Optimized wave functions for quantum Monte Carlo studies of atoms and solids

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

doi:10.1103/physrevb.53.9640

Cited by 61 publications

(64 citation statements)

References 22 publications

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“…However, because of its large band-gap, we expect that a single Slater determinant will give a good description of the nodal surface of MgO. The function J appearing in the Jastrow factor is a sum of parametrized one-body and two-body terms [20], the latter being designed to satisfy the cusp conditions. The free parameters in J are determined by requiring that the variance of the local energy in VMC be as small as possible [21,22].…”

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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“…The techniques employed are similar to those described elsewhere. 6,13 We use variational SlaterJastrow wave functions containing 24 parameters, 13 which are optimized by minimizing the variance of the energy. 14 The single particle functions were obtained from LDA calculations and were the same as those used in Fig.…”

Section: ͑1͒mentioning

confidence: 99%

Elimination of Coulomb finite-size effects in quantum many-body simulations

et al. 1997

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A model interaction is introduced for quantum many-body simulations of Coulomb systems using periodic boundary conditions. The interaction gives much smaller finite size effects than the standard Ewald interaction and is also much faster to compute. Variational quantum Monte Carlo simulations of diamond-structure silicon with up to 1000 electrons demonstrate the effectiveness of our method. ͓S0163-1829͑97͒51408-1͔Many-body simulation techniques such as the variational 1 and diffusion 2 quantum Monte Carlo ͑QMC͒ methods are capable of yielding highly accurate results for correlated systems. Large systems are normally modeled using a finite simulation cell subject to periodic boundary conditions. This, however, introduces ''finite size effects'' which are often very important, particularly for systems with long ranged interactions such as the Coulomb interaction. In this paper we introduce a method for dealing with long ranged interactions in quantum many-body simulations which greatly reduces these finite size effects. This method is a generalization of one we developed earlier for homogeneous systems such as jellium. 3 We illustrate our method with variational QMC calculations on diamond-structure silicon. The ideas described in this paper are of wide generality and can be applied to other quantum many-body schemes, such as the HF and ''GW'' ͑Ref. 4͒ methods, and to long ranged interactions other than the Coulomb interaction.The finite size effects encountered in QMC calculations for electronic systems can be divided into two terms: ͑i͒ the independent particle finite size effect ͑IPFSE͒ and ͑ii͒ the Coulomb finite size effect ͑CFSE͒. 3,5 The IPFSE and CFSE are most easily defined with reference to results of local density approximation ͑LDA͒ calculations. The IPFSE is the difference between the LDA energies per atom in the finite and infinite systems and the CFSE is the remainder of the finite size error. Recently we presented a method 6 for reducing the IPFSE in insulating systems by using the ''special k-points'' method borrowed from band-structure theory. 7 This method reduces the IPFSE by an order of magnitude and leaves the CFSE as the dominant finite size effect. The CFSE, which is the subject of this work, arises from the long range of the Coulomb interaction and is therefore of wide significance in many-body simulations.We illustrate the CFSE by comparing the results of LDA and Hartree-Fock calculations. To define the LDA and HF energies for simulation cells with periodic boundary conditions we must specify the form of the model electronelectron interaction used. This interaction acts only between the charges within the simulation cell, but is intended to model the forces that would act in the center of an infinite array of identical copies of that cell. Unfortunately, sums of Coulomb 1/r potentials in extended systems are only conditionally convergent, and hence these forces are not uniquely defined until the boundary conditions at infinity have been specified. It is standard to calculate the potential...

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“…A detailed description of this form of wave function can be found in Ref. [9]. Our VMC calculations follow the methodology described in Ref.…”

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Quantum Monte Carlo Investigation of Exchange and Correlation in Silicon

et al. 1997

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Realistic many-body wave functions for diamond-structure silicon are constructed for different values of the Coulomb coupling constant. The coupling-constant-integrated pair correlation function, the exchange-correlation hole, and the exchange-correlation energy density are calculated and compared with those obtained from the local density and average density approximations. We draw conclusions about the reasons for the success of the local density approximation and suggest a method for testing the effectiveness of exchange-correlation functionals. [S0031-9007(97) The standard computational tool of electronic-structure theory for solids is the local density approximation (LDA) within density-functional theory [1,2]. This has been applied successfully to systems, including those with quite rapidly varying densities, even though the LDA is based on approximating the system as locally homogeneous. However, when discrepancies between experiment and theory in solids arise it is difficult to improve upon the LDA systematically, although several schemes have been devised [3,4]. Since there is currently limited guidance for making improvements, we have used coupling constant integration and variational quantum Monte Carlo (VMC) techniques to calculate the quantities of central importance in density functional theory for a realistic inhomogeneous anisotropic solid. We have calculated the coupling-constant-integrated pair correlation function, the exchange-correlation hole, and the exchange-correlation energy density of diamond-structure silicon. In this Letter we describe our approach along with the insights gained by comparing these quantities with those from the LDA and the average density approximation (ADA) [3].In Kohn-Sham density functional theory there is an exact relationship [5] between the exchange-correlation energy, E xc , and the ground state many-electron wave functions C l associated with the different values of the Coulomb-coupling constant, l. The electronic density of each C l must equal the density at full coupling ͑l 1͒. This condition can be ensured by adding an additional external potential y l ͑r͒ to the many-body Hamiltonian in which the electron-electron interaction is multiplied by l. The coupling-constant-integrated pair correlation function g͑r, r 0 ͒, the exchange-correlation hole r xc ͑r, r 0 ͒, and the exchange-correlation energy density e xc ͑r͒ are related by [6] e xc ͑r͒ n͑r͒ 2 Z dr 0 r xc ͑r, r 0 ͒ jr 2 r 0 j ,r xc ͑r, r 0 ͒ n͑r 0 ͒ ͓g͑r, r 0 ͒ 2 1͔ .(2) The total exchange-correlation energy, E xc , is obtained by integrating e xc ͑r͒ over all space. Writing g in terms of its constituent spin componentsyields an equation involving the many-electron wave functions,where N is the number of electrons, n a ͑r͒ is the electronic density for spin a, and x i denotes the ith electron's spatial and spin components. In an unpolarized system such as silicon Eq. (3) reduces to g 1 4 P a,b g ab . Together Eqs. (1)-(4) specify the exact relationship between e xc ͑r͒ and the many-body wave function...

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Optimized wave functions for quantum Monte Carlo studies of atoms and solids

Cited by 61 publications

References 22 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

Elimination of Coulomb finite-size effects in quantum many-body simulations

Quantum Monte Carlo Investigation of Exchange and Correlation in Silicon

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