arXiv subjects

John P. Perdew

Publications and source records attributed to John P. Perdew.

At least 73 records · Page 4Linked to original sources

arXiv2015

SCAN: An Efficient Density Functional Yielding Accurate Structures and Energies of Diversely-Bonded Materials

Kohn-Sham density functional theory (DFT) is a widely-used electronic structure theory for materials as well as molecules. DFT is needed especially for large systems, ab initio molecular dynamics, and high-throughput searches for functional materials. DFT's accuracy and computational efficiency are limited by the approximation to its exchange-correlation energy. Currently, the local density approximation (LDA) and generalized gradient approximations (GGAs) dominate materials computation mainly due to their efficiency. We show here that the recently developed non-empirical strongly constrained and appropriately normed (SCAN) meta-GGA improves significantly over LDA and the standard Perdew-Burke-Ernzerhof GGA for geometries and energies of diversely-bonded materials (including covalent, metallic, ionic, hydrogen, and van der Waals bonds) at comparable efficiency. Thus SCAN may be useful even for soft matter. Often SCAN matches or improves upon the accuracy of a computationally expensive hybrid functional, at almost-GGA cost. SCAN is therefore expected to have a broad impact on materials science.

cond-mat.mtrl-sci↗

arXiv2015

Combinations of coupled cluster, density functionals, and the random phase approximation for describing static and dynamic correlation, and van der Waals interactions

Contrary to standard coupled cluster doubles (CCD) and Brueckner doubles (BD), singlet-paired analogues of CCD and BD (denoted here as CCD0 and BD0) do not break down when static correlation is present, but neglect substantial amounts of dynamic correlation. In fact, CCD0 and BD0 do not account for any contributions from multielectron excitations involving only same-spin electrons at all. We exploit this feature to add---without introducing double counting, self-interaction, or increase in cost---the missing correlation to these methods via meta-GGA density functionals (TPSS and SCAN). Furthermore, we improve upon these CCD0+DFT blends by invoking range separation: the short- and long-range correlations absent in CCD0/BD0 are evaluated with DFT and the direct random phase approximation (dRPA), respectively. This corrects the description of long-range van der Waals forces. Comprehensive benchmarking shows that the combinations presented here are very accurate for weakly correlated systems, while also providing a reasonable description of strongly correlated problems without resorting to symmetry breaking.

physics.chem-ph↗

arXiv2015

Strongly Constrained and Appropriately Normed Semilocal Density Functional

The ground-state energy, electron density, and related properties of ordinary matter can be computed efficiently when the exchange-correlation energy as a functional of the density is approximated semilocally. We propose the first meta-GGA (meta-generalized gradient approximation) that is fully constrained, obeying all 17 known exact constraints that a meta-GGA can. It is also exact or nearly exact for a set of appropriate norms, including rare-gas atoms and nonbonded interactions. This SCAN (strongly constrained and appropriately normed) meta-GGA achieves remarkable accuracy for systems where the exact exchange-correlation hole is localized near its electron, and especially for lattice constants and weak interactions.

cond-mat.mtrl-sci↗

arXiv2014

Gedanken Densities and Exact Constraints in Density Functional Theory

Approximations to the exact density functional for the exchange-correlation energy of a many-electron ground state can be constructed by satisfying constraints that are universal, i.e., valid for all electron densities. Gedanken densities are designed for the purpose of this construction, but need not be realistic. The uniform electron gas is an old gedanken density. Here, we propose a spherical two-electron gedanken density in which the dimensionless density gradient can be an arbitrary positive constant wherever the density is non-zero. The Lieb-Oxford lower bound on the exchange energy can be satisfied within a generalized gradient approximation (GGA) by bounding its enhancement factor or simplest GGA exchange-energy density. This enhancement-factor bound is well known to be sufficient, but our gedanken density shows that it is also necessary. The conventional exact exchange-energy density satisfies no such local bound, but energy densities are not unique, and the simplest GGA exchange-energy density is not an approximation to it. We further derive a strongly and optimally tightened bound on the exchange enhancement factor of a two-electron density, which is satisfied by the local density approximation but is violated by all published GGA's or meta-GGA's. Finally, some consequences of the non-uniform density-scaling behavior for the asymptotics of the exchange enhancement factor of a GGA or meta-GGA are given.

physics.chem-ph↗

arXiv2014

Self Interaction Corrected Density Functional Theory with Unitary Invariance: Applications to Molecules

Standard spin-density functionals for the exchange-correlation energy of a many-electron ground state make serious self-interaction errors which can be corrected by the Perdew-Zunger self-interaction correction (SIC). We propose a size-extensive construction of SIC orbitals which, unlike earlier constructions, makes SIC computationally efficient, and a true spin-density functional. The SIC orbitals are constructed from a unitary transformation that is explicitly dependent on the non-interacting one-particle density matrix. When this SIC is applied to the local spin-density approximation, improvements are found for the atomization energies of molecules.

cond-mat.mtrl-sci↗

arXiv2013

Density Functionals that Recognize Covalent, Metallic, and Weak Bonds

Computationally-efficient semilocal approximations of density functional theory at the level of the local spin density approximation (LSDA) or generalized gradient approximation (GGA) poorly describe weak interactions. We show improved descriptions for weak bonds (without loss of accuracy for strong ones) from a newly-developed semilocal meta-GGA (MGGA), by applying it to molecules, surfaces, and solids. We argue that this improvement comes from using the right MGGA dimensionless ingredient to recognize all types of orbital overlap.

cond-mat.mtrl-sci↗

arXiv2013

Semilocal and Hybrid Meta-Generalized Gradient Approximations Based on the Understanding of the Kinetic-Energy-Density Dependence

We present a global hybrid meta-generalized gradient approximation (meta-GGA) with three empirical parameters, as well as its underlying semilocal meta-GGA and a meta-GGA with only one empirical parameter. All of them are based on the new meta-GGA resulting from the understanding of kinetic-energy-density dependence [J. Chem. Phys. 137, 051101 (2012)]. The obtained functionals show robust performances on the considered molecular systems for the properties of heats of formation, barrier heights, and noncovalent interactions. The pair-wise additive dispersion corrections to the functionals are also presented.

physics.chem-ph↗

arXiv2010

Ionization potentials in the limit of large atomic number

By extrapolating the energies of non-relativistic atoms and their ions with up to 3000 electrons within Kohn-Sham density functional theory, we find that the ionization potential remains finite and increases across a row, even as $Z\rightarrow\infty$. The local density approximation becomes chemically accurate (and possibly exact) in some cases. Extended Thomas-Fermi theory matches the shell-average of both the ionization potential and density change. Exact results are given in the limit of weak electron-electron repulsion.

cond-mat.mtrl-sci↗

arXiv2009

Workhorse Semilocal Density Functional for Condensed Matter Physics and Quantum Chemistry

Semilocal density functionals for the exchange-correlation energy are needed for large electronic systems. The Tao-Perdew-Staroverov-Scuseria (TPSS) meta-generalized gradient approximation (meta-GGA) is semilocal and usefully accurate, but predicts too-long lattice constants. Recent "GGA's for solids" yield good lattice constants but poor atomization energies of molecules. We show that the construction principle for one of them (restoring the density gradient expansion for exchange over a wide range of densities) can be used to construct a "revised TPSS" meta-GGA with accurate lattice constants, surface energies, and atomization energies for ordinary matter.

cond-mat.mtrl-sci↗

arXiv2009

Exchange-Correlation Energy Functional Based on the Airy-Gas Reference System

In recent work, generalized gradient approximations (GGA's) have been constructed from the energy density of the Airy gas for exchange but not for correlation. We report the random phase approximation (RPA) conventional correlation energy density of the Airy gas, the simplest edge electron gas, in which the auxiliary noninteracting electrons experience a linear potential. By fitting the Airy-gas RPA exchange-correlation energy density and making an accurate short-range correction to RPA, we propose a simple beyond-RPA GGA density functional ("ARPA+") for the exchange-correlation energy. Our functional, tested for jellium surfaces, atoms, molecules and solids, improves mildly over the local spin density approximation for atomization energies and lattice constants without much worsening the already-good surface exchange-correlation energies.

cond-mat.mtrl-sci↗

arXiv2009

Assessing the Performance of Recent Density Functionals for Bulk Solids

We assess the performance of recent density functionals for the exchange-correlation energy of a nonmolecular solid, by applying accurate calculations with the GAUSSIAN, BAND, and VASP codes to a test set of 24 solid metals and non-metals. The functionals tested are the modified Perdew-Burke-Ernzerhof generalized gradient approximation (PBEsol GGA), the second-order GGA (SOGGA), and the Armiento-Mattsson 2005 (AM05) GGA. For completeness, we also test more-standard functionals: the local density approximation, the original PBE GGA, and the Tao-Perdew-Staroverov-Scuseria (TPSS) meta-GGA. We find that the recent density functionals for solids reach a high accuracy for bulk properties (lattice constant and bulk modulus). For the cohesive energy, PBE is better than PBEsol overall, as expected, but PBEsol is actually better for the alkali metals and alkali halides. For fair comparison of calculated and experimental results, we consider the zero-point phonon and finite-temperature effects ignored by many workers. We show how Gaussian basis sets and inaccurate experimental reference data may affect the rating of the quality of the functionals. The results show that PBEsol and AM05 perform somewhat differently from each other for alkali metal, alkaline earth metal and alkali halide crystals (where the maximum value of the reduced density gradient is about 2), but perform very similarly for most of the other solids (where it is often about 1). Our explanation for this is consistent with the importance of exchange-correlation nonlocality in regions of core-valence overlap.

cond-mat.mtrl-sci↗

arXiv2009

Exchange-Correlation Hole of a Generalized Gradient Approximation for Solids and Surfaces

We propose a generalized gradient approximation (GGA) for the angle- and system-averaged exchange-correlation hole of a many-electron system. This hole, which satisfies known exact constraints, recovers the PBEsol (Perdew-Burke-Ernzerhof for solids) exchange-correlation energy functional, a GGA that accurately describes the equilibrium properties of densely packed solids and their surfaces. We find that our PBEsol exchange-correlation hole describes the wavevector analysis of the jellium exchange-correlation surface energy in agreement with a sophisticated time-dependent density-functional calculation (whose three-dimensional wavevector analysis we report here).

cond-mat.mtrl-sci↗

arXiv2008

Exact condition on the Kohn-Sham kinetic energy, and modern parametrization of the Thomas-Fermi density

We study the asymptotic expansion of the neutral-atom energy as the atomic number Z goes to infinity, presenting a new method to extract the coefficients from oscillating numerical data. We find that recovery of the correct expansion is an exact condition on the Kohn-Sham kinetic energy that is important for the accuracy of approximate kinetic energy functionals for atoms, molecules and solids, when evaluated on a Kohn-Sham density. 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. We also give a modern, highly accurate parametrization of the Thomas-Fermi density of neutral atoms.

physics.atm-clus↗

arXiv2008

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

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. "Normal" regions are well described by semilocal approximations, 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. Because our mixing fraction tends to 1 in the high-density limit, we rigorously employ full exact exchange. However, the nonlocality of exchange also requires balanced nonlocality of correlation, which can demand at least five empirical parameters. Our local hybrid functional is perhaps the first size-consistent fourth-rung density functional or hyper-GGA with full exact exchange, is exact 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.

physics.chem-ph↗

arXiv2008

Collapse of the Electron Gas to Two Dimensions in Density Functional Theory

Local and semilocal density-functional approximations for the exchange-correlation energy fail badly in the zero-thickness limit of a quasi-two-dimensional electron gas, where the density variation is rapid almost everywhere. Here we show that a fully nonlocal fifth-rung functional, the inhomogeneous Singwi-Tosi-Land-Sjölander (STLS) approach, which employs both occupied and unoccupied Kohn-Sham orbitals, recovers the true two-dimensional STLS limit and appears to be remarkably accurate for any thickness of the slab (and thus for the dimensional crossover). We also show that this good behavior is only partly due to the use of the full exact exchange energy.

cond-mat.mtrl-sci↗

arXiv2008

Nonempirical Density Functionals Investigated for Jellium: Spin-Polarized Surfaces, Spherical Clusters, and Bulk Linear Response

Earlier tests show that the Tao-Perdew-Staroverov-Scuseria (TPSS) nonempirical meta-generalized gradient approximation (meta-GGA) for the exchange-correlation energy yields more accurate surface energies than the local spin density (LSD) approximation for spin-unpolarized jellium. In this study, work functions and surface energies of a jellium metal in the presence of ``internal'' and external magnetic fields are calculated with LSD, Perdew-Burke-Ernzerhof (PBE) GGA, and TPSS meta-GGA and its predecessor, the nearly nonempirical Perdew-Kurth-Zupan-Blaha (PKZB) meta-GGA, using self-consistent LSD orbitals and densities. The results show that: (i) For normal bulk densities, the surface correlation energy is the same in TPSS as in PBE, as it should be since TPSS strives to represent a self-correlation correction to PBE; (ii) Normal surface density profiles can be scaled uniformly to the low-density or strong-interaction limit, and TPSS provides an estimate for that limit that is consistent with (but probably more accurate than) other estimates; (iii) For both normal and low densities, TPSS provides the same description of surface magnetism as PBE, suggesting that these approximations may be generally equivalent for magnetism. The energies of jellium spheres with up to 106 electrons are calculated using density functionals and compared to those obtained with Diffusion Quantum Monte Carlo data, including our estimate for the fixed-node correction. Finally we calculate the linear response of bulk jellium using these density functionals, and find that not only LSD but also PBE GGA and TPSS meta-GGA yield a linear-response in good agreement with that of the Quantum Monte Carlo method, for wavevectors of the perturbing external potential up to twice the Fermi wavevector.

cond-mat.mtrl-sci↗

arXiv2007

Exact-exchange energy density in the gauge of a semilocal density functional approximation

Exact-exchange energy density and energy density of a semilocal density functional approximation are two key ingredients for modeling the static correlation, a strongly nonlocal functional of the density, through a local hybrid functional. Because energy densities are not uniquely defined, the conventional (Slater) exact-exchange energy density $e_\mathrm{x}^\mathrm{ex(conv)}$ is not necessarily well-suited for local mixing with a given semilocal approximation. We show how to transform $e_\mathrm{x}^\mathrm{ex(conv)}$ in order to make it compatible with an arbitrary semilocal density functional, taking the nonempirical meta-generalized gradient approximation of Tao, Perdew, Staroverov, and Scuseria (TPSS) as an example. Our additive gauge transformation function integrates to zero, satisfies exact constraints, and is most important where the density is dominated by a single orbital shape. We show that, as expected, the difference between semilocal and exact-exchange energy densities becomes more negative under bond stretching in He$_2^{+}$ and related systems. Our construction of $e_\mathrm{x}^\mathrm{ex(conv)}$ by a resolution-of-the-identity method requires uncontracted basis functions.

cond-mat.mtrl-sci↗

arXiv2007

High-Level Correlated Approach to the Jellium Surface Energy, Without Uniform-Electron-Gas Input

We resolve the long-standing controversy over the surface energy of simple metals: Density functional methods that require uniform-electron-gas input agree with each other at many levels of sophistication, but not with high-level correlated calculations like Fermi Hypernetted Chain and Diffusion Monte Carlo (DMC) that predict the uniform-gas correlation energy. Here we apply a very high-level correlated approach, the inhomogeneous Singwi-Tosi-Land-Sjölander (ISTLS) method, and find that the density functionals are indeed reliable (because the surface energy is "bulk-like"). ISTLS values are close to recently-revised DMC values. Our work also vindicates the previously-disputed use of uniform-gas-based nonlocal kernels in time-dependent density functional theory.

cond-mat.mtrl-sci↗