Optimized Jastrow-Slater wave functions for ground and excited states: Application to the lowest states of ethene

TL;DR

This paper introduces an advanced quantum Monte Carlo method for optimizing multi-determinantal Jastrow-Slater wave functions, improving the accuracy of ground and excited state calculations, demonstrated on ethene's lowest states.

Contribution

It develops a novel iterative optimization approach combining orbital and CI coefficient adjustments within the energy fluctuation potential framework.

Findings

Effective optimization of ground and excited states achieved.

Successful application to ethene's challenging singlet 1B_1u state.

Method compares favorably with stochastic reconfiguration techniques.

Abstract

A quantum Monte Carlo method is presented for determining multi-determinantal Jastrow-Slater wave functions for which the energy is stationary with respect to the simultaneous optimization of orbitals and configuration interaction coefficients. The approach is within the framework of the so-called energy fluctuation potential method which minimizes the energy in an iterative fashion based on Monte Carlo sampling and a fitting of the local energy fluctuations. The optimization of the orbitals is combined with the optimization of the configuration interaction coefficients through the use of additional single excitations to a set of external orbitals. A new set of orbitals is then obtained from the natural orbitals of this enlarged configuration interaction expansion. For excited states, the approach is extended to treat the average of several states within the same irreducible representation of the pointgroup of the molecule. The relationship of our optimization method with the stochastic reconfiguration technique by Sorella et al. is examined. Finally, the performance of our approach is illustrated with the lowest states of ethene, in particular with the difficult case of the singlet 1B_1u state.