A Symmetrical Quasi-Classical Spin-Mapping Model for the Electronic Degrees of Freedom in Non-Adiabatic Processes
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- 作者：Stephen J. Cotton ; William H. Miller
- 刊名：Journal of Physical Chemistry A
- 出版年：2015
- 出版时间：December 17, 2015
- 年：2015
- 卷：119
- 期：50
- 页码：12138-12145
- 全文大小：400K
- ISSN：1520-5215
文摘
A recent series of papers has shown that a symmetrical quasi-classical (SQC) windowing procedure applied to the Meyer鈥揗iller (MM) classical vibronic Hamiltonian provides a very good treatment of electronically nonadiabatic processes in a variety of benchmark model systems, including systems that exhibit strong quantum coherence effects and some which other approximate approaches have difficulty in describing correctly. In this paper, a different classical electronic Hamiltonian for the treatment of electronically nonadiabatic processes is proposed (and 鈥渜uantized鈥?via the SQC windowing approach), which maps the dynamics of F coupled electronic states to a set of F spin-1/2 degrees of freedom (DOF), similar to the Fermionic spin model described by Miller and White (J. Chem. Phys. 1986, 84, 5059). It is noted that this spin-mapping (SM) Hamiltonian is an exact Hamiltonian if treated as a quantum mechanical (QM) operator鈥攁nd thus QM鈥檒y equivalent to the MM Hamiltonian鈥攂ut that an analytically distinct classical analogue is obtained by replacing the QM spin-operators with their classical counterparts. Due to their analytic differences, a practical comparison is then made between the MM and SM Hamiltonians (when quantized with the SQC technique) by applying the latter to many of the same benchmark test problems successfully treated in our recent work with the SQC/MM model. We find that for every benchmark problem the MM model provides (slightly) better agreement with the correct quantum nonadiabatic transition probabilities than does the new SM model. This is despite the fact that one might expect, a priori, a more natural description of electronic state populations (occupied versus unoccupied) to be provided by DOF with only two states, i.e., spin-1/2 DOF, rather than by harmonic oscillator DOF which have an infinite manifold of states (though only two of these are ever occupied).