favorable electrostatic attraction.
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    19. 19
      Bürgi, H. B.; Dunitz, J. D.; Shefter, E. Geometrical reaction coordinates. II. Nucleophilic addition to a carbonyl group. J. Am. Chem. Soc. 1973, 95 (15), 5065– 5067,  DOI: 10.1021/ja00796a058
      19
      Geometrical reaction coordinates. II. Nucleophilic addition to a carbonyl group
      Burgi, H. B.; Dunitz, J. D.; Shefter, Eli
      Journal of the American Chemical Society (1973), 95 (15), 5065-7CODEN: JACSAT; ISSN:0002-7863.
      Analysis of intramol. N...C:O interactions obsd. in six crystal structures provides an exptl. basis for mapping the reaction coordinate (min. energy pathway) for the addn. reaction of a nucleophile to a carbonyl group. The line of approach of the nucleophile is not perpendicular to the C-O bond but is inclined at about 107° to it.
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    20. 20
      Bürgi, H. B.; Lehn, J. M.; Wipff, G. Ab initio study of nucleophilic addition to a carbonyl group. J. Am. Chem. Soc. 1974, 96 (6), 1956– 1957,  DOI: 10.1021/ja00813a062
      20
      Ab initio study of nucleophilic addition to a carbonyl group
      Buergi, H. B.; Lehn, J. M.; Wipff, G.
      Journal of the American Chemical Society (1974), 96 (6), 1956-7CODEN: JACSAT; ISSN:0002-7863.
      Ab initio SCF-LCGO (linear combination of Gaussian orbitals)-MO computations were performed on the reaction of hydride ion with HCHO, considered as model for nucleophilic addns. to the carbonyl group. Geometrical changes and electronic rearrangements were obtained as a function of the reaction coordinate. Orientational constraints in the course of the reaction bear relation to orbital steering, togetherness, and proximity effects considered in the literature. The calcd. geometrical changes correlate with the changes obsd. in crystal structures for the approach of an amino site toward a carbonyl group. A computation of the NH3-HCHO system at one fixed sepn. was also performed for comparison purposes.
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    21. 21
      Bürgi, H. B.; Dunitz, J. D.; Lehn, J. M.; Wipff, G. Stereochemistry of reaction paths at carbonyl centres. Tetrahedron 1974, 30 (12), 1563– 1572,  DOI: 10.1016/S0040-4020(01)90678-7
      21
      Stereochemistry of reaction paths at carbonyl centers
      Buergi, H. B.; Dunitz, J. D.; Lehn, J. M.; Wipff, G.
      Tetrahedron (1974), 30 (12), 1563-72CODEN: TETRAB; ISSN:0040-4020.
      Ab initio MO calcns. and crystal structure structure data were used to infer the reaction paths of nucleophilic addn. to carbonyl compds.
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    22. 22
      Frisch, M.; Trucks, G.; Schlegel, H.; Scuseria, G.; Robb, M.; Cheeseman, J.; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, G. Gaussian 16, Revision A.03; Gaussian Inc.: Wallingford, CT, 2016.
      There is no corresponding record for this reference.
    23. 23
      Zhao, Y.; Truhlar, D. G. The M06 suite of density functionals for main group thermochemistry, thermochemical kinetics, noncovalent interactions, excited states, and transition elements: two new functionals and systematic testing of four M06-class functionals and 12 other functionals. Theor. Chem. Acc. 2008, 120 (1–3), 215– 241,  DOI: 10.1007/s00214-007-0310-x
      23
      The M06 suite of density functionals for main group thermochemistry, thermochemical kinetics, noncovalent interactions, excited states, and transition elements: two new functionals and systematic testing of four M06-class functionals and 12 other functionals
      Zhao, Yan; Truhlar, Donald G.
      Theoretical Chemistry Accounts (2008), 120 (1-3), 215-241CODEN: TCACFW; ISSN:1432-881X. (Springer GmbH)
      We present two new hybrid meta exchange-correlation functionals, called M06 and M06-2X. The M06 functional is parametrized including both transition metals and nonmetals, whereas the M06-2X functional is a high-nonlocality functional with double the amt. of nonlocal exchange (2X), and it is parametrized only for nonmetals. The functionals, along with the previously published M06-L local functional and the M06-HF full-Hartree-Fock functionals, constitute the M06 suite of complementary functionals. We assess these four functionals by comparing their performance to that of 12 other functionals and Hartree-Fock theory for 403 energetic data in 29 diverse databases, including ten databases for thermochem., four databases for kinetics, eight databases for noncovalent interactions, three databases for transition metal bonding, one database for metal atom excitation energies, and three databases for mol. excitation energies. We also illustrate the performance of these 17 methods for three databases contg. 40 bond lengths and for databases contg. 38 vibrational frequencies and 15 vibrational zero point energies. We recommend the M06-2X functional for applications involving main-group thermochem., kinetics, noncovalent interactions, and electronic excitation energies to valence and Rydberg states. We recommend the M06 functional for application in organometallic and inorganometallic chem. and for noncovalent interactions.
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    24. 24
      Krishnan, R.; Binkley, J. S.; Seeger, R.; Pople, J. A. Self-consistent molecular orbital methods. XX. A basis set for correlated wave functions. J. Chem. Phys. 1980, 72 (1), 650– 654,  DOI: 10.1063/1.438955
      24
      Self-consistent molecular orbital methods. XX. A basis set for correlated wave functions
      Krishnan, R.; Binkley, J. S.; Seeger, R.; Pople, J. A.
      Journal of Chemical Physics (1980), 72 (1), 650-4CODEN: JCPSA6; ISSN:0021-9606.
      A contracted Gaussian basis set (6-311G**) is developed by optimizing exponents and coeffs. at the Moller-Plesset (MP) second-order level for the ground states of first-row atoms. This has a triple split in the valence s and p shells together with a single set of uncontracted polarization functions on each atom. The basis is tested by computing structures and energies for some simple mols. at various levels of MP theory and comparing with expt.
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    25. 25
      ADF2023; SCM, Theoretical Chemistry, Vrije Universiteit: Amsterdam, The Netherlands. http://www.scm.com (accessed 09/09/2023).
      There is no corresponding record for this reference.
    26. 26
      Fonseca Guerra, C.; Snijders, J. G.; te Velde, G.; Baerends, E. J. Towards an order- N DFT method. Theor. Chem. Acc. 1998, 99 (6), 391– 403,  DOI: 10.1007/s002140050353
      There is no corresponding record for this reference.
    27. 27
      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 (9), 931– 967,  DOI: 10.1002/jcc.1056
      27
      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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    28. 28
      Clementi, E.; Roetti, C. Roothaan-Hartree-Fock atomic wavefunctions. At. Data Nucl. Data Tables 1974, 14 (3–4), 177– 478,  DOI: 10.1016/S0092-640X(74)80016-1
      28
      Roothaan-Hartree-Fock atomic wave functions. Basis functions and their coefficients for ground and certain excited states of neutral and ionized atoms, Z .leq.54
      Clementi, Enrico; Roetti, Carla
      Atomic Data and Nuclear Data Tables (1974), 14 (3-4), 177-478CODEN: ADNDAT; ISSN:0092-640X.
      Tables are presented of the exponents of the basis functions and the coeffs. to be used in analytic wave functions expanded in the Roothaan-Hartree-Fock method. Values are tabulated for at. nos. Z ≤ 54, for neutral atoms, pos. and neg. ions, and a no. of isoelectronic series.
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    29. 29
      Van Lenthe, E.; Baerends, E. J. Optimized Slater-type basis sets for the elements 1–118. J. Comput. Chem. 2003, 24 (9), 1142– 1156,  DOI: 10.1002/jcc.10255
      29
      Optimized Slater-type basis sets for the elements 1-118
      Van Lenthe, E.; Baerends, E. J.
      Journal of Computational Chemistry (2003), 24 (9), 1142-1156CODEN: JCCHDD; ISSN:0192-8651. (John Wiley & Sons, Inc.)
      Seven different types of Slater type basis sets for the elements H (Z = 1) up to E118 (Z = 118), ranging from a double zeta valence quality up to a quadruple zeta valence quality, are tested in their performance in neutral at. and diat. oxide calcns. The exponents of the Slater type functions are optimized for the use in (scalar relativistic) zeroth-order regular approximated (ZORA) equations. At. tests reveal that, on av., the abs. basis set error of 0.03 kcal/mol in the d. functional calcn. of the valence spinor energies of the neutral atoms with the largest all electron basis set of quadruple zeta quality is lower than the av. abs. difference of 0.16 kcal/mol in these valence spinor energies if one compares the results of ZORA equation with those of the fully relativistic Dirac equation. This av. abs. basis set error increases to about 1 kcal/mol for the all electron basis sets of triple zeta valence quality, and to approx. 4 kcal/mol for the all electron basis sets of double zeta quality. The mol. tests reveal that, on av., the calcd. atomization energies of 118 neutral diat. oxides MO, where the nuclear charge Z of M ranges from Z = 1-118, with the all electron basis sets of triple zeta quality with two polarization functions added are within 1-2 kcal/mol of the benchmark results with the much larger all electron basis sets, which are of quadruple zeta valence quality with four polarization functions added. The accuracy is reduced to about 4-5 kcal/mol if only one polarization function is used in the triple zeta basis sets, and further reduced to approx. 20 kcal/mol if the all electron basis sets of double zeta quality are used. The inclusion of g-type STOs to the large benchmark basis sets had an effect of less than 1 kcal/mol in the calcn. of the atomization energies of the group 2 and group 14 diat. oxides. The basis sets that are optimized for calcns. using the frozen core approxn. (frozen core basis sets) have a restricted basis set in the core region compared to the all electron basis sets. On av., the use of these frozen core basis sets give at. basis set errors that are approx. twice as large as the corresponding all electron basis set errors and mol. atomization energies that are close to the corresponding all electron results. Only if spin-orbit coupling is included in the frozen core calcns. larger errors are found, esp. for the heavier elements, due to the addnl. approxn. that is made that the basis functions are orthogonalized on scalar relativistic core orbitals.
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    30. 30
      van Lenthe, E.; Snijders, J. G.; Baerends, E. J. The zero-order regular approximation for relativistic effects: The effect of spin–orbit coupling in closed shell molecules. J. Chem. Phys. 1996, 105 (15), 6505– 6516,  DOI: 10.1063/1.472460
      30
      The zero-order regular approximation for relativistic effects: The effect of spin-orbit coupling in closed shell molecules
      van Lenthe, E.; Snijders, J. G.; Baerends, E. J.
      Journal of Chemical Physics (1996), 105 (15), 6505-6516CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
      In this paper we will calc. the effect of spin-orbit coupling on properties of closed shell mols., using the zero-order regular approxn. to the Dirac equation. Results are obtained using d. functionals including d. gradient corrections. Close agreement with expt. is obtained for the calcd. mol. properties of a no. of heavy element diat. mols.
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    31. 31
      Svatunek, D.; Houk, K. N. autoDIAS: a python tool for an automated distortion/interaction activation strain analysis. J. Comput. Chem. 2019, 40 (28), 2509– 2515,  DOI: 10.1002/jcc.26023
      31
      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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  • Supporting Information

    Supporting Information

    The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.jctc.3c00907.

    • jmol file (XYZ)

    • Orbital overlaps (XLSX)

    • jmol file (XYZ)

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