arXiv subjects

John P. Perdew

Publications and source records attributed to John P. Perdew.

At least 55 records · Page 3Linked to original sources

arXiv2020

Constraint-based Wavevector- and Frequency-dependent Exchange-Correlation Kernel of the Uniform Electron Gas

According to time-dependent density functional theory, the exact exchange-correlation kernel f$_{xc}$(n, q, $ω$) determines not only the ground-state energy but also the excited-state energies/lifetimes and time-dependent linear density response of an electron gas of uniform density n $=$ 3/(4$π$r$^3_s$). Here we propose a parametrization of this function based upon the satisfaction of exact constraints. For the static ($ω$ = 0) limit, we modify the model of Constantin and Pitarke at small wavevector q to recover the known second-order gradient expansion, plus other changes. For all frequencies $ω$ at q $=$ 0, we use the model of Gross, Kohn, and Iwamoto. A Cauchy integral extends this model to complex $ω$ and implies the standard Kramers-Kronig relations. A scaling relation permits closed forms for not only the imaginary but also the real part of f$_{xc}$ for real $ω$. We then combine these ingredients by damping out the $ω$ dependence at large q in the same way that the q dependence is damped. Away from q $=$ 0 and $ω$ $=$ 0, the correlation contribution to the kernel becomes dominant over exchange, even at r$_s$ $=$ 4, the valence electron density of metallic sodium. The resulting correlation energy from integration over imaginary $ω$ is essentially exact. The plasmon pole of the density response function is found by analytic continuation of f$_{xc}$ to $ω$ just below the real axis, and the resulting plasmon lifetime first decreases from infinity and then increases as q grows from 0 toward the electron-hole continuum. A static charge-density wave is found for r$_s$ $>$ 69, and shown to be associated with softening of the plasmon mode. The exchange-only version of our static kernel confirms Overhauser's 1968 prediction that correlation enhances the charge-density wave.

physics.chem-ph↗

arXiv2019

A step in the direction of resolving the paradox of Perdew-Zunger self-interaction correction

Self-interaction (SI) error, which results when exchange-correlation contributions to the total energy are approximated, limits the reliability of many density functional approximations. The Perdew-Zunger SI correction (PZSIC), when applied in conjunction with the local spin density approximation (LSDA), improves the description of many properties, but overall, this improvement is limited. Here we propose a modification to PZSIC that uses an iso-orbital indicator to identify regions where local SI corrections should be applied. Using this local-scaling SIC (LSIC) approach with LSDA, we analyze predictions for a wide range of properties including, for atoms, total energies, ionization potentials, and electron affinities, and for molecules, atomization energies, dissociation energy curves, reaction energies, and reaction barrier heights. LSIC preserves the results of PZSIC-LSDA for properties where it is successful and provides dramatic improvements for many of the other properties studied. Atomization energies calculated using LSIC are better than those of the Perdew, Burke, and Ernzerhof (PBE) generalized gradient approximation (GGA) and close to those obtained with the Strongly Constrained and Appropriately Normed (SCAN) meta-GGA. LSIC also restores the uniform gas limit for the exchange energy that is lost in PZSIC-LSDA. Further performance improvements may be obtained by an appropriate combination or modification of the local scaling factor and the particular density functional approximation.

cond-mat.mtrl-sci↗

arXiv2019

Re-thinking CO adsorption on transition-metal surfaces: Density-driven error?

Adsorption of the molecule CO on metallic surfaces is an important unsolved problem in Kohn-Sham density functional theory (KS-DFT). We present a detailed study of carbon monoxide adsorption on fcc (111) surfaces of 3d, 4d and 5d metals using nonempirical semilocal density functionals for the exchange-correlation energy: the local-density approximation (LDA), two generalized gradient approximations or GGAs (PBE and PBEsol), and a meta-GGA (SCAN). The typical error pattern (as found earlier for free molecules and for free transition metal surfaces), in which results improve from LDA to PBE or PBEsol to SCAN, due to the satisfaction of more exact constraints, is not found here. Instead, for CO adsorption on transition metal surfaces, we find that, while SCAN overbinds much less than LDA, it overbinds slightly more than PBE. Moreover, the tested functionals often predict the wrong adsorption site, as first pointed out for LDA and GGA in the ``CO/Pt (111) puzzle". This abnormal pattern leads us to suspect that the errors of PBE and SCAN for this problem are density-driven self-interaction errors associated with incorrect charge transfer between molecule and metal surface. We point out that, by the variational principle, overbinding by an approximate functional would be reduced if that functional were applied not to its selfconsistent density for the adsorbed system but to an exact or more correct density for that system. Finally, we show for CO on Pt(111) that the site preference is corrected and the adsorption energy is improved for the PBE functional by using not the selfconsistent PBE density but a PBE+U density. The resulting correction to the PBE total energy is much larger for the adsorbed system than for its desorbed components, showing that the error is in the density of the adsorbed system. This seems to solve the ``CO/Pt (111) puzzle", in principle if not fully in practice.

cond-mat.mtrl-sci↗

arXiv2019

A simple self-interaction correction to RPA-like correlation energies

The random phase approximation (RPA) is exact for the exchange energy of a many-electron ground state, but RPA makes the correlation energy too negative by about 0.5 eV/electron. That large short-range error, which tends to cancel out of iso-electronic energy differences, is largely corrected by an exchange-correlation kernel, or (as in RPA+) by an additive local or semilocal correction. RPA+ is by construction exact for the homogeneous electron gas, and it is also accurate for the jellium surface. RPA+ often gives realistic total energies for atoms or solids in which spin-polarization corrections are absent or small. RPA and RPA+ also yield realistic singlet binding energy curves for H2 and N2, and thus RPA+ yields correct total energies even for spin-unpolarized atoms with fractional spins and strong correlation, as in stretched H2 or N2. However, RPA and RPA+ can be very wrong for spin-polarized one-electron systems (especially for stretched H2+), and also for the spin-polarization energies of atoms. The spin-polarization energy is often a small part of the total energy of an atom, but important for ionization energies, electron affinities, and the atomization energies of molecules. Here we propose a computationally efficient generalized RPA+ (gRPA+) that changes RPA+ only for spin-polarized systems by making gRPA+ exact for all one-electron densities, in the same simple semilocal way that the correlation energy densities of many meta-generalized gradent approximations are made self-correlation free. By construction, gRPA+ does not degrade the exact RPA+ description of jellium. gRPA+ is found to greatly improve upon RPA and RPA+ for the ionization energies and electron affinities of light atoms. Many versions of RPA with an approximate exchange-correlation kernel fail to be exact for all one-electron densities, and they can also be self-interaction corrected in this way.

physics.comp-ph↗

arXiv2019

Perdew-Zunger self-interaction correction: How wrong for uniform densities and large-Z atoms?

Semi-local density functionals for the exchange-correlation energy of a many-electron system cannot be exact for all one-electron densities. In 1981, Perdew and Zunger (PZ) subtracted the fully-nonlocal self-interaction error orbital-by-orbital, making the corrected functional exact for all collections of separated one-electron densities, and making no correction to the exact functional. Although the PZ self-interaction correction (SIC) eliminates many errors of semi-local functionals, it is often worse for equilibrium properties of sp-bonded molecules and solids. Non-empirical semi-local functionals are usually designed to be exact for electron gases of uniform density, and thus also make 0% error for neutral atoms in the limit of large atomic number Z, but PZ SIC is not so designed. For localized SIC orbitals, we show analytically that the LSDA-SIC correlation energy per electron of the uniform gas in the high-density limit makes an error of -50% in the spin-unpolarized case, and -100% in the fully-spin-polarized case. Then we extrapolate from the Ne, Ar, Kr, and Xe atoms to estimate the relative errors of the PZ SIC exchange-correlation energies (with localized SIC orbitals) in the limit of large atomic number: about +5.5% for the local spin density approximation (LSDA-SIC), and about -3.5% for nonempirical generalized gradient (PBE-SIC) and meta-generalized gradient (SCAN-SIC) approximations. The SIC errors are considerably larger than those that have been estimated for LSDA-SIC by approximating the localized SIC orbitals for the uniform gas, and may explain the errors of PZ SIC for equilibrium properties, opening the door to a generalized SIC that is more widely accurate.

physics.chem-ph↗

arXiv2019

Stretched or noded orbital densities and self-interaction correction in density functional theory

Semi-local approximations to the density functional for the exchange-correlation energy of a many-electron system necessarily fail for lobed one-electron densities, including not only the familiar stretched densities but also the less familiar but closely-related noded ones. The Perdew-Zunger (PZ) self-interaction correction (SIC) to a semi-local approximation makes that approximation exact for all one-electron ground- or excited-state densities and accurate for stretched bonds. When the minimization of the PZ total energy is made over real localized orbitals, the orbital densities can be noded, leading to energy errors in many-electron systems. Minimization over complex localized orbitals yields nodeless orbital densities, which reduce but typically do not eliminate the SIC errors of atomization energies. Other errors of PZ SIC remain, attributable to the loss of the exact constraints and appropriate norms that the semi-local approximations satisfy, and suggesting the need for a generalized SIC. These conclusions are supported by calculations for one-electron densities, and for many-electron molecules. While PZ SIC raises and improves the energy barriers of standard generalized gradient approximations (GGA's) and meta-GGA's, it reduces and often worsens the atomization energies of molecules. Thus PZ SIC raises the energy more as the nodality of the valence localized orbitals increases from atoms to molecules to transition states. PZ SIC is applied here in particular to the SCAN meta-GGA, for which the correlation part is already self-interaction-free. That property makes SCAN a natural first candidate for a generalized SIC.

physics.chem-ph↗

arXiv2018

Origin of the size-dependence of the equilibrium van der Waals binding between nanostructures

Nanostructures can be bound together at equilibrium by the van der Waals (vdW) effect, a small but ubiquitous many-body attraction that presents challenges to density functional theory. How does the binding energy depend upon the size or number of atoms in one of a pair of identical nanostructures? To answer this question, we treat each nanostructure properly as a whole object, not as a collection of atoms. Our calculations start from an accurate static dipole polarizability for each considered nanostructure, and an accurate equilibrium center-to-center distance for the pair (the latter from experiment, or from the vdW-DF-cx functional). We consider the competition in each term $-C_{2k}/d^{2k}$ ($k=3, 4, 5$) of the long-range vdW series for the interaction energy, between the size dependence of the vdW coefficient $C_{2k}$ and that of the $2k$-th power of the center-to-center distance $d$. The damping of these vdW terms can be negligible, but in any case it does not affect the size dependence for a given term in the absence of non-vdW binding. To our surprise, the vdW energy can be size-independent for quasi-spherical nanoclusters bound to one another by vdW interaction, even with strong nonadditivity of the vdW coefficient, as demonstrated for fullerenes. We also show that, for low-dimensional systems, the vdW interaction yields the strongest size-dependence, in stark contrast to that of fullerenes. We illustrate this with parallel planar polycyclic aromatic hydrocarbons. Other cases are between, as shown by sodium clusters.

physics.chem-ph↗

arXiv2017

Energy scaling law for nanostructured materials

The equilibrium binding energy is an important factor in the design of materials and devices. However, it presents great computational challenges for materials built up from nanostructures. Here we investigate the binding-energy scaling law from first-principles calculations. We show that the equilibrium binding energy per atom between identical nanostructures can scale up or down with nanostructure size. From the energy scaling law, we predict finite large-size limits of binding energy per atom. We find that there are two competing factors in the determination of the binding energy: Nonadditivities of van der Waals coefficients and center-to-center distance between nanostructures. To uncode the detail, the nonadditivity of the static multipole polarizability is investigated. We find that the higher-order multipole polarizability displays ultra-strong intrinsic nonadditivity, no matter if the dipole polarizability is additive or not.

cond-mat.mes-hall↗

arXiv2017

Ab initio theory and modeling of water

Water is of the utmost importance for life and technology. However, a genuinely predictive ab initio model of water has eluded scientists. We demonstrate that a fully ab initio approach, relying on the strongly constrained and appropriately normed (SCAN) density functional, provides such a description of water. SCAN accurately describes the balance among covalent bonds, hydrogen bonds, and van der Waals interactions that dictates the structure and dynamics of liquid water. Notably, SCAN captures the density difference between water and ice I{\it h} at ambient conditions, as well as many important structural, electronic, and dynamic properties of liquid water. These successful predictions of the versatile SCAN functional open the gates to study complex processes in aqueous phase chemistry and the interactions of water with other materials in an efficient, accurate, and predictive, ab initio manner.

cond-mat.soft↗

arXiv2017

Comparative first-principles studies of prototypical ferroelectric materials by LDA, GGA, and SCAN meta-GGA

Originating from a broken spatial inversion symmetry, ferroelectricity is a functionality of materials with an electric dipole that can be switched by external electric fields. Spontaneous polarization is a crucial ferroelectric property, and its amplitude is determined by the strength of polar structural distortions. Density functional theory (DFT) is one of the most widely used theoretical methods to study ferroelectric properties, yet it is limited by the levels of approximations in electron exchange-correlation. On the one hand, the local density approximation (LDA) is considered to be more accurate for the conventional perovskite ferroelectrics such as BaTiO3 and PbTiO3 than the generalized gradient approximation (GGA), which suffers from the so-called super-tetragonality error. On the other hand, GGA is more suitable for hydrogen-bonded ferroelectrics than LDA, which largely overestimates the strength of hydrogen bonding in general. We show here that the recently developed general-purpose strongly constrained and appropriately normed (SCAN) meta-GGA functional significantly improves over the traditional LDA/GGA for structural, electric, and energetic properties of diversely-bonded ferroelectric materials with a comparable computational effort, and thus enhances largely the predictive power of DFT in studies of ferroelectric materials. We also address the observed system-dependent performances of LDA and GGA for ferroelectrics from a chemical bonding point of view.

cond-mat.mtrl-sci↗

arXiv2017

Full self-consistency in Fermi-orbital self-interaction correction

The Perdew-Zunger self-interaction correction cures many common problems associated with semilocal density functionals, but suffers from a size-extensivity problem when Kohn-Sham orbitals are used in the correction. Fermi-Löwdin-orbital self-interaction correction (FLOSIC) solves the size-extensivity problem, allowing its use in periodic systems and resulting in better accuracy in finite systems. Although the previously published FLOSIC algorithm [J. Chem. Phys. 140, 121103 (2014)] appears to work well in many cases, it is not fully self-consistent. This would be particularly problematic for systems where the occupied manifold is strongly changed by the correction. In this paper we demonstrate a new algorithm for FLOSIC to achieve full self-consistency with only marginal increase of computational cost. The resulting total energies are found to be lower than previously reported non-self-consistent results.

physics.comp-ph↗

arXiv2017

Properties of real metallic surfaces: Effects of density functional semilocality and van der Waals nonlocality

We have computed the surface energies, work functions, and interlayer surface relaxations of clean (111), (110), and (100) surfaces of Al, Cu, Ru, Rh, Pd, Ag, Pt, and Au. Many of these metallic surfaces have technological or catalytic applications. We compare experimental reference values to those of the local density approximation (LDA), the Perdew-Burke-Ernzerhof (PBE) generalized gradient approximation (GGA), the PBEsol (PBE for solids) GGA, the SCAN meta-GGA, and SCAN+rVV10 (SCAN with a long-range van der Waals or vdW correction). The closest agreement with uncertain experimental values is achieved by the simplest density functional (LDA) and by the most sophisticated general-purpose one (SCAN+rVV10). The long-range vdW interaction increases the surface energies by about 10%, and the work functions by about 1%. LDA works for metal surfaces through a stronger-than-usual error cancellation. PBE yields the most-underestimated and presumably least accurate surface energies and work functions. Surface energies within the random phase approximation (RPA) are also reported. Interlayer relaxations from different functionals are in reasonable agreement with one another, and usually with experiment.

cond-mat.mtrl-sci↗

arXiv2017

Understanding Band Gaps of Solids in Generalized Kohn-Sham Theory

The fundamental energy gap of a periodic solid distinguishes insulators from metals and characterizes low-energy single-electron excitations. But the gap in the band-structure of the exact multiplicative Kohn-Sham (KS) potential substantially underestimates the fundamental gap, a major limitation of KS density functional theory. Here we give a simple proof of a new theorem: In generalized KS theory (GKS), the band gap of an extended system equals the fundamental gap for the approximate functional if the GKS potential operator is continuous and the density change is delocalized when an electron or hole is added. Our theorem explains how GKS band gaps from meta-generalized gradient approximations (meta-GGAs) and hybrid functionals can be more realistic than those from GGAs or even from the exact KS potential. The theorem also follows from earlier work. The band edges in the GKS one-electron spectrum are also related to measurable energies. A linear chain of hydrogen molecules, solid aluminum arsenide, and solid argon provide numerical illustrations.

cond-mat.mtrl-sci↗

arXiv2016

Rehabilitation of PBE-GGA for Layered Materials

The structural and energetic properties of layered materials propose a challenge to density functional theory with common semilocal approximations to the exchange-correlation. By combining the most-widely used semilocal generalized gradient approximation (GGA), Perdew--Burke--Ernzerhof (PBE), with the revised Vydrov--Van Voorhis non-local correlation functional (rVV10), both excellent structural and energetic properties of 28 layered materials were recovered with a judicious parameter selection. We term the resulting functional as PBE+rVV10L with "L" denoting for layered materials. Such combination is not new, and involves only refitting a single global parameter, however the resulting excellency suggests such corrected PBE for many aspects of theoretical studies on layered materials. For comparison, we also present the results for PBE+rVV10 where the parameter is determined by the 22 interaction energies between molecules.

cond-mat.mtrl-sci↗

arXiv2016

Towards efficient orbital-dependent density functionals for weak and strong correlation

We present a new paradigm for the design of exchange-correlation functionals in density-functional theory. Electron pairs are correlated explicitly by means of the recently developed second order Bethe-Goldstone equation (BGE2) approach. Here we propose a screened BGE2 (sBGE2) variant that efficiently regulates the coupling of a given electron pair. sBGE2 correctly dissociates H$_2$ and H$_2^+$, a problem that has been regarded as a great challenge in density-functional theory for a long time. The sBGE2 functional is then taken as a building block for an orbital-dependent functional, termed ZRPS, which is a natural extension of the PBE0 hybrid functional. While worsening the good performance of sBGE2 in H$_2$ and H$_2^{+}$, ZRPS yields a remarkable and consistent improvement over other density functionals across various chemical environments from weak to strong correlation.

cond-mat.mtrl-sci↗

arXiv2016

More-Realistic Band Gaps from Meta-Generalized Gradient Approximations: Only in a Generalized Kohn-Sham Scheme

Unlike the local density approximation (LDA) and the generalized gradient approximation (GGA), calculations with meta-generalized gradient approximations (meta-GGA) are usually done according to the generalized Kohn-Sham (gKS) formalism. The exchange-correlation potential of the gKS equation is non-multiplicative, which prevents systematic comparison of meta-GGA bandstructures to those of the LDA and the GGA. We implement the optimized effective potential (OEP) of the meta-GGA for periodic systems, which allows us to carry out meta-GGA calculations in the same KS manner as for the LDA and the GGA. We apply the OEP to several meta-GGAs, including the new SCAN functional [Phys. Rev. Lett. 115, 036402 (2015)]. We find that the KS gaps and KS band structures of meta-GGAs are close to those of GGAs. They are smaller than the more realistic gKS gaps of meta-GGAs, but probably close to the less-realistic gaps in the band structure of the exact KS potential, as can be seen by comparing with the gaps of the EXX+RPA OEP potential. The well-known grid sensitivity of meta-GGAs is much more severe in OEP calculations.

cond-mat.mtrl-sci↗

arXiv2016

SCAN+rVV10: A promising van der Waals density functional

The newly developed "strongly constrained and appropriately normed" (SCAN) meta-generalized-gradient approximation (meta-GGA) can generally improve over the non-empirical Perdew-Burke-Ernzerhof (PBE) GGA not only for strong chemical bonding, but also for the intermediate-range van der Waals (vdW) interaction. However, the long-range vdW interaction is still missing. To remedy this, we propose here pairing SCAN with the non-local correlation part from the rVV10 vdW density functional, with only two empirical parameters. The resulting SCAN+rVV10 yields excellent geometric and energetic results not only for molecular systems, but also for solids and layered-structure materials, as well as the adsorption of benzene on coinage metal surfaces. Especially, SCAN+rVV10 outperforms all current methods with comparable computational efficiencies, accurately reproducing the three most fundamental parameters---the inter-layer binding energies, inter-, and intra-layer lattice constants---for 28 layered-structure materials. Hence, we have achieved with SCAN+rVV10 a promising vdW density functional for general geometries, with minimal empiricism.

cond-mat.mtrl-sci↗

arXiv2016

Near-locality of exchange and correlation density functionals for 1- and 2-electron systems

The uniform electron gas and the hydrogen atom play fundamental roles in condensed matter physics and quantum chemistry. The former has an infinite number of electrons uniformly distributed over the neutralizing positively-charged background, and the latter only one electron bound to the proton. The uniform electron gas was used to derive the local spin density approximation (LSDA) to the exchange-correlation functional that undergirds the development of the Kohn-Sham density functional theory. We show here that the ground-state exchange-correlation energies of the hydrogen atom and many other 1- and 2-electron systems are modeled surprisingly well by a different local spin density approximation (LSDA0). Our LSDA0 is constructed to satisfy exact constraints, but agrees surprisingly well with the exact results for a uniform two-electron density in a finite, curved three-dimensional space. We also apply LSDA0 to excited or noded 1-electron densities. Furthermore, we show that the locality of an orbital can be measured by the ratio between the exact exchange energy and its optimal lower bound.

physics.chem-ph↗