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Bulletin of the American Physical Society

Spin-Orbit interactions in auxiliary field diffusion Monte Carlo

Jie Zhang, Kevin E. Schmidt

Published Mar 31, 2012• 0 citations
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The shifted-contour auxiliary-field Monte Carlo (SCAFMC) approach has been recently developed by Rom, Charutz and Neuhauser as an extension of the auxiliary-field Monte Carlo (AFMC) method. AFMC replaces the difficult fully interacting electrons problem by an ensemble of simpler problems where the electrons interact with a fluctuating electric field but not with each other. SCAFMC is based on shifting the auxiliary-field contour of integration to pass through the (imaginary) stationary point, leading to numerical stability at long propagation times. The new approach converges to the full CI energy in electronic structure calculations (both ground and low-lying excited states). Here we expand the application of SCAFMC from atomic to molecular problems. First, we calculate ground-state energies of a highly correlated transition-metal system (Cr2) with a moderate (12 orbitals) active space size, and demonstrate that SCAFMC is able to extract the energies accurately. In addition, we use SCAFMC to calculate a C–C bond-stretch energy in ethane with complete active spaces of up to 28 orbitals.

The Journal of Chemical Physics•Nov 15, 1998•26 citations
We present two diffusion Monte Carlo (DMC) algorithms for systems of ultracold quantum gases featuring synthetic spin-orbit interactions. The first one is a spin-integrated DMC method which provides fixed-phase energy estimates. The second one is a discrete spin generalisation of the T-moves spin-orbit DMC [Melton et al., J. Chem. Phys. 144, 244113 (2016)], which provides an upper bound to the fixed-phase energy. The former is a more accurate method but it is restricted to spin-independent two-body interactions. We report a comparison between both algorithms for different systems. As a check of the efficiency of both methods, we compare the DMC energies with results obtained with other numerical methods, finding agreement between both estimations.
The shifted-contour auxiliary-field Monte Carlo (SCAFMC) approach has been recently developed by Rom, Charutz and Neuhauser as an extension of the auxiliary-field Monte Carlo (AFMC) method. AFMC replaces the difficult fully interacting electrons problem by an ensemble of simpler problems where the electrons interact with a fluctuating electric field but not with each other. SCAFMC is based on shifting the auxiliary-field contour of integration to pass through the (imaginary) stationary point, leading to numerical stability at long propagation times. The new approach converges to the full CI energy in electronic structure calculations (both ground and low-lying excited states). Here we expand the application of SCAFMC from atomic to molecular problems. First, we calculate ground-state energies of a highly correlated transition-metal system (Cr2) with a moderate (12 orbitals) active space size, and demonstrate that SCAFMC is able to extract the energies accurately. In addition, we use SCAFMC to calculate a C–C bond-stretch energy in ethane with complete active spaces of up to 28 orbitals.