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

Area of Science:

• Quantum chemistry
• Computational physics
• Electronic structure theory

Background:

• Model space quantum Monte Carlo (MSQMC) extends full configuration interaction QMC.
• Existing methods struggle with quasi-degenerate and excited electronic states.
• Computational cost is a significant barrier for accurate electronic structure calculations.

Purpose of the Study:

• To introduce a novel, computationally efficient MSQMC algorithm for calculating multiple electronic states simultaneously.
• To analyze walker sampling in MSQMC for higher-order perturbation energies.
• To develop and implement size-consistency corrections for the initiator adaptation of MSQMC (i-MSQMC).

Main Methods:

• State-selective partitioning of the effective Hamiltonian using left eigenvectors.
• Stochastic algorithm for higher-order perturbation energies in the single reference limit.
• Three distinct size-consistency corrections: coupled electron pair approximation, a posteriori, and second-order perturbative corrections.

Main Results:

• The novel algorithm significantly reduces computational cost compared to original MSQMC.
• Analysis of walker sampling provides insights into MSQMC behavior.
• Developed size-consistency corrections effectively recover a major portion of the initiator error.

Conclusions:

• The new MSQMC algorithm enables simultaneous calculation of multiple electronic states with reduced computational expense.
• Size-consistency corrections are crucial for mitigating errors in the initiator approximation of MSQMC.
• This work advances the accuracy and efficiency of quantum Monte Carlo methods for electronic structure.