Quantum Monte Carlo calculations of the surface energy of an electron gas

Wood, Ben; Hine, Nicholas D. M.; Foulkes, W. M. C.; Garcı́a-González, P.

doi:10.1103/physrevb.76.035403

Cited by 39 publications

(43 citation statements)

References 34 publications

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“…Figure 1 shows surface energy enhancements relative to LSDA. The likely "range of the possible" for e surf xc extends from TPSS meta-GGA [3,7] or RPA+ [23] at the low end of what is possible (in agreement with the most recent Quantum Monte Carlo calculations [24]) to the RPA-like Pitarke-Perdew (PP) [25] value at the high end. The TPSS value probably provides the best value that a GGA should try to achieve.…”

supporting

confidence: 80%

Restoring the Density-Gradient Expansion for Exchange in Solids and Surfaces

et al. 2008

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supporting

confidence: 80%

Restoring the Density-Gradient Expansion for Exchange in Solids and Surfaces

et al. 2008

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“…Surface correlation energies 18 and surface exchange-correlation energies 19,20 have been obtained using extrapolated values to infinite size. In general, the values obtained for correlation surface energies obtained with spheres are consistent with the latest DMC results for jellium slabs 21 and other methods, but differ to some extent from the original DMC results from slab geometries 22 .…”

Section: Pacs Numberssupporting

confidence: 76%

Simple impurity embedded in a spherical jellium: Approximations of density functional theory compared to quantum Monte Carlo benchmarks

et al. 2011

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We study the electronic structure of a spherical jellium in the presence of a central Gaussian impurity. We test how well the resulting inhomogeneity effects beyond spherical jellium are reproduced by several approximations of density functional theory (DFT). Four rungs of Perdew's ladder of DFT functionals, namely local density approximation (LDA), generalized gradient approximation (GGA), meta-GGA and orbital-dependent hybrid functionals are compared against our quantum Monte Carlo (QMC) benchmarks. We identify several distinct transitions in the ground state of the system as the electronic occupation changes between delocalized and localized states. We examine the parameter space of realistic densities (1 ≤ rs ≤ 5) and moderate depths of the Gaussian impurity (Z < 7). The selected 18 electron system (with closed-shell ground state) presents 1d → 2s transitions while the 30 electron system (with open-shell ground state) exhibits 1f → 2p transitions. For the former system, the accuracy for the transitions is clearly improving with increasing sophistication of functionals with meta-GGA and hybrid functionals having only small deviations from QMC. However, for the latter system, we find much larger differences for the underlying transitions between our pool of DFT functionals and QMC. We attribute these failures to an insufficiently accurate treatment of exchange by these functionals. Additionally, we amplify the inhomogeneity effects by creating the system with spherical shell which leads to even larger errors in DFT approximations.

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“…This unexpected success of the LD approximation (for exchange and correlation) suggested that we try to understand what was behind it. Quantum Monte Carlo calculations confirmed the LD results many years later (Wood et al, 2007). 21 It has been shown (Colonna and Savin, 1999) that results for the He and Be series atoms using the two schemes are similar.…”

mentioning

confidence: 74%

Density functional theory: Its origins, rise to prominence, and future

2015

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In little more than 20 years, the number of applications of the density functional (DF) formalism in chemistry and materials science has grown in an astonishing fashion. The number of publications alone shows that DF calculations make up a huge success story, and many younger colleagues are surprised to learn that the widespread application of density functional methods, particularly in chemistry, began only after 1990. This is indeed unexpected, because the origins are usually traced to the papers of Hohenberg, Kohn, and Sham more than a quarter of a century earlier. The DF formalism, its applications, and prospects were reviewed for this journal in 1989. About the same time, the combination of DF calculations with molecular dynamics promised to provide an efficient way to study structures and reactions in molecules and extended systems. This paper reviews the development of density-related methods back to the early years of quantum mechanics and follows the breakthrough in their application after 1990. The two examples from biochemistry and materials science are among the many current applications that were simply far beyond expectations in 1990. The reasons why-50 years after its modern formulation and after two decades of rapid expansionsome of the most cited practitioners in the field are concerned about its future are discussed.

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Quantum Monte Carlo calculations of the surface energy of an electron gas

Cited by 39 publications

References 34 publications

Restoring the Density-Gradient Expansion for Exchange in Solids and Surfaces

Restoring the Density-Gradient Expansion for Exchange in Solids and Surfaces

Simple impurity embedded in a spherical jellium: Approximations of density functional theory compared to quantum Monte Carlo benchmarks

Density functional theory: Its origins, rise to prominence, and future

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