^{1,a)}, M. S. Johnson

^{1}, G. C. McBane

^{2}and R. Schinke

^{3,b)}

### Abstract

Global three dimensional potential energy surfaces and transition dipole moment functions are calculated for the lowest singlet and triplet states of carbonyl sulfide at the multireference configuration interaction level of theory. The first ultraviolet absorption band is then studied by means of quantum mechanical wave packet propagation. Excitation of the repulsive 2 ^{1} *A* ^{′} state gives the main contribution to the cross section. Excitation of the repulsive 1 ^{1} *A* ^{″} state is about a factor of 20 weaker at the absorption peak (*E* _{ph} ≈ 45 000 cm^{−1}) but becomes comparable to the 2 ^{1} *A* ^{′} state absorption with decreasing energy (35 000 cm^{−1}) and eventually exceeds it. Direct excitation of the repulsive triplet states is negligible except at photonenergies*E* _{ph} < 38 000 cm^{−1}. The main structure observed in the cross section is caused by excitation of the bound 2 ^{3} *A* ^{″} state, which is nearly degenerate with the 2 ^{1} *A* ^{′} state in the Franck-Condon region. The structure observed in the low energy tail of the spectrum is caused by excitation of quasi-bound bending vibrational states of the 2 ^{1} *A* ^{′} and 1 ^{1} *A* ^{″} electronic states. The absorption cross sections agree well with experimental data and the temperature dependence of the cross section is well reproduced.

We thank the Gesellschaft für wissenschaftliche Datenverarbeitung mbH Göttingen (GWDG) for computational resources. G.C.M. and J.A.S. are grateful to the MPIDS for hospitality and support. The authors thank Kirk Peterson and Gregory Hall for advice.

I. INTRODUCTION

II. POTENTIAL ENERGY SURFACES AND TRANSITION DIPOLE MOMENTS

A. Electronic structure calculations

B. Overview of the electronic states

C. Potential energy surfaces

1. Local ground statepotential energy surface

2. Global potential energy surfaces

D. Transition dipole moment functions

III. DYNAMICS CALCULATIONS

IV. RESULTS AND DISCUSSION

A. Autocorrelation function

B. State-resolved cross sections

C. Total cross section

D. The low-energy tail of the spectrum

V. SUMMARY AND OUTLOOK

### Key Topics

- Excitation energies
- 17.0
- Vibrational states
- 15.0
- Photodissociation
- 14.0
- Absorption spectra
- 12.0
- Ground states
- 12.0

## Figures

Upper panel: Potential energy surfaces for the 1–2 ^{1} *A* ^{′} states (black), the 3–5 ^{1} *A* ^{′} states (blue), and the first two ^{3} *A* ^{′} states (red) along the dissociation coordinate *R* for *r* = 2.2 *a* _{0} and γ = 5°. Lower panel: The same as in the upper panel but for states of *A* ^{″} symmetry.

Upper panel: Potential energy surfaces for the 1–2 ^{1} *A* ^{′} states (black), the 3–5 ^{1} *A* ^{′} states (blue), and the first two ^{3} *A* ^{′} states (red) along the dissociation coordinate *R* for *r* = 2.2 *a* _{0} and γ = 5°. Lower panel: The same as in the upper panel but for states of *A* ^{″} symmetry.

Same as in Fig. 1 but along the bending coordinate γ for *R* = 4.2 *a* _{0} and *r* = 2.2 *a* _{0}.

Same as in Fig. 1 but along the bending coordinate γ for *R* = 4.2 *a* _{0} and *r* = 2.2 *a* _{0}.

Two-dimensional contour representations of the local PES of the X state (1 ^{1} *A* ^{′}) with γ = 0° (a) and *r* = 2.2 *a* _{0} (b). The spacing between the contours is 0.25 eV and the red contours represent 0.25 eV which is approximately the vibrational zero point energy.

Two-dimensional contour representations of the local PES of the X state (1 ^{1} *A* ^{′}) with γ = 0° (a) and *r* = 2.2 *a* _{0} (b). The spacing between the contours is 0.25 eV and the red contours represent 0.25 eV which is approximately the vibrational zero point energy.

Two-dimensional contour representations of the potential energy surface of the A state (2 ^{1} *A* ^{′}) with γ = 25° (a) and *r* = 2.2 *a* _{0} (b). The spacing between the contours is 0.5 eV and the red contours represent 6.0 eV which is approximately the total energy, *E* _{ph} + *E* _{0}, following excitation at λ = 223 nm. The blue dots mark the A state FC point: *R* = 4.23 *a* _{0}, *r* = 2.18 *a* _{0}, and γ = 8.4°. The FC point for the A state is defined as the expectation value of *R*, *r*, and γ for the ground state vibrational wave function times the A state TDM, i.e., Ψ_{(0, 0, 0)} μ_{A}.

Two-dimensional contour representations of the potential energy surface of the A state (2 ^{1} *A* ^{′}) with γ = 25° (a) and *r* = 2.2 *a* _{0} (b). The spacing between the contours is 0.5 eV and the red contours represent 6.0 eV which is approximately the total energy, *E* _{ph} + *E* _{0}, following excitation at λ = 223 nm. The blue dots mark the A state FC point: *R* = 4.23 *a* _{0}, *r* = 2.18 *a* _{0}, and γ = 8.4°. The FC point for the A state is defined as the expectation value of *R*, *r*, and γ for the ground state vibrational wave function times the A state TDM, i.e., Ψ_{(0, 0, 0)} μ_{A}.

Two-dimensional contour representations of the potential energy surface of the B state (1 ^{1} *A* ^{″}) with γ = 25° (a) and *r* = 2.2 *a* _{0} (b). Details are the same as in Fig. 4. The blue dots mark the B state FC point: *R* = 4.23 *a* _{0}, *r* = 2.16 *a* _{0}, and γ = 7.0°.

Two-dimensional contour representations of the potential energy surface of the B state (1 ^{1} *A* ^{″}) with γ = 25° (a) and *r* = 2.2 *a* _{0} (b). Details are the same as in Fig. 4. The blue dots mark the B state FC point: *R* = 4.23 *a* _{0}, *r* = 2.16 *a* _{0}, and γ = 7.0°.

Two-dimensional contour representations of the potential energy surface of the C state (2 ^{1} *A* ^{″}) with γ = 25° (a) and *r* = 2.2 *a* _{0} (b). Details are the same as in Fig. 4. The blue dots mark the C state FC point: *R* = 4.24 *a* _{0}, *r* = 2.19 *a* _{0}, and γ = 6.3°.

Two-dimensional contour representations of the potential energy surface of the C state (2 ^{1} *A* ^{″}) with γ = 25° (a) and *r* = 2.2 *a* _{0} (b). Details are the same as in Fig. 4. The blue dots mark the C state FC point: *R* = 4.24 *a* _{0}, *r* = 2.19 *a* _{0}, and γ = 6.3°.

Two-dimensional contour representation of the potential energy surface of the c state (2 ^{3} *A* ^{″}) with γ = 25° (a) and *r* = 2.2 *a* _{0} (b). Details are the same as in Fig. 4. The blue dots mark the c state FC point: *R* = 4.22 *a* _{0}, *r* = 2.20 *a* _{0} and γ = 6.0°.

Two-dimensional contour representation of the potential energy surface of the c state (2 ^{3} *A* ^{″}) with γ = 25° (a) and *r* = 2.2 *a* _{0} (b). Details are the same as in Fig. 4. The blue dots mark the c state FC point: *R* = 4.22 *a* _{0}, *r* = 2.20 *a* _{0} and γ = 6.0°.

Cuts along γ of the TDMs between the electronic ground state and the different excited states. Panel (a): *A* ^{′} symmetry; panel (b): *A* ^{″} symmetry. The singlet and triplet states are shown in black and red, respectively. The cut is at *R* = 4.3 *a* _{0} and *r* = 2.2 *a* _{0}. The magnitudes of the transition dipole vectors are shown.

Cuts along γ of the TDMs between the electronic ground state and the different excited states. Panel (a): *A* ^{′} symmetry; panel (b): *A* ^{″} symmetry. The singlet and triplet states are shown in black and red, respectively. The cut is at *R* = 4.3 *a* _{0} and *r* = 2.2 *a* _{0}. The magnitudes of the transition dipole vectors are shown.

Two-dimensional contour representations of |μ_{A}| for *r* = 2.2 *a* _{0} The spacing between the contours is 0.05 au and the red contour represents 0.5 au. The blue dots marks the A state FC point (*R* = 4.23 *a* _{0} and γ = 8.4°).

Two-dimensional contour representations of |μ_{A}| for *r* = 2.2 *a* _{0} The spacing between the contours is 0.05 au and the red contour represents 0.5 au. The blue dots marks the A state FC point (*R* = 4.23 *a* _{0} and γ = 8.4°).

Modulus of the autocorrelation functions (multiplied by 100) for photodissociation via the A state of OCS (black line) and N_{2}O (red line). The initial vibrational state is (0, 0, 0).

Modulus of the autocorrelation functions (multiplied by 100) for photodissociation via the A state of OCS (black line) and N_{2}O (red line). The initial vibrational state is (0, 0, 0).

(a) Cross sections for excitation of the different singlet states A, B, and C; the initial vibrational state is (0, 0, 0). (b) The same as in (a) but for the triplet states a, b, c, and d.

(a) Cross sections for excitation of the different singlet states A, B, and C; the initial vibrational state is (0, 0, 0). (b) The same as in (a) but for the triplet states a, b, c, and d.

(a) The A state cross section for various initial vibrational states. (b) A state cross sections for various initial states multiplied by the Boltzmann weighting factor *w* _{ i } = *Q* ^{−1}(1 + *v* _{2})exp ( − *E* _{ i }/(*k* _{ B } *T*)) with *T* = 300 K and *Q* being the partition function.

(a) The A state cross section for various initial vibrational states. (b) A state cross sections for various initial states multiplied by the Boltzmann weighting factor *w* _{ i } = *Q* ^{−1}(1 + *v* _{2})exp ( − *E* _{ i }/(*k* _{ B } *T*)) with *T* = 300 K and *Q* being the partition function.

The total cross section (scaled by a factor of 1.3) compared with the experimental cross section of Wu *et al.* ^{17} (shifted upward by 0.25 for clarity of the presentation). The temperature in the calculation and the measurement is 170 K.

The total cross section (scaled by a factor of 1.3) compared with the experimental cross section of Wu *et al.* ^{17} (shifted upward by 0.25 for clarity of the presentation). The temperature in the calculation and the measurement is 170 K.

Temperature dependence of the total absorption cross section for four excitation energies. Calculations: solid lines (scaled by 1.3); measured cross sections:^{17} open squares.

Temperature dependence of the total absorption cross section for four excitation energies. Calculations: solid lines (scaled by 1.3); measured cross sections:^{17} open squares.

(a) Comparison of the calculated total cross section (multiplied by 1.3) and the measured cross section of Molina *et al.* ^{12} in the low-energy tail for two temperatures. (b) The contributions of the individual excited states as indicated for 295 K. (c) A state cross sections for initial vibrational states (0, *v* _{2}, 0). No extra scaling was applied in (b) and (c); none of the cross sections in (a), (b), and (c) was shifted on the energy scale.

(a) Comparison of the calculated total cross section (multiplied by 1.3) and the measured cross section of Molina *et al.* ^{12} in the low-energy tail for two temperatures. (b) The contributions of the individual excited states as indicated for 295 K. (c) A state cross sections for initial vibrational states (0, *v* _{2}, 0). No extra scaling was applied in (b) and (c); none of the cross sections in (a), (b), and (c) was shifted on the energy scale.

## Tables

Characteristics of the PESs of the excited singlet states A, B, and C and the triplet state c. The values *V* _{FC} and |μ_{FC}| were calculated at an approximate FC point (*R* = 4.2 *a* _{0}, *r* = 2.2 *a* _{0}, and γ = 5°). Numbers in parentheses indicate powers of 10.

Characteristics of the PESs of the excited singlet states A, B, and C and the triplet state c. The values *V* _{FC} and |μ_{FC}| were calculated at an approximate FC point (*R* = 4.2 *a* _{0}, *r* = 2.2 *a* _{0}, and γ = 5°). Numbers in parentheses indicate powers of 10.

Characteristics of the local ground state PES. Bond lengths are given in *a* _{0}, dissociation energy *D* _{0} in eV, and vibrational energies in cm^{−1}.

Characteristics of the local ground state PES. Bond lengths are given in *a* _{0}, dissociation energy *D* _{0} in eV, and vibrational energies in cm^{−1}.

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