Department of Chemistry and Kenneth S. Pitzer Center for Theoretical Chemistry, University of California, and Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA.
J Chem Phys. 2011 Mar 21;134(11):114104. doi: 10.1063/1.3563045.
Semiclassical instanton theory gives an approximate description of deep tunneling by means of periodic orbits on the inverted potential energy surface. There are two versions of the theory, one derived by taking a semiclassical limit of the exact flux-side time-correlation function and the other by starting from the "Im F" premise, in which the partition function is analytically continued into the complex plane. Here, we provide a derivation showing that the two versions of the theory are exactly equivalent. Unlike a previous derivation (which was restricted to a system-bath model), our derivation is completely general, and thus establishes that the "Im F" premise, which is behind such methods as quantum transition-state theory and ring polymer molecular dynamics rate-theory, is correct in the steepest-descent limit.
半经典瞬时理论通过在倒势能面上的周期轨道来近似描述深隧穿。该理论有两种版本，一种是通过对精确的流量侧时间相关函数进行半经典极限推导得到的，另一种是从“Im F”前提出发得到的，其中配分函数被解析延拓到复平面上。在这里，我们提供了一个证明，表明这两种理论版本完全等价。与之前的推导（仅限于系统-浴模型）不同，我们的推导是完全通用的，因此证明了量子跃迁态理论和环聚合物分子动力学速率理论等方法背后的“Im F”前提在最陡下降极限下是正确的。
