Fractional Charge by Fixed-Node Diffusion Monte Carlo Method.

Area of Science:

• Quantum many-body physics
• Computational chemistry
• Electronic structure theory

Background:

• The fixed-node diffusion Monte Carlo (FNDMC) method is a powerful stochastic approach for quantum many-body problems.
• Accurately describing electronic structure, especially with fractional electron numbers, remains a challenge in computational chemistry.
• Mean-field trial wave functions often lack exact features like derivative discontinuity.

Purpose of the Study:

• To investigate the ability of the FNDMC method to satisfy exact energy constraints, including piecewise linearity and derivative discontinuity, as a function of fractional electron number (N).
• To assess the performance of FNDMC when combined with mean-field trial wave functions that inherently miss these exact features.
• To demonstrate the efficacy of FNDMC for charged molecular systems.

Main Methods:

• Utilizing the fixed-node diffusion Monte Carlo (FNDMC) method, a stochastic quantum many-body technique.
• Examining the total energy E(N) behavior with respect to fractional electron number N.
• Employing ensemble and projector techniques within FNDMC to ensure correct charge localization.

Main Results:

• FNDMC successfully restores the piecewise linearity of the total energy E(N) for systems with fractional electron charges, such as H and Cl atoms.
• The method demonstrates superior performance for charged noncovalent systems, as exemplified by a water-solvated Cl⁻ complex.
• Ensemble and projector ingredients are key to achieving accurate charge localization.

Conclusions:

• The FNDMC method shows significant potential in electronic structure theory by accurately satisfying fundamental energy constraints.
• FNDMC effectively handles fractional electron numbers and improves the description of charged systems.
• This stochastic approach offers a robust pathway for advancing computational quantum chemistry.