ИСТИНА

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 Bβ v (β = x, y, z) (obtainable from high-resolution MW spectra) and non-empirical values of linear and quadratic vibration-rotation constants αβ r and γβ r,s plus a small electronic correction ob- tained through the rotational g-tensor (∆Bβ g = (me/mp)gααBα e ):1 Bβ v = Bβ e − ∑ r αβ r ( vr + 1 2 ) + ∑ r≥s γβ r,s ( vr + 1 2 ) ( vs + 1 2 ) + . . . (1) While linear constants αβ r can be trivially calculated using the second- order perturbation theory (VPT2), the evaluation of the quadratic constants γβ rs requires a number of complex rotational commutators and this problem was never solved systematically. Only a few experimental studies for the 32S16O2 molecule included evaluation of γβ rs. 2 3 The theoretical research include an early work by Brown4 and a recent review by Demaison et al.5 We propose the systematic procedure for evaluation of γβ r,s 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 γβ r,s can be obtained by comparing the operator form of the vibrationally transformed Hamiltonian ˆH(4) with the corresponding theoretical terms, Hvr = xyz∑ β J2 β ( Bβ e + Bβ α,γ,τ − ∑ r αβ r a† rar + ∑ r≥s γβ rsa† rara† sas + . . . ) . (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. Li ́evin, Mol. Phys., 120, e1950857(13pp) (2022). 6doi:10.1063/5.0142809, X. Chang, D. V. Millionshchikov, I. M. Efremov, S. V. Kras- noshchekov, J. Chem. Phys., 158, 104802(1–12) (2023).