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Recently we developed a nonlocal van der Waals density functional (VV09) that has a simple and well-behaved analytic form. In this article, we report a self-consistent implementation of VV09 with an atom-centered basis set. We compute binding energies for a diverse benchmark set and find that VV09 performs well in combination with Hartree–Fock exchange. We compare VV09 with its precursor, discuss likely sources of inaccuracies in both models, and identify some aspects of the methodology where further refinements are desirable. [ABSTRACT FROM AUTHOR]

We study real-time electron dynamics in a molecular junction with a variety of approximations to the electronic structure, toward the ultimate aim of determining what ingredients are crucial for the accurate prediction of charge transport. We begin with real-time, all electron simulations using some common density functionals that differ in how they treat long-range Hartree–Fock exchange. We find that the inclusion or exclusion of nonlocal exchange is the dominant factor determining the transport behavior, with all semilocal contributions having a smaller effect. In order to study nonlocal correlation, we first map our junction onto a simple Pariser–Parr–Pople (PPP) model Hamiltonian. The PPP dynamics are shown to faithfully reproduce the all electron results, and we demonstrate that nonlocal correlation can be readily included in the model space using the generator coordinate method (GCM). Our PPP-GCM simulations suggest that nonlocal correlation has a significant impact on the I-V character that is not captured even qualitatively by any of the common semilocal approximations to exchange and correlation. The implications of our results for transport calculations are discussed. [ABSTRACT FROM AUTHOR]

The nonlocal van der Waals density functional (vdW-DF) captures the essential physics of the dispersion interaction not only in the asymptotic regime but also for a general case of overlapping fragment densities. A balanced treatment of other energetic contributions, such as exchange, is crucial if we aim for accurate description of various properties of weakly bound systems. In this paper, the vdW-DF correlation functional is modified to make it better compatible with accurate exchange functionals. We suggest a slightly simplified construction of the nonlocal correlation, yielding more accurate asymptotic C6 coefficients. We also derive a gradient correction, containing a parameter that can be adjusted to suit an exchange functional of choice. We devise a particularly apt combination of exchange and correlation terms, which satisfies many important constraints and performs well for our benchmark tests. [ABSTRACT FROM AUTHOR]

Nearly all common density functional approximations fail to properly describe dispersion interactions responsible for binding in van der Waals complexes. Empirical corrections can fix some of the failures but cannot fully grasp the complex physics and may not be reliable for systems dissimilar to the fitting set. In contrast, the recently proposed nonlocal van der Waals density functional (vdW-DF) was derived from first principles, describes dispersion interactions in a seamless fashion, and yields the correct asymptotics. Implementation of this functional is somewhat cumbersome: Nonlocal dependence on the electron density requires numerical double integration over the space variables and functional derivatives are nontrivial. This paper shows how vdW-DF can be implemented self-consistently with Gaussian basis functions. The gradients of the energy with respect to nuclear displacements have also been derived and coded, enabling efficient geometry optimizations. We test the vdW-DF correlation functional in combination with several exchange approximations. We also study the sensitivity of the method to the basis set size and to the quality of the numerical quadrature grid. For weakly interacting systems, acceptable accuracy in semilocal exchange is achieved only with fine grids, whereas for nonlocal vdW-DF correlation even rather coarse grids are sufficient. The current version of vdW-DF is not well suited for pairing with Hartree–Fock exchange, leading to considerable overbinding. [ABSTRACT FROM AUTHOR]

The first n→π* transitions of 18 nitroso and 16 thiocarbonyl dyes have been computed by time-dependent density functional theory (TD-DFT) using pure as well as global and range-separated hybrid functionals. It turns out that the accuracy of all hybrids is relatively similar, i.e., the inclusion of a growing fraction of exact exchange does neither worsen nor improve significantly the raw TD-DFT estimations. However, after a simple linear regression, it appears that the range-separated hybrids provide a better accuracy than global hybrids. [ABSTRACT FROM AUTHOR]

The Perdew-Burke-Ernzerhof (PBE) generalized gradient approximation for the exchange-correlation energy functional has two nonempirical constructions, based on satisfaction of universal exact constraints on the hole density or on the energy. We show here that, by identifying one possible free parameter in exchange and a second in correlation, we can continue to satisfy these constraints while diminishing the gradient dependence almost to zero (i.e., almost recovering the local spin density approximation or LSDA). This points out the important role played by the Perdew-Wang 1991 nonempirical hole construction in shaping PBE and later constructions. Only the undiminished PBE is good for atoms and molecules, for reasons we present, but a somewhat diminished PBE could be useful for solids; in particular, the surface energies of solids could be improved. Even for atoms and molecules, a strongly diminished PBE works well when combined with a scaled-down self-interaction correction (although perhaps not significantly better than LSDA). This shows that the undiminished gradient dependence of PBE and related functionals works somewhat like a scaled-down self-interaction correction to LSDA. [ABSTRACT FROM AUTHOR]

In the exact theory, the ground state energy of an open system varies linearly when the electron number is changed between two adjacent integers. This linear dependence is not reproduced by common approximate density functionals. Deviation from linearity in this dependence has been suggested as a basis for the concept of many-electron self-interaction error (SIE). In this paper, we quantify many-electron SIE of a number of approximations by performing calculations on fractionally charged atoms. We demonstrate the direct relevance of these studies to such problems of common approximate functionals as instabilities of anions, spurious fractional charges on dissociated atoms, and poor description of charge transfer. Semilocal approximations have the largest many-electron SIE, which is only slightly reduced in typical global hybrids. In these approximations the energy versus fractional electron number curves upward, while in Hartree-Fock theory the energy curves downward. Perdew-Zunger self-interaction correction [Phys. Rev. B 23, 5048 (1981)] significantly reduces the many-electron SIE of semilocal functionals but impairs their accuracy for equilibrium properties. In contrast, a long-range corrected hybrid functional can be nearly many-electron SIE-free in many cases (for reasons we discuss) and at the same time performs remarkably well for many molecular properties. [ABSTRACT FROM AUTHOR]

The common density functionals for the exchange-correlation energy make serious self-interaction errors in the molecular dissociation limit when real or spurious noninteger electron numbers N are found on the dissociation products. An “M-electron self-interaction-free” functional for positive integer M is one that produces a realistic linear variation of total energy with N in the range of M-1≤Na=M, and so can avoid these errors. This desideratum is a natural generalization to all M of the more familiar one of one-electron self-interaction freedom. The intent of this paper is not to advocate for any functional, but to understand what is required for a functional to be M-electron self-interaction-free and thus correct even for highly stretched bonds. The original Perdew-Zunger self-interaction correction (SIC) and our scaled-down variant of it are exactly one- and nearly two-electron self-interaction-free, but only the former is nearly so for atoms with M>2. Thus all these SIC’s produce an exact binding energy curve for H2+, and an accurate one for He2+, but only the unscaled Perdew-Zunger SIC produces an accurate one for Ne2+, where there are more than two electrons on each fragment Ne+0.5. We also discuss LiH+, which is relatively free from self-interaction errors. We suggest that the ability of the original and unscaled Perdew-Zunger SIC to be nearly M-electron self-interaction-free for atoms of all M stems in part from its formal resemblance to the Hartree-Fock theory, with which it shares a sum rule on the exchange-correlation hole of an open system. [ABSTRACT FROM AUTHOR]

Common approximate exchange-correlation functionals suffer from self-interaction error, and as a result, their corresponding potentials have incorrect asymptotic behavior. The exact asymptote can be imposed by introducing range separation into the exchange component and replacing the long-range portion of the approximate exchange by the Hartree-Fock counterpart. The authors show that this long-range correction works particularly well in combination with the short-range variant of the Perdew-Burke-Ernzerhof (PBE) exchange functional. This long-range-corrected hybrid, here denoted LC-ωPBE, is remarkably accurate for a broad range of molecular properties, such as thermochemistry, barrier heights of chemical reactions, bond lengths, and most notably, description of processes involving long-range charge transfer. [ABSTRACT FROM AUTHOR]

This work reexamines the effect of the exchange screening parameter ω on the performance of the Heyd-Scuseria-Ernzerhof (HSE) screened hybrid functional. We show that variation of the screening parameter influences solid band gaps the most. Other properties such as molecular thermochemistry or lattice constants of solids change little with ω. We recommend a new version of HSE with the screening parameter ω=0.11 bohr-1 for further use. Compared to the original implementation, the new parametrization yields better thermochemical results and preserves the good accuracy for band gaps and lattice constants in solids. [ABSTRACT FROM AUTHOR]

Semilocal density functional approximations for the exchange-correlation energy can improperly dissociate a neutral molecule XY (Y≠X) to fractionally charged fragments X+q...Y-q with an energy significantly lower than X0...Y0. For example, NaCl can dissociate to Na+0.4...Cl-0.4. Generally, q is positive when the lowest-unoccupied orbital energy of atom Y0 lies below the highest-occupied orbital energy of atom X0. The first 24 open sp-shell atoms of the Periodic Table can form 276 distinct unlike pairs XY, and in the local spin density approximation 174 of these display fractional-charge dissociation. Finding these lowest-energy solutions with standard quantum chemistry codes, however, requires special care. Self-interaction-corrected (SIC) semilocal approximations are exact for one-electron systems and also reduce the spurious fractional charge q. The original SIC of Perdew and Zunger typically reduces q to 0. A scaled-down SIC with better equilibrium properties sometimes fails to reduce q all the way to 0. The desideratum of “many-electron self-interaction freedom” is introduced as a generalization of the one-electron concept. [ABSTRACT FROM AUTHOR]

We consider a general class of hybrid density functionals with decomposition of the exchange component into short-range and long-range parts. The admixture of Hartree-Fock (HF) exchange is controlled by three parameters: short-range mixing, long-range mixing, and range separation. We study how the variation of these parameters affects the accuracy of hybrid functionals for thermochemistry and kinetics. For the density functional component of the hybrids, we test three nonempirical approximations: local spin-density approximation, generalized gradient approximation (GGA), and meta-GGA. We find a great degree of flexibility in choosing the mixing parameters in range-separated hybrids. For the studied properties, short-range and long-range HF exchange seem to have a similar effect on the errors. One may choose to treat the long-range portion of the exchange by HF to recover the correct asymptotic behavior of the exchange potential and improve the description of density tail regions. If this asymptote is not important, as in solids, one may use screened hybrids, where long-range HF exchange is excluded. Screened hybrids retain most of the benefits of global hybrids but significantly reduce the computational cost in extended systems. [ABSTRACT FROM AUTHOR]

Semilocal density functional approximations (DFAs) for the exchange-correlation energy suffer from self-interaction error, which is believed to be the cause of many of the failures of common DFAs, such as poor description of charge transfer and transition states of chemical reactions. The standard self-interaction correction (SIC) of Perdew and Zunger mends some of these failures but spoils such essential properties as thermochemistry and equilibrium bond lengths. The Perdew-Zunger SIC seems to overcorrect many-electron systems. In this paper, we propose a modified SIC, which is scaled down in many-electron regions. The new SIC has an improved performance for many molecular properties, including total energies, atomization energies, barrier heights of chemical reactions, ionization potentials, electron affinities, and bond lengths. The local spin-density approximation (LSDA) benefits from SIC more than higher-level functionals do. The scaled-down SIC has only one adjustable parameter. Rationalization of the optimal value of this parameter enables us to construct an almost-nonempirical version of the scaled-down SIC-LSDA, which is significantly better than uncorrected LSDA and even better than the uncorrected generalized gradient approximation. We present an analysis of the formal properties of the scaled-down SIC and define possible directions for further improvements. In particular, we find that exactness for all one-electron densities does not guarantee correct asymptotics for the exchange-correlation potential of a many-electron system. [ABSTRACT FROM AUTHOR]

Using a self-consistent implementation of the Perdew–Zunger self-interaction corrected (PZ-SIC) density-functional theory, we have calculated ionization potentials (IP) and electron affinities (EA) of first- and second-row atoms and a set of small molecules. Several exchange-correlation functionals were tested. IPs and EAs were obtained by two methods: as the difference in self-consistent field (SCF) energies of neutrals and ions (ΔSCF) and as negatives of highest-occupied orbital energies. We found that, except for local spin-density approximation, PZ-SIC worsens ΔSCF IPs and EAs. On the other hand, PZ-SIC brings orbital eigenvalues into much better agreement with electron removal energies. The Perdew–Zunger SIC seems to overcorrect many-electron systems; for molecules it performs worse than for atoms. We also discuss several common approximations to PZ-SIC such as spherical averaging of orbital densities in atoms. [ABSTRACT FROM AUTHOR]

The Perdew–Zunger self-interaction-corrected density functional theory (SIC-DFT) was implemented self-consistently using a quasi-Newton direct minimization method. We calculated SIC-DFT energies for a number of atoms and molecules using various approximate density functionals, including hybrids. Self-interaction errors (SIE) of these functionals were compared and analyzed in terms of contributions from valence and core orbitals. We also calculated enthalpies of formation of the standard G2-1 set of 55 molecules and found that self-interaction-correction (SIC) improves agreement with experiment only for the LSDA functional, while all other functionals show worse performance upon introducing SIC. This is the first systematic study of the effect of SIC on thermochemical properties. We found no direct connection between the magnitude of the SIE contained in a functional and its performance for thermochemistry. Approximate functionals with large self-interaction errors can accurately reproduce enthalpies of formation. Our results do not support the popular belief that a smaller SIE of hybrid functionals is the main reason for their higher accuracy. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The method of Perdew and Zunger is commonly used to correct the self-interaction error of approximate density functionals. However, it has been shown that this orbital-based self-interaction correction (SIC) tends to overcorrect and often impairs molecular properties. We have recently proposed a method to improve the performance of the SIC by scaling it down in many-electron regions. In this communication, we present a simplification of this scheme. For every occupied orbital, we introduce a scaling factor determined by the ratio of the orbital density to the total spin-density. Thus, the magnitude of the correction is adjusted depending on how much orbital densities overlap with one another. Such a modification of the Perdew-Zunger SIC does not add any appreciable time to the computation, but significantly improves the accuracy for a number of benchmark properties. [ABSTRACT FROM AUTHOR]