Fixed-node errors in quantum Monte Carlo: interplay of electron density and node nonlinearities

We elucidate the origin of large differences (two-fold or more) in the fixed-node errors between the first- vs second-row systems for single-configuration trial wave functions in quantum Monte Carlo calculations. This significant difference in the fixed-node biases is studied across a set of atoms, molecules, and also Si, C solid crystals. The analysis is done over valence isoelectronic systems that share similar correlation energies, bond patterns, geometries, ground states, and symmetries. We show that the key features which affect the fixed-node errors are the differences in electron density and the degree of node nonlinearity. The findings reveal how the accuracy of the quantum Monte Carlo varies across a variety of systems, provide new perspectives on the origins of the fixed-node biases in electronic structure calculations of molecular and condensed systems, and carry implications for pseudopotential constructions for heavy elements