Spin Purification in Full-CI Quantum Monte Carlo via a First-Order Penalty Approach

In this Letter we demonstrate that a first-order spin penalty scheme can be efficiently applied to the Slater determinant based Full-CI Quantum Monte-Carlo (FCIQMC) algorithm, as a practical route towards spin purification. Two crucial applications are presented to demonstrate the validity and robustness of this scheme; the 1∆g ← 3Σg vertical excitation in O2 , and key spin gaps in a [Mn3 O4]3+ cluster. In the absence of a robust spin adaptation/purification technique, both applications would be unattainable by Slater determinant based ground state methods, with any starting wave function collapsing into the higher-spin ground state during the optimization. This strategy can be coupled to other algorithms that use FCIQMC as configuration interaction eigensolver, including the Stochastic Generalized Active Space, the similarity-transformed FCIQMC and second-order perturbation theory approaches. Moreover, in contrast to the GUGA-FCIQMC technique, this strategy features both spin projection and total spin adaptation, making it appealing when solving anisotropic Hamiltonians.