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

METHOD AND RESULTS OF DETERMINATION IN ANALYTICAL FORM

THE PARAMETERS OF TETRAHEDRAL SPLITTINGS AND BAND CENTERS IN THE XY_{4} SPHERICAL TOP MOLECULES:^{M}GeH_{4} AS AN

APPLICATION

\underline{O. N. ULENIKOV} , \underline{E. S. BEKHTEREVA} , \underline{O. V. GROMOVA} ,

\underline{A. L. FOMCHENKO} , \underline{P. A. GLUSHKOV} , National Research Tomsk Polytechnic

University, 30, av. Lenina, 634050 Tomsk, Russia; \underline{C. SYDOW} and \underline{S. BAUERECKER} , Institut für Physikalische und Theoretische Chemie, Technische

Universität Braunschweig, D - 38106, Braunschweig, Germany

The mathematical basis is discusses the for solving an important and up to the recent time unsolved problem of analytical describing a complicated tetrahedral structure of the spectra of spherical top molecules. The main difficulty of the problem until recently was the impossibility of an analytical presentation of the quantum– mechanical wave functions of such type molecules. Using the theory of irreducible tensor sets, we solved this problem and obtain the necessary results in the most general form for the vibrational problem (possible vibrational resonance interactions are also taken into account). Results are obtained for states of arbitrary symmetry which are united in polyads with a polyad quantum number P ≤ 8. As an illustration, band center values are predicted for all bands of the five isotopologues of ^{M}GeH_{4} (M = 70, 72, 73, 74, 76) up to 10000 cm^{−1}.

This work was supported by The Ministry of Science and Higher Education of the Russian Federation in part of the Science program (Project FSWW–2023–0003)

p-number: p015  Submitted on Sat, 27 May 2023 14:46:11 +0200