Binding and excitations in Si$_x$H$_y$ molecular systems using quantum Monte Carlo

TL;DR

This study uses quantum Monte Carlo methods to accurately compute binding energies and excitations in small silicon hydride molecules, analyzing fixed-node errors and demonstrating high precision in energy calculations.

Contribution

It provides a detailed assessment of fixed-node diffusion QMC errors in Si$_x$H$_y$ molecules, showing high accuracy and low bias across various states and excitations.

Findings

QMC atomization energies within 0.07 eV of exact results

Fixed-node biases between 1-3.5% with absolute errors up to 0.2 eV

Low fixed-node biases in silicon systems compared to other main group elements

Abstract

We present high-accuracy correlated calculations of small Si$_x$H$_y$ molecular systems both in the ground and excited states. We employ quantum Monte Carlo (QMC) together with a variety of many-body wave function approaches based on basis set expansions. The calculations are carried out in a valence-only framework using recently derived correlation consistent effective core potentials. Our primary goal is to understand the fixed-node diffusion QMC errors in both the ground and excited states with single-reference trial wave functions. Using a combination of methods, we demonstrate the very high accuracy of the QMC atomization energies being within $\approx$ 0.07 eV or better when compared with essentially exact results. By employing proper choices for trial wave functions, we have found that the fixed-node QMC biases for total energies are remarkably uniform ranging between $1-3.5$ % with absolute values at most $\approx$ 0.2 eV across the systems and several types of excitations such as singlets and triplets as well as low-lying and Rydberg-like states. Our results further corroborate that Si systems, and presumably also related main group IV and V elements of the periodic table (Ge, Sn, etc), exhibit some of the lowest fixed-node biases found in valence-only electronic structure QMC calculations.