Revisiting the generator coordinate approximation for calculating the ro‐vibrational energies of H\documentclass{article}\pagestyle{empty}Unknown environment 'document'

The Generator Coordinate Approximation, a relatively recent approximation formulated to solve systems of three or more bodies, is tested for its accuracy and viability by applying it to calculate the ro‐vibrational energies of the triatomic system H\documentclass{article}\pagestyle{empty}Unknown environment 'document'. We employ in this work a recently formulated basis called the Numerically Generated‐Discrete Variable Representation for the wave function and test it against the well‐known Finite Element Method basis. Comparison of the two results and with other results shows a tentative superiority of the Numerically Generated‐Discrete Variable Representation. In addition, many new physical properties of the Generator Coordinate Approximation were discovered. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 2028–2039, 2001

[1]  Peter Botschwina,et al.  Ab initio calculation of near‐equilibrium potential and multipole moment surfaces and vibrational frequencies of H+3 and its isotopomers , 1986 .

[2]  J. Tennyson,et al.  Overtone bands of H3+: First principle calculations , 1988 .

[3]  D. Colbert,et al.  A novel discrete variable representation for quantum mechanical reactive scattering via the S-matrix Kohn method , 1992 .

[4]  J. Griffin,et al.  Collective Motions in Nuclei by the Method of Generator Coordinates , 1957 .

[5]  John Archibald Wheeler,et al.  NUCLEAR CONSTITUTION AND THE INTERPRETATION OF FISSION PHENOMENA , 1953 .

[6]  I. Cacelli,et al.  Independent Electron Models: Hartree-Fock for Many-Electron Atoms , 1989 .

[7]  Joaquim José Soares Neto,et al.  Parallel algorithm for calculating ro‐vibrational states of diatomic molecules , 1994, J. Comput. Chem..

[8]  J. Muckerman Some useful discrete variable representations for problems in time-dependent and time-independent quantum mechanics , 1990 .

[9]  C. Mead The molecular Aharonov—Bohm effect in bound states , 1980 .

[10]  Philippe G. Ciarlet,et al.  The finite element method for elliptic problems , 2002, Classics in applied mathematics.

[11]  Søren B. Padkjær,et al.  Non-zero total angular momentum calculations of rovibrational levels for triatomic molecules using generator coordinates , 1992 .

[12]  F. V. Prudente,et al.  A novel finite element method implementation for calculating bound states of triatomic systems: Application to the water molecule , 1994 .

[13]  K. Morton Basic course in finite element methods , 1987 .

[14]  J. Linderberg,et al.  Kinetic energy functional in hyperspherical coordinates , 1985 .

[15]  C. Mead Superposition of reactive and nonreactive scattering amplitudes in the presence of a conical intersection , 1980 .

[16]  James N. Lyness,et al.  Moderate degree symmetric quadrature rules for the triangle j inst maths , 1975 .

[17]  S. Carter,et al.  A variational method for the calculation of vibrational energy levels of triatomic molecules using a Hamiltonian in hyperspherical coordinates , 1990 .

[18]  Vijay Sonnad,et al.  Solution of atomic Hartree–Fock equations with the P version of the finite element method , 1989 .