A new scheme for fixed node diffusion quantum Monte Carlo with pseudopotentials: Improving reproducibility and reducing the trial-wave-function bias

Abstract

Fixed node diffusion quantum Monte Carlo (FN-DMC) is an increasingly used computational approach for investigating the electronic structure of molecules, solids, and surfaces with controllable accuracy. It stands out among equally accurate electronic structure approaches for its favorable cubic scaling with system size, which often makes FN-DMC the only computationally affordable high-quality method in large condensed phase systems with more than 100 atoms. In such systems FN-DMC deploys pseudopotentials to substantially improve efficiency. In order to deal with non-local terms of pseudopotentials, the FN-DMC algorithm must use an additional approximation, leading to the so-called localization error. However, the two available approximations, the locality approximation (LA) and the T-move approximation (TM), have certain disadvantages and can make DMC calculations difficult to reproduce. Here we introduce a third approach, called the determinant localization approximation (DLA). DLA eliminates reproducibility issues and systematically provides good quality results and stable simulations that are slightly more efficient than LA and TM. When calculating energy differences -such as interaction and ionization energies -DLA is also more accurate than the LA and TM approaches. We believe that DLA paves the way to the automization of FN-DMC and its much easier application in large systems.

Variational and diffusion quantum Monte Carlo calculations with the CASINO code

“…143 The recently proposed "determinant locality approximation" in whichV Φ is simply approximated by (Ψ −1 SV Ψ S )Φ, where Ψ S is the Slater part of the wave function, has also been shown to deliver enhanced stability and resilience of the results against noise due to optimization of the Jastrow factor. 144 Both of these schemes are available in CASINO. Plane-wave DFT calculations normally use a Kleinman-Bylander representation of pseudopotentials.…”

Interactions between large molecules pose a puzzle for reference quantum mechanical methods

“…Unfortunately, a multireference ansatz implies a much larger computational effort, which is not yet possible on the large systems discussed here. Second, FN-DMC energies are sensitive to the time-step and we rely on recent improvements in FN-DMC algorithms 36,40 , that enable convergence of time-steps as large as 0.05 a.u. We used 0.03 a.u.…”

“…However, the quality of the Jastrow factor can be nonuniform for the bound complex and the noninteracting fragments, which can introduce a bias at larger time-steps. The recent DLA method in FN-DMC reduces this effect 36 and was applied to the C 60 @ [6]CPPA complex reported in Table 1 and also tested for GGG, C3A, and C2C2PD complexes (see Methods for further details). In all cases, FN-DMC with DLA is in agreement (95% confidence interval) with non-DLA FN-DMC interaction energies.…”

“…First, the energy reported in Fig. 3 and Table 1 is using the recently developed determinant localization approximation (DLA) 36 implementation CASINO v2.13.809 95 . The DLA gives: (i) better numerical stability than the LA algorithm allowing for more statistics to be accumulated, (ii) smaller dependence on the Jastrow factor, and (iii) addresses an indirect issue related to the use of non-local pseudopotentials.…”

“…The stochastic uncertainty associated with any DMC evaluation is inversely proportional to the square root of the sampling. In order to make this propagation efficient for an electronic wavefunction a few approximations are typically employed: the fixed node (FN) constraint 15 , the use of pseudopotentials [36][37][38][39] , and solutions enhancing the stability of walker populations 40,41 . In non-covalent interactions, the challenge for FN-DMC is to provide precise and accurate evaluations of the interaction energy E int , despite E int being a tiny fraction of the total energy, e.g., it is circa 1/10 4 of the total energy in the C 60 @ [6]CPPA complex.…”