Different thermodynamic pathways to the solvation free energy of a spherical cavity in a hard sphere fluid

Chen, Yng-Gwei; Weeks, John D.

doi:10.1063/1.1563592

Cited by 10 publications

(35 citation statements)

References 23 publications

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“…Density pathways can also be used for atomic and molecular systems to check the accuracy of the V T s used, since results using the exact V T s would be independent of path. 27,28 …”

Section: A Herring's Pathwaymentioning

confidence: 98%

“…Many possible pathways can be used to construct T s ͓͔ by functional integration of V T s ͑r ; ͓͔͒. 27,28 If the exact V T s ͑r ; ͓͔͒ is used and the integration is carried out exactly, then all pathways would give the same exact result for T s ͓͔. However, when an approximate V T s ͑r ; ͓͔͒ is used, different pathways will give different results for the kinetic energy.…”

Section: Pathways From V T S "R; † ‡… To T S † ‡mentioning

confidence: 99%

“…But this "thermodynamic inconsistency" is small if reasonably good approximations are used, since the integration tends to smooth out local errors that may exist in the density. 7,28 More problematic is the fact that most pathways require additional results for partially coupled systems as the external field or density perturbation is gradually turned on, which adds to the computational burden. In particular, most earlier work has used a "potential energy pathway," where the external potential is scaled by a coupling parameter.…”

Section: Pathways From V T S "R; † ‡… To T S † ‡mentioning

confidence: 99%

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Orbital-free density functional theory: Kinetic potentials andab initiolocal pseudopotentials

Chai

Weeks

2007

Phys. Rev. B

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In the density functional ͑DF͒ theory of Kohn and Sham, the kinetic energy of the ground state of a system of noninteracting electrons in a general external field is calculated using a set of orbitals. Orbital-free methods attempt to calculate this directly from the electron density by approximating the universal but unknown kinetic energy density functional. However, simple local approximations are inaccurate, and it has proven very difficult to devise generally accurate nonlocal approximations. We focus instead on the kinetic potential, the functional derivative of the kinetic energy DF, which appears in the Euler equation for the electron density. We argue that the kinetic potential is more local and more amenable to simple physically motivated approximations in many relevant cases, and describe two pathways by which the value of the kinetic energy can be efficiently calculated. We propose two nonlocal orbital free kinetic potentials that reduce to known exact forms for both slowly varying and rapidly varying perturbations and also reproduce exact results for the linear response of the density of the homogeneous system to small perturbations. A simple and systematic approach for generating accurate and weak ab initio local pseudopotentials which produce a smooth slowly varying valence component of the electron density is proposed for use in orbital-free DF calculations of molecules and solids. The use of these local pseudopotentials further minimizes the possible errors from the kinetic potentials. Our theory yields results for the total energies and ionization energies of atoms, and for the shell structure in the atomic radial density profiles that are in very good agreement with calculations using the full Kohn-Sham theory.

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“…Density pathways can also be used for atomic and molecular systems to check the accuracy of the V T s used, since results using the exact V T s would be independent of path. 27,28 …”

Section: A Herring's Pathwaymentioning

confidence: 98%

Section: Pathways From V T S "R; † ‡… To T S † ‡mentioning

confidence: 99%

Section: Pathways From V T S "R; † ‡… To T S † ‡mentioning

confidence: 99%

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Orbital-free density functional theory: Kinetic potentials andab initiolocal pseudopotentials

Chai

Weeks

2007

Phys. Rev. B

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“…[34]. Experience with the classical analogue of the KP method applied to nonuniform hard sphere fluids [46] has shown that errors from this path dependence can be small (e.g., less than one percent for the surface tension at a hard wall) when used with particular pathways that do not excessively weight regions poorly described by an approximate theory for the nonuniform density.…”

Section: Density Pathwaymentioning

confidence: 99%

“…[34], an integration pathway is needed to determine the value of T s [ρ] from a given V Ts (r; [ρ]) [43,44,45,46]. If the exact V Ts (r; [ρ]) is used and the integration is carried out exactly, then all pathways would give the same exact result for T s [ρ].…”

Section: Density Pathwaymentioning

confidence: 99%

Orbital-free density functional theory: Linear scaling methods for kinetic potentials, and applications to solid Al and Si

Chai¹,

Lignères²,

Ho³

et al. 2009

Chemical Physics Letters

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In orbital-free density functional theory the kinetic potential (KP), the functional derivative of the kinetic energy density functional, appears in the Euler equation for the electron density and may be more amenable to simple approximations. We study properties of two solid-state systems, Al and Si, using two nonlocal KPs that gave good results for atoms. Very accurate results are found for Al, but results for Si are much less satisfactory, illustrating the general need for a better treatment of extended covalent systems. A different integration pathway in the KP formalism may prove useful in attacking this fundamental problem.

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Modified Statistical Treatment of Kinetic Energy in the Thomas−Fermi Model

Chai

Weeks

2004

J. Phys. Chem. B

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We try to improve the Thomas-Fermi model for the total energy and electron density of atoms and molecules by directly modifying the Euler equation for the electron density, which we argue is less affected by nonlocal corrections. Here we consider the simplest such modification by adding a linear gradient term to the Euler equation. For atoms, the coefficient of the gradient term can be chosen so that the correct exponential decay constant far from the nucleus is obtained. This model then gives a much improved description of the electron density at smaller distances, yielding in particular a finite density at the nucleus that is in good qualitative agreement with exact results. The cusp condition differs from the exact value by a factor of two. Values for the total energy of atomic systems, obtained by coupling parameter integration of the densities given by the Euler equation, are about as accurate as those given by very best Thomas-Fermi-Weizsäcker models, and the density is much more accurate. Possible connections to orbital-free methods for the kinetic-energy functional in density functional theory are discussed.

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Different thermodynamic pathways to the solvation free energy of a spherical cavity in a hard sphere fluid

Cited by 10 publications

References 23 publications

Orbital-free density functional theory: Kinetic potentials andab initiolocal pseudopotentials

Orbital-free density functional theory: Kinetic potentials andab initiolocal pseudopotentials

Orbital-free density functional theory: Linear scaling methods for kinetic potentials, and applications to solid Al and Si

Modified Statistical Treatment of Kinetic Energy in the Thomas−Fermi Model

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