Excited state calculations using phaseless auxiliary-field quantum Monte Carlo: potential energy curves of low lying C2 singlet states

TL;DR

This paper demonstrates that phaseless auxiliary-field quantum Monte Carlo (AFQMC) can effectively compute excited state potential energy curves, offering a promising alternative to traditional quantum chemistry methods especially for challenging molecules.

Contribution

The study extends the phaseless AFQMC method to excited states, showing it can accurately predict potential energy curves of low-lying states without extensive trial wave function optimization.

Findings

Good agreement with full configuration interaction for small basis sets

Accurate spectroscopic constants with large basis sets

Effective control of the Fermion sign/phase problem in excited states

Abstract

We show that the recently developed phaseless auxiliary-field quantum Monte Carlo (AFQMC) method can be used to study excited states, providing an alternative to standard quantum chemistry methods. The phaseless AFQMC approach, whose computational cost scales as M^3-M^4 with system size M, has been shown to be among the most accurate many-body methods in ground state calculations. For excited states, prevention of collapse into the ground state and control of the Fermion sign/phase problem are accomplished by the approximate phaseless constraint with a trial wave function. Using the challenging C2 molecule as a test case, we calculate the potential energy curves of the ground and two low-lying singlet excited states. The trial wave function is obtained by truncating complete active space wave functions, with no further optimization. The phaseless AFQMC results using a small basis set are in good agreement with exact full configuration interaction calculations, while those using large basis sets are in good agreement with experimental spectroscopic constants.