Finite-size effects and Coulomb interactions in quantum Monte Carlo calculations for homogeneous systems with periodic boundary conditions

Fraser, Louisa; Foulkes, W. M. C.; Rajagopal, G.; Needs, R. J.; Kenny, Steven D.; Williamson, Andrew

doi:10.1103/physrevb.53.1814

Cited by 302 publications

(271 citation statements)

References 26 publications

(34 reference statements)

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“…To improve this convergence, we follow the common practice [33] of correcting for this error by using separate DFT calculations: we add to the DMC energies the difference ∆E Γ→k between the DFT-LDA energy calculated with a very large set of k-points and the DFT-LDA energy calculated using the same sampling as in the DMC calculation. The question of correcting for finite size errors in the Coulomb energy has been addressed in recent papers [28,29,30], and a method known as the model periodic Coulomb (MPC) interaction has been developed. The finite size error in the Ewald interaction energy arises from the exchange-correlation energy, which can be written as the interaction of the electrons with their exchange-correlation holes.…”

Section: Techniquesmentioning

confidence: 99%

Quantum Monte Carlo calculations of the structural properties and the B1-B2 phase transition of MgO

et al. 2005

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We report diffusion Monte Carlo (DMC) calculations on MgO in the rock-salt and CsCl structures. The calculations are based on Hartree-Fock pseudopotentials, with the single-particle orbitals entering the correlated wave function being represented by a systematically convergeable cubic-spline basis. Systematic tests are presented on system-size errors using periodically repeating cells of up to over 600 atoms. The equilibrium lattice parameter of the rock-salt structure obtained within DMC is almost identical to the Hartree-Fock result, which is close to the experimental value. The DMC result for the bulk modulus is also in good agreement with the experimental value. The B1-B2 transition pressure (between the rock-salt and CsCl structures) is predicted to be just below 600 GPa, which is beyond the experimentally accessible range, in accord with other predictions based on Hartree-Fock and density functional theories.

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Section: Techniquesmentioning

confidence: 99%

Quantum Monte Carlo calculations of the structural properties and the B1-B2 phase transition of MgO

et al. 2005

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“…1. This allows us to see explicitly that in the case of solids and finite systems MPC improves convergence considerably (over the more traditional Ewald scheme), due to the fact that for such systems MPC yields the correct quadratic behavior of S k as k → 0.…”

Section: Discussionmentioning

confidence: 91%

“…[1][2][3][4][5] As QMC calculations of solids need to be carried out within a supercell, the Coulomb interaction is typically replaced by the so-called Ewald interaction that is compatible with the supercell geometry. 6 This, in turn, is equivalent to dealing with an infinite system with a periodically repeated exchange-correlation (xc) hole.…”

Section: Introductionmentioning

confidence: 99%

Momentum-space finite-size corrections for quantum Monte Carlo calculations

2012

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Extended solids are frequently simulated as finite systems with periodic boundary conditions, which due to the long-range nature of the Coulomb interaction may lead to slowly decaying finite-size errors. In the case of quantum Monte Carlo simulations, which are based on real space, both real-space and momentum-space solutions to this problem exist. Here, we describe a hybrid method which using real-space data models the spherically averaged structure factor in momentum space. We show that (i) by integration our hybrid method exactly maps onto the real-space model periodic Coulomb-interaction (MPC) method and (ii) therefore our method combines the best of both worlds (real space and momentum space). One can use known momentum-resolved behavior to improve convergence where MPC fails (e.g., at surfacelike systems). In contrast to pure momentum-space methods, our method only deals with a simple single-valued function and hence better lends itself to interpolation with exact small-momentum data as no directional information is needed. By virtue of integration, the resulting finite-size corrections can be written as an addition to MPC.

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“…The k-point shift (from Γ to L), similar to the "special k-point method" in DFT, frequently works well for insulators. 59,60 The MPC (model periodic Coulomb interaction) 61,62 and CCMH (Chiesa, Ceperley, Martin, and Holzmann) 63 schemes are known to be effective two-body schemes.…”

Section: Introductionmentioning

confidence: 99%

Diffusion Monte Carlo Study of Para-Diiodobenzene Polymorphism Revisited

Hongo

Watson

Iitaka

et al. 2015

J. Chem. Theory Comput.

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We revisit our investigation of the diffusion Monte Carlo (DMC) simulation of p-DIB molecular crystal polymorphism. [J. Phys. Chem. Lett. 2010Lett. , 1, 1789Lett. -1794 We perform, for the first time, a rigorous study of finite-size effects and choice of nodal surface on the prediction of polymorph stability in molecular crystals using fixed-node DMC. Our calculations are the largest which are currently feasible using the resources of the K computer and provide insights into the formidable challenge of predicting such properties from first principles. In particular, we show that finite-size effects can influence the trial nodal surface of a small (1×1×1) simulation cell considerably. We therefore repeated our DMC simulations with a 1×3×3 simulation cell, which is the largest such calculation to date. We used a DFT nodal surface generated with the PBE functional and we accumulated statistical samples with ∼ 6.4 × 10 5 core-hours for each polymorph. Our final results predict a polymorph stability consistent with experiment, but indicate that results in our previous paper were somewhat fortuitous.We analyze the finite-size errors using model periodic Coulomb (MPC) interactions and kinetic energy corrections, according to the CCMH scheme of Chiesa, Ceperley, Martin, and Holzmann. We investigate the dependence of the finite-size errors on different aspect ratios of the simulation cell (k-mesh convergence) in order to understand how to choose an appropriate ratio for the DMC calculations. Even in the most expensive simulations currently possible, we show that the finite size errors in the DMC total energies are far larger than the energy difference between the two polymorphs, although error cancellation means that the polymorph prediction is accurate. Finally, we found that the T -move scheme is essential for these massive DMC simulations in order to circumvent population explosions and large time-step biases.

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Finite-size effects and Coulomb interactions in quantum Monte Carlo calculations for homogeneous systems with periodic boundary conditions

Cited by 302 publications

References 26 publications

Quantum Monte Carlo calculations of the structural properties and the B1-B2 phase transition of MgO

Quantum Monte Carlo calculations of the structural properties and the B1-B2 phase transition of MgO

Momentum-space finite-size corrections for quantum Monte Carlo calculations

Diffusion Monte Carlo Study of Para-Diiodobenzene Polymorphism Revisited

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