Vanícek Jirí, Miller William H, Castillo Jesús F, Aoiz F Javier
Department of Chemistry and Kenneth S. Pitzer Center for Theoretical Chemistry, University of California, Berkeley, California 94720, USA.
J Chem Phys. 2005 Aug 1;123(5):054108. doi: 10.1063/1.1946740.
A general quantum-mechanical method for computing kinetic isotope effects is presented. The method is based on the quantum-instanton approximation for the rate constant and on the path-integral Metropolis-Monte Carlo evaluation of the Boltzmann operator matrix elements. It computes the kinetic isotope effect directly, using a thermodynamic integration with respect to the mass of the isotope, thus avoiding the more computationally expensive process of computing the individual rate constants. The method should be more accurate than variational transition-state theories or the semiclassical instanton method since it does not assume a single tunneling path and does not use a semiclassical approximation of the Boltzmann operator. While the general Monte Carlo implementation makes the method accessible to systems with a large number of atoms, we present numerical results for the Eckart barrier and for the collinear and full three-dimensional isotope variants of the hydrogen exchange reaction H + H2 --> H2 + H. In all seven test cases, for temperatures between 250 and 600 K, the error of the quantum instanton approximation for the kinetic isotope effects is less than approximately 10%.
本文提出了一种计算动力学同位素效应的通用量子力学方法。该方法基于速率常数的量子瞬子近似以及玻尔兹曼算符矩阵元的路径积分Metropolis - 蒙特卡罗评估。它通过对同位素质量进行热力学积分直接计算动力学同位素效应，从而避免了计算各个速率常数时计算量更大的过程。该方法应该比变分过渡态理论或半经典瞬子方法更准确，因为它不假设单一的隧穿路径，也不使用玻尔兹曼算符的半经典近似。虽然通用的蒙特卡罗实现方式使该方法适用于具有大量原子的系统，但我们给出了埃卡特势垒以及氢交换反应H + H₂→H₂ + H的共线和全三维同位素变体的数值结果。在所有七个测试案例中，对于250至600 K的温度范围，动力学同位素效应的量子瞬子近似误差小于约10%。
