Quantum Monte Carlo with variable spins

Abstract

We investigate the inclusion of variable spins in electronic structure quantum Monte Carlo, with a focus on diffusion Monte Carlo with Hamiltonians that include spin-orbit interactions. Following our previous introduction of fixed-phase spin-orbit diffusion Monte Carlo (FPSODMC), we thoroughly discuss the details of the method and elaborate upon its technicalities. We present a proof for an upper-bound property for complex nonlocal operators, which allows for the implementation of T-moves to ensure the variational property. We discuss the time step biases associated with our particular choice of spin representation. Applications of the method are also presented for atomic and molecular systems. We calculate the binding energies and geometry of the PbH and Sn 2 molecules, as well as the electron affinities of the 6p row elements in close agreement with experiments.

Spin-orbit interactions in electronic structure quantum Monte Carlo methods

“…The resulting energy is not necessarily variational, however, the variational property can be recovered with an appropriate modification [13] of the T-moves algorithm [14]. Continuous spin and its updates.…”

“…The Jastrow factor includes electron-ion, electron-electron and, possibly, higher order terms. Since U (R) depends only on the spatial coordinates, the spin integrations in the nonlocal operator can be done explicitly and the rest is similar to the treatment of nonlocality in static spin calculations [11,13]. The short-time approximation for the importance sampled propagator [3,4] is a product of the dynamical and reweighting factors G(R, S; R , S ) = G dyn e −∆t(E loc +E loc −2E T )/2 , where E loc (R, S) = [HΨ T ]/Ψ T .…”

“…Note that the success of the method depends on the local energies to be mildly varying since large fluctuations could cause very large variance of the exponentials and make the sampling very inefficient. More details about this fixed-phase spin-orbit DMC (FPSODMC) method are further elaborated elsewhere [13]. Atomic calculations: excitations in Pb, Bi, and W atoms.…”

Assessing the accuracy of the Jastrow antisymmetrized geminal power in the H4 model system

“…Thanks to well established advances 9,10 in this field, it is possible nowadays to compute the total energy of a given correlated ansatz and to optimize several variational parameters with a computational effort scaling at most with the fourth power of the number of electrons.A good variational ansatz allows a good description of the ground state by energy optimization. Moreover an even better characterization can be obtain by applying the so called diffusion Monte Carlo (DMC) method with the Fixed Node approximation (FNA) 11,12 . Within this projection method it is possible to obtain the lowest energy state constrained to have the same signs of a chosen trial WF, in the configuration space where electron positions and spins are given.…”

“…A good variational ansatz allows a good description of the ground state by energy optimization. Moreover an even better characterization can be obtain by applying the so called diffusion Monte Carlo (DMC) method with the Fixed Node approximation (FNA) 11,12 . Within this projection method it is possible to obtain the lowest energy state constrained to have the same signs of a chosen trial WF, in the configuration space where electron positions and spins are given.…”