Full Wave Function Optimization with Quantum Monte Carlo—A Study of the Dissociation Energies of ZnO, FeO, FeH, and CrS

Abstract

The dissociation energies of four transition metal dimers are determined using diffusion Monte Carlo. The Jastrow, CI, and molecular orbital parameters of the wave function are both partially and fully optimized with respect to the variational energy. The pivotal role is thereby ascribable to the optimization of the molecular orbital parameters of a complete active space wave function in the presence of a Jastrow correlation function. Excellent results are obtained for ZnO, FeO, FeH, and CrS. In addition, potential energy curves are computed for the first three compounds at multi-reference diffusion Monte Carlo (MR-DMC) level, from which spectroscopic constants such as the equilibrium bond distance, the harmonic frequency, and the anharmonicity are extracted. All of those quantities agree well with the experiment. Furthermore, it is shown for CrS that a restricted active space calculation can yield improved initial orbitals by including 1 single and double excitations from the original active space into a set of virtual orbitals.We demonstrated in this study that the fixed-node error in DMC can be systematically reduced for multi-reference systems by orbital optimization in compact active spaces.While DMC calculations with a large number of determinants are possible and very accurate, our results demonstrate that compact wave functions may be sufficient in order to obtain accurate nodal surfaces, which determine the accuracy of DMC, even in the case of transition metal compounds.

Toward Compact Selected Configuration Interaction Wave Functions with Quantum Monte Carlo─A Case Study of C2

“…The Jastrow correlation function having a nonzero overlap with the determinant expansion, it is essential to reoptimize the expansion coefficients (as well as the MO parameters). This is corroborated by a previous study of ours which focused on the computation of accurate dissociation energies for transition metal dimers 65 as well as by many other works. 18,31,33,66 It should be noted, that the Jas+CI curves are much steeper than the ones for the fully optimized wave functions, which seem to be close to convergence already.…”

“…This was already shown by Dash et al in their work on 1,3-trans-butadiene. 83 The comparison between CIPSI and CAS justifies the transition from CAS initial wave functions�used in several of our previous studies 65,79 �to CIPSI expansions, leaving behind the limitations of CASSCF and paving the way toward the investigation of larger systems.…”

Orbital optimized unitary coupled cluster theory for quantum computer

“…In addition, the measurement introduces statistical errors. In that sense, OO-UCCD (OO-VQE) is related to the multiconfigurational self-consistent field methods; these are based on stochastic electron correlation approaches such as full configuration interaction quantum Monte Carlo [56,57], the heat-bath CI [58], and variational Monte Carlo [59][60][61][62][63][64]. The costs and errors owing to the measurements can be reduced using simultaneous measurements and/or other techniques.…”

Taming the fixed-node error in diffusion Monte Carlo via range separation

“…73 Orbitals obtained in the presence of a Jastrow factor are generally superior to KS orbitals. 63,[74][75][76] The description of electron correlation within DFT is very different from correlated methods such as FCI or CC. As mentioned above, within KS-DFT, one solves a mean-field problem with a modified potential incorporating the effects of electron correlation while maintaining the exact ground state density, whereas in correlated methods the real Hamiltonian is used and the electron-electron interaction is explicitly considered.…”