# Full Wave Function Optimization with Quantum Monte Carlo -- A study of the Dissociation Energies of ZnO, FeO, FeH, and CrS

## TL;DR

This study uses diffusion Monte Carlo with optimized wave functions to accurately determine dissociation energies and spectroscopic constants of transition metal dimers, demonstrating that compact wave functions can effectively reduce fixed-node errors.

## Contribution

It introduces a systematic approach to optimize wave functions in DMC for transition metal compounds, improving accuracy with compact active spaces.

## Key findings

- Accurate dissociation energies for ZnO, FeO, FeH, and CrS.
- Computed potential energy curves and spectroscopic constants consistent with experiments.
- Demonstrated that orbital optimization in active spaces reduces fixed-node errors in DMC.

## Abstract

The dissociation energies of four transition metal dimers are determined using diffusion Monte Carlo. The Jastrow, CI, and molecular orbital parameters of the wave function are both partially and fully optimized with respect to the variational energy. The pivotal role is thereby ascribable to the optimization of the molecular orbital parameters of a complete active space wave function in the presence of a Jastrow correlation function. Excellent results are obtained for ZnO, FeO, FeH, and CrS. In addition, potential energy curves are computed for the first three compounds at multi-reference diffusion Monte Carlo (MR-DMC) level, from which spectroscopic constants such as the equilibrium bond distance, the harmonic frequency, and the anharmonicity are extracted. All of those quantities agree well with the experiment. Furthermore, it is shown for CrS that a restricted active space calculation can yield improved initial orbitals by including single and double excitations from the original active space into a set of virtual orbitals. We demonstrated in this study that the fixed-node error in DMC can be systematically reduced for multi-reference systems by orbital optimization in compact active spaces. While DMC calculations with a large number of determinants are possible and very accurate, our results demonstrate that compact wave functions may be sufficient in order to obtain accurate nodal surfaces, which determine the accuracy of DMC, even in the case of transition metal compounds.