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We show that the recently developed phaseless auxiliary-field quantum MonteCarlo (AFQMC) method can be used to study excited states, providing analternative to standard quantum chemistry methods. The phaseless AFQMCapproach, whose computational cost scales as M^3-M^4 with system size M, hasbeen shown to be among the most accurate many-body methods in ground statecalculations. For excited states, prevention of collapse into the ground stateand control of the Fermion sign/phase problem are accomplished by theapproximate phaseless constraint with a trial wave function. Using thechallenging C2 molecule as a test case, we calculate the potential energycurves of the ground and two low-lying singlet excited states. The trial wavefunction is obtained by truncating complete active space wave functions, withno further optimization. The phaseless AFQMC results using a small basis setare in good agreement with exact full configuration interaction calculations,while those using large basis sets are in good agreement with experimentalspectroscopic constants.

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