Monte Carlo integration of density functional theory: Fermions in a harmonic well

Hoffman, Gary G.; Pratt, Lawrence R.; Harris, R. Adron

doi:10.1016/0009-2614(88)87278-6

Cited by 11 publications

(11 citation statements)

References 11 publications

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“…The results above are more fully discussed elsewhere (Hoffman et al 1988;Pratt et al 1990;). The derivation of (1) indicates that the p oo limit should provide the correct density.…”

Section: Theorymentioning

confidence: 71%

“…The result that motivates these analyses describes the density as the diagonal part (r = r')of the formula (Hoffman et al 1988(Hoffman et al , 1990Pratt et al 1990)…”

Section: Theorymentioning

confidence: 99%

“…The brackets indicate the average over the surface of the hypersphere of radius z and the points {r0, rx, ...,rp} identify a segmented path from = to = For numerical work, the integration of (2) can be treated in normal mode coordinates {ax,..., a x} which diagonalize the quadradic form lp; this permits a straightforward sampling of the coordinates {ax, . .., average (Hoffman et al 1988). The calculations below are, however, entirely analytical and, therefore, the physical spatial coordinates provide a satisfactory definition of the problem.…”

Section: Theorymentioning

confidence: 99%

“…Recently, it has been shown th a t electron densities can be calculated by a statistical method based upon an electron density functional formalism (Harris & P ra tt 1985; Yang 1987Yang , 1988P ra tt et al 1988Hoffman et al 1988). In this paper, th at statistical formulation is used to establish an alternative derivation of the multiple scattering perturbation theory derived many years ago by March & Murray (March & Murray 1961;March et al 1967).…”

Section: Introductionmentioning

confidence: 98%

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Statistical theory of electron densities: multiple scattering perturbation theory

Hoffman

Pratt

1991

Proc. R. Soc. Lond. A

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A multiple scattering perturbation theory for electron densities, originally discussed by N. H. March and A. M. Murray, is derived in a new way. The new derivation does not depend on special choices for the origin of the energy scale. Therefore, it clarifies the point that the result of the perturbation calculation, the electron density, should be independent of the energy origin chosen for the purposes of the calculation even though the individual terms of the series do depend on that choice. This point is not evident in the previous derivations. Appreciation of this point permits adoption of an origin of the energy scale which varies with position without any change in form of the perturbation expansion. This extends the original theory beyond the significant limitation that the zero-order result is the uniform density of the free-electron gas. In particular, the energy origin can be chosen so that the zero-order contribution reproduces any physical model electron density. The theory then gives successive corrections and allows investigation of the usefulness of physical models by an analysis of the low-order corrections. These ideas permit a compact new derivation of the Thomas–Fermi theory, a derivation which also produces explicit formulae for corrections of all orders. An especially useful choice for the energy origin yields the optimized Thomas–Fermi theory as the zero-order contribution. Therefore, new results of this development are explicit formulae for the corrections to that simple theory.

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“…The results above are more fully discussed elsewhere (Hoffman et al 1988;Pratt et al 1990;). The derivation of (1) indicates that the p oo limit should provide the correct density.…”

Section: Theorymentioning

confidence: 71%

“…The result that motivates these analyses describes the density as the diagonal part (r = r')of the formula (Hoffman et al 1988(Hoffman et al , 1990Pratt et al 1990)…”

Section: Theorymentioning

confidence: 99%

Section: Theorymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 98%

See 2 more Smart Citations

Statistical theory of electron densities: multiple scattering perturbation theory

Hoffman

Pratt

1991

Proc. R. Soc. Lond. A

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“…A notable early effort in this direction-like the present work, statistical in nature, and aimed at computing dynamically-evolving forces for large systems-is the elegant path integral formulation of Pratt and co-workers. [110][111][112][113] Harris and Pratt used a discretized propagator method to show 110 that the electron density ρ(r) of a system could be expressed in terms of an effective single-particle potential 114 via a p-dimensional integral over the coordinates of all possible p-segment paths initiating and terminating at r = r 0 = r p . The expression is remarkably simple:…”

Section: B Energy-density Dualitymentioning

confidence: 99%

Embedding quantum statistical excitations in a classical force field

Atlas

2021

Preprint

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Quantum-mechanically-driven charge polarization and charge transfer are ubiquitous in biomolecular systems, controlling reaction rates, allosteric interactions, ligand-protein binding, membrane transport, and dynamically-driven structural transformations. Molecular dynamics (MD) simulations of these processes require quantum mechanical (QM) information in order to accurately describe their reactive dynamics. However, current techniques-empirical force fields, subsystem approaches, ab initio MD, and machine learning-vary in their ability to achieve a consistent chemical description across multiple atom types, and at scale. Here we present a physics-based, atomistic force field, the ensemble DFT charge-transfer embedded-atom method, in which QM forces are described at a uniform level of theory across all atoms, avoiding the need for explicit solution of the Schrödinger equation or large, precomputed training datasets. Coupling between the electronic and atomistic length scales is effected through an ensemble density functional theory formulation of the embedded atom method originally developed for elemental materials. Charge transfer is expressed in terms of ensembles of ionic states basis densities of individual atoms, and charge polarization, in terms of atomic excited state basis densities. This provides a highly compact yet general representation of the force field, encompassing both local and system-wide effects. Charge rearrangement is realized through the evolution of ensemble weights, adjusted at each dynamical timestep via chemical potential equalization.

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Multigrid methods in density functional theory

Beck

Iyer

Merrick

1997

Int. J. Quant. Chem.

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A multigrid method for real-space solution of the Kohn᎐Sham equations is presented. By using this multiscale approach, the problem of critical slowing down typical of iterative real-space solvers is overcome. The method scales linearly in computer time with the number of electrons if the orbitals are localized. Here, we describe details of our multigrid method, present preliminary many-electron numerical results illustrating the efficiency of the solver, and discuss its strengths and limitations.

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Monte Carlo integration of density functional theory: Fermions in a harmonic well

Cited by 11 publications

References 11 publications

Statistical theory of electron densities: multiple scattering perturbation theory

Statistical theory of electron densities: multiple scattering perturbation theory

Embedding quantum statistical excitations in a classical force field

Multigrid methods in density functional theory

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