Communication: fixed-node errors in quantum Monte Carlo: interplay of electron density and node nonlinearities.

Area of Science:

• Computational Quantum Chemistry
• Materials Science

Background:

• Quantum Monte Carlo (QMC) methods are powerful tools for electronic structure calculations.
• Fixed-node errors are a primary source of inaccuracy in QMC, particularly for systems with complex electronic structures.
• Observed large discrepancies in fixed-node errors between first- and second-row elements necessitate further investigation.

Purpose of the Study:

• To elucidate the origin of significant differences in fixed-node errors between first- and second-row systems in QMC calculations.
• To identify the key electronic and nodal properties influencing these fixed-node biases.
• To provide insights into the accuracy of QMC across diverse chemical and material systems.

Main Methods:

• Systematic study of fixed-node errors in single-configuration trial wave functions.
• Analysis across a range of systems including atoms, molecules, and solid crystals (Si, C).
• Investigation of electron density distributions and nodal structure nonlinearity.

Main Results:

• Identified differences in electron density and degree of node nonlinearity as primary drivers of fixed-node errors.
• Quantified the two-fold or greater variation in fixed-node errors between first- and second-row systems.
• Demonstrated the impact of these factors on QMC accuracy for diverse systems.

Conclusions:

• The accuracy of QMC calculations is system-dependent, influenced by electron density and nodal properties.
• Understanding these factors offers new perspectives on fixed-node biases in molecular and condensed matter systems.
• Findings have implications for developing improved pseudopotentials for heavy element calculations.