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Increase of Radiative Forcing through Midinfrared Absorption by Stable CO2 Dimers?

Cite this: J. Phys. Chem. A 2022, 126, 19, 2966–2975
Publication Date (Web):May 9, 2022
https://doi.org/10.1021/acs.jpca.2c00857

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Abstract

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We performed matrix-isolation infrared (MI-IR) spectroscopy of carbon dioxide monomers, CO2, and dimers, (CO2)2, trapped in neon and in air. On the basis of vibration configuration interaction (VCI) calculations accounting for mode coupling and anharmonicity, we identify additional infrared-active bands in the MI-IR spectra due to the (CO2)2 dimer. These bands are satellite bands next to the established CO2 monomer bands, which appear in the infrared window of Earth’s atmosphere at around 4 and 15 μm. In a systematic carbon dioxide mixing ratio study using neon matrixes, we observe a significant fraction of the dimer at mixing ratios above 300 ppm, with a steep increase up to 1000 ppm. In neon matrix, the dimer increases the IR absorbance by about 15% at 400 ppm compared to the monomer absorbance alone. This suggests a high fraction of the (CO2)2 dimer in our matrix experiments. In atmospheric conditions, such increased absorbance would significantly amplify radiative forcings and, thus, the greenhouse warming. To enable a comparison of our laboratory experiment with various atmospheric conditions (Earth, Mars, Venus), we compute the thermodynamics of the dimerization accordingly. The dimerization is favored at low temperatures and/or high carbon dioxide partial pressures. Thus, we argue that matrix isolation does not trap the gas composition “as is”. Instead, the gas is precooled to 40 K, where CO2 dimerizes before being trapped in the matrix, already at very low carbon dioxide partial pressures. In the context of planetary atmospheres, our results improve understanding of the greenhouse effect for planets of rather thick CO2 atmospheres such as Venus, where a significant fraction of the (CO2)2 dimer can be expected. There, the necessity of including the mid-IR absorption by stable (CO2)2 dimers in databases used for modeling radiative forcing, such as HITRAN, arises.

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 Special Issue

Published as part of The Journal of Physical Chemistry virtual special issue “10 Years of the ACS PHYS Astrochemistry Subdivision”.

Introduction

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Carbon dioxide is the preeminent anthropogenic greenhouse gas on Earth. (1) In thermal equilibrium with the sun, the Earth’s surface temperature should be 255 K according to Stefan–Boltzmann’s law. The actual surface temperature, however, is 288 K, implying a warming of 33 K caused by its atmospheric greenhouse gases. While CO2 is a trace gas on Earth, Venus has a much denser atmosphere composed of mainly 96.5% CO2 and 92 bar of surface pressure. (2) Hence, the greenhouse effect on Venus is about 15 times stronger than that on Earth. The Earth’s atmospheric CO2 mixing ratio increased from 270 ± 10 ppm in 1750 to about 417 ppm in May 2020, where annual increases have reached 3 ppm in the past decade. (3) Consequently, the temperature has risen by +2.50 ± 0.14 °C for Northern hemisphere landmasses comparing 2020 with 1884. (4) By year 2100, CO2 mixing ratios might climb to 830 ppm according to the SSP3 scenario that predicts an increase of global mean surface temperature by 4.1 °C, (5) far above the Paris Agreement aims of 1.5 °C. (6) This scenario seems to be a path closely resembling that of the global development in the past few years. (7)
A skyrocketing atmospheric CO2 mixing ratio favors CO2 dimerization and raises the question of what the impact of (CO2)2 on greenhouse warming might be. Up to now, no carbon dioxide dimers have been detected in Earth’s atmosphere. However, once dimers appear in significant amounts in planetary atmospheres, we expect increasing radiative forcing due to additional infrared (IR) absorption and, thus, global warming beyond the greenhouse effect of the monomers. If there were carbon dioxide dimers in the troposphere, revision of contemporary climate models could be necessary because of potentially unaccounted (CO2)2 infrared absorptions. A step in this direction has been done by considering collision-induced absorption (CIA) due to unstable (CO2)2 dimers for dense CO2 atmospheres. (8) CIA has been included in the HITRAN database for the (CO2)2 dimers, together with a variety of other dimers and other collision complexes. (9) However, dimerization may also result in stable dimers (or tightly bound dimers), which have been recently considered in broad-band spectra. (10) In the mid-IR, such stable dimers would lead to permanent additional absorptions in the vicinity of the monomer’s IR absorption. Those additional IR bands are usually hard to distinguish from the rotational–vibrational spectrum of the pure monomer.
Thus, we investigate the IR spectrum of carbon dioxide using matrix isolation to quench rotational transitions and use anharmonic calculations to assign all observed vibrational transitions. Previously, we successfully assigned all CO2 monomer bands, (11) where we also provided a short review of the theoretical and experimental spectroscopy of carbon dioxide and its dimer. For a detailed review on computational studies on the (CO2)2 dimer and also recent calculations we refer to Maystrovsky et al., (12) who demonstrated that variational calculations using a tailor-made potential energy surface for the dimer on explicitly correlated coupled cluster theory yield excellent results. In the present work, we investigate the infrared absorption of the (CO2)2 dimer in the mid-IR and discuss its importance to different planetary atmospheres, specifically Mars, Venus, and Earth in comparison. On the basis of two matrix-isolation experiments, we demonstrate the characteristics of the mid-IR spectrum of the (CO2)2 dimer: (a) a mixing ratio series study of carbon dioxide isolated in neon matrix and (b) direct matrix isolation of laboratory air (containing about 417 ppm carbon dioxide). In addition to the experimental data, we provide ab initio calculations of the vibrational spectrum of the monomer and dimer, relying on multimode potential energy surfaces (13) and vibrational self-consistent field (VSCF) and configuration interaction (VCI) computations. (14,15) This approach allows us to unequivocally identify dimer absorptions by minimizing the discrepancy between experiment and calculation based on the inclusion of mode coupling and anharmonicity. (16) Finally, we calculate the equilibrium constant for the monomer–dimer equilibrium to estimate the fraction of dimers for different CO2 partial pressures and temperatures.

Experimental Methodology and Computational Details

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Matrix-Isolation Infrared Spectroscopy of Carbon Dioxide in Neon

We performed infrared spectroscopy measurements of mixtures of gases in frozen neon matrixes, i.e., matrix-isolation infrared (MI-IR) spectroscopy. Former studies (17,18) have shown that the composition of an atmosphere trapped in a frozen matrix resembles the gas phase composition. Thus, MI-IR spectroscopy is a suitable analytical technique for investigating short-lived and unstable species from the gas phase. As matrix isolation inhibits molecular rotation, i.e., quenches the rotational–vibrational transitions, the complexity of the MI-IR spectra is reduced compared to a gas-phase IR spectrum. Consequently, observation of pure vibrational features in MI-IR spectra facilitates the distinction of different molecules, conformers, and clusters as well as dimers and oligomers. For studying the carbon dioxide dimerization with increasing carbon dioxide mixing ratio, we employed MI-IR experiments using neon as a host. Compared to other rare gases as a matrix material, neon minimizes matrix effects such as matrix shifts or multiple trapping sites. (11) Hence, MI-IR spectroscopy using neon as a host provides particularly clean spectra and facilitates studying carbon dioxide dimerization.
We used a 12C16O2 sample of high purity (99.9995%, Messer Austria, order no. 1290102114, lot 27531923) to deposit CO2/Ne mixtures as a frozen, immobile solid on a cold mirror. The neon matrix containing carbon dioxide is then probed in the mid-infrared using a Vertex 80v Bruker spectrometer. The mixing ratio of carbon dioxide in neon, from now on denoted as ρ, was adjusted and quantified by barometric monitoring. This setup is detailed elsewhere. (11,19) In our main experiments, matrix isolation and IR spectroscopy were performed at 6 K. We accumulated the IR spectra (resolution, 0.3 cm–1; scans, 512) within roughly 30 min. To study the influence of initial gas temperature during mixing on the dimerization, the CO2/Ne mixtures were equilibrated at either 25 °C (cf. the spectra in Figure S4) or 65 °C (cf. spectra in Figure S5). The relative band areas for the monomer and dimer at these different mixing temperatures (cf. Figure S6, parts b and c) show no significant difference.
As neon has a comparably high vapor pressure in comparison to, e.g., argon, we probed the thermal stability of our neon matrixes. All gas mixtures were deposited at 6 K, and then slowly heated in steps of 0.5 K up to 12 K. In each step, we accumulated “quick” spectra (resolution, 0.3 cm–1; scans, 32) within about 1 min. Neon evaporation from the matrix commences at roughly 9 K. Afterward we further increased the temperature beyond 12 K by turning off the helium cryostat and keeping the heater on. In roughly 2 min steps, we accumulated spectra up to a temperature of about 100 K. Figure S7 shows for ρ = 500 ppm that solid carbon dioxide residues remain after neon evaporation. We observed very similar behavior for the other carbon dioxide mixing ratios in our study.

MI-IR Spectroscopy of Isolated Air (Carbon Dioxide in Nitrogen–Oxygen–Argon)

When isolating air at 12 K, all trace gases in the air, including carbon dioxide, are trapped in a solid matrix of N2/O2/Ar, with their volume mixing ratio of 78:21:1 in the atmosphere. For this experiment, we used a different high-vacuum setup, also employing a helium cryostat. The cryostat was used to cool a cesium iodide window to 12 K. By introducing air into the chamber through a needle valve, we could deposit air onto this window slowly. During the deposition, the window was monitored in situ, where the entire vacuum chamber is placed inside the sample chamber of an IR spectrometer (Varian Excalibur 4500). The sample chamber of the spectrometer was constantly flooded with nitrogen to remove IR-active trace gases from the air, through which the beam passes. Over 800 spectra, with a resolution of 0.25 cm–1, were collected and combined to a single measurement. We isolated air on November 15, 2020 at Innrain 52c, Innsbruck, Austria. The deposition times were long enough to avoid significant heating of the air matrix.

Monomer–Dimer Thermodynamic Equilibrium

The free energy of the dimer dissociation (CO2)2 ↔ 2CO2 is computed as ΔG (kJ mol–1) = 2GCO2f – G(CO2)2f, where G(CO2)2f and GCO2f are the free energy of formation of the dimer and the monomer. First, we calculated the electronic energies and the harmonic frequencies of the monomer and dimer at the CCSD(T)-F12 level of theory with the VTZ-F12 basis set using the MOLPRO software package. (20) Second, we estimated the free energies of formation within the rigid rotor harmonic oscillator (RRHO) approach using the KiSThelP program. (21) This approach computes thermodynamic properties from partition functions based on previously calculated electronic energies, harmonic frequencies, rotational constants, as well as the molecular symmetry and mass. Note that calculated thermodynamics and the equilibrium constants for temperatures close to 0 K may potentially be inaccurate as the approximations break down. However, for the temperature range we are interested in (above 30 K) the RRHO approximations can be expected to be valid.

In Vacuo VSCF/VCI Calculations of Carbon Dioxide and Its Dimer

Our present band assignment to monomer or dimer vibrational modes relies on VSCF and VCI computations using the MOLPRO software package. (20) Starting from the global equilibrium structure of the carbon dioxide dimer, which has C2h symmetry, (22) we performed a harmonic frequency calculation using the distinguishable cluster approach with a double-ζ basis (DCSD-F12a/VDZ-F12) (23,24) to obtain the normal modes of the dimer. The multimode potential energy surface (PES) is expanded up to 3D terms, i.e., three mode couplings, using the XSURF algorithm, (25) as implemented in MOLPRO 2020. Hereby, intermolecular as well as intramolecular modes are coupled. Within this approach we used DCSD-F12a/cc-pVDZ-F12 single points to construct the grid representation of the PES. To estimate whether addition of diffuse functions improves the description of the CO2 dimer, we also computed a PES relying on DCSD-F12a/aug-cc-pVDZ single points (cf. Table S2). However, the results were very similar and will not be considered in detail here. The grid representation of the PES is transformed into an analytic representation using polynomials. (26) On the basis of this polynomial representation, anharmonic vibrational frequencies are computed using the vibrational self-consistent field and configuration interaction (VSCF/VCI) approach (27) as implemented in MOLPRO. In the VCI approach, single to quadruple (SDTQ) excitations are considered. Vibrational intensities are computed within the same approach using a multimode dipole moment surface (DMS) at the HF/VTZ-F12 level of theory. For the carbon dioxide monomer in D∞h symmetry, we followed the same procedure using up to three mode couplings. Our previous studies on the CO2 monomer using the same computational approach show excellent agreement between VCI computations and MI-IR spectra. (11)
The (CO2)2 dimer can be distinguished from the monomer by consideration of its structure and symmetry. The linear CO2 monomer (Figure 1a) comprises four normal modes (3N – 5 with N = 3) and is in the D∞h point group. Only three modes are in the IR-active irreducible representation A1u or E1u, namely, the antisymmetric stretch ν3(A1u) and the bending ν2(E1u). The bending occurs as two degenerate normal modes; hence, only two distinguishable IR-active vibrations are considered in total. Considering the structure of the (CO2)2 dimer, Kalugina et al. (22) suggested the slipped-parallel 60–60–0 conformer as the global minimum. Other conformers are transition states (T-shaped and crossed dimer) or higher in energy (linear dimer). For the assignment of our MI-IR spectra, the consideration of the mentioned slipped-parallel dimer is sufficient; hence, we omit any anharmonic calculations of the other conformers.

Figure 1

Figure 1. Symmetry elements of CO2 and (CO2)2. (a) CO2 in the D∞h point group is highly symmetric. It contains an inversion center (black arrow), an infinite-fold improper rotation axis (green), and an infinite-fold proper rotation axis (yellow). There are infinite choices of degrees of rotation for the infinite-fold axes. Additionally, there is an infinite set of vertical symmetry planes and 2-fold proper rotation axes (blue). (b) In contrast, (CO2)2 in its equilibrium geometry, as a slipped-parallel structure of C2h symmetry, contains only three symmetry elements: an inversion center (black arrow), a 2-fold rotation axis (blue), and a horizontal symmetry plane (blue). Due to its lower symmetry, it features more IR-active bands than the monomer.

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The slipped-parallel (CO2)2 dimer (Figure 1b) is in the C2h point group and has 12 vibrational modes (3N – 6 with N = 6). Six out of 12 modes are in the IR-active irreducible representation Au or Bu, namely, the in-phase antisymmetric stretch ν9(Bu), the in-phase symmetric stretch ν10(Bu), the in-phase out-of-plane bending ν7(Au), the in-phase in-plane bending ν11(Bu), and two intermolecular modes ν8(Au) and ν12(Bu). While the intermolecular modes are outside the atmospheric IR window in the far-infrared region, (28) the remaining four are inside the atmospheric window. The ν10(Bu) vibration in the atmospheric window is too weak to be detected in the present work. That said, an IR spectrum containing (CO2)2 dimers comprises three additional mid-IR bands compared to that of a pure monomer spectrum. In the following experimental spectra, we make use of these differences to elaborate on the impact of the (CO2)2 dimer spectral features relative to the CO2 monomer features.

Results and Discussion

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Figure 2 depicts the calculated temperature dependence of the equilibrium constant Keq for the (CO2)2 dimer dissociation reaction. For temperatures above 50 K, the monomer is thermodynamically favored (cf. thermochemistry data in Figure S1), and the equilibrium constant Keq is on the CO2 monomer side. This is the case for various planetary atmospheres. While the equilibrium constant Keq increases steeply for temperatures above 300 K (like Earth’s atmosphere), it reaches a maximum at around 700 K (like Venus’s atmosphere). The dimer dissociation, however, depends also on the partial pressure of carbon dioxide p(CO2) in the respective environment (cf. the pressure dependence of the degree of dissociation in Figure S2). On Earth and Mars, the partial pressure of carbon dioxide is very low (p(CO2) ≪ 1 bar), leading to high degrees of dissociation. On Venus, however, the high partial pressure (p(CO2) ∼ 90 bar) leads to a lower degree of dissociation α, although the high temperature favors dissociation.

Figure 2

Figure 2. Temperature-dependent equilibrium constant Keq for (CO2)2 → 2CO2 between 30 and 1000 K calculated within the rigid rotor harmonic oscillator (RRHO) approximation in the KiSTheIP program by Canneaux et al. (ref (21)) and relying on the electronic energy and the harmonic frequencies at the CCSD(T)-F12/VTZ-F12 level of theory.

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For Venus, the very dense atmosphere composed of 96.5% carbon dioxide results in a significant fraction of dimers. According to our thermodynamic estimations, the ratio of monomers to dimers is approximately 12:1, resulting in a partial pressure of (CO2)2 dimers of 6.98 bar on Venus (7.6 vol %). Mars has an atmosphere that is composed of 95.1% carbon dioxide but is about 15 000 times thinner than that of Venus (6.36 mbar vs 92 bar). Consequently, the dimer is only a trace species on Mars, despite the much colder climate on Mars (210 vs 737 K). Hence, the monomer-to-dimer ratio is about 5.4 × 105:1, and the (CO2)2 partial pressure is only 0.111 μbar (17 ppmv). By contrast to Mars and Venus, CO2 is only a trace species in our atmosphere (410 ppmv in a 1 bar atmosphere). This leads to a very high monomer-to-dimer ratio of 1.3 × 106:1 and a (CO2)2 partial pressure of only 0.317 nbar (312 pptv) in the boundary layer above Earth’s surface at 288 K.
If (CO2)2 exists in the troposphere, then it is merely at a mixing ratio on the order of parts per trillion (ppt). At higher altitude, e.g., in the tropopause at ∼20 km or the mesopause at ∼80 km, temperatures are much lower, namely, about 200 and 150 K, respectively. Partial pressures are also lower, namely, by a factor of 102 and 105 at such altitudes. While the lower temperatures favor dimerization, the lower partial pressure disfavoring dimers is much stronger. This leads to much smaller dimer fractions in the higher layers of our atmosphere. Consequently, it is a huge challenge in terms of detection limit and sensitivity to spectroscopically observe (CO2)2 dimers on Mars and Earth. For comparison, our estimated mixing ratio of dimers (CO2)2 of 312 pptv on Earth is on the same scale as that of the OH radical (2) or prominent ozone-depleting halocarbons, currently in between ∼80 pptv (CCl4) and ∼490 pptv (CFC-12) according to measurements at Manua Loa, Hawaii within the NOAA/GML in situ halocarbons program.
In both our neon matrix and the air-freezing experiments detailed below, we in fact do observe a considerable amount of (CO2)2 dimers. However, as we will also show below, the monomer/dimer ratio in our matrix experiments does not represent the ratio at 25 °C (or 65 °C). Rather than that, the gas precools to 40 K prior to being trapped in the matrix. Cooling of the gas from room temperature (or above) to 40 K shifts the equilibrium massively to the side of the dimers. That is, in our matrix experiment we trap an atmosphere enriched in dimers, where the monomer/dimer ratio is about 8:1 (see Table 1).
Table 1. Estimation of the (CO2)2 Partial Pressure and Monomer/Dimer Ratioa
 temp (K)KeqpCO2p(CO2)2ratio (monomer/dimer)
Mars2103256.00 × 10–3 bar (∼95.1 vol %)0.111 × 10–6 bar (∼17 ppmv)54 157:1
Earth2885720.426 × 10–3 bar (∼426 ppmv)0.317 × 10–9 bar (∼312 pptv)1 344 231:1
Venus73795888.8 bar (∼96.5 vol %)6.98 bar (∼7.6 vol %)12:1
“matrix”400.002730.400 × 10–3 bar0.460 × 10–6 bar (∼46 ppmv)8:1
a

Equilibrium constants Keq for a given temperature are taken from the calculation shown in Figure 2. Calculation of the dimer fraction p(CO2)2 and monomer/dimer ratio is detailed in the Supporting Information. The characteristic temperatures and carbon dioxide partial pressures pCO2 of Mars, Earth, and Venus are taken from ref (29).

Let us now turn to our experimental observations obtained for CO2/Ne mixtures after deposition as matrixes at 6 K. Figure 3a shows the IR spectra recorded in transmission–reflection for carbon dioxide mixing ratios ρ = 100–700 ppm. Other spectra for ρ = 700–4000 ppm are shown in Figures S4 and S5. At ρ = 100 ppm, the well-known CO2 monomer bands dominate the spectra. In the antisymmetric stretch region (Figure 3c), we observe the CO2 ν3(A1u) transition at 2348.3 cm–1. In the bending region (Figure 3d), we observe the CO2 ν2(E1u) transition as a doublet at 668.5 and 667.9 cm–1. (11) Note that doublet splitting was observed in earlier studies for both the antisymmetric stretch and the bending region for carbon dioxide in argon and krypton matrixes but not in xenon, nitrogen, and deuterium matrixes. (30−36) These doublets were identified as a matrix effect, reflecting that the monomer, of linear geometry, was in two different surroundings referred to as matrix cages. While we reproduced this splitting in argon matrixes, in neon matrixes we observe only a splitting for the CO2 ν2(E1u) transition. (11) It has been shown that the matrix environment makes the two degenerate bending vibrations distinguishable, leading to the observed splitting of the band that corresponds to the bending vibration. (37−39)

Figure 3

Figure 3. Matrix isolation of (CO2)2 dimers from gas-phase CO2/Ne mixtures at 6 K. (a) The mid-IR spectrum between 4000 cm–1 (2.5 μm) and 500 cm–1 (20 μm) exhibits three major absorption regions: (b) the Fermi resonance overtone region, which we do not consider in detail, (c) the antisymmetric stretch region, containing the (CO2)2 ν9(Bu) transition, and (d) the bending region, containing the (CO2)2 ν8(Au) and ν11(Bu) transitions. The assignment relies on frequencies calculated in vacuo, shown as colored lines. To better compare with the experiment, we scale all calculated frequencies by a factor of 0.9989 in panel c and 0.9924 in panel d and the calculated intensities by 0.2397.

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For ρ ≥ 200 ppm, satellite bands appear, shifted from the assigned monomer bands by just a few wavenumbers. Specifically, two bands in the antisymmetric stretch region are shifted by +1.9 and −1.8 cm–1 compared to the CO2 ν3(A1u) transition (Figure 3c), and two bands in the bend region are shifted by +1.8/+2.4 and −3.3/–3.9 cm–1 compared to the CO2 ν2(E1u) transition (Figure 3d). As the shift between the satellite bands and the established monomer bands agrees with our VCI-calculated monomer–dimer shifts, we assign the satellite bands to the (CO2)2 dimer. Our VCI calculations of the slipped-parallel dimer in the C2h point group reveal monomer–dimer shifts that are very similar to the experiment, namely, +2.2 cm–1 for the antisymmetric stretch and +3.9 and −3.9 cm–1 for the bend (cf. the line spectra in Figure 3, parts c and d). On the basis of these calculations, we assign the (CO2)2 bands as follows: the band at 2350.2 cm–1 to the (CO2)2 ν9(Bu) transition and the bands at 670.3 and 664.6 cm–1 to the (CO2)2 ν8(Au) and ν11(Bu) transitions, respectively.
The present VCI calculations systematically overestimate the experimental frequencies by approximately 5 cm–1. In parts c and d of Figure 3, we scale the VCI frequencies of the monomer in each the antisymmetric region by a factor of 0.9989 and the bending region by 0.9924 to match our neon MI-IR experiments. Consequently, we use the scaling factors derived from the monomer bands also for the dimer bands in the respective spectral regions. Table 2, Table S1, and Table S2 comprise the unscaled calculated frequencies, and we provide a variant of Figure 3 with unscaled calculated frequencies in Figure S3. The systematic overestimation of VCI frequencies compared to those of the MI-IR experiment is due to matrix effects (11) and residual anharmonicity. Matrix effects could be computationally modeled by including the matrix atoms explicitly. (40) In the present work, however, we rely on comparing shifts of bands rather than absolute wavenumbers. This strategy largely eliminates the impact of matrix effects on our comparison of experimental and computational IR spectra. As the matrix shift is very similar for dimers and monomers, it cancels out by inspecting differences in monomer and dimer band positions. For this reason, calculated and observed shifts between monomers and dimers (or similarly between conformers) are of crucial importance in the assignment. We have demonstrated this concept earlier for conformers of carbonic acid (17) and monomers and dimers of carbonic acid hemiester (18,41) trapped in noble gas matrixes.
Table 2. Monomer–Dimer Shift of the Stretching and Bending Regionsa
 ref(CO2)2 ν9(Bu)shift ←CO2 ν3(A1u)(CO2)2 ν8(Au)shift ←CO2 ν2(E1u)shift →(CO2)2 ν11(Bu)
VCIthis study2353.22.22351.0677.03.9673.1–3.9669.2
air (N2/Ar/O2)this study2350.92.22348.7663.51.2662.3  
neonthis study2350.21.92348.3670.31.8668.5–3.9664.6
2.4667.9–3.3
nitrogen N2 (30)  2348.6664.32.0662.3–1.7660.6
argon (30)2345.81.32344.5664.10.7663.4–3.5659.9
2.2661.8–2.0
  (31)2346.52.02344.5664.20.8663.4–3.8659.6
2.4661.8–2.2
  (36)2346.72.72345.0664.40.7663.7–3.8659.9
2.5661.9–2.0
krypton (31)2342.52.02340.5662.21.0661.2–2.6658.6
2.0660.2–1.6
xenon (31)2336.01.52334.5661.21.2660.0–1.5658.5
deuterium D2 (33)  2344.0666.31.2665.1–2.1663.0
a

Monomer–dimer shifts derived from absolute (unscaled) frequencies as assigned to the CO2 monomer and (CO2)2 dimer in various matrix-isolation experiments from literature and in the matrix-isolation experiments and VCI computations from this study. All values are in wavenumbers (cm–1).

Table 2 summarizes the monomer–dimer shifts, including our experiments and calculations as well as literature data. Our dimer assignment agrees with earlier observations of satellite bands in the IR spectroscopy of carbon dioxide in various matrixes. (30−36) The frequency shifts due to dimerization are very systematic through all these experiments, which further confirms our assignment of the dimer bands. The upshifted band in the antisymmetric stretch region amounts to 1.3–2.7 cm–1 in argon, krypton, and xenon matrixes, (30−36) 1.9 cm–1 in neon matrixes, and 2.2 cm–1 in the VCI calculation. The experimentally observed, downshifted band at 2346.5 cm–1 in the antisymmetric stretch region is not present in our calculations on CO2 and (CO2)2. We speculate that this band originates from larger (CO2)n clusters, where an assignment would require computations of the trimer (n = 3) or even higher oligomers (n ≥ 4). In previous MI-IR experiments, such downshifted bands have been assigned to higher oligomers of carbon dioxide. (30−36) In the bending region, the upshifts are 0.7–2.5 cm–1 and the downshifts are −1.5 to −3.8 cm–1 in N2, Ar, Kr, Xe, and D2 matrixes, (30−36) compared to +3.9 and −3.9 cm–1 in VCI calculations and +1.8/+2.4 and −3.3/–3.9 cm–1 in the neon matrix. In this context, we emphasize that wavenumbers in neon matrixes agree best with gas-phase spectra, i.e., the matrix effect in neon is the smallest one among all matrixes, (11) which is why we decided to study the CO2 dimerization in neon matrixes.
The present VCI calculations allow for a correct assignment as they generally reproduce the positive monomer–dimer shift in the antisymmetric stretch region (Figure 3c) and one positive and one negative monomer–dimer shift in the bending region (Figure 3d). In the latter region, the calculated monomer–dimer shift from CO2 ν2(E1u) to (CO2)2 ν11(Bu) agrees with the experiment, whereas the shift from CO2 ν2(E1u) to (CO2)2 ν8(Au) is slightly overestimated. Further improvement in our VCI calculations may be achieved by an extension of the multimode potential energy surface to couple more than three modes. However, we do not expect such calculations to improve the assignment; hence, we consider them as beyond the scope of the present work. Note that VSCF and VCI calculations including up to three mode couplings have been previously performed by Maystrovsky et al. (12) Considering the mbCO2/grid/VCI calculations in ref (12), the monomer–dimer shift from CO2 ν2(E1u) to (CO2)2 ν11(Bu) would be −4.5 cm–1, the shift from CO2 ν2(E1u) to (CO2)2 ν8(Au) would be +13.7 cm–1, and the shift from CO2 ν2(E1u) to (CO2)2 ν11(Bu) would be +4.7 cm–1. These shifts do not agree with our or any previous MI-IR experiments, (30−36) which is why we rely on our present VCI calculations for the final assignment. The discrepancy of the monomer–dimer shifts from ref (12) is most likely rooted in the VCI results of the dimer, where the authors correctly stress that the VCI eigenvectors are very sensitive to small changes in the computation (12) and emphasize the value of additional investigations. The assigned monomer–dimer shifts observed from our and previous MI-IR experiments may be a reference for future VCI investigations.
In addition to the band positions, the band intensities are also of interest. In the region of 1400–1200 cm–1, we do not observe the (CO2)2 ν10(Bu) transition. This agrees with the calculated IR intensities, where the intensity of ν10(Bu) is 3–4 orders of magnitude weaker than the intensities of the other transitions, so we are not sensitive enough in our spectroscopy experiment to detect this very weak absorption. The observed intensities allow us to give a first estimate of the monomer/dimer ratio in our experiment. To match the monomer-to-dimer intensity ratio as observed for ρ = 700 ppm (black trace in Figure 3, parts c and d), the VCI-calculated intensities of the dimer bands in Figure 3, parts c and d, need to be scaled by 0.2397. In other words, for ρ = 700 ppm, the monomer is the dominant species with a ratio of 4:1 compared to the dimer. A better quantification of the monomer/dimer ratio from the experiment is possible by investigation of the band areas, as explained below. On the basis of our assignment, we proceed to the central task of the present study, namely, quantifying the additional IR absorption of the (CO2)2 dimers from the experimental spectrum itself.
On the basis of the assigned dimer and monomer bands, we retrieve the band areas by numeric integration, as described in the Supporting Information. Figure S4 details this numerical integration of the monomer and dimer bands. Figure S6 shows the absolute areas of monomer and dimer bands individually in Figure S6a, with relative areas given in Figure S6, parts b and c. This quantification enables us to (1) estimate the monomer/dimer ratio in the matrix experiment and (2) quantify the increase in IR absorption (and thus radiative forcing) by the occurrence of dimers. This estimate of the dimer abundance based on band areas is more rigorous and accurate than the rough estimate based on band intensities detailed above.
We may compare the monomer/dimer ratio from our experiment with the estimation we gave in Table 1 from our thermochemical calculation. For ρ = 400 ppm in our neon matrix experiment, we obtain a monomer-per-dimer ratio of 0.83/0.15 = 5.5 in the asymmetric stretch region or 0.87/0.13 = 6.7 in the bending region (cf. the relative dimer band areas in Figure S6b). For ρ = 400 ppm, our thermochemical calculation predicts a monomer/dimer ratio of 8 at a temperature of 40 K. This implies that the composition in the neon matrix does not correspond to the gas-phase composition at room temperature, but to the gas-phase composition at roughly 40 K. While ideally we would like to trap the ambient-temperature gas-phase composition “as is”, this is apparently not the case in the matrix-isolation studies. We explain this observation by gas-phase molecules bouncing back from the matrix instead of being trapped right away. The gas-phase molecules are precooled during this hitting of the matrix and bounce back before eventually being trapped, apparently to 40 K in our experimental setup.
The analysis of band areas also allows us to quantify the impact of dimers on radiative forcing and greenhouse warming. Assuming an equal absorption coefficient for the monomer and dimer, we can provide an estimate of how much the radiative forcing of carbon dioxide is increased by the occurrence of dimers. The (relative) dimer contribution to radiative forcing is then calculated from the increase of the total band area due to dimerization Ω = , where a(dim) is the area under the dimer bands and a(mono) is the area under the monomer band. Figure 4 shows Ω in red for the antisymmetric stretch and blue for the bending bands. For example, at ρ = 400 ppm Ω is 18% in the asymmetric stretch region. In general, both spectral regions provide two central observations: (1) Ω increases with increasing carbon dioxide mixing ratio ρ. (2) Ω increases steeply at lower ρ and less steeply at higher ρ (beyond 1000 ppm). In particular, Ω increases steeply from approximately 3–6% at ρ = 100 ppm to 15–20% at ρ = 400 ppm, and further to 22–26% at ρ = 700 ppm. Beyond ρ = 1000 ppm, Ω increases flatly from 25% to almost 50% at 4000 ppm.

Figure 4

Figure 4. Amplification of the mid-IR absorption caused by (CO2)2 at different mixing ratios. The curve depicts how the overall mid-IR absorption is amplified due to additional dimer bands compared to that of the monomer alone. The red and blue curves are based on bands near 4.3 and 15.0 μm, respectively. Note that this graph applies to the precooled gas phase (presumably at 40 K) and is based on nonrotating molecules trapped in a neon matrix. The increase of the total band area due to dimerization is calculated by the relation Ω = .

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Our observation of significant absorption due to dimers in neon matrixes even at ρ = 400 ppm prompted us to study the MI-IR spectrum of ambient air. This was done by very slow deposition of air onto a cesium iodide window at 15 K, where the lab was well-vented with outdoor air right before the deposition. In this experiment the matrix is composed of air (N2/O2/Ar) itself, as opposed to neon in the mixing ratio series described above. Figure 5 depicts a deposition-time sequence of spectra in the antisymmetric stretch and bend regions. Figure S8 covers additional spectral regions, where we observe, besides CO2, bands arising from H2O, NO, and NO2 (most likely from traffic pollution) as well as clusters, e.g., (H2O)2 or CO2–N2, in the matrix. As shown in Table S3, the deviation of the band positions of these species from literature data measured in a N2 matrix is less than 1 cm–1.

Figure 5

Figure 5. Matrix-isolation IR spectra of air (from Innsbruck on November 15, 2020; roughly 417 ppm of carbon dioxide) deposited at 15 K, where the main components of air act as the matrix material (N2/O2/Ar) and trace components are trapped as isolated molecules. The antisymmetric stretch region (a) and the bending region (b) of carbon dioxide are studied as a function of the deposition time (15 min, 30 min, 3, 4, 6, and 8 h). Assignment [a] refers to that of ref (30) and [b] to ref (36). Additional spectral regions are shown in the Supporting Information.

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Unlike the neon matrix spectra in Figure 3a–d, the mixing ratio of carbon dioxide in ambient air is constant (ρ = 417 ppm). Hence, we do not perform a mixing ratio series here, yet we increase the thickness of the air matrix with deposition time in Figure 5 to improve the signal-to-noise ratio. The interaction between CO2 and the matrix material air (N2/O2/Ar) is stronger than the interaction with the matrix material neon. This leads to a significant broadening of bands, a change of band intensities, and a more pronounced matrix shift. Despite the broadening, we see direct evidence for the presence of (CO2)2 in isolated air, namely, shoulders at 2350.9 and 663.5 cm–1. The shoulder assignment relies on the assignment of the monomer and dimer shown in Figure 3, parts c and d, as well as earlier literature on matrix isolation of carbon dioxide in nitrogen matrixes in ref (30) and in ref (36). Similar to the neon matrix spectra, the dimer bands are shifted by +2.2 and +1.2 cm–1 compared to the monomer bands. However, we do not observe the downshifted bending band as it is of very low intensity in N2 matrixes (and hence also in air matrixes). (30) The downshifted band in the stretch region is missing, too. Thus, we assume that trimers and higher oligomers of CO2 are not present in the air matrix, as opposed to the neon matrix.
We have decomposed the bands shown in Figure 5 using three Gaussian functions to obtain more information on the monomer/dimer ratio in this matrix experiment. Figure S9 depicts this decomposition, where the black line represents the measured band, the red line the sum of three Gaussian functions, and the green lines the individual Gaussian peaks. To correctly reproduce the bending region, we used two Gaussian functions for the dimer and one for the monomer. For the stretch region, we need two Gaussian functions for the monomer, which is probably a consequence of the cage geometry: a cage splitting occurs for the monomer in the stretch region and a splitting for the dimer in the bending region. The splitting amounts to 1.3 and 0.4 cm–1, with very similar band areas and intensities for the Gaussian functions, indicating the cage splitting. In this analysis, each dimer band area is about 6–10 times smaller than the monomer band areas. We estimate that the IR absorption increases by about 13 ± 4% due to the dimers, which compares very well with the estimation from our neon experiments (see Figure 4). Also in this matrix experiment, the dimers are very likely present because the air is precooled before being trapped at the spectroscopy window. Upon precooling, a large fraction of monomers associate to produce dimers. The presence of such large fractions of carbon dioxide dimers in the air at ambient temperature is ruled out based on thermodynamics calculations.

Conclusion

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We here provide a systematic matrix-isolation study of carbon dioxide with increasing mixing ratios up to 4000 ppm. High-level VCI calculations that account for mode coupling and anharmonicity allow us to clearly identify monomer and dimer bands. As expected, while we barely observe any dimers at mixing ratios of 100 ppm, we observe a strong increase of the dimer fraction at higher mixing ratios. Similarly, we observe carbon dioxide dimers by trapping laboratory air (mainly N2/O2/Ar) containing approximately 417 ppm of CO2. On the basis of calculations of the equilibrium constants for the carbon dioxide monomer–dimer equilibrium, we conclude that the matrix composition represents the gas phase in thermodynamic equilibrium at 40 K. Accordingly, carbon dioxide is precooled before being trapped in the neon and air matrixes. Upon precooling, dimers and higher oligomers form. In the matrix experiment, the IR absorption due to carbon dioxide dimers is significant. The mid-IR absorption compared to that of monomers alone increases between 18% (at 400 ppm) and 35% (at 4000 ppm) due to dimerization. Although it is a rather weakly bound system, the (CO2)2 dimer can introduce additional mid-IR bands.
The fraction of carbon dioxide dimers in the current atmosphere of Earth (∼288 K) is in the parts-per-trillion range (see Table 1). In the coming 20 years, the carbon dioxide mixing ratio in the atmosphere will likely be doubled in comparison to preindustrial times and reach approximately 500 ppm. Although the increasing carbon dioxide mixing ratio will lead to a higher fraction of dimers, more sensitive methods will be necessary to identify dimers in Earth’s atmosphere spectroscopically. In contrast, we roughly estimate a 12:1 monomer/dimer ratio in the Venus atmosphere at 737 K and 88.8 bar of carbon dioxide. Consequently, climate models for Venus based on monomer bands alone would severely underestimate radiative forcing. Considering temperature and pressure broadening effects as the only mechanisms for IR band broadening (2) would be insufficient. Hence, to properly account for band broadening, the occurrence of dimer satellite bands also ought to be considered. We tentatively propose that the (CO2)2 dimer is an underestimated driver for the Venus greenhouse effect that has previously not been recognized. On Earth and Mars, the (CO2)2 dimer fraction is too small to considerably increase IR absorption and act as a driver for the greenhouse effect of these planets.

Supporting Information

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The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.jpca.2c00857.

  • Additional text explaining the results of the calculations and experiments in more detail, calculated frequencies of the monomer and dimer, experimentally observed bands in solid air, thermochemistry of the dimer dissociation, pressure dependence of the dissociation and dimer fraction, MI-IR spectra and calculated spectra without scaling, band integration of all MI-IR spectra of the dilution series in neon matrix (25 and 65 °C, gas phase), results of the band integration (absolute and relative area under the peak), heating experiment, complete MI-IR spectrum of isolated air, band integration of the MI-IR spectrum of isolated air, and additional references (PDF)

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Most electronic Supporting Information files are available without a subscription to ACS Web Editions. Such files may be downloaded by article for research use (if there is a public use license linked to the relevant article, that license may permit other uses). Permission may be obtained from ACS for other uses through requests via the RightsLink permission system: http://pubs.acs.org/page/copyright/permissions.html.

Author Information

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  • Corresponding Authors
  • Authors
    • Dennis F. Dinu - Institute of General, Inorganic and Theoretical Chemistry, University of Innsbruck, A-6020 Innsbruck, Austria;  Institute of Physical Chemistry, University of Innsbruck, A-6020 Innsbruck, Austria;  Institute of Materials Chemistry, Technische Universität Wien, A-1060 Vienna, Austria;  Orcidhttps://orcid.org/0000-0001-8239-7854
    • Pit Bartl - Institute of Physical Chemistry, University of Innsbruck, A-6020 Innsbruck, Austria
    • Patrick K. Quoika - Institute of General, Inorganic and Theoretical Chemistry, University of Innsbruck, A-6020 Innsbruck, Austria;  Orcidhttps://orcid.org/0000-0002-6227-5443
    • Maren Podewitz - Institute of General, Inorganic and Theoretical Chemistry, University of Innsbruck, A-6020 Innsbruck, Austria;  Institute of Materials Chemistry, Technische Universität Wien, A-1060 Vienna, Austria;  Orcidhttps://orcid.org/0000-0001-7256-1219
    • Klaus R. Liedl - Institute of General, Inorganic and Theoretical Chemistry, University of Innsbruck, A-6020 Innsbruck, Austria;  Orcidhttps://orcid.org/0000-0002-0985-2299
  • Notes
    The authors declare no competing financial interest.

Acknowledgments

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The authors are grateful to the Center for Molecular Water Sciences Hamburg (CMWS) for financial support. Christoph Rameshan is thanked for providing samples of pure carbon dioxide.

References

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    Croatica Chemica Acta (2012), 85 (4), 379-390CODEN: CCACAA; ISSN:0011-1643. (Croatian Chemical Society)
    This feature article discusses some selected aspects in the field of vibrational structure calcns. based on vibrational SCF, VSCF, and vibrational CI, VCI, theory. As the quality of such calcns. depends strongly on the accuracy of the underlying multi-dimensional potential energy surface, PES, some techniques will be discussed to establish high-quality PESs in a fully automated manner. As an alternative to VCI theory multiconfiguration SCF, VMCSCF, theory and in particular specific aspects concerning the integral evaluation relevant to both approaches will also be presented. Further aspects concern the efficient calcn. of IR intensities and Franck-Condon factors in vibronic transitions.
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  15. 15
    Christiansen, O. Vibrational Structure Theory: New Vibrational Wave Function Methods for Calculation of Anharmonic Vibrational Energies and Vibrational Contributions to Molecular Properties. Phys. Chem. Chem. Phys. 2007, 9 (23), 2942,  DOI: 10.1039/b618764a
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    15
    Vibrational structure theory: new vibrational wave function methods for calculation of anharmonic vibrational energies and vibrational contributions to molecular properties
    Christiansen, Ove
    Physical Chemistry Chemical Physics (2007), 9 (23), 2942-2953CODEN: PPCPFQ; ISSN:1463-9076. (Royal Society of Chemistry)
    A review. A no. of recently developed theor. methods for the calcn. of vibrational energies and wave functions are reviewed. Methods for constructing the appropriate quantum mech. Hamilton operator are briefly described before reviewing a particular branch of theor. methods for solving the nuclear Schrodinger equation. The main focus is on wave function methods using the vibrational SCF (VSCF) as starting point, and includes vibrational CI (VCI), vibrational Moller-Plesset (VMP) theory, and vibrational coupled cluster (VCC) theory. The convergence of the different methods towards the full vibrational CI (FVCI) result is discussed. Finally, newly developed vibrational response methods for calcn. of vibrational contributions to properties, energies, and transition probabilities are discussed.
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  16. 16
    Dinu, D. F.; Podewitz, M.; Grothe, H.; Liedl, K. R.; Loerting, T. Toward Elimination of Discrepancies between Theory and Experiment: Anharmonic Rotational–Vibrational Spectrum of Water in Solid Noble Gas Matrices. J. Phys. Chem. A 2019, 123 (38), 8234– 8242,  DOI: 10.1021/acs.jpca.9b07221
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    16
    Toward Elimination of Discrepancies between Theory and Experiment: Anharmonic Rotational-Vibrational Spectrum of Water in Solid Noble Gas Matrices
    Dinu, Dennis F.; Podewitz, Maren; Grothe, Hinrich; Liedl, Klaus R.; Loerting, Thomas
    Journal of Physical Chemistry A (2019), 123 (38), 8234-8242CODEN: JPCAFH; ISSN:1089-5639. (American Chemical Society)
    Rotational-vibrational spectroscopy of water in solid noble gas matrixes has been studied for many decades. In spite of that, discrepancies persist in literature about the assignment of specific bands. We tackle the involved rotational-vibrational spectrum of the water isotopologues H216O, HD16O and D216O with an unprecedented combination of exptl. high-resoln. matrix isolation IR (MI-IR) spectroscopy and computational anharmonic vibrational spectroscopy by Vibrational CI (VCI) on high-level ab initio Potential Energy Surfaces. With VCI, the av. deviation to gas-phase expts. is reduced from >100 cm-1 to ≈1 cm-1, when compared to harmonic vibrational spectra. Discrepancies between MI-IR and VCI spectra are identified as matrix effects rather than missing anharmonicity in the theor. approach. Matrix effects are small in Ne (≈1.5 cm-1) and a bit larger in Ar (≈10 cm-1). Controversial assignments in Ne MI-IR spectra are resolved, e.g., concerning the ν3 triad in HDO. We identify new transitions, e.g., the ν2 101←110 transition in D2O and H2O or the ν3 000←101 transition in D2O, and reassign bands, e.g., the band at 3718.9 cm-1 that is newly assigned as the 110←111 transition. The identification and soln. of discrepancies for a well-studied benchmark system such as water, proves the importance of an iterative and one-hand combination of theory and expt. in the field of high-resoln. IR spectroscopy of single mols. As the computational costs involved in the VCI approach are reasonably low, such combined exptl./theor. studies can be extended to mols. larger than triatomics.
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  17. 17
    Bernard, J.; Huber, R. G.; Liedl, K. R.; Grothe, H.; Loerting, T. Matrix Isolation Studies of Carbonic Acid - The Vapor Phase above the β-Polymorph. J. Am. Chem. Soc. 2013, 135 (20), 7732– 7737,  DOI: 10.1021/ja4020925
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    17
    Matrix Isolation Studies of Carbonic Acid-The Vapor Phase above the β-Polymorph
    Bernard, Juergen; Huber, Roland G.; Liedl, Klaus R.; Grothe, Hinrich; Loerting, Thomas
    Journal of the American Chemical Society (2013), 135 (20), 7732-7737CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
    Twenty years ago two different polymorphs of carbonic acid, α- and β-H2CO3, were isolated as thin, cryst. films. They were characterized by IR and, of late, by Raman spectroscopy. Detn. of the crystal structure of these two polymorphs, using cryopowder and thin film X-ray diffraction techniques, has failed so far. Recently, we succeeded in sublimating α-H2CO3 and trapping the vapor phase in a noble gas matrix, which was analyzed by IR spectroscopy. In the same way we have now investigated the β-polymorph. Unlike α-H2CO3, β-H2CO3 was regarded to decomp. upon sublimation. Still, we have succeeded in isolation of undecomposed carbonic acid in the matrix and recondensation after removal of the matrix here. This possibility of sublimation and recondensation cycles of β-H2CO3 adds a new aspect to the chem. of carbonic acid in astrophys. environments, esp. because there is a direct way of β-H2CO3 formation in space, but none for α-H2CO3. Assignments of the FTIR spectra of the isolated mols. unambiguously reveal two different carbonic acid monomer conformers (C2v and Cs). In contrast to the earlier study on α-H2CO3, we do not find evidence for centrosym. (C2h) carbonic acid dimers here. This suggests that two monomers are entropically favored at the sublimation temp. of 250 K for β-H2CO3, whereas they are not at the sublimation temp. of 210 K for α-H2CO3.
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  18. 18
    Köck, E.-M.; Bernard, J.; Podewitz, M.; Dinu, D. F.; Huber, R. G.; Liedl, K. R.; Grothe, H.; Bertel, E.; Schlögl, R.; Loerting, T. Alpha-Carbonic Acid Revisited: Carbonic Acid Monomethyl Ester as a Solid and Its Conformational Isomerism in the Gas Phase. Chem. Eur. J. 2020, 26 (1), 285– 305,  DOI: 10.1002/chem.201904142
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    Dinu, D. F.; Podewitz, M.; Grothe, H.; Loerting, T.; Liedl, K. R. On the Synergy of Matrix-Isolation Infrared Spectroscopy and Vibrational Configuration Interaction Computations. Theor. Chem. Acc. 2020, 139 (12), 174,  DOI: 10.1007/s00214-020-02682-0
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    19
    On the synergy of matrix-isolation infrared spectroscopy and vibrational configuration interaction computations
    Dinu, Dennis F.; Podewitz, Maren; Grothe, Hinrich; Loerting, Thomas; Liedl, Klaus R.
    Theoretical Chemistry Accounts (2020), 139 (12), 174CODEN: TCACFW; ISSN:1432-2234. (Springer)
    A review. The key feature of matrix-isolation IR (MI-IR) spectroscopy is the isolation of single guest mols. in a host system at cryogenic conditions. The matrix mostly hinders rotation of the guest mol., providing access to pure vibrational features. Vibrational SCF (VSCF) and CI computations (VCI) on ab initio multimode potential energy surfaces (PES) give rise to anharmonic vibrational spectra. In a single-sourced combination of these exptl. and computational approaches, we have established an iterative spectroscopic characterization procedure. The present article reviews the scope of this procedure by highlighting the strengths and limitations based on the examples of water, carbon dioxide, methane, methanol, and fluoroethane. An assessment of setups for the construction of the multimode PES on the example of methanol demonstrates that CCSD(T)-F12 level of theory is preferable to compute (a) accurate vibrational frequencies and (b) equil. or vibrationally averaged structural parameters. Our procedure has allowed us to uniquely assign unknown or disputed bands and enabled us to clarify problematic spectral regions that are crowded with combination bands and overtones. Besides spectroscopic assignment, the excellent agreement between theory and expt. paves the way to tackle questions of rather fundamental nature as to whether or not matrix effects are systematic, and it shows the limits of conventional notations used by spectroscopists.
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  20. 20
    Werner, H. J.; Knowles, P. J.; Manby, F. R.; Black, J. A.; Doll, K.; Heßelmann, A.; Kats, D.; Köhn, A.; Korona, T.; Kreplin, D. A. The Molpro Quantum Chemistry Package. J. Chem. Phys. 2020, 152 (14), 144107,  DOI: 10.1063/5.0005081
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    20
    The Molpro quantum chemistry package
    Werner, Hans-Joachim; Knowles, Peter J.; Manby, Frederick R.; Black, Joshua A.; Doll, Klaus; Hesselmann, Andreas; Kats, Daniel; Koehn, Andreas; Korona, Tatiana; Kreplin, David A.; Ma, Qianli; Miller, Thomas F.; Mitrushchenkov, Alexander; Peterson, Kirk A.; Polyak, Iakov; Rauhut, Guntram; Sibaev, Marat
    Journal of Chemical Physics (2020), 152 (14), 144107CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
    Molpro is a general purpose quantum chem. software package with a long development history. It was originally focused on accurate wavefunction calcns. for small mols. but now has many addnl. distinctive capabilities that include, inter alia, local correlation approxns. combined with explicit correlation, highly efficient implementations of single-ref. correlation methods, robust and efficient multireference methods for large mols., projection embedding, and anharmonic vibrational spectra. In addn. to conventional input-file specification of calcns., Molpro calcns. can now be specified and analyzed via a new graphical user interface and through a Python framework. (c) 2020 American Institute of Physics.
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  21. 21
    Canneaux, S.; Bohr, F.; Henon, E. KiSThelP: A Program to Predict Thermodynamic Properties and Rate Constants from Quantum Chemistry Results. J. Comput. Chem. 2014, 35 (1), 82– 93,  DOI: 10.1002/jcc.23470
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    21
    KiSThelP: A program to predict thermodynamic properties and rate constants from quantum chemistry results
    Canneaux, Sebastien; Bohr, Frederic; Henon, Eric
    Journal of Computational Chemistry (2014), 35 (1), 82-93CODEN: JCCHDD; ISSN:0192-8651. (John Wiley & Sons, Inc.)
    Kinetic and Statistical Thermodynamical Package (KiSThelP) is a cross-platform free open-source program developed to est. mol. and reaction properties from electronic structure data. To date, three computational chem. software formats are supported (Gaussian, GAMESS, and NWChem). Some key features are: gas-phase mol. thermodn. properties (offering hindered rotor treatment), thermal equil. consts., transition state theory rate coeffs. (transition state theory (TST), variational transition state theory (VTST)) including one-dimensional (1D) tunneling effects (Wigner, and Eckart) and Rice-Ramsperger-Kassel-Marcus (RRKM) rate consts., for elementary reactions with well-defined barriers. KiSThelP is intended as a working tool both for the general public and also for more expert users. It provides graphical front-end capabilities designed to facilitate calcns. and interpreting results. KiSThelP enables to change input data and simulation parameters directly through the graphical user interface and to visually probe how it affects results. Users can access results in the form of graphs and tables. The graphical tool offers customizing of 2D plots, exporting images and data files. These features make this program also well-suited to support and enhance students learning and can serve as a very attractive courseware, taking the teaching content directly from results in mol. and kinetic modeling. © 2013 Wiley Periodicals, Inc.
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  22. 22
    Kalugina, Y. N.; Buryak, I. A.; Ajili, Y.; Vigasin, A. A.; Jaidane, N. E.; Hochlaf, M. Explicit Correlation Treatment of the Potential Energy Surface of CO 2 Dimer. J. Chem. Phys. 2014, 140 (23), 234310,  DOI: 10.1063/1.4882900
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    22
    Explicit correlation treatment of the potential energy surface of CO2 dimer
    Kalugina, Yulia N.; Buryak, Ilya A.; Ajili, Yosra; Vigasin, Andrei A.; Jaidane, Nejm Eddine; Hochlaf, Majdi
    Journal of Chemical Physics (2014), 140 (23), 234310/1-234310/10CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
    We present an extensive study of the four-dimensional potential energy surface (4D-PES) of the carbon dioxide dimer, (CO2)2. This PES is developed over the set of intermol. coordinates. The electronic computations are carried out at the explicitly correlated coupled cluster method with single, double, and perturbative triple excitations [CCSD(T)-F12] level of theory in connection with the augmented correlation-consistent aug-cc-pVTZ basis set. An analytic representation of the 4D-PES is derived. Our extensive calcns. confirm that "Slipped Parallel" is the most stable form and that the T-shaped structure corresponds to a transition state. Later on, this PES is employed for the calcns. of the vibrational energy levels of the dimer. Moreover, the temp. dependence of the dimer second virial coeff. and of the first spectral moment of rototranslational collision-induced absorption spectrum is derived. For both quantities, a good agreement is found between our values and the exptl. data for a wide range of temps. This attests to the high quality of our PES. Generally, our PES and results can be used for modeling CO2 supercrit. fluidity and examn. of its role in planetary atmospheres. It can be also incorporated into dynamical computations of CO2 capture and sequestration. This allows deep understanding, at the microscopic level, of these processes. (c) 2014 American Institute of Physics.
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    Kats, D.; Manby, F. R. Communication: The Distinguishable Cluster Approximation. J. Chem. Phys. 2013, 139 (2), 021102,  DOI: 10.1063/1.4813481
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    Communication: The distinguishable cluster approximation
    Kats, Daniel; Manby, Frederick R.
    Journal of Chemical Physics (2013), 139 (2), 021102/1-021102/4CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
    We present a method that accurately describes strongly correlated states and captures dynamical correlation. It is derived as a modification of coupled-cluster theory with single and double excitations (CCSD) through consideration of particle distinguishability between dissocd. fragments, while retaining the key desirable properties of particle-hole symmetry, size extensivity, invariance to rotations within the occupied and virtual spaces, and exactness for two-electron subsystems. The resulting method, called the distinguishable cluster approxn., smoothly dissocs. difficult cases such as the nitrogen mol., with the modest N6 computational cost of CCSD. Even for mols. near their equil. geometries, the new model outperforms CCSD. It also accurately describes the massively correlated states encountered when dissocg. hydrogen lattices, a proxy for the metal-insulator transition, and the fully dissocd. system is treated exactly. (c) 2013 American Institute of Physics.
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  24. 24
    Kats, D. Communication: The Distinguishable Cluster Approximation. II. the Role of Orbital Relaxation. J. Chem. Phys. 2014, 141 (6), 061101,  DOI: 10.1063/1.4892792
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    24
    Communication: The distinguishable cluster approximation. II. The role of orbital relaxation
    Kats, Daniel
    Journal of Chemical Physics (2014), 141 (6), 061101/1-061101/4CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
    The distinguishable cluster approxn. proposed in Paper I [D. Kats and F. R. Manby, J. Chem. Phys.139, 021102 (2013)] has shown intriguing abilities to accurately describe potential energy surfaces in various notoriously difficult cases. The question that still remained open is to what extend the accuracy and the stability of the method is due to the special choice of orbital-relaxation treatment. In this paper we introduce orbital relaxation in terms of Brueckner orbitals, orbital optimization, and projective singles into the distinguishable cluster approxn. and investigate its importance in single- and multireference cases. All three resulting methods are able to cope with many multiple-bond breaking problems, but in some difficult cases where the Hartree-Fock orbitals seem to be entirely inadequate the orbital-optimized version turns out to be superior. (c) 2014 American Institute of Physics.
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    Ziegler, B.; Rauhut, G. Rigorous Use of Symmetry within the Construction of Multidimensional Potential Energy Surfaces. J. Chem. Phys. 2018, 149 (16), 164110,  DOI: 10.1063/1.5047912
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    25
    Rigorous use of symmetry within the construction of multidimensional potential energy surfaces
    Ziegler, Benjamin; Rauhut, Guntram
    Journal of Chemical Physics (2018), 149 (16), 164110/1-164110/12CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
    A method is presented, which allows for the rigorous use of symmetry within the construction of multidimensional potential energy surfaces (PESs). This approach is based on a crude but very fast energy est., which retains the symmetry of a mol. This enables the efficient use of coordinate systems, which mix mol. and permutational symmetry, as, for example, in the case of normal coordinates with subsets of localized normal coordinates. The impact of symmetry within the individual terms of an expansion of the PES is studied together with a symmetry consideration within the individual electronic structure calcns. A trade between symmetry within the surface and the electronic structure calcns. has been obsd. and has been investigated in dependence on different coordinate systems. Differences occur between mols. belonging to Abelian point groups in contrast to non-Abelian groups, in which further benefits can be achieved by rotating normal coordinates belonging to degenerate vibrational frequencies. In general, the exploitation of surface symmetry was found to be very important within the construction of PESs of small and medium-sized mols.-irresp. of the coordinate system. Benchmark calcns. are provided for formaldehyde, ethene, chloromethane, and cubane. (c) 2018 American Institute of Physics.
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    Ziegler, B.; Rauhut, G. Efficient Generation of Sum-of-Products Representations of High-Dimensional Potential Energy Surfaces Based on Multimode Expansions. J. Chem. Phys. 2016, 144 (11), 114114,  DOI: 10.1063/1.4943985
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    Efficient generation of sum-of-products representations of high-dimensional potential energy surfaces based on multimode expansions
    Ziegler, Benjamin; Rauhut, Guntram
    Journal of Chemical Physics (2016), 144 (11), 114114/1-114114/11CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
    The transformation of multi-dimensional potential energy surfaces (PESs) from a grid-based multimode representation to an anal. one is a std. procedure in quantum chem. programs. Within the framework of linear least squares fitting, a simple and highly efficient algorithm is presented, which relies on a direct product representation of the PES and a repeated use of Kronecker products. It shows the same scalings in computational cost and memory requirements as the POTFIT approach. In comparison to customary linear least squares fitting algorithms, this corresponds to a speed-up and memory saving by several orders of magnitude. Different fitting bases are tested, namely, polynomials, B-splines, and distributed Gaussians. Benchmark calcns. are provided for the PESs of a set of small mols. (c) 2016 American Institute of Physics.
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    Rauhut, G. Configuration Selection as a Route towards Efficient Vibrational Configuration Interaction Calculations. J. Chem. Phys. 2007, 127 (18), 184109,  DOI: 10.1063/1.2790016
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    Configuration selection as a route towards efficient vibrational configuration interaction calculations
    Rauhut, Guntram
    Journal of Chemical Physics (2007), 127 (18), 184109/1-184109/11CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
    A configuration selective vibrational CI approach is presented that efficiently reduces the variational space and thus leads to significant speedups in comparison to std. vibrational CI implementations. Deviations with respect to ref. calcns. are well below the accuracy of the underlying electronic structure calcns. for the potential and hence are essentially negligible. Parallel implementations of the presented configuration selective vibrational CI approaches lead to further significant time savings. Benchmark calcns. based on potential energy surfaces of coupled-cluster quality are presented for the fundamental modes of cis- and trans-difluoroethylene. The size-consistency error within the vibrational CI calcns. of the difluoroethylene dimer has been studied in dependence on the excitation level.
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    Norooz Oliaee, J.; Dehghany, M.; Rezaei, M.; McKellar, A. R. W.; Moazzen-Ahmadi, N. Five Intermolecular Vibrations of the CO2 Dimer Observed via Infrared Combination Bands. J. Chem. Phys. 2016, 145 (17), 174302,  DOI: 10.1063/1.4966146
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    Five intermolecular vibrations of the CO2 dimer observed via infrared combination bands
    Norooz Oliaee, J.; Dehghany, M.; Rezaei, Mojtaba; McKellar, A. R. W.; Moazzen-Ahmadi, N.
    Journal of Chemical Physics (2016), 145 (17), 174302/1-174302/6CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
    The weakly bound van der Waals dimer (CO2)2 has long been of considerable theor. and exptl. interest. Here, we study its low frequency intermol. vibrations by means of combination bands in the region of the CO2 monomer ν3 fundamental (≈2350 cm-1), which are obsd. using a tunable IR laser to probe a pulsed supersonic slit jet expansion. With the help of a recent high level ab initio calcn. by Wang, Carrington, and Dawes, four intermol. frequencies are assigned: the in-plane disrotatory bend (22.26 cm-1); the out-of-plane torsion (23.24 cm-1); twice the disrotatory bend (31.51 cm-1); and the in-plane conrotatory bend (92.25 cm-1). The disrotatory bend and torsion, sepd. by only 0.98 cm-1, are strongly mixed by Coriolis interactions. The disrotatory bend overtone is well behaved, but the conrotatory bend is highly perturbed and could not be well fitted. The latter perturbations could be due to tunneling effects, which have not previously been obsd. exptl. for CO2 dimer. A fifth combination band, located 1.3 cm-1 below the conrotatory bend, remains unassigned. (c) 2016 American Institute of Physics.
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    Fredin, L.; Nelander, B.; Ribbegård, G. On the Dimerization of Carbon Dioxide in Nitrogen and Argon Matrices. J. Mol. Spectrosc. 1974, 53 (3), 410– 416,  DOI: 10.1016/0022-2852(74)90077-0
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    Dimerization of carbon dioxide in nitrogen and argon matrixes
    Fredin, Leif; Nelander, Bengt; Ribbegard, Goran
    Journal of Molecular Spectroscopy (1974), 53 (3), 410-16CODEN: JMOSA3; ISSN:0022-2852.
    The ir spectrum of CO2 in solid N and Ar matrixes was studied. In N the N-N stretching vibration becomes ir-active in the presence of CO2. Concn. dependency and diffusion studies allowed the identification of a CO2 dimer in solid Ar. In solid N, no clear evidence for a dimer was obtained.
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    Guasti, R.; Schettino, V.; Brigot, N. The Structure of Carbon Dioxide Dimers Trapped in Solid Rare Gas Matrices. Chem. Phys. 1978, 34 (3), 391– 398,  DOI: 10.1016/0301-0104(78)85181-7
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    The structure of carbon dioxide dimers trapped in solid rare gas matrices
    Guasti, R.; Schettino, V.; Brigot, N.
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    The IR spectra of CO2 trapped in solid rare gas matrixes (Ar,Kr,Xe) were studied. The concn. and diffusion dependence of the spectra showed that dimers are formed in the matrixes. In the ν3 region dimer absorption occurs at higher frequency than the monomer absorption while in the bending region it occurs both at higher and lower frequencies. Selection rules and calcns. of the dimer frequencies using a resonant dipole-dipole interaction potential show that the dimer has a structure with the 2 mols. parallel to each other and correlated by an inversion center.
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    Evidence is presented that the cause of the doubling of the IR bands of CO2 in an Ar lattice is the presence of 2 types of acceptable sites for the CO2 mol. The nature of these sites is discussed; it is concluded that the sites are double substitutional sites, in which a CO2 mol. occupies the place of 2 adjacent Ar atoms, and single substitution sites, in which the CO2 mol. occupies the place of a single Ar atom. A CO2 mol. in a double substitutional site is a more stable situation than a CO2 mol. in a single substitutional site: the former gives a higher ν3 and lower ν2 frequency than the latter.
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    The IR spectra of CO2 isolated in deuterium matrixes at ∼6 K are reported for molar ratios of D2/CO2 between 50 and 3200. The bending mode ν2 of CO2 appears as a narrow doublet in the matrix spectra. Bands due to CO2 dimers are identified in the ν2 region from their concn. dependence and from mixed isotope spectra (12CO2 and 13CO2). No dimer bands were obsd. in the monomer antisym. stretching region. In this respect the spectra of CO2 in D2 matrixes resemble those in N2 matrixes. The obsd. dimer spectrum is compared with those predicted on the basis of T-shaped and staggered parallel configurations for the dimer and is interpreted as favoring the latter configuration. The desirability of obtaining matrix spectra at sufficiently high resoln. is stressed.
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    Chemical Physics Letters (2021), 779 (), 138874CODEN: CHPLBC; ISSN:0009-2614. (Elsevier B.V.)
    The IR spectrum of CO2-Ne complex is studied in the region of the CO2 ν3 fundamental vibration. The vibrational fundamentals for both CO2-20Ne and CO2-22Ne are analyzed in combination with available microwave data. In addn., combination bands involving the intermol. bending mode are obsd., leading to the detn. of the bending frequency. For the hot band CO2 transition, (0111) ← (0110), detection of the weak CO2-Ne spectrum reveals the symmetry breaking of the CO2 ν2 bending mode induced by the Ne atom, with the out-of-plane component detd. to lie 0.057 cm-1 higher in energy than the in-plane component.
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    Carbonic acid monoethyl ester as a pure solid and its conformational isomerism in the gas-phase
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    The monoesters of carbonic acid are deemed to be unstable and decomp. to alc. and carbon dioxide. In spite of this, we here report the isolation of the elusive carbonic acid monoethyl ester (CAEE) as a pure solid from ethanolic solns. of potassium bicarbonate. The hemiester is surprisingly stable in acidic soln. and does not experience hydrolysis to carbonic acid. Furthermore, it is also stable in the gas phase, which we demonstrate by subliming the hemiester without decompn. This could not be achieved in the past for any hemiester of carbonic acid. In the gas phase the hemiester experiences conformational isomerism at 210 K. Interestingly, the thermodynamically favored conformation is only reached for the torsional movement of the terminal Et group, but not the terminal hydrogen atom on the millisecond time scale. Accordingly, IR spectra of the gas phase trapped in an argon matrix are best explained on the basis of a 5 : 1 mixt. of monomeric conformers. Our findings necessitate reevaluation of claims of the formation of a carbonic acid polymorph in methanolic soln., which is the subject of a forthcoming publication.
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  1. Ryan C. Fortenberry, Robert J. McMahon, Ralf I. Kaiser. 10 Years of the ACS PHYS Astrochemistry Subdivision. The Journal of Physical Chemistry A 2022, 126 (38) , 6571-6574. https://doi.org/10.1021/acs.jpca.2c06091
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  • Abstract

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    Figure 1

    Figure 1. Symmetry elements of CO2 and (CO2)2. (a) CO2 in the D∞h point group is highly symmetric. It contains an inversion center (black arrow), an infinite-fold improper rotation axis (green), and an infinite-fold proper rotation axis (yellow). There are infinite choices of degrees of rotation for the infinite-fold axes. Additionally, there is an infinite set of vertical symmetry planes and 2-fold proper rotation axes (blue). (b) In contrast, (CO2)2 in its equilibrium geometry, as a slipped-parallel structure of C2h symmetry, contains only three symmetry elements: an inversion center (black arrow), a 2-fold rotation axis (blue), and a horizontal symmetry plane (blue). Due to its lower symmetry, it features more IR-active bands than the monomer.

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    Figure 2

    Figure 2. Temperature-dependent equilibrium constant Keq for (CO2)2 → 2CO2 between 30 and 1000 K calculated within the rigid rotor harmonic oscillator (RRHO) approximation in the KiSTheIP program by Canneaux et al. (ref (21)) and relying on the electronic energy and the harmonic frequencies at the CCSD(T)-F12/VTZ-F12 level of theory.

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    Figure 3

    Figure 3. Matrix isolation of (CO2)2 dimers from gas-phase CO2/Ne mixtures at 6 K. (a) The mid-IR spectrum between 4000 cm–1 (2.5 μm) and 500 cm–1 (20 μm) exhibits three major absorption regions: (b) the Fermi resonance overtone region, which we do not consider in detail, (c) the antisymmetric stretch region, containing the (CO2)2 ν9(Bu) transition, and (d) the bending region, containing the (CO2)2 ν8(Au) and ν11(Bu) transitions. The assignment relies on frequencies calculated in vacuo, shown as colored lines. To better compare with the experiment, we scale all calculated frequencies by a factor of 0.9989 in panel c and 0.9924 in panel d and the calculated intensities by 0.2397.

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    Figure 4

    Figure 4. Amplification of the mid-IR absorption caused by (CO2)2 at different mixing ratios. The curve depicts how the overall mid-IR absorption is amplified due to additional dimer bands compared to that of the monomer alone. The red and blue curves are based on bands near 4.3 and 15.0 μm, respectively. Note that this graph applies to the precooled gas phase (presumably at 40 K) and is based on nonrotating molecules trapped in a neon matrix. The increase of the total band area due to dimerization is calculated by the relation Ω = .

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    Figure 5

    Figure 5. Matrix-isolation IR spectra of air (from Innsbruck on November 15, 2020; roughly 417 ppm of carbon dioxide) deposited at 15 K, where the main components of air act as the matrix material (N2/O2/Ar) and trace components are trapped as isolated molecules. The antisymmetric stretch region (a) and the bending region (b) of carbon dioxide are studied as a function of the deposition time (15 min, 30 min, 3, 4, 6, and 8 h). Assignment [a] refers to that of ref (30) and [b] to ref (36). Additional spectral regions are shown in the Supporting Information.

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      Update of the HITRAN collision-induced absorption section
      Karman, Tijs; Gordon, Iouli E.; van der Avoird, Ad; Baranov, Yury I.; Boulet, Christian; Drouin, Brian J.; Groenenboom, Gerrit C.; Gustafsson, Magnus; Hartmann, Jean-Michel; Kurucz, Robert L.; Rothman, Laurence S.; Sun, Kang; Sung, Keeyoon; Thalman, Ryan; Tran, Ha; Wishnow, Edward H.; Wordsworth, Robin; Vigasin, Andrey A.; Volkamer, Rainer; van der Zande, Wim J.
      Icarus (2019), 328 (), 160-175CODEN: ICRSA5; ISSN:0019-1035. (Elsevier Inc.)
      Correct parameterization of the Collision-induced Absorption (CIA) phenomena is essential for accurate modeling of planetary atmospheres. The HITRAN spectroscopic database provides these parameters in a dedicated section. Here, we significantly revise and extend the HITRAN CIA data with respect to the original effort described in Richard et al. [JQSRT 113, 1276 (2012)]. The extension concerns new collisional pairs as well as wider spectral and temp. ranges for the existing pairs. The database now contains CIA for N2-N2, N2-H2, N2-CH4, N2-H2O, N2-O2, O2-O2, O2-CO2, CO2-CO2, H2-H2, H2-He, H2-CH4, H2-H, H-He, CH4-CH4, CH4-CO2, CH4-He, and CH4-Ar collision pairs. The sources of data as well as their validation and selection are discussed. A wish list to eliminate remaining deficiencies or lack of data from the astrophysics perspective is also presented.
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    10. 10
      Odintsova, T. A.; Serov, E. A.; Balashov, A. A.; Koshelev, M. A.; Koroleva, A. O.; Simonova, A. A.; Tretyakov, M. Y.; Filippov, N. N.; Chistikov, D. N.; Finenko, A. A. CO2–CO2 and CO2–Ar Continua at Millimeter Wavelengths. J. Quant. Spectrosc. Radiat. Transfer 2021, 258, 107400,  DOI: 10.1016/j.jqsrt.2020.107400
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      10
      CO2-CO2 and CO2-Ar continua at millimeter wavelengths
      Odintsova, T. A.; Serov, E. A.; Balashov, A. A.; Koshelev, M. A.; Koroleva, A. O.; Simonova, A. A.; Tretyakov, M. Yu.; Filippov, N. N.; Chistikov, D. N.; Finenko, A. A.; Lokshtanov, S. E.; Petrov, S. V.; Vigasin, A. A.
      Journal of Quantitative Spectroscopy & Radiative Transfer (2021), 258 (), 107400CODEN: JQSRAE; ISSN:0022-4073. (Elsevier Ltd.)
      Broadband spectra of the continuum absorption in pure CO2 gas and its mixt. with Ar are studied at room temp. using a resonator spectrometer within 105-240 GHz. The expected pressure and frequency dependence is obsd. The obtained data are validated by two independent calcns. of the interaction-induced absorption using a semiclassical trajectory-based method. The obsd. continuum is interpreted in terms of bimol. absorption, including a significant contribution from true bound dimers. A simplified formula describing both frequency and temp. dependency of the CO2-Ar continuum within a frequency range from 60 GHz to 450 GHz at temps. from 200 K to 400 K is suggested for use in atm. studies.
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    11. 11
      Dinu, D. F.; Podewitz, M.; Grothe, H.; Loerting, T.; Liedl, K. R. Decomposing Anharmonicity and Mode-Coupling from Matrix Effects in the IR Spectra of Matrix-Isolated Carbon Dioxide and Methane. Phys. Chem. Chem. Phys. 2020, 22 (32), 17932– 17947,  DOI: 10.1039/D0CP02121K
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      11
      Decomposing anharmonicity and mode-coupling from matrix effects in the IR spectra of matrix-isolated carbon dioxide and methane
      Dinu, Dennis F.; Podewitz, Maren; Grothe, Hinrich; Loerting, Thomas; Liedl, Klaus R.
      Physical Chemistry Chemical Physics (2020), 22 (32), 17932-17947CODEN: PPCPFQ; ISSN:1463-9076. (Royal Society of Chemistry)
      Gas-phase IR spectra of carbon dioxide and methane are nowadays well understood, as a consequence of their pivotal roles in atm.- and astrochem. However, once those mols. are trapped in noble gas matrixes, their spectroscopic properties become difficult to conceptualize. Still, such spectra provide valuable insights into the vibrational structure. In this study, we combine new matrix-isolation IR (MI-IR) spectra at 6 K in argon and neon with in vacuo anharmonic spectra computed by vibrational SCF (VSCF) and vibrational CI (VCI). The aim is to sep. anharmonicity from matrix effects in the mid-IR spectra of 12C16O2, 12CH4, and 12CD4. The accurate description of anharmonic potential energy surfaces including mode-coupling allows to reproduce gas-phase data with deviations of below 3 cm-1. Consequently, the remaining difference between MI-IR and VSCF/VCI can be attributed to matrix effects. Frequency shifts and splitting patterns turn out to be unsystematic and dependent on the particular combination of analyte and noble gas. While in the case of neon matrixes these effects are small, they are pronounced in xenon, krypton, and argon matrixes. Our strategy allows us to suggest that methane rotates in neon matrixes - in contrast to previous reports.
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    12. 12
      Maystrovsky, S.; Keçeli, M.; Sode, O. Understanding the Anharmonic Vibrational Structure of the Carbon Dioxide Dimer. J. Chem. Phys. 2019, 150 (14), 144302,  DOI: 10.1063/1.5089460
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      12
      Understanding the anharmonic vibrational structure of the carbon dioxide dimer
      Maystrovsky, Samuel; Keceli, Murat; Sode, Olaseni
      Journal of Chemical Physics (2019), 150 (14), 144302/1-144302/10CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
      Understanding the vibrational structure of the CO2 system is important to confirm the potential energy surface and interactions in such van der Waals complexes. In this work, we use our previously developed mbCO2 potential function to explore the vibrational structure of the CO2 monomer and dimer. The potential function has been trained to reproduce the potential energies at the CCSD(T)-F12b/aug-cc-pVTZ level of electronic structure theory. The harmonic approxn., as well as anharmonic corrections using vibrational structure theories such as vibrational SCF, vibrational second-order Moller-Plesset perturbation, and vibrational CI (VCI), is applied to address the vibrational motions. We compare the vibrational results using the mbCO2 potential function with traditional electronic structure theory results and to exptl. frequencies. The anharmonic results for the monomer most closely match the exptl. data to within 3 cm-1, including the Fermi dyad frequencies. The intermol. and intramol. dimer frequencies were treated sep. and show good agreement with the most recent theor. and exptl. results from the literature. The VCI treatment of the dimer vibrational motions accounts for vibrational mixing and delocalization, such that we observe the dimer Fermi resonance phenomena, both in the intramol. and intermol. regions. (c) 2019 American Institute of Physics.
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    13. 13
      Bowman, J. M. Beyond Platonic Molecules. Science (80-.) 2000, 290, 724,  DOI: 10.1126/science.290.5492.724
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    14. 14
      Oschetzki, D.; Neff, M.; Meier, P.; Pfeiffer, F.; Rauhut, G. Selected Aspects Concerning the Efficient Calculation of Vibrational Spectra beyond the Harmonic Approximation. Croat. Chem. Acta 2012, 85 (4), 379– 390,  DOI: 10.5562/cca2149
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      14
      Selected aspects concerning the efficient calculation of vibrational spectra beyond the harmonic approximation
      Oschetzki, Dominik; Neff, Michael; Meier, Patrick; Pfeiffer, Florian; Rauhut, Guntram
      Croatica Chemica Acta (2012), 85 (4), 379-390CODEN: CCACAA; ISSN:0011-1643. (Croatian Chemical Society)
      This feature article discusses some selected aspects in the field of vibrational structure calcns. based on vibrational SCF, VSCF, and vibrational CI, VCI, theory. As the quality of such calcns. depends strongly on the accuracy of the underlying multi-dimensional potential energy surface, PES, some techniques will be discussed to establish high-quality PESs in a fully automated manner. As an alternative to VCI theory multiconfiguration SCF, VMCSCF, theory and in particular specific aspects concerning the integral evaluation relevant to both approaches will also be presented. Further aspects concern the efficient calcn. of IR intensities and Franck-Condon factors in vibronic transitions.
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    15. 15
      Christiansen, O. Vibrational Structure Theory: New Vibrational Wave Function Methods for Calculation of Anharmonic Vibrational Energies and Vibrational Contributions to Molecular Properties. Phys. Chem. Chem. Phys. 2007, 9 (23), 2942,  DOI: 10.1039/b618764a
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      15
      Vibrational structure theory: new vibrational wave function methods for calculation of anharmonic vibrational energies and vibrational contributions to molecular properties
      Christiansen, Ove
      Physical Chemistry Chemical Physics (2007), 9 (23), 2942-2953CODEN: PPCPFQ; ISSN:1463-9076. (Royal Society of Chemistry)
      A review. A no. of recently developed theor. methods for the calcn. of vibrational energies and wave functions are reviewed. Methods for constructing the appropriate quantum mech. Hamilton operator are briefly described before reviewing a particular branch of theor. methods for solving the nuclear Schrodinger equation. The main focus is on wave function methods using the vibrational SCF (VSCF) as starting point, and includes vibrational CI (VCI), vibrational Moller-Plesset (VMP) theory, and vibrational coupled cluster (VCC) theory. The convergence of the different methods towards the full vibrational CI (FVCI) result is discussed. Finally, newly developed vibrational response methods for calcn. of vibrational contributions to properties, energies, and transition probabilities are discussed.
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    16. 16
      Dinu, D. F.; Podewitz, M.; Grothe, H.; Liedl, K. R.; Loerting, T. Toward Elimination of Discrepancies between Theory and Experiment: Anharmonic Rotational–Vibrational Spectrum of Water in Solid Noble Gas Matrices. J. Phys. Chem. A 2019, 123 (38), 8234– 8242,  DOI: 10.1021/acs.jpca.9b07221
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      16
      Toward Elimination of Discrepancies between Theory and Experiment: Anharmonic Rotational-Vibrational Spectrum of Water in Solid Noble Gas Matrices
      Dinu, Dennis F.; Podewitz, Maren; Grothe, Hinrich; Liedl, Klaus R.; Loerting, Thomas
      Journal of Physical Chemistry A (2019), 123 (38), 8234-8242CODEN: JPCAFH; ISSN:1089-5639. (American Chemical Society)
      Rotational-vibrational spectroscopy of water in solid noble gas matrixes has been studied for many decades. In spite of that, discrepancies persist in literature about the assignment of specific bands. We tackle the involved rotational-vibrational spectrum of the water isotopologues H216O, HD16O and D216O with an unprecedented combination of exptl. high-resoln. matrix isolation IR (MI-IR) spectroscopy and computational anharmonic vibrational spectroscopy by Vibrational CI (VCI) on high-level ab initio Potential Energy Surfaces. With VCI, the av. deviation to gas-phase expts. is reduced from >100 cm-1 to ≈1 cm-1, when compared to harmonic vibrational spectra. Discrepancies between MI-IR and VCI spectra are identified as matrix effects rather than missing anharmonicity in the theor. approach. Matrix effects are small in Ne (≈1.5 cm-1) and a bit larger in Ar (≈10 cm-1). Controversial assignments in Ne MI-IR spectra are resolved, e.g., concerning the ν3 triad in HDO. We identify new transitions, e.g., the ν2 101←110 transition in D2O and H2O or the ν3 000←101 transition in D2O, and reassign bands, e.g., the band at 3718.9 cm-1 that is newly assigned as the 110←111 transition. The identification and soln. of discrepancies for a well-studied benchmark system such as water, proves the importance of an iterative and one-hand combination of theory and expt. in the field of high-resoln. IR spectroscopy of single mols. As the computational costs involved in the VCI approach are reasonably low, such combined exptl./theor. studies can be extended to mols. larger than triatomics.
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    17. 17
      Bernard, J.; Huber, R. G.; Liedl, K. R.; Grothe, H.; Loerting, T. Matrix Isolation Studies of Carbonic Acid - The Vapor Phase above the β-Polymorph. J. Am. Chem. Soc. 2013, 135 (20), 7732– 7737,  DOI: 10.1021/ja4020925
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      17
      Matrix Isolation Studies of Carbonic Acid-The Vapor Phase above the β-Polymorph
      Bernard, Juergen; Huber, Roland G.; Liedl, Klaus R.; Grothe, Hinrich; Loerting, Thomas
      Journal of the American Chemical Society (2013), 135 (20), 7732-7737CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
      Twenty years ago two different polymorphs of carbonic acid, α- and β-H2CO3, were isolated as thin, cryst. films. They were characterized by IR and, of late, by Raman spectroscopy. Detn. of the crystal structure of these two polymorphs, using cryopowder and thin film X-ray diffraction techniques, has failed so far. Recently, we succeeded in sublimating α-H2CO3 and trapping the vapor phase in a noble gas matrix, which was analyzed by IR spectroscopy. In the same way we have now investigated the β-polymorph. Unlike α-H2CO3, β-H2CO3 was regarded to decomp. upon sublimation. Still, we have succeeded in isolation of undecomposed carbonic acid in the matrix and recondensation after removal of the matrix here. This possibility of sublimation and recondensation cycles of β-H2CO3 adds a new aspect to the chem. of carbonic acid in astrophys. environments, esp. because there is a direct way of β-H2CO3 formation in space, but none for α-H2CO3. Assignments of the FTIR spectra of the isolated mols. unambiguously reveal two different carbonic acid monomer conformers (C2v and Cs). In contrast to the earlier study on α-H2CO3, we do not find evidence for centrosym. (C2h) carbonic acid dimers here. This suggests that two monomers are entropically favored at the sublimation temp. of 250 K for β-H2CO3, whereas they are not at the sublimation temp. of 210 K for α-H2CO3.
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    18. 18
      Köck, E.-M.; Bernard, J.; Podewitz, M.; Dinu, D. F.; Huber, R. G.; Liedl, K. R.; Grothe, H.; Bertel, E.; Schlögl, R.; Loerting, T. Alpha-Carbonic Acid Revisited: Carbonic Acid Monomethyl Ester as a Solid and Its Conformational Isomerism in the Gas Phase. Chem. Eur. J. 2020, 26 (1), 285– 305,  DOI: 10.1002/chem.201904142
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      There is no corresponding record for this reference.
    19. 19
      Dinu, D. F.; Podewitz, M.; Grothe, H.; Loerting, T.; Liedl, K. R. On the Synergy of Matrix-Isolation Infrared Spectroscopy and Vibrational Configuration Interaction Computations. Theor. Chem. Acc. 2020, 139 (12), 174,  DOI: 10.1007/s00214-020-02682-0
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      19
      On the synergy of matrix-isolation infrared spectroscopy and vibrational configuration interaction computations
      Dinu, Dennis F.; Podewitz, Maren; Grothe, Hinrich; Loerting, Thomas; Liedl, Klaus R.
      Theoretical Chemistry Accounts (2020), 139 (12), 174CODEN: TCACFW; ISSN:1432-2234. (Springer)
      A review. The key feature of matrix-isolation IR (MI-IR) spectroscopy is the isolation of single guest mols. in a host system at cryogenic conditions. The matrix mostly hinders rotation of the guest mol., providing access to pure vibrational features. Vibrational SCF (VSCF) and CI computations (VCI) on ab initio multimode potential energy surfaces (PES) give rise to anharmonic vibrational spectra. In a single-sourced combination of these exptl. and computational approaches, we have established an iterative spectroscopic characterization procedure. The present article reviews the scope of this procedure by highlighting the strengths and limitations based on the examples of water, carbon dioxide, methane, methanol, and fluoroethane. An assessment of setups for the construction of the multimode PES on the example of methanol demonstrates that CCSD(T)-F12 level of theory is preferable to compute (a) accurate vibrational frequencies and (b) equil. or vibrationally averaged structural parameters. Our procedure has allowed us to uniquely assign unknown or disputed bands and enabled us to clarify problematic spectral regions that are crowded with combination bands and overtones. Besides spectroscopic assignment, the excellent agreement between theory and expt. paves the way to tackle questions of rather fundamental nature as to whether or not matrix effects are systematic, and it shows the limits of conventional notations used by spectroscopists.
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    20. 20
      Werner, H. J.; Knowles, P. J.; Manby, F. R.; Black, J. A.; Doll, K.; Heßelmann, A.; Kats, D.; Köhn, A.; Korona, T.; Kreplin, D. A. The Molpro Quantum Chemistry Package. J. Chem. Phys. 2020, 152 (14), 144107,  DOI: 10.1063/5.0005081
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      20
      The Molpro quantum chemistry package
      Werner, Hans-Joachim; Knowles, Peter J.; Manby, Frederick R.; Black, Joshua A.; Doll, Klaus; Hesselmann, Andreas; Kats, Daniel; Koehn, Andreas; Korona, Tatiana; Kreplin, David A.; Ma, Qianli; Miller, Thomas F.; Mitrushchenkov, Alexander; Peterson, Kirk A.; Polyak, Iakov; Rauhut, Guntram; Sibaev, Marat
      Journal of Chemical Physics (2020), 152 (14), 144107CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
      Molpro is a general purpose quantum chem. software package with a long development history. It was originally focused on accurate wavefunction calcns. for small mols. but now has many addnl. distinctive capabilities that include, inter alia, local correlation approxns. combined with explicit correlation, highly efficient implementations of single-ref. correlation methods, robust and efficient multireference methods for large mols., projection embedding, and anharmonic vibrational spectra. In addn. to conventional input-file specification of calcns., Molpro calcns. can now be specified and analyzed via a new graphical user interface and through a Python framework. (c) 2020 American Institute of Physics.
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    21. 21
      Canneaux, S.; Bohr, F.; Henon, E. KiSThelP: A Program to Predict Thermodynamic Properties and Rate Constants from Quantum Chemistry Results. J. Comput. Chem. 2014, 35 (1), 82– 93,  DOI: 10.1002/jcc.23470
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      21
      KiSThelP: A program to predict thermodynamic properties and rate constants from quantum chemistry results
      Canneaux, Sebastien; Bohr, Frederic; Henon, Eric
      Journal of Computational Chemistry (2014), 35 (1), 82-93CODEN: JCCHDD; ISSN:0192-8651. (John Wiley & Sons, Inc.)
      Kinetic and Statistical Thermodynamical Package (KiSThelP) is a cross-platform free open-source program developed to est. mol. and reaction properties from electronic structure data. To date, three computational chem. software formats are supported (Gaussian, GAMESS, and NWChem). Some key features are: gas-phase mol. thermodn. properties (offering hindered rotor treatment), thermal equil. consts., transition state theory rate coeffs. (transition state theory (TST), variational transition state theory (VTST)) including one-dimensional (1D) tunneling effects (Wigner, and Eckart) and Rice-Ramsperger-Kassel-Marcus (RRKM) rate consts., for elementary reactions with well-defined barriers. KiSThelP is intended as a working tool both for the general public and also for more expert users. It provides graphical front-end capabilities designed to facilitate calcns. and interpreting results. KiSThelP enables to change input data and simulation parameters directly through the graphical user interface and to visually probe how it affects results. Users can access results in the form of graphs and tables. The graphical tool offers customizing of 2D plots, exporting images and data files. These features make this program also well-suited to support and enhance students learning and can serve as a very attractive courseware, taking the teaching content directly from results in mol. and kinetic modeling. © 2013 Wiley Periodicals, Inc.
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    22. 22
      Kalugina, Y. N.; Buryak, I. A.; Ajili, Y.; Vigasin, A. A.; Jaidane, N. E.; Hochlaf, M. Explicit Correlation Treatment of the Potential Energy Surface of CO 2 Dimer. J. Chem. Phys. 2014, 140 (23), 234310,  DOI: 10.1063/1.4882900
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      22
      Explicit correlation treatment of the potential energy surface of CO2 dimer
      Kalugina, Yulia N.; Buryak, Ilya A.; Ajili, Yosra; Vigasin, Andrei A.; Jaidane, Nejm Eddine; Hochlaf, Majdi
      Journal of Chemical Physics (2014), 140 (23), 234310/1-234310/10CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
      We present an extensive study of the four-dimensional potential energy surface (4D-PES) of the carbon dioxide dimer, (CO2)2. This PES is developed over the set of intermol. coordinates. The electronic computations are carried out at the explicitly correlated coupled cluster method with single, double, and perturbative triple excitations [CCSD(T)-F12] level of theory in connection with the augmented correlation-consistent aug-cc-pVTZ basis set. An analytic representation of the 4D-PES is derived. Our extensive calcns. confirm that "Slipped Parallel" is the most stable form and that the T-shaped structure corresponds to a transition state. Later on, this PES is employed for the calcns. of the vibrational energy levels of the dimer. Moreover, the temp. dependence of the dimer second virial coeff. and of the first spectral moment of rototranslational collision-induced absorption spectrum is derived. For both quantities, a good agreement is found between our values and the exptl. data for a wide range of temps. This attests to the high quality of our PES. Generally, our PES and results can be used for modeling CO2 supercrit. fluidity and examn. of its role in planetary atmospheres. It can be also incorporated into dynamical computations of CO2 capture and sequestration. This allows deep understanding, at the microscopic level, of these processes. (c) 2014 American Institute of Physics.
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      Kats, D.; Manby, F. R. Communication: The Distinguishable Cluster Approximation. J. Chem. Phys. 2013, 139 (2), 021102,  DOI: 10.1063/1.4813481
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      23
      Communication: The distinguishable cluster approximation
      Kats, Daniel; Manby, Frederick R.
      Journal of Chemical Physics (2013), 139 (2), 021102/1-021102/4CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
      We present a method that accurately describes strongly correlated states and captures dynamical correlation. It is derived as a modification of coupled-cluster theory with single and double excitations (CCSD) through consideration of particle distinguishability between dissocd. fragments, while retaining the key desirable properties of particle-hole symmetry, size extensivity, invariance to rotations within the occupied and virtual spaces, and exactness for two-electron subsystems. The resulting method, called the distinguishable cluster approxn., smoothly dissocs. difficult cases such as the nitrogen mol., with the modest N6 computational cost of CCSD. Even for mols. near their equil. geometries, the new model outperforms CCSD. It also accurately describes the massively correlated states encountered when dissocg. hydrogen lattices, a proxy for the metal-insulator transition, and the fully dissocd. system is treated exactly. (c) 2013 American Institute of Physics.
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    24. 24
      Kats, D. Communication: The Distinguishable Cluster Approximation. II. the Role of Orbital Relaxation. J. Chem. Phys. 2014, 141 (6), 061101,  DOI: 10.1063/1.4892792
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      24
      Communication: The distinguishable cluster approximation. II. The role of orbital relaxation
      Kats, Daniel
      Journal of Chemical Physics (2014), 141 (6), 061101/1-061101/4CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
      The distinguishable cluster approxn. proposed in Paper I [D. Kats and F. R. Manby, J. Chem. Phys.139, 021102 (2013)] has shown intriguing abilities to accurately describe potential energy surfaces in various notoriously difficult cases. The question that still remained open is to what extend the accuracy and the stability of the method is due to the special choice of orbital-relaxation treatment. In this paper we introduce orbital relaxation in terms of Brueckner orbitals, orbital optimization, and projective singles into the distinguishable cluster approxn. and investigate its importance in single- and multireference cases. All three resulting methods are able to cope with many multiple-bond breaking problems, but in some difficult cases where the Hartree-Fock orbitals seem to be entirely inadequate the orbital-optimized version turns out to be superior. (c) 2014 American Institute of Physics.
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    25. 25
      Ziegler, B.; Rauhut, G. Rigorous Use of Symmetry within the Construction of Multidimensional Potential Energy Surfaces. J. Chem. Phys. 2018, 149 (16), 164110,  DOI: 10.1063/1.5047912
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      25
      Rigorous use of symmetry within the construction of multidimensional potential energy surfaces
      Ziegler, Benjamin; Rauhut, Guntram
      Journal of Chemical Physics (2018), 149 (16), 164110/1-164110/12CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
      A method is presented, which allows for the rigorous use of symmetry within the construction of multidimensional potential energy surfaces (PESs). This approach is based on a crude but very fast energy est., which retains the symmetry of a mol. This enables the efficient use of coordinate systems, which mix mol. and permutational symmetry, as, for example, in the case of normal coordinates with subsets of localized normal coordinates. The impact of symmetry within the individual terms of an expansion of the PES is studied together with a symmetry consideration within the individual electronic structure calcns. A trade between symmetry within the surface and the electronic structure calcns. has been obsd. and has been investigated in dependence on different coordinate systems. Differences occur between mols. belonging to Abelian point groups in contrast to non-Abelian groups, in which further benefits can be achieved by rotating normal coordinates belonging to degenerate vibrational frequencies. In general, the exploitation of surface symmetry was found to be very important within the construction of PESs of small and medium-sized mols.-irresp. of the coordinate system. Benchmark calcns. are provided for formaldehyde, ethene, chloromethane, and cubane. (c) 2018 American Institute of Physics.
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      Ziegler, B.; Rauhut, G. Efficient Generation of Sum-of-Products Representations of High-Dimensional Potential Energy Surfaces Based on Multimode Expansions. J. Chem. Phys. 2016, 144 (11), 114114,  DOI: 10.1063/1.4943985
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      Efficient generation of sum-of-products representations of high-dimensional potential energy surfaces based on multimode expansions
      Ziegler, Benjamin; Rauhut, Guntram
      Journal of Chemical Physics (2016), 144 (11), 114114/1-114114/11CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
      The transformation of multi-dimensional potential energy surfaces (PESs) from a grid-based multimode representation to an anal. one is a std. procedure in quantum chem. programs. Within the framework of linear least squares fitting, a simple and highly efficient algorithm is presented, which relies on a direct product representation of the PES and a repeated use of Kronecker products. It shows the same scalings in computational cost and memory requirements as the POTFIT approach. In comparison to customary linear least squares fitting algorithms, this corresponds to a speed-up and memory saving by several orders of magnitude. Different fitting bases are tested, namely, polynomials, B-splines, and distributed Gaussians. Benchmark calcns. are provided for the PESs of a set of small mols. (c) 2016 American Institute of Physics.
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      Rauhut, G. Configuration Selection as a Route towards Efficient Vibrational Configuration Interaction Calculations. J. Chem. Phys. 2007, 127 (18), 184109,  DOI: 10.1063/1.2790016
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      Configuration selection as a route towards efficient vibrational configuration interaction calculations
      Rauhut, Guntram
      Journal of Chemical Physics (2007), 127 (18), 184109/1-184109/11CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
      A configuration selective vibrational CI approach is presented that efficiently reduces the variational space and thus leads to significant speedups in comparison to std. vibrational CI implementations. Deviations with respect to ref. calcns. are well below the accuracy of the underlying electronic structure calcns. for the potential and hence are essentially negligible. Parallel implementations of the presented configuration selective vibrational CI approaches lead to further significant time savings. Benchmark calcns. based on potential energy surfaces of coupled-cluster quality are presented for the fundamental modes of cis- and trans-difluoroethylene. The size-consistency error within the vibrational CI calcns. of the difluoroethylene dimer has been studied in dependence on the excitation level.
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      Norooz Oliaee, J.; Dehghany, M.; Rezaei, M.; McKellar, A. R. W.; Moazzen-Ahmadi, N. Five Intermolecular Vibrations of the CO2 Dimer Observed via Infrared Combination Bands. J. Chem. Phys. 2016, 145 (17), 174302,  DOI: 10.1063/1.4966146
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      Five intermolecular vibrations of the CO2 dimer observed via infrared combination bands
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      Journal of Chemical Physics (2016), 145 (17), 174302/1-174302/6CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
      The weakly bound van der Waals dimer (CO2)2 has long been of considerable theor. and exptl. interest. Here, we study its low frequency intermol. vibrations by means of combination bands in the region of the CO2 monomer ν3 fundamental (≈2350 cm-1), which are obsd. using a tunable IR laser to probe a pulsed supersonic slit jet expansion. With the help of a recent high level ab initio calcn. by Wang, Carrington, and Dawes, four intermol. frequencies are assigned: the in-plane disrotatory bend (22.26 cm-1); the out-of-plane torsion (23.24 cm-1); twice the disrotatory bend (31.51 cm-1); and the in-plane conrotatory bend (92.25 cm-1). The disrotatory bend and torsion, sepd. by only 0.98 cm-1, are strongly mixed by Coriolis interactions. The disrotatory bend overtone is well behaved, but the conrotatory bend is highly perturbed and could not be well fitted. The latter perturbations could be due to tunneling effects, which have not previously been obsd. exptl. for CO2 dimer. A fifth combination band, located 1.3 cm-1 below the conrotatory bend, remains unassigned. (c) 2016 American Institute of Physics.
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      The ir spectrum of CO2 in solid N and Ar matrixes was studied. In N the N-N stretching vibration becomes ir-active in the presence of CO2. Concn. dependency and diffusion studies allowed the identification of a CO2 dimer in solid Ar. In solid N, no clear evidence for a dimer was obtained.
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      The IR spectra of CO2 trapped in solid rare gas matrixes (Ar,Kr,Xe) were studied. The concn. and diffusion dependence of the spectra showed that dimers are formed in the matrixes. In the ν3 region dimer absorption occurs at higher frequency than the monomer absorption while in the bending region it occurs both at higher and lower frequencies. Selection rules and calcns. of the dimer frequencies using a resonant dipole-dipole interaction potential show that the dimer has a structure with the 2 mols. parallel to each other and correlated by an inversion center.
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      Evidence is presented that the cause of the doubling of the IR bands of CO2 in an Ar lattice is the presence of 2 types of acceptable sites for the CO2 mol. The nature of these sites is discussed; it is concluded that the sites are double substitutional sites, in which a CO2 mol. occupies the place of 2 adjacent Ar atoms, and single substitution sites, in which the CO2 mol. occupies the place of a single Ar atom. A CO2 mol. in a double substitutional site is a more stable situation than a CO2 mol. in a single substitutional site: the former gives a higher ν3 and lower ν2 frequency than the latter.
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      Irvine, M.; Pullin, A. The Infrared Matrix Isolation Spectra of Carbon Dioxide. I. Deuterium Matrices : Identification of Bands Due to Carbon Dioxide Dimers. Aust. J. Chem. 1982, 35 (10), 1961,  DOI: 10.1071/CH9821961
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      The IR spectra of CO2 isolated in deuterium matrixes at ∼6 K are reported for molar ratios of D2/CO2 between 50 and 3200. The bending mode ν2 of CO2 appears as a narrow doublet in the matrix spectra. Bands due to CO2 dimers are identified in the ν2 region from their concn. dependence and from mixed isotope spectra (12CO2 and 13CO2). No dimer bands were obsd. in the monomer antisym. stretching region. In this respect the spectra of CO2 in D2 matrixes resemble those in N2 matrixes. The obsd. dimer spectrum is compared with those predicted on the basis of T-shaped and staggered parallel configurations for the dimer and is interpreted as favoring the latter configuration. The desirability of obtaining matrix spectra at sufficiently high resoln. is stressed.
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      Knoezinger, E.; Beichert, P. Matrix Isolation Studies of CO2 Clusters Emerging from Adiabatic Expansion. J. Phys. Chem. 1995, 99 (14), 4906– 4911,  DOI: 10.1021/j100014a006
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      FT-IR spectroscopic studies of the relaxation of binary solid nonequil. mixts. of CO2 and Ar or Kr (1:1000 molar ratio) are reported. The samples were prepd. by embedding carbon dioxide in solid rare gas, either after thermal effusion or after adiabatic expansion. The resulting matrixes then contained exclusively isolated monomer CO2 or both monomer and aggregate species, resp. These two nonequil. systems were subjected to appropriate thermal treatment, which initiated a stepwise transition to the same final state, namely, the equil. solid. The relaxation paths traced by monitoring the asym. stretching vibration of 13CO2 in natural abundance are, however, fundamentally different. They include an intermediate amorphous and a CO2 cluster phase, resp. The studies were preferentially carried out in Kr matrix, since the initial spectrum indicates the presence of only one substitutional site for the CO2 monomer, whereas in Ar there are four sites. To facilitate the interpretation of the IR spectra, ab initio calcns. were performed on small CO2 clusters.
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      Gómez Castaño, J. A.; Fantoni, A.; Romano, R. M. Matrix-Isolation FTIR Study of Carbon Dioxide: Reinvestigation of the CO2 Dimer and CO2···N2 Complex. J. Mol. Struct. 2008, 881 (1–3), 68– 75,  DOI: 10.1016/j.molstruc.2007.08.035
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      Gomez Castano, Jovanny A.; Fantoni, Adolfo; Romano, Rosana M.
      Journal of Molecular Structure (2008), 881 (1-3), 68-75CODEN: JMOSB4; ISSN:0022-2860. (Elsevier B.V.)
      Carbon dioxide isolated in argon and nitrogen matrixes was reinvestigated through FTIR spectroscopy. The study of the variation of the IR absorptions with the concn. of CO2 in the matrix, and also with the addn. of different amts. of N2 (present as an impurity in the Ar gas) was performed. Some of the bands were reassigned to the CO2 dimer and CO2···N2 complex and some others, like the sym. stretching mode for the CO2 dimer and the (ν 1 + ν 3) and (2ν 2 + ν 3) combination bands for the CO2 dimer and that of the CO2···N2 complex, were reported for the first time. The bonding properties of the (CO2)2 and CO2···N2 complexes have been interpreted by a Natural Bond Orbital (NBO) anal. in terms of "donor-acceptor" interactions.
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      Schriver, A.; Schriver-Mazzuoli, L.; Vigasin, A. A. Matrix Isolation Spectra of the Carbon Dioxide Monomer and Dimer Revisited. Vib. Spectrosc. 2000, 23 (1), 83– 94,  DOI: 10.1016/S0924-2031(99)00087-9
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      Matrix isolation spectra of the carbon dioxide monomer and dimer revisited
      Schriver, A.; Schriver-Mazzuoli, L.; Vigasin, A. A.
      Vibrational Spectroscopy (2000), 23 (1), 83-94CODEN: VISPEK; ISSN:0924-2031. (Elsevier Science B.V.)
      New FTIR CO2 high resoln. spectra are recorded in Ar and N matrixes at 11 K at high diln. Their evolution with CO2 diffusion at higher temp. is traced. New observations are discussed in regard to previous works. Monomer CO2 spectra was reassigned in an argon matrix and the three ν3 bands are assigned. Even at high diln. (1/10,000), the temp. increase causes appearance of several bands both in Ar and N. Identification of CO2 dimer absorptions is tentatively proposed.
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      Gartner, T. A.; Barclay, A. J.; McKellar, A. R. W.; Moazzen-Ahmadi, N. Symmetry Breaking of the Bending Mode of CO2in the Presence of Ar. Phys. Chem. Chem. Phys. 2020, 22 (37), 21488– 21493,  DOI: 10.1039/D0CP02674C
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      Symmetry breaking of the bending mode of CO2 in the presence of Ar
      Gartner, T. A.; Barclay, A. J.; McKellar, A. R. W.; Moazzen-Ahmadi, N.
      Physical Chemistry Chemical Physics (2020), 22 (37), 21488-21493CODEN: PPCPFQ; ISSN:1463-9076. (Royal Society of Chemistry)
      The weak IR spectrum of CO2-Ar corresponding to the (0111) ← (0110) hot band of CO2 is detected in the region of the carbon dioxide ν3 fundamental vibration (≈2340 cm-1), using a tunable OPO laser source to probe a pulsed supersonic slit jet expansion. While this method was previously thought to cool clusters to the lowest rotational states of the ground vibrational state, here we show that under suitable jet expansion conditions, sufficient population remains in the first excited bending mode of CO2 (1-2%) to enable observation of vibrationally hot CO2-Ar, and thus to investigate the symmetry breaking of the intramol. bending mode of CO2 in the presence of Ar. The bending mode of the CO2 monomer splits into an in-plane and an out-of-plane mode, strongly linked by a Coriolis interaction. Anal. of the spectrum yields a direct measurement of the in-plane/out-of-plane splitting measured to be 0.8770 cm-1. Calcns. were carried out to det. if key features of our results, i.e., the sign and magnitude of the shift in the energy for the two intramol. bending modes, are consistent with a quantum chem. potential energy surface. This aspect of intramol. interactions has received little previous exptl. and theor. consideration. Therefore, we provide an addnl. avenue by which to study the intramol. dynamics of this simplest dimer in its bending modes. Similar results should be possible for other weakly-bound complexes.
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      Barclay, A. J.; McKellar, A. R. W.; Moazzen-Ahmadi, N. New Infrared Spectra of CO2 – Ne: Fundamental for CO2 – 22Ne Isotopologue, Intermolecular Bend, and Symmetry Breaking of the Intramolecular CO2 Bend. Chem. Phys. Lett. 2021, 779 (July), 138874,  DOI: 10.1016/j.cplett.2021.138874
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      New infrared spectra of CO2 - Ne: Fundamental for CO2 -22Ne isotopologue, intermolecular bend, and symmetry breaking of the intramolecular CO2 bend
      Barclay, A. J.; McKellar, A. R. W.; Moazzen-Ahmadi, N.
      Chemical Physics Letters (2021), 779 (), 138874CODEN: CHPLBC; ISSN:0009-2614. (Elsevier B.V.)
      The IR spectrum of CO2-Ne complex is studied in the region of the CO2 ν3 fundamental vibration. The vibrational fundamentals for both CO2-20Ne and CO2-22Ne are analyzed in combination with available microwave data. In addn., combination bands involving the intermol. bending mode are obsd., leading to the detn. of the bending frequency. For the hot band CO2 transition, (0111) ← (0110), detection of the weak CO2-Ne spectrum reveals the symmetry breaking of the CO2 ν2 bending mode induced by the Ne atom, with the out-of-plane component detd. to lie 0.057 cm-1 higher in energy than the in-plane component.
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      Sode, O.; Ruiz, J.; Peralta, S. Theoretical Investigation of the Vibrational Structure of the Ar–CO2 Complex. J. Mol. Spectrosc. 2021, 380, 111512,  DOI: 10.1016/j.jms.2021.111512
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      Theoretical investigation of the vibrational structure of the Ar-CO2 complex
      Sode, Olaseni; Ruiz, Jesus; Peralta, Steve
      Journal of Molecular Spectroscopy (2021), 380 (), 111512CODEN: JMOSA3; ISSN:0022-2852. (Elsevier B.V.)
      We develop a new flexible-monomer two-body ab initio potential energy surface (PES) for the Ar - CO2 complex. The accuracy of this new potential function is validated by its agreement in the vibrational spectrum of the complex. Vibrational SCF theory (VSCF) and vibrational CI (VCI) theory were employed to solve the complete vibrational Hamiltonian, including both intermol. and intramol. degrees of freedom. We observe excellent agreement with theor. and exptl. results for the vibrational energy levels in the Terahertz region. In the intramol. region, we confirm the slight splitting of the bending modes of the CO2 monomer, where the in-plane bend is 0.83 cm-1 less energetic than the out-of-plane mode. We also explore the combination bands in the asym. stretching region of the CO2 monomer that involve the intermol. motions, and show that these results compare favorably to the fundamental intermol. vibrational energy levels.
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      Bader, F.; Lindic, T.; Paulus, B. A Validation of Cluster Modeling in the Description of Matrix Isolation Spectroscopy. J. Comput. Chem. 2020, 41 (8), 751– 758,  DOI: 10.1002/jcc.26123
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      A Validation of Cluster Modeling in the Description of Matrix Isolation Spectroscopy
      Bader, Frederik; Lindic, Tilen; Paulus, Beate
      Journal of Computational Chemistry (2020), 41 (8), 751-758CODEN: JCCHDD; ISSN:0192-8651. (John Wiley & Sons, Inc.)
      Matrix isolation is a fundamental tool for the synthesis and characterization of highly reactive novel species and study of unusual bonding situations. Ab initio descriptions of guest-host interactions in matrix isolation are highly demanding, as the weak interactions between guest and host can influence the former's oftentimes challenging electronic structure. The matrix effects on a single CO2 mol. in an Ar matrix were studied with dispersion-cor. d. functional theory calcns. Three different guest-host structures were described by bulk models employing periodic boundary conditions as well as cluster models. The calcns. were analyzed with respect to structural features of the CO2 mol. and its immediate surroundings. Also, the mol.'s harmonic frequencies were detd. The calcd. frequencies were in qual. agreement with exptl. observations. The cluster models produced comparable results given that the clusters were large enough to reproduce the structural features of the bulk model. © 2019 Wiley Periodicals, Inc.
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      Bernard, J.; Köck, E.-M.; Huber, R. G.; Liedl, K. R.; Call, L.; Schlögl, R.; Grothe, H.; Loerting, T. Carbonic Acid Monoethyl Ester as a Pure Solid and Its Conformational Isomerism in the Gas-Phase. RSC Adv. 2017, 7 (36), 22222– 22233,  DOI: 10.1039/C7RA02792C
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      Carbonic acid monoethyl ester as a pure solid and its conformational isomerism in the gas-phase
      Bernard, Juergen; Koeck, Eva-Maria; Huber, Roland G.; Liedl, Klaus R.; Call, Ludwig; Schloegl, Robert; Grothe, Hinrich; Loerting, Thomas
      RSC Advances (2017), 7 (36), 22222-22233CODEN: RSCACL; ISSN:2046-2069. (Royal Society of Chemistry)
      The monoesters of carbonic acid are deemed to be unstable and decomp. to alc. and carbon dioxide. In spite of this, we here report the isolation of the elusive carbonic acid monoethyl ester (CAEE) as a pure solid from ethanolic solns. of potassium bicarbonate. The hemiester is surprisingly stable in acidic soln. and does not experience hydrolysis to carbonic acid. Furthermore, it is also stable in the gas phase, which we demonstrate by subliming the hemiester without decompn. This could not be achieved in the past for any hemiester of carbonic acid. In the gas phase the hemiester experiences conformational isomerism at 210 K. Interestingly, the thermodynamically favored conformation is only reached for the torsional movement of the terminal Et group, but not the terminal hydrogen atom on the millisecond time scale. Accordingly, IR spectra of the gas phase trapped in an argon matrix are best explained on the basis of a 5 : 1 mixt. of monomeric conformers. Our findings necessitate reevaluation of claims of the formation of a carbonic acid polymorph in methanolic soln., which is the subject of a forthcoming publication.
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    • Additional text explaining the results of the calculations and experiments in more detail, calculated frequencies of the monomer and dimer, experimentally observed bands in solid air, thermochemistry of the dimer dissociation, pressure dependence of the dissociation and dimer fraction, MI-IR spectra and calculated spectra without scaling, band integration of all MI-IR spectra of the dilution series in neon matrix (25 and 65 °C, gas phase), results of the band integration (absolute and relative area under the peak), heating experiment, complete MI-IR spectrum of isolated air, band integration of the MI-IR spectrum of isolated air, and additional references (PDF)


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