Multi-state effective Hamiltonian and size-consistency corrections in stochastic configuration interactions

Abstract

Model space quantum Monte Carlo (MSQMC) is an extension of full configuration interaction QMC (FCIQMC) 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 pertrubative 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.

arXiv comment9 pges, 5 figures

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• Full Coupled-Cluster Reduction for Accurate Description of Strong Electron Correlation
• The HANDE-QMC project: open-source stochastic quantum chemistry from the ground state up
• The Adaptive Shift Method in Full Configuration Interaction Quantum Monte Carlo: Development and Applications
• An efficient and accurate perturbative correction to initiator full configuration interaction quantum Monte Carlo
• Diagrammatic Coupled Cluster Monte Carlo
• Taming the fixed-node error in diffusion Monte Carlo via range separation
• Non-linear biases, stochastically-sampled effective Hamiltonians and spectral functions in quantum Monte Carlo methods
• Nonunitary projective transcorrelation theory inspired by the F12 ansatz
• A hybrid approach to extending selected configuration interaction and full configuration interaction quantum Monte Carlo
• Theory and Implementation of a Novel Stochastic Approach to Coupled Cluster
• Fixed and partial-node approximations in Slater determinant space for molecules
• Stochastic evaluation of four-component relativistic second-order many-body perturbation energies: A potentially quadratic-scaling correlation method