All-particle Hamiltonians for Polyatomic-molecules .2. Born-oppenheimer and Other Adiabatic Approximations
(1992) Chemical Physics Letters — Vol. 197, n° 6, p. 635-642 (1992)
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- Abstract
- A non-relativistic exact quantum-mechanical expression of the Hamiltonian operator is derived for a molecular system made up of nu-electrons and N nuclei, by following a body-fixed quantization procedure recently introduced. The BF frame origin is at the total centre of mass. The arrangement of the nuclei is described by 3N - 6 internal coordinates, and the 3-nu-electron body-fixed Cartesian coordinates are used. All terms that contribute, beyond the Born-Oppenheimer electronic Hamiltonian, to the non-adiabatic couplings are identified. The difference between the Born-Oppenheimer approximation (based on the infinitely slow nuclear motion hypothesis and no distinction between the body-fixed and space-fixed frames, i.e. no overall rotation), and the adiabatic approximations based on the infinitely slow nuclear motion hypothesis and no total or nuclear angular momentum, is emphasized. The separability of the total Hamiltonian operator is discussed.
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Citations
Hounkonnou, MN., Sana, M., Kalonda, O., & Chapuisat, X. (1992). All-particle Hamiltonians for Polyatomic-molecules .2. Born-oppenheimer and Other Adiabatic Approximations. Chemical Physics Letters, 197(6), 635-642. https://doi.org/10.1016/0009-2614(92)85827-W (Original work published 1992)