Quantum Monte Carlo studies of density functional theory (original) (raw)
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Physical Review B, 2003
We use a variational quantum Monte Carlo realization of the adiabatic connection technique to calculate the most relevant quantities in Hohenberg-Kohn-Sham density functional theory for several strongly inhomogeneous electron-gas systems. Results for the coupling-constant dependence of the exchange-correlation energy, the pair-correlation function, the exchange-correlation hole, and the exchange and correlation energy densities are presented. Comparisons are made with the interaction strength interpolation ͑ISI͒ approximation, the local density approximation ͑LDA͒, the gradient expansion approximation ͑GEA͒, the generalized gradient approximation ͑GGA͒, and the weighted density approximation ͑WDA͒. The coupling-constant dependence of the exchange-correlation energy is accurately described by an ISI model that incorporates information on the strong-interaction limit. Unlike either the LDA or GEA, the WDA is successful in describing the nonlocal structure of the exchange-correlation hole. The LDA errors in the exchange-correlation energy density show a remarkable correlation with the Laplacian of the density. The GGA worsens the error in the integrated exchange-correlation energy as the inhomogeneity of the systems increases. This failure is shared by current meta-GGA functionals and is shown to be caused by the inability of these functionals to describe the LDA overestimation ͑in absolute value͒ of the exchange energy density around density maxima. It is suggested that this effect could be taken into account by including Laplacian terms in semilocal density functionals.
Quantum Monte Carlo analysis of exchange and correlation in the strongly inhomogeneous electron gas
Physical review letters, 2001
We use the variational quantum Monte Carlo method to calculate the density-functional exchange-correlation hole n(xc), the exchange-correlation energy density e(xc), and the total exchange-correlation energy E(xc) of several strongly inhomogeneous electron gas systems. We compare our results with the local density approximation and the generalized gradient approximation. It is found that the nonlocal contributions to e(xc) contain an energetically significant component, the magnitude, shape, and sign of which are controlled by the Laplacian of the electron density.
Monte Carlo implementation of density-functional theory
Physical Review B, 2012
We propose a conceptually easy and relatively straigthforward numerical method for calculating the groundstate properties of many-particle systems based on the Hohenberg-Kohn theorems. In this "density-functional Monte Carlo" method a direct numerical minimization of the energy functional is performed by a Monte Carlo algorithm in which the density is simulated by a distribution of Bernoulli walkers. The total number of particles is conserved by construction, unlike for other implementations of density-functional theory. The feasibility of the method is illustrated by applying it to a nanoshell.
Comments on the quantum Monte Carlo method and the density matrix theory
The Journal of Chemical Physics, 2003
Density matrix theory is implemented in a variational quantum Monte Carlo computation of electronic properties of atoms and molecules. Differences between electronic densities from conventional and density matrix methods are detected. However, calculated properties present similar behavior and partial antisymmetry can be ignored in the cases studied.
Exact-exchange density-functional theory applied to a strongly inhomogeneous electron gas
Physical Review B, 2003
A recently developed quasi two-dimensional exact-exchange formalism within the framework of Density Functional Theory has been applied to a strongly inhomogeneous interacting electron gas, and the results were compared with state-of-the-art Variational Quantum Monte Carlo (VMC) numerical simulations for a three-dimensional electron gas under a strong external potential. The VMC results, extremely demanding from the computational point of view, could be considered as a benchmark for the present theory. We observe a remarkable qualitative and quantitative agreement between both methods from the comparison of the exchange-hole densities, exchange-energy densities, and total exchange-energies per particle. This agreement is increasingly improved with the strength of the external potential when the electron gas becomes quasi-two-dimensional.
Monte Carlo integration of density functional theory: Fermions in a harmonic well
Chemical Physics Letters, 1988
The first numerical results with a recently developed path integration formulation of electron density functional theory are presented. The many-dimensional integral which provides the fundamental expression for the density is presented in a rearranged form amenable to straightforward Monte Carlo estimation. This method is then applied to the case of independent electrons in a harmonic well. The numerical results satisfactorily reproduce the structured electron densities which reflect fermion level filing for this simple problem. These encouraging results also exemplify the algorithmic problems which must be overcome before the present formulation of electron density functional theory shall be of important practical use.
Density-density functionals and effective potentials in many-body electronic structure calculations
2008
We demonstrate the existence of different density-density functionals designed to retain selected properties of the many-body ground state in a non-interacting solution starting from the standard density functional theory ground state. We focus on diffusion quantum Monte Carlo applications that require trial wave functions with optimal Fermion nodes. The theory is extensible and can be used to understand current practices in several electronic structure methods within a generalized density functional framework. The theory justifies and stimulates the search of optimal empirical density functionals and effective potentials for accurate calculations of the properties of real materials, but also cautions on the limits of their applicability. The concepts are tested and validated with a near-analytic model.
2005
We construct a quantum Monte Carlo algorithm for interacting fermions using the two-body density as the fundamental quantity. The central idea is mapping the interacting fermionic system onto an auxiliary system of interacting bosons. The correction term is approximated using correlated wave functions for the interacting system, resulting in an effective potential that represents the nodal surface. We calculate the properties of 3He and find good agreement with experiment and with other theoretical work. In particular, our results for the total energy agree well with other calculations where the same approximations were implemented but the standard quantum Monte Carlo algorithm was used
Path-Integral Monte Carlo Simulation of the Warm Dense Homogeneous Electron Gas
Physical Review Letters, 2013
We perform calculations of the 3D finite-temperature homogeneous electron gas (HEG) in the warm-dense regime (rs ≡ (3/4πn) 1/3 a −1 B = 1.0−40.0 and Θ ≡ T /TF = 0.0625−8.0) using restricted path integral Monte Carlo (RPIMC). Precise energies, pair correlation functions, and structure factors are obtained. For all densities, we find a significant discrepancy between the ground state parameterized local density approximation (LDA) and our results around TF . These results can be used as a benchmark for improved functionals, as well as input for orbital-free DFT formulations.