Linear-scaling fixed-node diffusion quantum Monte Carlo: accounting for the nodal information in a density...

Area of Science:

• Computational Quantum Chemistry
• Quantum Monte Carlo Methods
• Electronic Structure Theory

Background:

• The fixed-node diffusion quantum Monte Carlo (FN-DQMC) method is a powerful tool for electronic structure calculations.
• Previous density matrix-based approaches for variational QMC achieved linear scaling but lost essential nodal information.
• Preserving nodal information is critical for confining random walkers in FN-DQMC simulations.

Purpose of the Study:

• To reformulate the FN-DQMC method using the N-particle density matrix.
• To reduce the computational effort for local energy evaluation to linear scaling.
• To retain the nodal information of the trial function within the FN-DQMC framework.

Main Methods:

• Reformulation of FN-DQMC in terms of the N-particle density matrix.
• Utilizing off-diagonal elements of the N-particle density matrix (rhoN T(R;R')) to preserve nodal information.
• Development of a scheme for single-electron moves within the N-particle density matrix Quantum Monte Carlo (N-PDM QMC).

Main Results:

• Achieved linear scaling for the evaluation of local energy in FN-DQMC.
• Successfully incorporated nodal information into the density matrix formulation.
• Demonstrated the efficiency of the new method through exemplary calculations.

Conclusions:

• The N-particle density matrix reformulation provides a computationally efficient and accurate approach to FN-DQMC.
• This method overcomes the limitation of lost nodal information in previous density matrix-based QMC techniques.
• The developed scheme is applicable to both all-electron and single-electron move calculations.