Craig Ian R, Manolopoulos David E
Physical and Theoretical Chemistry Laboratory, Oxford University, South Parks Road, Oxford OX1 3QZ, United Kingdom.
J Chem Phys. 2005 Feb 22;122(8):84106. doi: 10.1063/1.1850093.
We show how the ring-polymer molecular dynamics method can be adapted to calculate approximate Kubo-transformed flux-side correlation functions, and hence rate coefficients for condensed phase reactions. An application of the method to the standard model for a chemical reaction in solution--a quartic double-well potential linearly coupled to a bath of harmonic oscillators--is found to give results of comparable accuracy to those of the classical Wigner model and the centroid molecular dynamics method. However, since the present method does not require that one evaluate the Wigner transform of a thermal flux operator or that one perform a separate path integral calculation for each molecular dynamics time step, we believe it will prove easier to apply to more general problems than either of these alternative techniques. We also present a (logarithmic) discretization scheme for the Ohmic bath in the system-bath model that gives converged results with just nine bath modes--a surprisingly small number for a model of a condensed phase reaction. Finally, we present some calculations of the transmission through an Eckart barrier which show that the present method provides a satisfactory (although not perfect) description of the deep quantum tunneling regime. Part of the reason for the success of the method is that it gives the exact quantum-mechanical rate constant for the transmission through a parabolic barrier, as we demonstrate analytically in the Appendix.
我们展示了如何调整环聚合物分子动力学方法来计算近似的久保变换通量-边关联函数，从而得到凝聚相反应的速率系数。将该方法应用于溶液中化学反应的标准模型——一个与谐振子浴线性耦合的四次双阱势——发现其结果的精度与经典维格纳模型和质心分子动力学方法相当。然而，由于本方法不需要评估热通量算符的维格纳变换，也不需要在每个分子动力学时间步进行单独的路径积分计算，我们认为它比这两种替代技术更容易应用于更一般的问题。我们还为系统-浴模型中的欧姆浴提出了一种（对数）离散化方案，该方案仅用九个浴模就能得到收敛结果——对于凝聚相反应模型来说，这个数字小得出奇。最后，我们给出了一些通过埃卡特势垒的透射计算结果，表明本方法对深量子隧穿区域提供了令人满意（尽管并不完美）的描述。该方法成功的部分原因是，正如我们在附录中通过解析证明的那样，它给出了通过抛物线势垒的精确量子力学速率常数。
