An excited-state approach within full configuration interaction quantum Monte Carlo

TL;DR

This paper introduces a new, efficient method within FCIQMC to compute multiple low-energy excited states simultaneously, avoiding trial functions and additional partitioning, demonstrated on the carbon dimer.

Contribution

A novel Gram-Schmidt orthogonalization technique integrated into FCIQMC for excited state calculations, maintaining computational efficiency and simplicity.

Findings

Successfully applied to the carbon dimer with results comparable to existing methods.

Requires minimal modifications to existing FCIQMC algorithms.

Enables study of excited states with similar computational cost as ground states.

Abstract

We present a new approach to calculate excited states with the full configuration interaction quantum Monte Carlo (FCIQMC) method. The approach uses a Gram-Schmidt procedure, instantaneously applied to the stochastically evolving distributions of walkers, to orthogonalize higher energy states against lower energy ones. It can thus be used to study several of the lowest-energy states of a system within the same symmetry. This additional step is particularly simple and computationally inexpensive, requiring only a small change to the underlying FCIQMC algorithm. No trial wave functions or partitioning of the space is needed. The approach should allow excited states to be studied for systems similar to those accessible to the ground-state method, due to a comparable computational cost. As a first application we consider the carbon dimer in basis sets up to quadruple-zeta quality, and compare to existing results where available.