On the determination of spectroscopic constants as functions of intramolecular parameters

Abstract

The symmetrised form of the operator Van Vleck perturbation theory is considered (the irreducible tensorial set theory is used as the mathematical basis of this consideration). General formulae which define spectroscopic rotational, centrifugal and resonance constants of molecules as functions of reduced matrix elements of vibrational operators are obtained. Algorithms for the ES-1055 computer have been derived on the basis of the formulae obtained, and a system of analytical calculations using the language 'REDUCE' has been created. The dyad and pentad of the CH,-type molecule are considered for illustration. Formulae are obtained which connect spectroscopic and intramolecular constants not only for isolated but also for interacting vibrational states.

On the “expanded local mode” approach applied to the methane molecule

“…[23,28] are exactly the same with the exception of the fact that the resonance interaction between the states ðv 1 v 2 v 3 v 4 Þ and ðv 1 v 2 AE 1 v 3 v 4 Ç 1Þ are taken into account in Ref. [28]. good quantitative correspondence between values predicted on their basis and high accurate experimental data.…”

“…At the same time, it would not be strange, if the derived simple model with only two free parameters gives not very 1 Formulas in Refs. [23,28] are exactly the same with the exception of the fact that the resonance interaction between the states ðv 1 v 2 v 3 v 4 Þ and ðv 1 v 2 AE 1 v 3 v 4 Ç 1Þ are taken into account in Ref. [28].…”

High resolution analysis of C2D4 in the region of 600–1150 cm−1

“…[63][64][65]), and operator perturbation theory, Refs. [66,67]. Without details, we mention here that it is possible to show that for substitution of all four nuclei H by D in the C 2 H 4 molecule, centrifugal distortion coefficients P and P 0 of the ground vibrational states of the main, C 2 H 4 , and substituted, C 2 D 4 , species can be connected with each other by the following approximate relations:…”

Precise ro-vibrational analysis of molecular bands forbidden in absorption: The ν8+ν10 band of the 12C2H4 molecule

“…At the same time (it can be estimated, for example, on the basis of the operator perturbation theory, see, e.g., Refs. [39,[55][56][57][58]), values of many of the resonance interaction coefficients in Eqs. (4)-(8) are comparable with values of even the largest centrifugal distortion parameters.…”