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Title: An efficient method for energy levels calculation using full symmetry and exact kinetic energy operator: Tetrahedral molecules

A simultaneous use of the full molecular symmetry and of an exact kinetic energy operator (KEO) is of key importance for accurate predictions of vibrational levels at a high energy range from a potential energy surface (PES). An efficient method that permits a fast convergence of variational calculations would allow iterative optimization of the PES parameters using experimental data. In this work, we propose such a method applied to tetrahedral AB{sub 4} molecules for which a use of high symmetry is crucial for vibrational calculations. A symmetry-adapted contracted angular basis set for six redundant angles is introduced. Simple formulas using this basis set for explicit calculation of the angular matrix elements of KEO and PES are reported. The symmetric form (six redundant angles) of vibrational KEO without the sin(q){sup −2} type singularity is derived. The efficient recursive algorithm based on the tensorial formalism is used for the calculation of vibrational matrix elements. A good basis set convergence for the calculations of vibrational levels of the CH{sub 4} molecule is demonstrated.
Authors:
 [1] ;  [2] ; ;  [3]
  1. Laboratory of Theoretical Spectroscopy, V.E. Zuev Institute of Atmospheric Optics, SB RAS, 1, Academician Zuev square, 634021 Tomsk (Russian Federation)
  2. (Russian Federation)
  3. Groupe de Spectrométrie Moléculaire et Atmosphérique, UMR CNRS 7331, Université de Reims, U.F.R. Sciences, B.P. 1039, 51687 Cedex 2 Reims (France)
Publication Date:
OSTI Identifier:
22416213
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Chemical Physics; Journal Volume: 142; Journal Issue: 9; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ALGORITHMS; CONVERGENCE; ENERGY LEVELS; ITERATIVE METHODS; KINETIC ENERGY; MATRIX ELEMENTS; METHANE; MOLECULES; POTENTIAL ENERGY; SINGULARITY; SURFACES; SYMMETRY; VARIATIONAL METHODS