Optimization Stability in Excited-State-Specific Variational Monte Carlo

Abstract

We investigate the issue of optimization stability in variance-based state-specific variational Monte Carlo, discussing the roles of the objective function, the complexity of wave function ansatz, the amount of sampling effort, and the choice of minimization algorithm. Using a small cyanine dye molecule as a test case, we systematically perform minimizations using variants of the linear method as both a standalone algorithm and in a hybrid combination with accelerated descent. We demonstrate that adaptive step control is crucial for maintaining the linear method's stability when optimizing complicated wave functions and that the hybrid method enjoys both greater stability and minimization performance.

Ensemble variational Monte Carlo for optimization of correlated excited state wave functions

“…In many systems, optimal orbitals for describing an excited state are quite different from the optimal ground-state orbitals, so large determinant expansions are required to accurately represent these states using a shared set of orbitals. An optimization approach using variance of the local energy has been used to target excited states without state averaging [12][13][14][15]; however, relying on the variance leads to difficulty optimizing to the correct minimum in some situations [16]. An alternative method avoids state averaging and variance optimization by penalizing the wave function's overlap with a set of known eigenstates [17,18].…”

Partial Separability of the Schrödinger Equation Combined with a Jastrow Factor

“…However, when larger systems are considered, the method becomes more complicated and less elegant. Nowadays, explicitly correlated wave functions are widely employed in electronic structure calculations of atoms and molecules by using numerical integration schemes such as those based on the Quantum Monte Carlo methods or other schemes such as the Explicitly Correlated R12/F12 or the Transcorrelated methods, see, e.g., refs − .…”