Potential Scaling in Density Functional Theory
Authors: Peter Elliott, Kieron Burke
Abstract
Density scaling has a rich history in density functional theory, providing exact conditions for use in the construction of ever more accurate approximations to the unknown exchange-correlation functional. We define a conjugate potential scaling for each density scaling. This provides exact relations on various important density functionals, in particular, relating functionals evaluated on exact densities of different potentials. We illustrate these conditions on the two- and four-electron ion series.
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Closest papers
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Some Remarks on Scaling Relations in Density Functional TheoryWei-Tao Yang · 1987 · cited 13 times · Not summarized yet
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Relevance of the slowly varying electron gas to atoms, molecules, and solids.J. Perdew, L. Constantin, Espen Sagvolden et al. · 2006 · Physical Review Letters · cited 88 times · Not summarized yet
Abstract
We present a Thomas-Fermi-inspired density scaling under which electron densities of atomic, molecular, or condensed matter become both large and slowly varying, so that semiclassical approximations and second-order density gradient expansions are asymptotically exact for the kinetic and exchange energies. Thus, even for atoms and molecules, density-functional approximations should recover the universal second-order gradient expansions in this limit. We also explain why common generalized gradient approximations for exchange do not.
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Rationale for mixing exact exchange with density functional approximationsJ. Perdew, M. Ernzerhof, K. Burke · 1996 · Journal of Chemical Physics · cited 5,775 times · Not summarized yet
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Potential functionals: dual to density functionals and solution to the v-representability problem.Wei-Tao Yang, P. Ayers, Qin Wu · 2004 · Physical Review Letters · cited 94 times · Not summarized yet
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Finite-Size Scaling of Charge Carrier Mobility in Disordered Organic SemiconductorsPascal Kordt, Thomas Speck, Denis Andrienko · 2015 · Phys. Rev. B 94, 014208 (2016) · cited 18 times · Not summarized yet
Abstract
Simulations of charge transport in amorphous semiconductors are often performed in microscopically sized systems. As a result, charge carrier mobilities become system-size dependent. We propose a simple method for extrapolating a macroscopic, nondispersive mobility from the system-size dependence of a microscopic one. The method is validated against a temperature-based extrapolation [Phys. Rev. B 82, 193202 (2010)]. In addition, we provide an analytic estimate of system sizes required to perform nondispersive charge transport simulations in systems with finite charge carrier density, derived from a truncated Gaussian distribution. This estimate is not limited to lattice models or specific ra…
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A short derivation of Feynman formulaAlejandro Rivero · 1998 · Quantum Physics · preprint, not peer reviewed · cited 6 times · Not summarized yet
Abstract
The complex exponential weighting of Feynman formalism is seen to happen at the classical level. (Finiteness of) Feynman path integral formula is suspected then to appear as a consistency condition for the existence of certain Dirac measures over functional spaces.
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Orbital currents and charge density waves in a generalized Hubbard ladderJ. O. Fjaerestad, J. B. Marston, U. Schollwoeck · 2004 · Ann. Phys. (N.Y.) 321, 894 (2006) · cited 7 times · Not summarized yet
Abstract
We study a generalized Hubbard model on the two-leg ladder at zero temperature, focusing on a parameter region with staggered flux (SF)/d-density wave (DDW) order. To guide our numerical calculations, we first investigate the location of a SF/DDW phase in the phase diagram of the half-filled weakly interacting ladder using a perturbative renormalization group (RG) and bosonization approach. For hole doping delta away from half-filling, finite-size density-matrix renormalization-group (DMRG) calculations are used to study ladders with up to 200 rungs for intermediate-strength interactions. In the doped SF/DDW phase, the staggered rung current and the rung electron density both show periodic s…
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Condition on the Kohn-Sham kinetic energy and modern parametrization of the Thomas-Fermi density.Donghyung Lee, L. Constantin, J. Perdew et al. · 2008 · Journal of Chemical Physics · cited 68 times · Not summarized yet
Abstract
We study the asymptotic expansion of the neutral-atom energy as the atomic number Z-->infinity, presenting a new method to extract the coefficients from oscillating numerical data. Recovery of the correct expansion yields a condition on the Kohn-Sham kinetic energy that is important for the accuracy of approximate kinetic energy functionals for atoms, molecules, and solids. For example, this determines the small gradient limit of any generalized gradient approximation and conflicts somewhat with the standard gradient expansion. Tests are performed on atoms, molecules, and jellium clusters using densities constructed from Kohn-Sham orbitals. We also give a modern, highly accurate parametrizat…
Prior work it builds on
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Density-functional exchange correlation through coordinate scaling in adiabatic connection and correlation hole.M. Levy · 1991 · Physical Review A. Atomic, Molecular, and Optical Physics · cited 223 times · Not summarized yet
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Adiabatic connection from accurate wave-function calculationsDerek Frydel, William H. Terilla, K. Burke · 1999 · Journal of Chemical Physics · cited 46 times · Not summarized yet
Abstract
An extremely easy method for accurately calculating the adiabatic connection of density functional theory is presented, and its accuracy tested on both Hooke’s atom and the He atom. The method is easy because calculations are needed only for different values of parameters in the external potential, which can be achieved with almost any electronic structure code. Application of the method to accurate calculations on small systems should lead to benchmark adiabatic connection curves.
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Universal variational functionals of electron densities, first-order density matrices, and natural spin-orbitals and solution of the v-representability problem.M. Levy · 1979 · Proceedings of the National Academy of Sciences of the United States of America · cited 1,707 times · Not summarized yet
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Sixth-order term of the gradient expansion of the kinetic-energy density functionalD. R. Murphy · 1981 · Physical Review A · cited 115 times · Not summarized yet
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Accurate exchange-correlation potentials and total-energy components for the helium isoelectronic series.C. Umrigar, X. Gonze · 1994 · Physical Review A. Atomic, Molecular, and Optical Physics · cited 285 times · Not summarized yet
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Updated on 6 November 2026.