Bias cancellation in one-determinant fixed-node diffusion Monte Carlo: Insights from fermionic occupation numbers

Area of Science:

• Quantum chemistry
• Computational physics
• Electronic structure theory

Background:

• Fixed-node diffusion Monte Carlo (FNDMC) accuracy relies on the quality of the trial wavefunction's nodal surface.
• Practical FNDMC methods for large systems often use single Slater determinants (SD) as trial wavefunctions.
• The suitability of SD nodes can vary significantly between different chemical systems, potentially leading to inaccurate energy differences.

Purpose of the Study:

• To develop a method for estimating the nonequivalence or appropriateness of Slater determinants (SD) in FNDMC calculations.
• To provide a qualitative measure of the expected bias in FNDMC energy differences arising from the choice of SD.
• To assess the reliability of SDs for FNDMC by analyzing their nodal properties.

Main Methods:

• Utilizing a measure based on the Euclidean distance between the natural orbital occupation number (NOON) vector of the SD and the exact solution in the NOON vector space.
• Calculating the NOON vector difference as an indicator of SD suitability.
• Applying the NOON-based measure to small noncovalent complexes and the dissociation of Si2 vs N2.

Main Results:

• The NOON-based measure effectively quantifies the nonequivalence of SDs.
• This measure serves as a qualitative indicator of nondynamic correlation bias in FNDMC energy differences.
• The NOON-based approach accurately reflects the magnitude and sign of bias observed in FNDMC calculations for the studied systems.

Conclusions:

• The developed NOON-based measure provides valuable insights into the reliability of SDs for FNDMC.
• It helps in understanding and predicting the bias in FNDMC energy differences.
• This method offers a way to assess the appropriateness of trial wavefunctions, improving the accuracy of FNDMC results.