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On the numerical solution of the multidimensional vibrational time‐independent Schroedinger equation
Author(s) -
AlvarezCollado J.R.,
Buenker Robert J.
Publication year - 1992
Publication title -
journal of computational chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.907
H-Index - 188
eISSN - 1096-987X
pISSN - 0192-8651
DOI - 10.1002/jcc.540130203
Subject(s) - eigenvalues and eigenvectors , finite element method , harmonic oscillator , ab initio , harmonic , schrödinger equation , molecule , mathematical analysis , finite difference , mathematics , physics , computational chemistry , quantum mechanics , chemistry , thermodynamics
A preliminary study of the capability of the finite difference and finite element methods (FDM, FEM) to evaluate eigenvalues of one‐, two‐, and three‐dimensional self‐adjoint operators is reported with reference to applications dealing with the description of vibrational levels. Results of harmonic oscillator model potentials and ab initio PES for the water molecule are obtained by using the FDM. In spite of the large matrices used, low accuracy, nonvariational results are found. A different method, based on FEM and normal coordinates, is therefore proposed. Two nearly harmonic cases are studied and it is shown that variational results with higher accuracy can be obtained with a moderate cost. The vibrational levels of the water molecule are also calculated in order to compare the results with those of the FDM treatment.