使用多行列式计算水分子的能量：一种简单、高效的算法。

Computing the energy of a water molecule using multideterminants: a simple, efficient algorithm.

机构信息

Princeton Center For Theoretical Science, Princeton University, Princeton, New Jersey 08544, USA.

出版信息

J Chem Phys. 2011 Dec 28;135(24):244105. doi: 10.1063/1.3665391.

Abstract

Quantum Monte Carlo (QMC) methods such as variational Monte Carlo and fixed node diffusion Monte Carlo depend heavily on the quality of the trial wave function. Although Slater-Jastrow wave functions are the most commonly used variational ansatz in electronic structure, more sophisticated wave functions are critical to ascertaining new physics. One such wave function is the multi-Slater-Jastrow wave function which consists of a Jastrow function multiplied by the sum of Slater determinants. In this paper we describe a method for working with these wave functions in QMC codes that is easy to implement, efficient both in computational speed as well as memory, and easily parallelized. The computational cost scales quadratically with particle number making this scaling no worse than the single determinant case and linear with the total number of excitations. Additionally, we implement this method and use it to compute the ground state energy of a water molecule.

摘要

量子蒙特卡罗（QMC）方法，如变分蒙特卡罗和固定节点扩散蒙特卡罗，严重依赖于试探波函数的质量。虽然 Slater-Jastrow 波函数是电子结构中最常用的变分假设，但更复杂的波函数对于确定新物理至关重要。多 Slater-Jastrow 波函数就是这样一种波函数，它由一个 Jastrow 函数乘以 Slater 行列式的和组成。在本文中，我们描述了一种在 QMC 代码中处理这些波函数的方法，该方法易于实现，在计算速度和内存方面都很高效，并且易于并行化。计算成本与粒子数呈二次方关系，使得这种扩展情况与单个行列式情况一样差，并且与总激发数呈线性关系。此外，我们实现了这种方法，并使用它来计算水分子的基态能量。