A Symmetrical Quasi-Classical Spin-Mapping Model for the Electronic Degrees of Freedom in Non-Adiabatic Processes
A Symmetrical Quasi-Classical Spin-Mapping Model for the Electronic Degrees of Freedom in Non-Adiabatic Processes
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DOI：
10.1021/acs.jpca.5b05906
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发表时间：
2015-12-17
影响因子：
2.9
通讯作者：
Miller, William H.
中科院分区：
文献类型：
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作者：
Cotton, Stephen J.;Miller, William H.
最近的一系列论文表明，对称准经典（SQC）窗口程序应用于迈耶-米勒（MM）的经典振动哈密顿量提供了一个很好的处理电子非绝热过程中的各种基准模型系统，包括系统表现出强量子相干效应和一些其他近似方法难以正确描述。本文提出了一种不同的经典电子哈密顿量来处理电子非绝热过程（并通过SQC窗口方法“量化”），其将F耦合电子态的动力学映射到一组F自旋-（1）/（2）自由度（DOF），类似于由米勒和白色描述的费米自旋模型（化学物理杂志1986，84，5059）。值得注意的是，如果把这种自旋映射（SM）哈密顿量看作量子力学（QM）算符，则它是一个精确的哈密顿量，因而QM与MM哈密顿量是等价的，但用它们的经典对应物代替QM自旋算符，则得到了一个解析上不同的经典类似物。由于他们的分析差异，一个实际的比较，然后MM和SM哈密顿（当量化与SQC技术）通过应用后者的许多相同的基准测试问题成功地处理在我们最近的工作与SQC/MM模型。我们发现，对于每一个基准问题的MM模型提供（略）更好的协议，正确的量子非绝热跃迁概率比新的SM模型。尽管事实上，人们可能先验地期望DOF仅提供两个状态对电子状态种群（占用与未占用）的更自然描述，即，自旋-（1）/（2）自由度，而不是谐振子自由度，谐振子自由度具有无限多个状态（尽管只有其中两个被占据）。
A recent series of papers has shown that a symmetrical quasi-classical (SQC) windowing procedure applied to the Meyer-Miller (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 "quantized" 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-and thus QM'ly equivalent to the MM Hamiltonian-but 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).