HRMS, 28th Colloquium, Dijon, France, Aug. 28 - Sept. 1, 2023

QUADRATIC VIBRATION-ROTATION CONSTANTS γ_{r,s}^{β} AND SEMI-EXPERIMENTAL^{32}S^{16}O_{2} EQUILIBRIUM GEOMETRY

\underline{S. V. KRASNOSHCHEKOV} , E. O. DOBROLYUBOV,

I. V. POLYAKOV, Dept. of Chemistry, Lomonosov Moscow State University, Leninskiye Gory 1-3, 119991 Moscow, Russia; A. V. BELYAKOV, St. Petersburg

State Technological Institute, 190013, Russia

Probably the most precise geometrical nuclear configuration of a semi-rigid molecule can be obtained through the wide-spread technique combining experimental values of rotational constants B_{v}^{β}(β = x, y, z) (obtainable from high-resolution MW spectra) and non-empirical values of linear and quadratic vibration-rotation constants α_{r}^{β} and γ_{r,s}^{β} plus a small electronic correction obtained through the rotational g-tensor (ΔB_{g}^{β} = (m_{e}/m_{p})g^{αα}B_{e}^{α}):^{1}

B_{v}^{β} = B_{e}^{β} − ∑_{r} α_{r}^{β} (v_{r} + \frac{1}{2}) + ∑_{r≥s} γ_{r,s}^{β} (v_{r} + \frac{1}{2}) (v_{s} + \frac{1}{2}) + … (1)

While linear constants α_{r}^{β} can be trivially calculated using the second-order perturbation theory (VPT2), the evaluation of the quadratic constants γ_{rs}^{β} requires a number of complex rotational commutators and this problem was never solved systematically. Only a few experimental studies for the^{32}S^{16}O_{2} molecule included evaluation of γ_{rs}^{β}. ^{2} ^{3} The theoretical research include an early work by Brown^{4} and a recent review by Demaison et al.^{5}

We propose the systematic procedure for evaluation of γ_{r,s}^{β} using the fourth-order canonical Van Vleck perturbation theory (CVPT4). This approach is largely based on evaluation of vibrational and rotational commutators using the normal ordering of ladder operators of angular momentum.^{6} The values of γ_{r,s}^{β} can be obtained by comparing the operator form of the vibrationally transformed Hamiltonian Ĥ^{(4)} with the corresponding theoretical terms,

H_{vib−rot} = ∑_{β}^{xyz} J_{β}^{2}(B_{e}^{β} − ∑_{r} α_{r}^{β}a_{r}^{†}a_{r} + ∑_{r≥s} γ_{rs}^{β}a_{r}^{†}a_{r}a_{s}^{†}a_{s} + …).  (2)

1doi:10.1021/acs.jctc.7b00279, M. Mendolicchio, E. Penocchio, D. Licari, N. Tasinato, V. Barone, J. Chem. Theory Comput., 13, 3060–3075 (2017).

2doi:10.1006/jmsp.1993.1245, J.-M. Flaud, W. J. Lafferty, J. Mol. Spectrosc., 161, 396–402 (1993).

3doi:10.1006/jmsp.1993.1245, Y. Morino, M. Tanimoto, J. Mol. Spectrosc., 166, 310–320 (1994).

4doi:10.1016/0022-2852(71)90050-6, J. M. Brown, J. Mol. Spectrosc., 37, 179–195 (1971).

5doi:10.1080/00268976.2021.1950857, J. Demaison, J. Liévin, Mol. Phys., 120, e1950857(13pp)

(2022).

6doi:10.1063/5.0142809, X. Chang, D. V. Millionshchikov, I. M. Efremov, S. V. Krasnoshchekov, J.

Chem. Phys., 158, 104802(1–12) (2023).

p-number: p082  Submitted on Wed, 12 Jul 2023 10:25:39 +0200