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Unified approach to molecular structure and molecular vibrations
Author(s) -
Cohen Joel M.,
Goodson David Z.
Publication year - 1996
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/(sici)1097-461x(1996)59:6<445::aid-qua2>3.0.co;2-y
Subject(s) - hamiltonian (control theory) , quadratic equation , continuation , physics , potential energy , bent molecular geometry , schrödinger equation , quantum mechanics , møller–plesset perturbation theory , ground state , vibration , perturbation (astronomy) , perturbation theory (quantum mechanics) , harmonic oscillator , dissociation (chemistry) , born–oppenheimer approximation , classical mechanics , mathematical physics , molecule , chemistry , mathematics , geometry , mathematical optimization , organic chemistry , computer science , programming language
First‐order dimensional perturbation theory is used to construct a Hamiltonian for the H + 2 molecule without the Born‐Oppenheimer approximation. The physical model that emerges has the three particles undergoing harmonic oscillations about a bent symmetric configuration. Despite its simplicity, the theory yields correct results for the ground‐state energy, for the equilibrium internuclear distance, and for vibrational frequencies. Although the standard dimensional continuation of the Schrödinger equation leads to dissociation at large D , this model remains stable due to a quadratic polynomial in 1/ D that is included in the potential energy. This Hamiltonian is a suitable starting point for a large‐order perturbation expansion in 1/ D . © 1996 John Wiley & Sons, Inc.