Simulated Electronic Absorption Spectra of Sulfur-Containing

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Simulated Electronic Absorption Spectra of SulfurContaining Molecules Present in Earth's Atmosphere Sara Farahani, Benjamin Normann Frandsen, Henrik Grum Kjaergaard, and Joseph R. Lane J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.9b04668 • Publication Date (Web): 08 Jul 2019 Downloaded from pubs.acs.org on July 20, 2019

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The Journal of Physical Chemistry

Simulated Electronic Absorption Spectra of Sulfur-Containing Molecules Present in Earth's Atmosphere

Sara Farahani,

†

Benjamin N. Frandsen,

‡

Lane

‡

Henrik G. Kjaergaard,

and Joseph R.

∗,†

†School of Science, University of Waikato, Private Bag 3105, Hamilton 3240, New Zealand. ‡Department of Chemistry, University of Copenhagen, DK-2100 Copenhagen Ø, Denmark E-mail: [email protected]

Phone: +64-7-837-9391

1

ACS Paragon Plus Environment

The Journal of Physical Chemistry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Abstract We have calculated, ab initio, the electronic absorption spectrum of sulfuric acid (H2 SO4 ) under atmospherically relevant conditions using a nuclear ensemble approach. The experimental electronic spectrum of H2 SO4 is unknown so we benchmark our theoretical results by also considering other related sulfur-containing molecules, namely, sulfur dioxide (SO2 ), sulfur trioxide (SO3 ), hydrogen sulde (H2 S), carbonyl sulde (OCS) and carbon disulde (CS2 ), where experimental spectra are available. In general, we nd very good agreement between our calculated spectra, which are based on underlying EOM-CCSD electronic structure calculations, and the available experimental spectra. We show that the computational cost of these calculated spectra can be substantively reduced with negligible loss of accuracy by using a combination of results obtained with the aug-cc-pV(D+d)Z+3 and aug-cc-pV(T+d)Z+3 basis sets. Our calculated cross-section for H2 SO4 in the UV/VUV region is larger than previous theoretical estimates and greater than the experimentally measured upper limits. We suggest that further experimental attempts to measure the electronic absorption spectrum of H2 SO4 in the actinic region (4.0-7.5 eV, 313-167 nm) region are warranted.

1

Introduction

Sulfur compounds with their role in forming aerosol and cloud condensation nuclei (CCN), have been the subject of many atmospheric studies. 17 In Earth's atmosphere, these aerosol particles provide sites for heterogeneous chemical reactions, some of which lead to depletion of ozone (O3 ) in the polar regions, 2,4 and aect the Earth's climate by scattering sunlight. 2 Sulfur compounds are also the main candidates for proposed geoengineering solutions to oset climate change in Earth's atmosphere. 810 There is increasing interest in the role of sulfur compounds in other planets' atmospheres such as Venus and many aspects of the Venusian atmosphere have been studied. 1117 Recent developments in Venusian sulfur chemistry show the importance of accurately calculating cross-sections to amend modeling. 1823 2


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Sulfuric acid (H2 SO4 ) is the dominant sulfur compound in Earth's atmosphere after sulfur dioxide (SO2 ) and sulfur trioxide (SO3 ). 2,24 The form H2 SO4 is found in, depends on the altitude. In lower altitudes, between 15 and 35 km and where water exists, H2 SO4 is predominantly in aerosols, while in higher altitudes (above 35 km) it is mostly found in the gas phase. 24 Despite its atmospheric importance, the electronic absorption spectrum of H2 SO4 has not yet been experimentally measured. The low vapor pressure of H2 SO4 and spectral interference by SO3 and H2 O have been reported as technical challenges in recording the experimental absorption spectra of this molecule. 25 The previous experimental attempts have led to upper limits for the cross-section of H2 SO4 in three spectral regions: 10−21 cm2 molecule−1 (330195 nm), 10−19 cm2 molecule−1 (195-170 nm) and 10−18 cm2 molecule−1 (170-140 nm). 24,25 These upper limits for the electronic absorption spectrum of H2 SO4 have been corroborated by calculated vertical excitation energies and oscillator strengths obtained with the CIS, TDDFT, CASSCF and MRCISD methods. 25,26 More recently, the electronic transitions of H2 SO4 have been systematically investigated with a range of coupled cluster response methods (CCS, CC2, CCSD, CC3) and correlation consistent basis sets (up to quadruple-ζ ). 27,28 To facilitate direct comparison of these theoretical results with the experimental limits, the electronic absorption cross-section was modeled by empirically convoluting the calculated electronic transitions using a Gaussian function. This approach, while simplistic, gave absorption cross-sections that were generally consistent with the reported experimental upper limits, although in some spectral regions the calculated cross-sections were higher. 25 The results were also used to corroborate a previously proposed OH-stretching vibrational overtone photodissociation mechanism and to estimate the contribution of Lyman-α photons for photodissociation. 2,24,25,27,28 In the present work, we make two signicant improvements to the earlier modelled electronic spectrum of H2 SO4 . Firstly, we directly simulate the absorption cross-section without relying on a simple empirical convolution for the electronic band prole. Secondly, we con3



sider both the lowest energy C2 conformer of H2 SO4 as well as the Cs conformer, which has previously been calculated to be ∼3-5 kJ mol−1 higher in energy, 29 and would have a non-negligible abundance (vide infra ) under atmospherically relevant conditions. We use the Newton-X package (NX) 30 to simulate absorption spectra within the nuclear ensemble approximation using a Wigner sampling procedure. The underlying electronic excited energies and oscillator strengths are calculated using dierent electronic structure packages interfaced with NX. We investigate the optimal level of theory for the electronic structure calculations, as well as the dierent simulation parameters, using a series of sulfurcontaining molecules where experimental spectra are available. The theoretical approach that gave the best t for the ve molecules for which there are experimental data is then used to simulate the absorption cross-sections of H2 SO4 . Finally, we reconsider the atmospheric signicance of the various proposed photodissociation mechanisms for H2 SO4 as a function of altitude. 2,27

2

Computational details

Geometry optimization and vibrational frequency calculations of SO2 , SO3 , H2 S, OCS, CS2 and the C2 and Cs conformers of H2 SO4 were done at the coupled-cluster singles and doubles with additional perturbative triples [CCSD(T)] level of theory with the aug-cc-pV(T+d)Z basis set in CFOUR. 31 To simulate the electronic absorption spectra, the Newton-X package was used, 30 which is based on the nuclear ensemble approach and interfaces to multiple electronic structure packages. 32 An ensemble of nuclear geometries was constructed by sampling the CCSD(T)/aug-cc-pV(T+d)Z vibrational modes of the electronic ground state and calculating transition energies and oscillator strengths for each geometry in the ensemble. The transitions to the excited states considered for each nuclear structure are then convoluted with a narrow empirical band shape, typically a Lorentzian or Gaussian function, to yield the overall electronic absorption spectrum. 32 Unless otherwise specied, each ensemble includes

4


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2000 geometric structures and is based on a Wigner distribution. We calculate electronic transition energies and oscillator strengths with the equation of motion coupled cluster singles and doubles method (EOM-CCSD) in Gaussian 09, 33 and with the resolution-of-the-identity second-order approximate coupled cluster (RI-CC2) and second-order algebraic diagrammatic construction [ADC(2)] methods in Turbomole. 34 For all three methods, the correlation consistent aug-cc-pV(X+d)Z basis sets are used, 35 with the addition of very diuse 3s3p3d functions on the central atom of each molecule (S:SO2 , S:SO2 , S:H2 S, C:OCS, C:CS2 ), denoted aug-cc-pV(X+d)Z+3. This is similar to approach previously used, but with functions placed on the central atom rather than the center of mass. 27 We restrict our investigations to these coupled cluster methods and correlation consistent basis sets as previous studies of H2 SO4 27,28 have shown that EOM-CCSD results provide reasonably well-converged excitation energies and oscillator strengths.

3 3.1

Results and Discussion Benchmarking molecules

We consider a series of representative sulfur-containing molecules, including sulfur dioxide (SO2 ), sulfur trioxide (SO3 ), hydrogen sulde (H2 S), carbonyl sulde (OCS) and carbon disulde (CS2 ), where experimental spectra are available. 3640 These molecules have highquality experimental spectra and are small enough to thoroughly investigate the dierent theoretical methods and parameters that could be used. To avoid selection bias and "tuning" our simulated spectra to articially match the experimental spectra, we rst undertake a comprehensive investigation of the electronic spectrum of SO2 in section 3.1.1 and then apply the recommended combination of theoretical methods and parameters for SO2 to the remaining molecules (SO3 , H2 S, OCS and CS2 ) in section 3.1.2.

5



3.1.1

SO2

The EOM-CCSD/aug-cc-pV(D+d)Z+3 level of theory has been previously shown to give reliable results for calculating electronic transitions in sulfur-containing molecules at moderate computational cost. 27,28 As such, we use this level of theory to undertake our initial investigation into some of the sampling and convolution parameters that aect our NX simulated electronic absorption spectra. For SO2 , we include the rst 16 electronic excited states, which includes a mixture of valence and Rydberg states. 27 In Figure 1, we present the EOM-CCSD/aug-cc-pV(D+d)Z+3 electronic absorption spectrum for SO2 obtained with nuclear ensembles including 100, 1000, 2000 and 5000 geometries. Also included in Figure 1 are the numerical integration errors for each of the simulated spectra. As expected, due to the more comprehensive sampling, the numerical integration error reduces as the number of geometries in the ensemble increases. However, the computational cost also increases linearly as the number geometries in an ensemble increases. Crespo et. al. have previously shown that for furan, benzene and 2-phenylfuran, a total of 350, 500 and 850 geometries, respectively, were sucient to simulate the electronic absorption spectra. 32 For SO2 , it is clear that 100 geometries is far too few, as large gaps in the spectrum between the main absorption features appear, and a very large integration error occurs at higher energies. The spectra obtained with ensembles of 1000-5000 geometries are generally similar and we suggest that 2000 geometries provides an appropriate balance between computational cost and sampling error, with most regions showing small numerical integration error bars. In Figure 2, we present the electronic absorption spectra for SO2 obtained from EOMCCSD/aug-cc-pV(D+d)Z+3 results. We have used either a Gaussian or Lorenztian function with a full width at half maximum (FWHM) (δ ) of 0.1 eV to convolute each of the calculated transitions. We compare our calculated spectra to the experimental spectrum from Manatt and Lane. 41 The two calculated spectra have similar cross-sections near the band maxima, but are appreciably dierent in the trough regions between the band maxima. The spectrum obtained using a Lorentzian band shape has a higher cross-section away from the band 6


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Figure 1: Calculated electronic absorption spectra and numeric integration error bars for SO2 for ensembles including 100, 1000, 2000 and 5000 geometries. Obtained from EOMCCSD/aug-cc-pV(D+d)Z+3 results, convoluted using a Gaussian band shape with a broadening width of 0.1 eV. 7



maxima than the spectrum obtained using a Gaussian band shape, owing to the slower decay of a Lorentzian function as compared to a Gaussian function. Consequently, the Lorenztian-based spectrum tends to overestimate the cross-section in the trough regions as compared to experiment, whereas the Gaussian-based spectrum tends to underestimate the cross-section. As such, it is not obvious which of the two band shapes yields the better spectrum. For H2 SO4 , we are particularly interested in the low-energy tail region of its spectrum. If we focus on this region for SO2 , we nd that the Gaussian-based spectrum drops away to zero consistent with experiment, whereas the Lorentzian-based spectrum decreases to a non-physical plateau of approximately 10−19 cm2 molecule−1 . As such, we suggest that a Gaussian band shape is likely more appropriate.

Figure 2: Calculated electronic absorption spectra of SO2 obtained with either a Gaussian or Lorentzian band shape and compared to the experimental spectrum from Manatt and Lane. 41 Obtained from EOM-CCSD/aug-cc-pV(D+d)Z+3 results, convoluted using a broadening width of 0.1 eV. In Figure 3, we present the electronic absorption spectra for SO2 obtained from EOMCCSD/aug-cc-pV(D+d)Z+3 results, using a Gaussian function for convolution, with dierent values of δ from 0.01-0.20 eV, and compare these to the experimental spectrum from 8


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Manatt and Lane. 41 We nd that the overall band shape and widths of the spectra are generally similar for the dierent values of δ , which is encouraging and shows that this arbitrary constant does not substantially impact the vibrational band prole. However, as expected, there is more numerical noise for the smaller values of δ than the larger values. Overall, we nd that δ =0.1 eV appears to be in best agreement with experiment, with small numerical noise and no signicant dierence in the width of the band for each electronic transition as compared to δ =0.2 eV.

Figure 3: Calculated electronic absorption spectra of SO2 obtained with dierent broadening widths and compared to the experimental spectrum from Manatt and Lane. 41 Obtained from EOM-CCSD/aug-cc-pV(D+d)Z+3 results, convoluted using a Gaussian function. We now consider how the underlying electronic structure method that is used, aects the calculated spectra. To do this, we use a consistent ensemble of 2000 geometries sampled from CCSD(T)/aug-cc-pV(T+d)Z vibrational frequencies, and convolute the results with a Gaussian band shape with δ =0.1 eV. In Figure 4, we present the electronic absorption spectra of SO2 obtained from EOM-CCSD, RI-CC2 and ADC(2) results with the aug-cc-pV(D+d)Z+3 basis set, and compare these to the experimental spectrum from Manatt and Lane. 41 While we nd that the three methods yield somewhat similar electronic absorption spectra in the 9



lower energy regions, above approximately 8 eV there is a substantive dierence between the EOM-CCSD results and the less computationally demanding RI-CC2 and ADC(2) results. For the lowest energy band that is centered around 4.5 eV, the three methods give crosssections in good agreement with experiment, although the ADC(2) band maximum is a little bit lower in energy. For the second band that is centered around 6 eV, the experimental agreement is similar, with the ADC(2) method again giving a band maximum a little bit lower in energy. For the higher energy bands, only the spectrum based on the EOM-CCSD results continues to exhibit good agreement with experiment. In this region, we nd that the band maxima of the spectra based on the RI-CC2 and ADC(2) results are much too low in energy. Consequently, the RI-CC2 and ADC(2) cross-sections drops markedly above 9.8 eV, which is indicative of the need to include a larger number of states with these methods in this region. Finally, it is worth noting that we expect the present EOM-CCSD results to be reasonably well-converged as compared to higher order coupled cluster methods. The dierences in vertical excitation energies and oscillator strengths for sulfur-containing molecules calculated with the CCSD and CC3 methods were about ∼0.1 eV on energies and ∼ 10% in oscillator strengths. 27 In Figure 5, we present the electronic absorption spectra of SO2 obtained from EOMCCSD results with the aug-cc-pV(D+d)Z+3, aug-cc-pV(T+d)Z+3, aug-cc-pV(Q+d)Z+3 basis sets, and compare these to the experimental spectrum from Manatt and Lane. 41 We nd that the calculated electronic absorption spectra are quite similar for the three basis sets up to approximately 8.5 eV. Above this point, the overall band shapes obtained with the three basis sets are similar, but the positions of the bands converge to increasing energy from the double-ζ to quadruple-ζ results. This variation with basis set suggests that the electronic excited states below 8.5 eV have signicant valence character, whereas those states above 8.5 eV have signicant Rydberg character. 42 Overall, we conclude that the electronic absorption spectrum obtained using the aug-cc-pV(T+d)Z+3 basis set is reasonably well-converged and should be sucient for most purposes. 10


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Figure 4: Calculated electronic absorption spectra of SO2 obtained from ADC(2), RI-CC2 and EOM-CCSD results and compared to the experimental spectrum from Manatt and Lane. 41 Obtained using the aug-cc-pV(D+d)Z+3 basis set, convoluted using a Gaussian function with δ =0.1 eV. Note that the sharp drop in cross-section for the ADC(2) and RICC2 methods above 9.8 eV energies is articial, see text for details. While it is feasible to calculate electronic absorption spectra for a small molecule like SO2 at the EOM-CCSD/aug-cc-pV(T+d)Z+3 level of theory, for larger molecules this becomes computationally prohibitive. For SO2 , calculating the electronic transition energies and oscillator strengths for each geometry in the ensemble take approximately 2 hours with the aug-cc-pV(D+d)Z+3 basis set, 17 hours with the aug-cc-pV(T+d)Z+3 basis set and 72 hours with the aug-cc-pV(Q+d)Z+3 basis set. Given the predictable convergence of results with coupled cluster methods and correlation consistent basis sets, and the fact that the general band shapes of the electronic transitions in Figure 5 are well-produced even with the smallest double-ζ basis set, we now consider whether a combination of the aug-ccpV(D+d)Z+3 and aug-cc-pV(T+d)Z+3 basis sets can produce spectra of greater accuracy at reduced computational cost. We randomly pick 10 of the 2000 geometries in the ensemble and calculate vertical excitation energies and oscillator strengths with the EOM-CCSD method using the aug-cc11



Figure 5: Calculated electronic absorption spectra of SO2 obtained from results with dierent basis sets and compared to the experimental spectrum from Manatt and Lane. 41 Obtained from EOM-CCSD results, convoluted using a Gaussian function with δ =0.1 eV. pV(D+d)Z+3 and aug-cc-pV(T+d)Z+3 basis sets, and compare the results. We calculate the absolute dierence in the vertical excitation energies and the percentage change in the oscillator strengths on a state by state basis for each of the 10 sets of results obtained with the two basis sets. We then average the dierences for each state across the 10 sets of results and apply these averaged dierences to the remaining 1990 EOM-CCSD/aug-cc-pV(D+d)Z+3 results in the ensemble. We then sum the corrected results to produce an approximate EOM-CCSD/aug-cc-pV(T+d)Z+3 spectrum of SO2 , which is presented in Figure 6. In Figure 6, we compare the approximate EOM-CCSD/aug-cc-pV(T+d)Z+3 spectrum to the full uncorrected spectra obtained from either the EOM-CCSD/aug-cc-pV(D+d)Z+3 or EOM-CCSD/aug-cc-pV(T+d)Z+3 results. In general, we nd that the approximate spectrum is in very good agreement with the full uncorrected EOM-CCSD/aug-cc-pV(T+d)Z+3 spectrum, while its cost is not very dierent from that of the uncorrected EOM-CCSD/augcc-pV(D+d)Z+3 spectrum. The exception is the band maximum around 9 eV, where the position is slightly o-set, leading to a dierence in cross-section of up to a factor of three. 12


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In terms of computational saving, the approximate spectrum used 4170 hours of CPU time whereas the full EOM-CCSD/aug-cc-pV(T+d)Z+3 spectrum required 34000 hours of CPU time. Overall, we nd there to be reasonably good agreement between the approximate EOM-CCSD/aug-cc-pV(T+d)Z+3 calculated spectrum and the experimental spectrum, 36 particularly given the cross-section spans ve orders of magnitude for the spectral region that is considered.

Figure 6: Calculated electronic absorption spectra of SO2 obtained with results using the aug-cc-pV(D+d)Z+3 and aug-cc-pV(T+d)Z+3 basis sets and compared to the experimental spectrum from Manatt and Lane. 41 Obtained from EOM-CCSD results, convoluted using a Gaussian function with δ =0.1 eV.

3.1.2

SO3 , H2 S, CS2 , and OCS

To validate and conrm our ndings for SO2 from section 3.1.1, we now calculate spectra for some other sulfur-containing molecules using the combination of theoretical parameters that was considered most appropriate for SO2 i.e. those used to produce the Approx. augcc-pV(T+d)Z+3 spectrum in Figure 6. In Figure 7, we present the calculated spectrum of SO3 and compare this to the exper13



imental spectra from Burkholder et al. (from 4.8-6.4 eV) and Hintze et. al (from 6.4-8.9 eV). 25,39 Our calculated spectrum includes the 18 lowest energy electronic excited states for SO3 . The electronic absorption spectrum of SO3 can be described in terms of a strong absorption band centered around 8.4 eV and a much weaker absorption feature around 6 eV, which is formally symmetry forbidden and only gains intensity by coupling to the umbrella bending vibrational mode of SO3 . 25,39 Overall, our calculated spectrum shows good agreement with the experimental spectra. The most notable dierence occurs in the lowest energy region below 6 eV, where the calculated cross-section of the lowest-energy absorption band decreases somewhat faster than the experimental cross-section. This is due to the spin-forbidden singlet-triplet transition in this region, 25,39 which is not considered in our calculated spectrum as Newton-X is limited to transitions between states of the same multiplicity.

Figure 7: Calculated electronic absorption spectrum of SO3 compared to the experimental spectrum from Burkholder et al. (4.8-6.4 eV) and Hintze et. al (6.4-8.9 eV). 25,39 Obtained from EOM-CCSD results using a combination of the aug-cc-pV(D+d)Z+3 and augcc-pV(T+d)Z+3 basis sets, convoluted using a Gaussian function with δ =0.1 eV. See text for details. In Figure 8, we present the calculated spectrum of H2 S and compare this to the ex14


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perimental spectrum, which is a composite from Grosch et al. (5.0-6.3 eV), Wu and Chen (6.3-7.7 eV), and Feng et al (7.7-9.6 eV). 38,43,44 Our calculated spectrum includes the 18 lowest energy electronic excited states for H2 S. The electronic absorption spectrum of H2 S is dominated by a broad absorption band centered around 6.2 eV and a series of sharper absorption bands that overlap to create a continuum from 7.5-9.5 eV. Our calculated results well-reproduce the position, intensity and band shape of the broad absorption band and provide a good rolling-average description of the higher energy region, but do not capture the sharper peaks and troughs that are evident in the experimental spectrum. The other notable dierence between our calculated spectrum and the experimental spectrum occurs around 7.5 eV, where the experimental cross-section does not decrease as rapidly as the calculated cross-section. Nonetheless, the overall agreement between the calculated and experimental electronic absorption spectrum for H2 S is very good.

Figure 8: Calculated electronic absorption spectrum of H2 S compared to the experimental spectrum from Grosch et al. (5.0-6.3 eV), Wu and Chen (6.3-7.7 eV), and Feng et al (7.7-9.6 eV).. 38,43,44 Obtained from EOM-CCSD results using a combination of the aug-ccpV(D+d)Z+3 and aug-cc-pV(T+d)Z+3 basis sets, convoluted using a Gaussian function with δ =0.1 eV. See text for details. In Figure 9, we present the calculated spectrum of CS2 and compare this to the exper15



imental spectrum, which is a composite from Grosch et al. (3.3-6.0 eV), Sunanda et al. (6.0-6.7 eV) and Rabalais et al. (6.7-8.2 eV). 40,43,45 Our calculated spectrum includes the 18 lowest energy electronic excited states for CS2 . Overall, we nd that our calculated spectrum is in good agreement with the experimental spectrum. The calculated energy and intensity of the rst, weak absorption band is slightly underestimated with respect to experiment whereas the second, much stronger absorption band is slightly overestimated both in terms of the energy of the band maximum and the intensity. The vibrational ne structure of the second band is also not replicated in our calculations, due to the non-quantised approach that is used to construct the underlying nuclear ensemble. This issue is also evident with some of the other absorption features from 6.8-8.2 eV that are otherwise in good agreement with experiment.

Figure 9: Calculated electronic absorption spectrum of CS2 compared to the experimental spectrum, which is a composite from Grosch et al. (3.3-6.0 eV), Sunanda et al. (6.0-6.7 eV) and Rabalais et al. (6.7-8.2 eV). 40,43,45 Obtained from EOM-CCSD results using a combination of the aug-cc-pV(D+d)Z+3 and aug-cc-pV(T+d)Z+3 basis sets, convoluted using a Gaussian function with δ =0.1 eV. See text for details. In Figure 10, we present the calculated spectrum of OCS and compare this to the experimental spectrum, which is a composite from Molina et. al (4.1-4.8 eV) and Limão-Vieira et 16


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al. (4.8-9.3 eV) 46,47 Our calculated spectrum includes the 18 lowest energy electronic excited states for OCS. In general, our calculated spectrum for OCS is in very good agreement with experiment, with two noticeable exceptions. Firstly, there is a sharp trough in our calculated spectrum around 6.2 eV between the rst two broad absorption bands, which is not seen in the experimental spectrum. Secondly, like CS2 , the vibrational ne structure that can be seen in the experimental bands between 6.8 and 9.5 eV is not replicated in our calculated spectrum, again due to the non-quantised approach that is used to construct the underlying nuclear ensemble.

Figure 10: Calculated electronic absorption spectrum of OCS compared to the experimental spectrum from Molina et. al (4.1-4.8 eV) and Limão-Vieira et al. (4.8-9.3 eV). 46,47 Obtained from EOM-CCSD results using a combination of the aug-cc-pV(D+d)Z+3 and aug-cc-pV(T+d)Z+3 basis sets, convoluted using a Gaussian function with δ =0.1 eV. See text for details. In summary, we nd that the combination of theoretical parameters that was considered suitable for calculating the electronic absorption spectrum of SO2 , can also be used to calculate absorption spectra for SO3 , H2 S, CS2 and OCS that are in good agreement with experiment. This gives condence that the approach used to calculate the electronic absorption spectra is versatile and robust, and hence is expected to give reliable results for other 17



related molecules, such as H2 SO4 . Based on a comparison of the calculated and experimental spectra for SO2 , SO3 , H2 S, CS2 and OCS in Figures 6-10, we expect that the same theoretical approach should yield calculated intensities within a factor of 5 of experiment for other molecules, at least for the lower energy transitions. Near the band maxima, where there is good sampling around the vertical excitation energy, the agreement with experiment is expected to be even better. In terms of the position of the band maxima, we estimate an accuracy of approximately

∼0.1 eV, based on a comparison of the calculated and experimental spectra and considering the likely convergence of the underlying CCSD vertical excitation energies in relation to equivalent CC3 results. 27

18


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3.2

H2 SO4

H2 SO4 has two low energy conformers, C2 and Cs , which are separated by a dierence in electronic energy of 3-5 kJ mol−1 with the MP2/cc-pV(T+d)Z and MP2/aug-cc-pV(Q+d)Z methods. 29 While experimental measurements of H2 SO4 are dicult in the gas-phase, there is some corroborative evidence of the higher energy Cs conformer in vibrational spectra. 25,48 Previous theoretical investigations into the electronic spectroscopy of H2 SO4 have only considered the lowest energy C2 conformer. In the present work, we use statistical mechanics with input from the CCSD(T)/aug-cc-pV(T+d)Z electronic energies, rotational constants and vibrational frequencies, to calculate the Gibbs energies of the C2 and Cs conformers of H2 SO4 as a function of altitude in Earth's atmosphere. These results are presented in the Supporting Information, along with the corresponding atmospheric conditions (temperature, pressure and altitude) that were used. The dierence in the Gibbs energies of the two conformers was then used to calculate their relative atmospheric abundance in Earth's atmosphere. We nd that the Cs conformer represents 24-26% of the population of H2 SO4 , depending on altitude, and hence both conformers need to be considered.

3.2.1

Electronic absorption spectrum

In Figure 11, we present the calculated spectra of the C2 and Cs conformers of H2 SO4 obtained using the same combination of theoretical parameters as in section 3.1.2. For each conformer, the 18 lowest energy electronic excited states of H2 SO4 were included. Also shown in Figure 11 is the weighted spectrum of H2 SO4 , which includes contributions from the spectra of the two conformers, proportional to their abundance at 30 km altitude, corresponding to T=226.5 K and P=1197 Pa. Perhaps not surprisingly, the two conformers generally exhibit similar electronic absorption spectra. We nd that the spectrum of the Cs conformer is slightly redshifted compared to the dominant C2 conformer, leading to a higher cross-section at lower energies, particularly those below 8 eV. In the region around 10.2 eV, where absorption of Lyman-α radiation can be important at high altitudes, the Cs conformer 19



has a cross-section that is approximately ∼20% lower than that of the C2 conformer. The spectra of both conformers exhibit some oscillation in the cross-section below approximately 7 eV. This is not vibrational ne structure but is due to the relatively small number of geometries from the nuclear ensembles that make contributions to this region of the spectra. The weighted spectrum improves this situation somewhat, as it is eectively based on an ensemble that includes twice as many geometries (4000), which reduces the uncertainty in the cross-sections. Nonetheless, some caution should be exercised when interpreting the cross-section in this region, even if the same theoretical approach gave reasonably accurate low-energy absorption tails for the other sulfur-containing molecules considered in section 3.1. To assess the accuracy of our calculated cross-sections in this region, we have undertaken a number of sensitivity analyses, the details of which are included in the Supporting Information. In the rst analysis, we used the same ensemble of 4000 total geometries (C2 and Cs ) and either double (0.2 eV) or halve (0.05 eV) the width of the Gaussian function that is used for convolution. As expected, the oscillation in the spectrum becomes larger if the width is halved and becomes smaller if the width is doubled. The integrated cross-section in the region from 3-7 eV varies to a small extent with the dierent convolution widths and is 1.4×10−15 cm molecule−1 (0.05 eV), 1.5×10−15 cm molecule−1 (0.10 eV) and 1.6×10−15 cm molecule−1 (0.20 eV). In the second analysis, we construct a second ensemble of 4000 geometries (C2 and Cs ) that is separately sampled, including only four excited states to reduce the computational cost. As expected, we nd no substantive dierences in the cross-sections near the band maximum at 8.5 eV or down to approximately 7 eV. Below 7 eV, we observe more variation between the cross-sections generated from the two equally valid ensembles, although there is little dierence between the overall integrated cross-sections: 1.5×10−15 cm molecule−1 for the rst ensemble and 1.5×10−15 cm molecule−1 for the second ensemble. Finally, in the third analysis we have taken the original ensemble of 4000 geometries (C2 20


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and Cs ) and progressively included 1000 additional geometries (C2 and Cs ) from the second ensemble, to give spectra sampled with a total of 4000, 5000, 6000, 7000 and 8000 geometries. As expected, we nd that the oscillation in the cross-sections decreases as the number of geometries that are included in the ensemble increases, although even with the ensemble of 8000 geometries, oscillation still remains. The integrated cross-section in the region below 7 eV is found to be 1.5×10−15 cm molecule−1 (4000 geometries), 1.5×10−15 cm molecule−1 (5000 geometries), 1.4×10−15 cm molecule−1 (6000 geometries), 1.5×10−15 cm molecule−1 (7000 geometries) and 1.5×10−15 cm molecule−1 (8000 geometries).

Figure 11: Calculated electronic absorption spectra of the C2 and Cs conformers of H2 SO4 , and a weighted combination of the two, proportional to the conformer abundances at 30 km altitude. Obtained from EOM-CCSD results using a combination of the aug-ccpV(D+d)Z+3 and aug-cc-pV(T+d)Z+3 basis sets, convoluted using a Gaussian function with δ =0.1 eV. See text for details. In Figure 12, we present the weighted electronic absorption spectrum of H2 SO4 and compare this with the previous simulated spectrum from Lane et al. 27 and the experimental upper limits of Burkholder et al. 24 and Hintze et al. 25 Given the uncertainties with the crosssection in the low-energy tail region, the spectrum in Figure 12 is a compilation of results. In the region above 8 eV, the spectrum is the same as Figure 11 (4000 geometries, 18 excited 21



states), whereas in the region below 8 eV it is based on an ensemble of 8000 geometries but only four excited states to reduce the eects of undersampling (Figure S4 of the Supporting Information). Our present calculated spectrum and the previous simulated spectrum in Figure 12 rely on almost identical vertical excitation energies and oscillator strengths (at least for geometries close to the equilibrium structure), there are some appreciable dierences in the resulting cross-sections. It is worth noting that the previous simulated spectrum was based on a simple convolution of the vertical excitation energies and oscillator strengths calculated at the experimental equilibrium geometry, using wide Gaussian functions of 0.9 eV for the lower energy valence states and 0.3 eV for the higher energy Rydberg states. 27 These values were determined by tting to comparable transitions in SO2 .

Figure 12: Present calculated electronic absorption spectrum of H2 SO4 versus the previous simulated spectrum, 27 experimental cross-section upper limits. 24,25 Spectra are a weighted average of the Cs and C2 conformers, obtained from EOM-CCSD results using a combination of the aug-cc-pV(D+d)Z+3 and aug-cc-pV(T+d)Z+3 basis sets, and convoluted using a Gaussian function with δ =0.1 eV. See text for details. We nd that our calculated spectrum of H2 SO4 has broader spectral features than the earlier simulated spectrum, 27 and with exception of the band maximum around 10 eV, the present calculated cross-sections are also consistently higher. The most signicant dierence 22


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between the present calculated spectrum and the previous simulated spectrum occurs in the low energy tail region, below 7.5 eV. Our present work shows that the cross-section decreases approximately linearly on the log/linear plot (i.e. exponentially on a linear/linear plot), whereas the previous simulated cross-section decreases more rapidly with decreasing energy due to the Gaussian function that was used for convolution. Both spectra are mostly consistent with the experimental upper limits of the cross-section for H2 SO4 from Burkholder

et al 24 and Hintze et al., 25 with the calculated cross-sections generally within an order of magnitude of the limits. That said, it is worth noting that Burkholder et al. did measure a sloping noisy background signal, appearing to increase with energy in the 330-195 nm region (3.76-6.52 eV), which could possibly be due to the low energy tail of H2 SO4 . 25 As discussed in Section 3.1.2, we expect that our calculated spectra will generally be within a factor of 5 as compared to the experimental measured cross-section. Given our present calculated cross-section for H2 SO4 in the 330-195 nm region (3.76-6.52 eV) is up to a factor of 20 higher than the experimental upper limit, we suggest that further experimental investigation in this region is warranted.

3.2.2

Atmospheric implications

The photodissociation rate constant (J ) for H2 SO4 can be calculated using the following equation:

J=

Z

I(ν)Φ(ν)σ(ν)dν

(1)

where I(ν) is the frequency dependent solar ux, Φ(ν) is the quantum yield and σ(ν) is the cross-section. In Figure 13, we present our calculated electronic absorption spectrum for H2 SO4 (with a weighted conformer abundance of 25% Cs and 75% C2 at 80 km; T=198.6 K, P=1.01 Pa) along with the experimental OH-stretching vibrational overtone absorption cross-sections of Feierabend et al. 49 and the averaged solar ux at 80 km altitude from Lane et

al. 27 Also included in Figure 13 is an approximated cross-section of H2 SO4 in its low-energy tail region, which was obtained by tting the calculated cross-section to an exponential 23



function in the 5.5-8.0 eV region. This simple approximation should provide a reasonable estimate of the true cross-section of H2 SO4 in the low energy tail region, in spite of the unphysical oscillation in the cross-section due to the inherently low sampling of geometries in the ensemble away from the band maximum.

Figure 13: Calculated electronic absorption spectrum of H2 SO4 , experimental OH-stretching cross-sections, 49 and the solar ux at 80 km. 27 Spectra are a weighted average of the Cs and C2 conformers, obtained from EOM-CCSD results using a combination of the aug-ccpV(D+d)Z+3 and aug-cc-pV(T+d)Z+3 basis sets, and convoluted using a Gaussian function with δ =0.1 eV. See text for details. In general, there is poor overlap between the cross-section of H2 SO4 and the solar ux, which has led to three separate photodissociation mechanisms having been proposed: 2,27 1. UV photodissociation via absorption of UV/VUV light 2. OH-stretching overtone vibrational photodissociation via absorption of visible light 3. Lyman-α photodissociation via absorption of light at 121.6 nm (10.2 eV) In Figure 14, we present the J -values for photodissociation of H2 SO4 for the three dierent mechanisms. These are calculated as previously, 27 but with the present calculated electronic 24


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absorption cross-sections. The visible mechanism is based on the experimental cross-sections of the third and fourth OH-stretching overtone transitions of H2 SO4 , assuming a quantum yield of one. 49 It should be noted that the weighted electronic absorption cross-sections used in the UV and Lyman-alpha J -value calculations vary slightly with altitude, due to the changing populations of the C2 and Cs conformers with altitude (Supporting Information). Also included in Figure 14 is a much simpler calculation of the UV photodissociation J values (UV exp. decay), which was obtained using the approximate cross-section of H2 SO4 from Figure 13 and is based on a simple exponential decrease in the cross-section in the low-energy tail region.

Figure 14: J -values for the photodissociation of H2 SO4 at dierent altitudes. See text for details. We nd that all three photodissociation mechanisms can be considered most important, depending on the altitude. Below 35 km, the visible OH-stretching vibrational overtone mechanism is dominant; between 35-75 km altitude the UV photodissociation mechanism is dominant; and above 75 km altitude the Lyman-α photodissociation mechanism is dominant. These results are in partial agreement with earlier ndings, where the OH-stretching vibrational overtone mechanism was found to be dominant up to 60 km altitude and the 25



Lyman-α mechanism was found to be dominant above this altitude. Given the solar ux and OH-stretching vibrational cross-sections are identical between the two studies, the dierence in J−values is simply attributable to the dierence in the electronic absorption spectra below 7.5 eV (in the UV region) and at 10.2 eV (Lyman-α radiation). As discussed earlier and shown in Figure 12, our calculated cross-section for H2 SO4 below 7.5 eV is appreciably higher than the earlier simulated spectrum, 27 which makes the UV mechanism more important than in the previous work. However, some caution should be exercised when interpreting this result as the calculated J−value is very sensitive in this spectral region, with the solar ux increasing exponentially and the tail of the calculated absorption cross-section decreasing exponentially from 7.5 eV to 4 eV. There is little uncertainty in the solar ux in this region, although the same cannot be said for the calculated absorption cross-section. While the same theoretical approach performed reasonably well for SO2 , SO3 , H2 S, CS2 and OCS in their respective low-energy tail regions, for H2 SO4 we are considering the cross-section even further from the band maximum and consequently we would again stress the need for further experimental investigation of the electronic absorption spectrum of H2 SO4 in the region below 7.5 eV. Finally, our calculated J−values for absorption of Lyman-α radiation are slightly smaller than those calculated for the previous simulated spectrum, principally due to the broader band prole for H2 SO4 , which results in a lower cross-section at 10.2 eV. 27 However, this does not substantively change the relative importance of this photodissociation mechanism compared to the previous work.

4

Conclusions

We have calculated the electronic absorption spectra of six atmospherically important sulfurcontaining molecules, namely SO2 , SO3 , H2 S, CS2 , OCS, and H2 SO4 , using a nuclear ensemble approach. For SO2 , we comprehensively investigated the dierent theoretical parameters

26


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that aect the calculated spectra, and by comparison to the experimental spectrum, determined an appropriate balance of computational cost and accuracy. We then used this same combination of theoretical parameters to calculate electronic absorption spectra for SO3 , H2 S, CS2 and OCS. In general, we found very good agreement between our calculated spectra and the experimental spectra, with exception of the vibrational ne detail. This suggests that the approach used is reasonably versatile and should give reliable low-resolution results for other related sulfur-containing molecules. We then calculated electronic absorption spectra for the C2 and Cs conformers of H2 SO4 , and weighted these proportionally by their atmospheric abundance. We found that our weighted calculated spectrum for H2 SO4 is in broad agreement with the previous simulated spectrum for the lowest energy C2 confomer and with the experimental upper limits for the absorption cross-section, but with some notable dierences. Most signicantly, we predict a higher, albeit uncertain, cross-section in the low-energy tail region from 4.0-7.5 eV, and a slightly lower cross-section at 10.2 eV. This higher cross-section in the low energy region would lead to a dominance of the UV/VUV photodissociation mechanism from 35-75 km altitude. However, the result is strongly dependent on the cross-section of H2 SO4 in this region, and hence we suggest that further experimental investigation is necessary to understand the relative importance of the dierent H2 SO4 photodissociation mechanisms.

Acknowledgement We acknowledge the University of Waikato, the University of Copenhagen, and the New Zealand eScience Infrastructure (NeSI) for computing time. We are also grateful to the Royal Society of New Zealand for a Marsden grant.

27



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Supporting Information Available Results from the sensitivity analysis of the H2 SO4 cross-section, and the relative abundance of the Cs and C2 conformers of H2 SO4 are available in the supporting information.

References (1) Mills, M. J.; Toon, O. B.; Vaida, V.; Hintze, P. E.; Kjaergaard, H. G.; Schoeld, D. P.; Robinson, T. W. Photolysis of sulfuric acid vapor by visible light as a source of the polar stratospheric CN layer. Journal of Geophysical Research: Atmospheres

2005,

110, 21562202. (2) Vaida, V.; Kjaergaard, H. G.; Hintze, P. E.; Donaldson, D. J. Photolysis of sulfuric acid vapor by visible solar radiation. Science

2003,

299, 15661568.

(3) Hofmann, D. J.; Rosen, J. M. Condensation nuclei events at 30 km and possible inuences of solar cosmic rays. Nature

1983,

302, 511.

(4) Hofmann, D. J.; Rosen, J. M.; Harder, J. A.; Rolf, S. R. Ozone and aerosolmeasurements in the springtime Antarctic stratosphere in 1985. Geophysical Research

Letters

1986,

13, 12521255.

(5) Donaldson, D. J.; Kroll, J. A.; Vaida, V. Gas-phase hydrolysis of triplet SO2 : A possible direct route to atmospheric acid formation. Scientic Reports

2016,

6, 30000.

(6) Kroll, J. A.; Frandsen, B. N.; Rapf, R. J.; Kjaergaard, H. G.; Vaida, V. Reactivity of electronically excited SO2 with alkanes. The Journal of Physical Chemistry A

2018,

122, 77827789. (7) Kroll, J. A.; Frandsen, B. N.; Kjaergaard, H. G.; Vaida, V. Atmospheric hydroxyl radical source: Reaction of triplet SO2 and water. The Journal of Physical Chemistry

A 2018, 122, 44654469. 28


Page 29 of 34 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(8) Wigley, T. M. L. A combined mitigation/geoengineering approach to climate stabilization. Science

2006,

314, 452454.

(9) Crutzen, P. J. Albedo enhancement by stratospheric sulfur injections: A contribution to resolve a policy dilemma? Climatic Change

2006,

77, 211.

(10) Robock, A.; Marquardt, A.; Kravitz, B.; Stenchikov, G. Benets, risks, and costs of stratospheric geoengineering. Geophysical Research Letters

2009,

36, L19703.

(11) Krasnopolsky, V. A photochemical model for the Venus atmosphere at 47112 km.

Icarus

2012,

218, 230246.

(12) Zhang, X.; Liang, M. C.; Mills, F. P.; Belyaev, D. A.; Yung, Y. L. Sulfur chemistry in the middle atmosphere of Venus. Icarus

2012,

217, 714739.

(13) Esposito, L. W.; Copley, M.; Eckert, R.; Gates, L.; Stewart, A. I. F.; Worden, H. Sulfur dioxide at the Venus cloud tops, 19781986. Journal of Geophysical Research:

Atmospheres

1988,

93, 52675276.

(14) Encrenaz, T.; Greathouse, T. K.; Richter, M. J.; Lacy, J.; Widemann, T.; Bézard, B.; Fouchet, T.; deWitt, C.; Atreya, S. K. HDO and SO2 thermal mapping on Venus. A&A 2013,

559, A65.

(15) Marcq, E.; Belyaev, D.; Montmessin, F.; Fedorova, A.; Bertaux, J.-L.; Vandaele, A. C.; Neefs, E. An investigation of the SO2 content of the venusian mesosphere using SPICAVUV in nadir mode. Icarus

2011,

211, 5869.

(16) Yung, Y. L.; Demore, W. B. Photochemistry of the stratosphere of Venus: Implications for atmospheric evolution. Icarus

1982,

51, 199247.

(17) Jessup, K. L.; Marcq, E.; Mills, F.; Mahieux, A.; Limaye, S.; Wilson, C.; Allen, M.; Bertaux, J.-L.; Markiewicz, W.; Roman, T. et al. Coordinated Hubble space telescope and Venus express observations of Venus' upper cloud deck. Icarus 29


2015,

258, 309336.


Page 30 of 34

(18) Lo, W.-J.; Wu, Y.-J.; Lee, Y.-P. Ultraviolet absorption spectrum of cyclic S2 O in solid Ar. Journal of Physical Chemistry A

2003,

107, 69446947.

(19) Frandsen, B. N.; Wennberg, P. O.; Kjaergaard, H. G. Identication of OSSO as a near-UV absorber in the Venusian atmosphere. Geophysical Research Letters

2016,

11,

146155. (20) Perez-Hoyos, S.; Sanchez-Lavega, A.; Garcia-Muñoz, A.; Irwin, P. G. J.; Peralta, J.; Holsclaw, G.; McClintock, W. M.; Sanz-Requena, J. F. Venus upper clouds and the UVabsorber from MESSENGER/MASCS observations. Journal of Geophysical Research

Planets

2018,

123, 145162.

(21) Krasnopolsky, V. A. Disulfur dioxide and its near-UV absorption in the photochemical model of Venus atmosphere. Icarus

2018,

299, 294 299.

(22) Wu, Z.; Wan, H.; Xu, J.; Lu, B.; Lu, Y.; Eckhardt, A. K.; Schreiner, P. R.; Xie, C.; Guo, H.; Zeng, X. The near-UV absorber OSSO and its isomers. Chem. Commun. 2018,

54, 45174520.

(23) Marcq, E.; Baggio, L.; Lefèvre, F.; Stolzenbach, A.; Montmessin, F.; Belyaev, D.; Korablev, O.; Bertaux, J.-L. Discovery of cloud top ozone on Venus. Icarus

2019,

319,

491 498. (24) Burkholder, J. B.; Mills, M.; McKeen, S. Upper limit for the UV absorption cross sections of H2 SO4 . Geophysical Research Letters

2000,

27, 24932496.

(25) Hintze, P. E.; Kjaergaard, H. G.; Vaida, V.; Burkholder, J. B. Vibrational and electronic spectroscopy of sulfuric acid vapor. Journal of Physical Chemistry A

2003,

107, 1112

1118. (26) Robinson, T. W.; Schoeld, D. P.; Kjaergaard, H. G. High level ab initio studies of the

30


Page 31 of 34 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


excited states of sulfuric acid and sulfur trioxide. Journal of Chemical Physics

2003,

118, 72267232. (27) Lane, J. R.; Kjaergaard, H. G. Calculated Electronic Transitions in Sulfuric Acid and Implications for Its Photodissociation in the Atmosphere. Journal of Physical Chemistry

A 2008, 112, 49584964. (28) Kjaergaard, H. G.; Lane, J. R.; Garden, A. L.; Schoeld, D. P.; Robinson, T. W.; Mills, M. J. Advances in Quantum Chemistry ; Elsevier, 2008; Vol. 55; Chapter Atmospheric photolysis of sulfuric acid, pp 137158. (29) Demaison, J.; Herman, M.; Liévin, J.; Rudolph, H. D. Equilibrium structure of sulfuric acid. Journal of Physical Chemistry A

2007,

111, 26022609.

(30) Barbatti, M.; Granucci, G.; Ruckenbauer, M.; Plasser, F.; Crespo-Otero, R.; Pittner, J.; Persico, M.; Lischka, H. NEWTON-X: A package for Newtonian dynamics close to the crossing seam. 2016; www.newtonx.org. (31) Stanton, J. F.; Gauss, J.; Harding, M.; Szalay, P.; Auer, A.; Bartlett, R.; Benedikt, U.; Berger, C.; Bernholdt, D.; Bomble, Y. et al. CFOUR. http://www.cfour.de. (32) Crespo, R.; Barbatti, M. Spectrum simulation and decomposition with nuclear ensemble: Formal derivation and application to benzene, furan and 2-phenylfuran. Theoretical

Chemistry Accounts

2012,

131, 1237.

(33) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Petersson, G. A.; Nakatsuji, H. et al. Gaussian 09 Revision D.01. Gaussian Inc. Wallingford CT 2016. (34) TURBOMOLE V6.2 2010,

a development of University of Karlsruhe and

Forschungszentrum Karlsruhe GmbH, 1989-2007, TURBOMOLE GmbH, since 2007; available from http://www.turbomole.com. 31



Page 32 of 34

(35) Dunning Jr, T. H.; Peterson, K. A.; Wilson, A. K. Gaussian basis sets for use in correlated molecular calculations. X. The atoms aluminum through argon revisited.

Journal of Chemical Physics

2001,

114, 92449253.

(36) Feng, R.; Cooper, G.; Burton, G. R.; Brion, C. E.; Avaldi, L. Absolute photoabsorption oscillator strengths by electron energy loss methods: the valence and S 2p and 2s inner shells of sulphur dioxide in the discrete and continuum regions (3.5-260 eV). Chemical

Physics

1999,

240, 371386.

(37) Feng, R.; Cooper, G.; Brion, C. E. Quantitative studies of the photoabsorption of carbonyl sulphide in the valence-shell, S 2p,2s and C 1s inner-shell regions (4-360 eV) by dipole electron impact spectroscopies. Chemical Physics

2000,

252, 359378.

(38) Feng, R.; Cooper, G.; Brion, C. E. Absolute oscillator strengths for hydrogen sulphide: I. Photoabsorption in the valence-shell and the S 2p and 2s inner-shell regions (4-260 eV). Chemical Physics

1999,

244, 127142.

(39) Burkholder, J. B.; Stuart, M. UV absorption cross sections for SO3 . Geophysical Re-

search Letters

1997,

24, 32013204.

(40) Sunanda, K.; Shastri, A.; Das, A. K.; Raja Sekhar, B. N. Electronic states of carbon disulphide in the 5.511.8eV region by VUV photo absorption spectroscopy. Journal of

Quantitative Spectroscopy and Radiative Transfer

2015,

151, 7687.

(41) Manatt, S. L.; Lane, A. L. A compilation of the absorption cross-sections of SO2 from 106 to 403 nm. Journal of Quantitative Spectroscopy and Radiative Transfer

1993,

50,

267 276. (42) Christansen, O.; Gauss, J.; Stanton, J.; Jorgensen, P. The electronic spectrum of pyrrole. J. Chem. Phys.

1999,

111, 525537.

32


Page 33 of 34 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(43) Grosch, H.; Fateev, A.; Clausen, S. UV absorption cross-sections of selected sulfurcontaining compounds at temperatures up to 500◦ C. Journal of Quantitative Spec-

troscopy and Radiative Transfer

2015,

154, 2834.

(44) Wu, C. Y. R.; Chen, F. Z. Temperature-dependent photoabsorption cross sections of H2 S in the 16002600 Å region. Journal of Quantitative Spectroscopy and Radiative

Transfer

1998,

60, 17 23.

(45) Rabalais, J. W.; McDonald, J. R.; Scherr, V. M.; McGlynn, S. P. Electronic spectoscopy of isoelectronic molecules. II. Linear triatomic groupings containing sixteen valence electrons. Chemical Reviews

1971,

71, 73108.

(46) Molina, L. T.; Lamb, J. J.; Molina, M. J. Temperature dependent UV absorption cross sections for carbonyl sulde. Geophysical Research Letters

1981,

8, 10081011.

(47) Limão Vieira, P.; Ferreira da Silva, F.; Almeida, D.; Hoshino, M.; Tanaka, H.; Mogi, D.; Tanioka, T.; Mason, N. J.; Homann, S. V.; Hubin-Franskin, M.-J. et al. Electronic excitation of carbonyl sulphide (COS) by high-resolution vacuum ultraviolet photoabsorption and electron-impact spectroscopy in the energy region from 4 to 11 eV. The

Journal of Chemical Physics

2015,

142, 064303.

(48) Havey, D.; Feierabend, K.; Vaida, V. Ab initio study of H2 SO4 rotamers. J. Molec.

Struct. (THEOCHEM)

2004,

680, 243247.

(49) Feierabend, K. J.; Havey, D. K.; Brown, S. S.; Vaida, V. Experimental absolute intensities of the 4v9 and 5v9 O-H stretching overtones of H2 SO4 . Chemical Physics Letters 2006,

420, 438442.

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Simulated Electronic Absorption Spectra of Sulfur-Containing

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