Bias Cancellation in One-Determinant Fixed-Node Diffusion Monte Carlo: Insights from Fermionic Occupation Numbers

Abstract

Accuracy of the fixed-node diffusion Monte Carlo (FN-DMC) depends on the node location of the best available trial state ${\Psi }_T$. The practical FN-DMC approaches available for large systems rely on compact yet effective ${\Psi }_T$s containing explicitly correlated single Slater determinant (SD). However, SD nodes may be better suited to one system than to another, which may possibly lead to inaccurate FN-DMC energy differences. It remains a challenge, how to estimate inequivalency or appropriateness of SDs. Here we use the differences of a measure based on Euclidean distance between the natural orbital occupation number (NOON) vector of the Slater determinant (SD) from the exact solution in the NOON vector space, that can be viewed as a measure of SD inequivalency and a measure of the expected degree of nondynamic-correlation-related bias in FN-DMC energy differences. This is explored on a set of small noncovalent complexes and covalent bond breaking of Si${}_2$ vs. N${}_2$. It turns out that NOON-based measures well reflect the magnitude and sign of the bias present in the data available, thus providing new insights to the nature of bias cancellation in SD FN-DMC energy differences.

References in corpus (12)

• Continuum variational and diffusion quantum Monte Carlo calculations
• A spin-adapted Density Matrix Renormalization Group algorithm for quantum chemistry
• On the accuracy of DFT exchange-correlation functionals for H bonds in small water clusters II: The water hexamer and van der Waals interactions
• Applications of quantum Monte Carlo methods in condensed systems
• Multi-Determinant Wave-functions in Quantum Monte Carlo
• Separation of Dynamic and Nondynamic Correlation
• Pinning of Fermionic Occupation Numbers
• Water on hexagonal boron nitride from diffusion Monte Carlo
• Dissociation energy of the water dimer from Quantum Monte Carlo calculations
• Quantum Monte Carlo calculations of structural properties of FeO under pressure
• Generalized Pauli conditions on the spectra of one-electron reduced density matrices of atoms and molecules
• Water on BN doped benzene: A hard test for exchange-correlation functionals and the impact of exact exchange on weak binding