The exact molecular wavefunction as a product of an electronic and a nuclear wavefunction
Abstract
The Born-Oppenheimer approximation is a basic approximation in molecular science. In this approximation, the total molecular wavefunction is written as a product of an electronic and a nuclear wavefunction. Hunter [Int. J. Quantum Chem. 9, 237 (1975)] has argued that the exact total wavefunction can also be factorized as such a product. In the present work, a variational principle is introduced which shows explicitly that the total wavefunction can be exactly written as such a product. To this end, a different electronic Hamiltonian has to be defined. The Schroedinger equation for the electronic wavefunction follows from the variational ansatz and is presented. As in the Born-Oppenheimer approximation, the nuclear motion is shown to proceed in a potential which is the electronic energy. In contrast to the Born-Oppenheimer approximation, the separation of the center of mass can be carried out exactly. The electronic Hamiltonian and the equation of motion of the nuclei resulting after the exact separation of the center of mass motion are explicitly given. A simple exactly solvable model is used to illustrate some aspects of the theory.
- Authors:
-
- Theoretische Chemie, Physikalisch-Chemisches Institut, Universitaet Heidelberg, Im Neuenheimer Feld 229, D-69120 Heidelberg (Germany)
- Publication Date:
- OSTI Identifier:
- 22118607
- Resource Type:
- Journal Article
- Journal Name:
- Journal of Chemical Physics
- Additional Journal Information:
- Journal Volume: 138; Journal Issue: 22; Other Information: (c) 2013 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0021-9606
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; BORN-OPPENHEIMER APPROXIMATION; EQUATIONS OF MOTION; EXACT SOLUTIONS; HAMILTONIANS; SCHROEDINGER EQUATION; VARIATIONAL METHODS; WAVE FUNCTIONS
Citation Formats
Cederbaum, Lorenz S. The exact molecular wavefunction as a product of an electronic and a nuclear wavefunction. United States: N. p., 2013.
Web. doi:10.1063/1.4807115.
Cederbaum, Lorenz S. The exact molecular wavefunction as a product of an electronic and a nuclear wavefunction. United States. https://doi.org/10.1063/1.4807115
Cederbaum, Lorenz S. 2013.
"The exact molecular wavefunction as a product of an electronic and a nuclear wavefunction". United States. https://doi.org/10.1063/1.4807115.
@article{osti_22118607,
title = {The exact molecular wavefunction as a product of an electronic and a nuclear wavefunction},
author = {Cederbaum, Lorenz S.},
abstractNote = {The Born-Oppenheimer approximation is a basic approximation in molecular science. In this approximation, the total molecular wavefunction is written as a product of an electronic and a nuclear wavefunction. Hunter [Int. J. Quantum Chem. 9, 237 (1975)] has argued that the exact total wavefunction can also be factorized as such a product. In the present work, a variational principle is introduced which shows explicitly that the total wavefunction can be exactly written as such a product. To this end, a different electronic Hamiltonian has to be defined. The Schroedinger equation for the electronic wavefunction follows from the variational ansatz and is presented. As in the Born-Oppenheimer approximation, the nuclear motion is shown to proceed in a potential which is the electronic energy. In contrast to the Born-Oppenheimer approximation, the separation of the center of mass can be carried out exactly. The electronic Hamiltonian and the equation of motion of the nuclei resulting after the exact separation of the center of mass motion are explicitly given. A simple exactly solvable model is used to illustrate some aspects of the theory.},
doi = {10.1063/1.4807115},
url = {https://www.osti.gov/biblio/22118607},
journal = {Journal of Chemical Physics},
issn = {0021-9606},
number = 22,
volume = 138,
place = {United States},
year = {Fri Jun 14 00:00:00 EDT 2013},
month = {Fri Jun 14 00:00:00 EDT 2013}
}