Graduate School of Science, Technology, and Innovation, Kobe University, Nada-ku, Kobe 657-8501, Japan.
J Chem Phys. 2017 Dec 28;147(24):244107. doi: 10.1063/1.5003222.
Model space quantum Monte Carlo (MSQMC) is an extension of full configuration interaction QMC that allows us to calculate quasi-degenerate and excited electronic states by sampling the effective Hamiltonian in the model space. We introduce a novel algorithm based on the state-selective partitioning for the effective Hamiltonian using left eigenvectors to calculate several electronic states simultaneously at much less computational cost than the original MSQMC with the energy-dependent partitioning. The sampling of walkers in MSQMC is analyzed in the single reference limit using a stochastic algorithm for higher-order perturbation energies by the analogy of the deterministic case utilizing a full configuration interaction program. We further develop size-consistency corrections of the initiator adaptation (i-MSQMC) in three different ways, i.e., the coupled electron pair approximation, a posteriori, and second-order perturbative corrections. It is clearly demonstrated that most of the initiator error is originating from the deficiency of proper scaling of correlation energy due to its truncated CI nature of the initiator approximation and that the greater part of the error can be recovered by the size-consistency corrections developed in this work.
模型空间量子蒙特卡罗（MSQMC）是全组态相互作用 QMC 的扩展，它允许我们通过在模型空间中采样有效哈密顿量来计算准简并和激发电子态。我们引入了一种新的算法，该算法基于有效哈密顿量的状态选择分区，使用左特征向量同时计算几个电子态，计算成本远低于原始的基于能量相关分区的 MSQMC。在单参考极限下，通过类比利用全组态相互作用程序的确定性情况来分析 walker 在 MSQMC 中的采样，采用更高阶微扰能量的随机算法。我们进一步以三种不同的方式开发了引发子自适应的大小一致性校正（i-MSQMC），即耦合电子对近似、后验和二阶微扰校正。清楚地表明，引发子误差的大部分源于由于引发子近似的截断 CI 性质导致相关能的适当缩放不足，并且可以通过本文开发的大小一致性校正来恢复大部分误差。
