Left-right correlation energy

Handy, Nicholas C.; Cohen, Aron J.

doi:10.1080/00268970010018431

Cited by 1,549 publications

(1,184 citation statements)

References 26 publications

(19 reference statements)

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“…The settings for both runs were identical and started from the same well-equilibrated configuration. The influence of the XC functional on the properties calculated was investigated in a series of additional runs using a variety of different semilocal XC functionals 86,90,[115][116][117] . The statistics in each of these reference runs were accumulated for at least 30 ps after an equilibration of 20 ps, resulting in more than 1 ns of AIMD simulations.…”

Section: Liquid Water a Structural And Dynamical Properties Of Lmentioning

confidence: 99%

Microscopic properties of liquid water from combined ab initio molecular dynamics and energy decomposition studies

Khaliullin

Kühne

2013

Phys. Chem. Chem. Phys.

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The application of newly developed first-principle modeling techniques to liquid water deepens our understanding of the microscopic origins of its unusual macroscopic properties and behaviour. Here, we review two novel ab initio computational methods: second-generation Car-Parrinello molecular dynamics and decomposition analysis based on absolutely localized molecular orbitals. We show that these two methods in combination not only enable ab initio molecular dynamics simulations on previously inaccessible time and length scales, but also provide unprecedented insights into the nature of hydrogen bonding between water molecules. We discuss recent applications of these methods to water clusters and bulk water. CONTENTS

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Section: Liquid Water a Structural And Dynamical Properties Of Lmentioning

confidence: 99%

Microscopic properties of liquid water from combined ab initio molecular dynamics and energy decomposition studies

Khaliullin

Kühne

2013

Phys. Chem. Chem. Phys.

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“…After a conference talk some years ago on the functionals OPTX 83 and OLYP 84 that do not respect the UEG limit, Nicholas Handy verbalized his own choice as follows: "I don't know about you chaps in America, but at Cambridge we have never been able to synthesize jellium!" It should be added, though, that the performance of OPTX/OLYP deteriorates for heavy atoms because the LDA does become exact, in a relative-error sense, in the infinite Z limit.…”

Section: Other Strokesmentioning

confidence: 99%

Perspective: Fifty years of density-functional theory in chemical physics

Becke

2014

The Journal of Chemical Physics

1,319

964

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Since its formal inception in 1964-1965, Kohn-Sham density-functional theory (KS-DFT) has become the most popular electronic structure method in computational physics and chemistry. Its popularity stems from its beautifully simple conceptual framework and computational elegance. The rise of KS-DFT in chemical physics began in earnest in the mid 1980s, when crucial developments in its exchange-correlation term gave the theory predictive power competitive with welldeveloped wave-function methods. Today KS-DFT finds itself under increasing pressure to deliver higher and higher accuracy and to adapt to ever more challenging problems. If we are not mindful, however, these pressures may submerge the theory in the wave-function sea. KS-DFT might be lost. I am hopeful the Kohn-Sham philosophical, theoretical, and computational framework can be preserved. This Perspective outlines the history, basic concepts, and present status of KS-DFT in chemical physics, and offers suggestions for its future development. © 2014 AIP Publishing LLC.

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“…Thus, the three terms in the last line of Eq. (7) represent respectively exact exchange, the fully nonlocal part of correlation including "left-right" [56] static or near-degeneracy correlation important in molecules, and the semilocal dynamic correlation. Instead of thinking of a(r) as the fraction of exact exchange mixed locally with semilocal exchange, it is more correct to think of [1 − a(r)] as the fraction of the nonlocal energy difference [ǫ sl x (r) − ǫ ex x (r)] added to exact exchange plus semilocal correlation.…”

Section: Local Hybrid Form Of the Hyper-ggamentioning

confidence: 99%

Density functional with full exact exchange, balanced nonlocality of correlation, and constraint satisfaction

et al. 2008

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We construct a nonlocal density functional approximation with full exact exchange, while preserving the constraint-satisfaction approach and justified error cancellations of simpler semilocal functionals. This is achieved by interpolating between different approximations suitable for two extreme regions of the electron density. In a "normal" region, the exact exchange-correlation hole density around an electron is semilocal because its spatial range is reduced by correlation and because it integrates over a narrow range to −1. These regions are well described by popular semilocal approximations (many of which have been constructed nonempirically), because of proper accuracy for a slowly-varying density or because of error cancellation between exchange and correlation. "Abnormal" regions, where nonlocality is unveiled, include those in which exchange can dominate correlation (one-electron, nonuniform high-density, and rapidly-varying limits), and those open subsystems of fluctuating electron number over which the exact exchange-correlation hole integrates to a value greater than −1. Regions between these extremes are described by a hybrid functional mixing exact and semilocal exchange energy densities locally, i.e., with a mixing fraction that is a function of position r and a functional of the density. Because our mixing fraction tends to 1 in the high-density limit, we employ full exact exchange according to the rigorous definition of the exchange component of any exchange-correlation energy functional. Use of full exact exchange permits the satisfaction of many exact constraints, but the nonlocality of exchange also requires balanced nonlocality of correlation. We find that this nonlocality can demand at least five empirical parameters, corresponding roughly to the four kinds of abnormal regions. Our local hybrid functional is perhaps the first accurate fourth-rung density functional or hyper-generalized gradient approximation, with full exact exchange, that is size-consistent in the way that simpler functionals are. It satisfies other known exact constraints, including exactness for all one-electron densities, and provides an excellent fit to the 223 molecular enthalpies of formation of the G3/99 set and the 42 reaction barrier heights of the BH42/03 set, improving both (but especially the latter) over most semilocal functionals and global hybrids. Exact constraints, physical insights, and paradigm examples hopefully suppress "overfitting".

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Left-right correlation energy

Cited by 1,549 publications

References 26 publications

Microscopic properties of liquid water from combined ab initio molecular dynamics and energy decomposition studies

Microscopic properties of liquid water from combined ab initio molecular dynamics and energy decomposition studies

Perspective: Fifty years of density-functional theory in chemical physics

Density functional with full exact exchange, balanced nonlocality of correlation, and constraint satisfaction

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