Direct optimization of nodal hypersurfaces in approximate wave functions

Area of Science:

• Computational Quantum Chemistry
• Many-Body Physics
• Quantum Monte Carlo Methods

Background:

• The fixed-node diffusion quantum Monte Carlo (FN-DMC) method approximates solutions to the Schrödinger equation for many-electron systems.
• A key limitation of FN-DMC is the "node location error," arising from inaccuracies in the nodal hypersurface of trial wave functions.
• Accurate nodal hypersurfaces are crucial for obtaining exact eigenvalues.

Purpose of the Study:

• To develop and validate local criteria for assessing the accuracy of nodal hypersurfaces in FN-DMC.
• To introduce direct optimization methods for improving nodal hypersurfaces based on these criteria.
• To demonstrate the efficacy of nodal optimization for simple atomic and molecular systems.

Main Methods:

• Development of local criteria evaluating the proximity of nodal hypersurfaces of PsiT, TPsiT, and HPsiT.
• Implementation of direct optimization algorithms targeting the nodal hypersurface.
• Application and verification using FN-DMC calculations for the Be atom and C2 molecule.

Main Results:

• Established local criteria to quantify nodal accuracy.
• Demonstrated successful direct optimization of nodal hypersurfaces.
• Verified improved accuracy through FN-DMC calculations for benchmark systems.

Conclusions:

• The developed criteria provide a reliable measure of nodal accuracy.
• Direct nodal optimization offers a pathway to reduce the node location error in FN-DMC.
• This approach enhances the precision of quantum Monte Carlo simulations for electronic structure problems.