Self-consistent field perturbation theory of molecular vibrations
- 1 February 1998
- journal article
- research article
- Published by Informa UK Limited in Molecular Physics
- Vol. 93 (3), 477-484
- https://doi.org/10.1080/002689798169168
Abstract
Perturbation theory is used to perform non-iterative calculations of energy eigenvalues of the coupled ordinary differential equations that result from imposing separability assumptions in terms of normal coordinates on vibrational wavefunctions. Various model Hamiltonians with 2 or 3 coupled normal modes are studied and the increase of computational cost with the number of degrees of freedom is analysed. Quadratic Padé approximants of the perturbation expansions are rapidly convergent, and directly yield complex numbers for resonance eigenvalues. For a 3-mode system, results are obtained within partial separability assumptions, with a pair of modes left coupled. Large-order perturbation theory with partial separability is suggested as an alternative to low-order exact perturbation theory.Keywords
This publication has 32 references indexed in Scilit:
- Dimensional perturbation theory for vibration–rotation spectra of linear triatomic moleculesThe Journal of Chemical Physics, 1997
- Perturbation theory for coupled anharmonic oscillatorsThe Journal of Chemical Physics, 1997
- Summation of the eigenvalue perturbation series by multi-valued Pade approximants: application to resonance problems and double wellsJournal of Physics A: General Physics, 1995
- Anharmonic Wave Functions of Proteins: Quantum Self-Consistent Field Calculations of BPTIScience, 1995
- A linear algebraic method for exact computation of the coefficients of the 1/D expansion of the Schrödinger equationThe Journal of Chemical Physics, 1994
- A truncation/recoupling method for basis set calculations of eigenvalues and eigenvectorsThe Journal of Chemical Physics, 1991
- Vibrational correlation energies for deuterated H + 3 moleculesJournal of the Chemical Society, Faraday Transactions 2: Molecular and Chemical Physics, 1988
- Vibrational levels and tunneling dynamics by the optimal coordinates, self-consistent field method: a study of hydrocyanic acid .dblarw. hydroisocyanic acidThe Journal of Physical Chemistry, 1986
- Large N expansions work: A semi-classical perturbation theory for quantum mechanicsProgress in Particle and Nuclear Physics, 1982
- Quantum dynamical tunneling in bound statesThe Journal of Chemical Physics, 1981