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首页> 外文期刊>The journal of physical chemistry, A. Molecules, spectroscopy, kinetics, environment, & general theory >Nonradiative Electronic Relaxation Rate Constants from Approximations Based on Linearizing the Path-Integral Forward-Backward Action
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Nonradiative Electronic Relaxation Rate Constants from Approximations Based on Linearizing the Path-Integral Forward-Backward Action

机译：基于线性积分路径向前-向后动作的近似非辐射电子弛豫速率常数

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摘要

We consider two different semiclassical approximations for nonadiabatic quantum-mechanical correlation functions of the form Tr[A e~(iH_et/h)B e~(-iH_gt/h)],where H_g(not =)H_e represent the nuclear Hamiltonians of two different electronic states.The first approximation is based on direct linearization(DL)of the forward-backward(FB)action in the exact path integral expression for this correlation function.The second approximation is based on linearizing the FB action in an equivalent quantum expression for this correlation function,which is given in terms of the Meyer-Miller mapping Hamiltonian(MML).The two approximations have several features in common,namely:(1)They are given in terms of an integral over a classical-like phase space;(2)The relevant operators are replaced by their Wigner transforms;(3)The dynamics is purely classical and governed by a Hamiltonian that represents an average over H_g and H_e;(4)The fact that H_g(not =)H_e gives rise to a phase factor of the form e~(iH_et/h)dtau where U = H_e - H_g.The main differences between the two approximations are:(1)The MML approximation involves an additional phase-space integral and Wigner transforms that correspond to the continuous variables representing the electronic degree of freedom;(2)The DL and MML approximations involve different averaged Hamiltonians,namely,//av =(Hg+//e)/2 in the case of the DL approximation,as opposed to different relative weights of H_g and H_e,which depend on the electronic degree of freedom,in the case of the MML approximation.The two approximations are tested within the framework of a nonradiative electronic relaxation(NRER)benchmark problem.Although the NRER rate constants are accurately reproduced by both methods,the DL approximation is consistently found to perform somewhat better.A discussion is provided of a feasible scheme for implementing those approximations in the case of anharmonic systems as well as the relationship to previous work.
机译：对于形式为Tr [A e〜（iH_et / h）B e〜（-iH_gt / h）]的非绝热量子力学相关函数，我们考虑了两种不同的半经典近似，其中H_g（not =）H_e表示两个原子核的哈密顿量不同的电子状态。第一近似基于该相关函数的精确路径积分表达式中的正向（FB）作用的直接线性化（DL）。第二近似基于等效方程式中的FB作用线性化。对于这种相关函数，这是根据Meyer-Miller映射哈密顿量（MML）给出的。这两个近似具有共同的几个特征，即：（1）它们在类经典相空间上的积分中给出;（2）相关运算符被其Wigner变换所取代;（3）动力学纯粹是经典的，并由表示H_g和H_e上平均值的哈密顿量控制;（4）H_g（not =）H_e产生的事实到形式为e〜（iH_e t / h）dtau其中U = H_e-H_g。两个近似之间的主要区别是：（1）MML近似涉及一个附加的相空间积分和Wigner变换，它们对应于代表电子自由度的连续变量; （2）DL和MML近似涉及不同的平均哈密顿量，即在DL近似的情况下，// av =（Hg + // e）/ 2，与H_g和H_e的不同相对权重不同，后者取决于电子自由度，在MML近似的情况下。在非辐射电子弛豫（NRER）基准问题的框架内测试了这两种近似。尽管两种方法都精确地再现了NRER速率常数，但始终可以找到DL近似讨论了在非谐系统情况下实现这些近似值的可行方案以及与先前工作的关系。

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