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    188宝金博页面版: Quantum simulation of vibration states and Franck-Condon overlap in non-separable potentials

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    内容提示： Theor Chim Acta (1989) 76:137-145 Theoretica Chimica Acta ?9 Springer-Verlag 1989 Quantum simulation of vibration states and Franek- Condon overlap in non-separable potentials W. Lorenz and O. Heitzsch Sektion Chemie, Karl-Marx-Universit~it Leipzig, DDR-7010 Leipzig, German Democratic Republic (Received December 2, 1988; revised March 10/Accepted March 24, 1989) Summary. Taking into consideration nuclear motion in non-separable poten- tials, we have probed the solution of the Schr6dinger equation by random...

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    Theor Chim Acta (1989) 76:137-145 Theoretica Chimica Acta ?9 Springer-Verlag 1989 Quantum simulation of vibration states and Franek- Condon overlap in non-separable potentials W. Lorenz and O. Heitzsch Sektion Chemie, Karl-Marx-Universit~it Leipzig, DDR-7010 Leipzig, German Democratic Republic (Received December 2, 1988; revised March 10/Accepted March 24, 1989) Summary. Taking into consideration nuclear motion in non-separable poten- tials, we have probed the solution of the Schr6dinger equation by random walk sampling in imaginary time on a two-dimensional example. Evaluation of the many-dimensional Franck-Condon overlap and the chemical species conversion rate is outlined. Key words: Quantum simulation--Non-separable vibrations -- Franck- Condon overlap I. Introduction Our aim in this paper is to prepare for further numerical exploration of local chemical processes in condensed systems or at interfaces [1, 2]. As a starting point of the following, we note that in the chemical species conversion probabil- ity expression P 2rt (a~.b) = -~ AvITba[23(AE "ab + AE), (1) the vibrational, or Franck-Condon overlap (qSblq~ ~ ) contained in the transition matrix elements Tb~, is not restricted to separable vibration states; ~b,, q~b are the vibration state functions of the initial and final state in diabatic or quasi-adia- batic potentials. In Eq. (1), AE rib is the change of vibration energy in the conversion process, AE the difference of total energy zero points of states (a) and (b), Av indicates thermal weighting. Taking into consideration general potential surface characteristics, the question of including non-separable anharmonic vibrations in the transition matrix treatment arises.

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