Pollak Eli, Upadhyayula Sameernandan, Liu Jian
Chemical and Biological Physics Department, Weizmann Institute of Science, 76100 Rehovoth, Israel.
Beijing National Laboratory for Molecular Sciences, Institute of Theoretical and Computational Chemistry, College of Chemistry and Molecular Engineering, Peking University, Beijing 100871, China.
J Chem Phys. 2022 Jun 28;156(24):244101. doi: 10.1063/5.0088163.
A coherent state phase space representation of operators, based on the Husimi distribution, is used to derive an exact expression for the symmetrized version of thermal correlation functions. In addition to the time and temperature independent phase space representation of the two operators whose correlation function is of interest, the integrand includes a non-negative distribution function where only one imaginary time and one real time propagation are needed to compute it. The methodology is exemplified for the flux side correlation function used in rate theory. The coherent state representation necessitates the use of a smeared Gaussian flux operator whose coherent state phase space representation is identical to the classical flux expression. The resulting coherent state expression for the flux side correlation function has a number of advantages as compared to previous formulations. Since only one time propagation is needed, it is much easier to converge it with a semiclassical initial value representation. There is no need for forward-backward approximations, and in principle, the computation may be implemented on the fly. It also provides a route for analytic semiclassical approximations for the thermal rate, as exemplified by a computation of the transmission factor through symmetric and asymmetric Eckart barriers using a thawed Gaussian approximation for both imaginary and real time propagations. As a by-product, this example shows that one may obtain "good" tunneling rates using only above barrier classical trajectories even in the deep tunneling regime.
基于胡西米分布的算符的相干态相空间表示，被用于推导热关联函数对称形式的精确表达式。除了感兴趣的两个算符的与时间和温度无关的相空间表示外，被积函数还包括一个非负分布函数，计算它仅需一次虚时间和一次实时间传播。该方法以速率理论中使用的通量侧关联函数为例进行说明。相干态表示需要使用一个涂抹的高斯通量算符，其相干态相空间表示与经典通量表达式相同。与先前的公式相比，由此得到的通量侧关联函数的相干态表达式具有许多优点。由于只需要一次时间传播，用半经典初值表示来使其收敛要容易得多。不需要前后近似，原则上，计算可以实时进行。它还为热速率的解析半经典近似提供了一条途径，例如通过对虚时间和实时间传播都使用解冻高斯近似来计算通过对称和非对称埃卡特势垒的透射因子。作为一个副产品，这个例子表明，即使在深隧穿区域，仅使用势垒上方的经典轨迹也可以获得“良好”的隧穿速率。
