Department of Chemistry and Supercomputing Institute, University of Minnesota, Minneapolis, Minnesota 55455-0431, USA.
J Chem Phys. 2010 Feb 28;132(8):084109. doi: 10.1063/1.3310296.
This paper describes and illustrates a way to construct multidimensional representations of reactive potential energy surfaces (PESs) by a multiconfiguration Shepard interpolation (MCSI) method based only on gradient information, that is, without using any Hessian information from electronic structure calculations. MCSI, which is called multiconfiguration molecular mechanics (MCMM) in previous articles, is a semiautomated method designed for constructing full-dimensional PESs for subsequent dynamics calculations (classical trajectories, full quantum dynamics, or variational transition state theory with multidimensional tunneling). The MCSI method is based on Shepard interpolation of Taylor series expansions of the coupling term of a 2 x 2 electronically diabatic Hamiltonian matrix with the diagonal elements representing nonreactive analytical PESs for reactants and products. In contrast to the previously developed method, these expansions are truncated in the present version at the first order, and, therefore, no input of electronic structure Hessians is required. The accuracy of the interpolated energies is evaluated for two test reactions, namely, the reaction OH+H(2)-->H(2)O+H and the hydrogen atom abstraction from a model of alpha-tocopherol by methyl radical. The latter reaction involves 38 atoms and a 108-dimensional PES. The mean unsigned errors averaged over a wide range of representative nuclear configurations (corresponding to an energy range of 19.5 kcal/mol in the former case and 32 kcal/mol in the latter) are found to be within 1 kcal/mol for both reactions, based on 13 gradients in one case and 11 in the other. The gradient-based MCMM method can be applied for efficient representations of multidimensional PESs in cases where analytical electronic structure Hessians are too expensive or unavailable, and it provides new opportunities to employ high-level electronic structure calculations for dynamics at an affordable cost.
本文描述并说明了一种基于梯度信息而无需使用电子结构计算中的任何 Hessian 信息的多组态 Shepard 插值（MCSI）方法来构建反应势能面（PES）的多维表示的方法。MCSI 在前几篇文章中被称为多组态分子力学（MCMM），它是一种半自动方法，用于构建全维 PES，以便进行后续动力学计算（经典轨迹、全量子动力学或多维隧穿的变分过渡态理论）。MCSI 方法基于 2 x 2 电子离绝热哈密顿矩阵的耦合项的 Shepard 插值，该矩阵的对角元素代表反应物和产物的非反应分析 PES。与以前开发的方法不同，在当前版本中，这些展开式在一阶截断，因此不需要输入电子结构 Hessians。对于两个测试反应，即 OH+H(2)-->H(2)O+H 和从模型中提取氢自由基的阿尔法生育酚的氢原子，评估了插值能量的准确性。后者反应涉及 38 个原子和一个 108 维 PES。在广泛的代表性核构型范围内（分别对应于前一种情况的 19.5 kcal/mol 和后一种情况的 32 kcal/mol 的能量范围），基于一种情况下的 13 个梯度和另一种情况下的 11 个梯度，发现平均未签名误差在两种情况下均在 1 kcal/mol 以内。基于梯度的 MCMM 方法可用于在分析电子结构 Hessians 过于昂贵或不可用时有效地表示多维 PES，并且为以可承受的成本使用高级电子结构计算进行动力学提供了新的机会。
