Nonlocal van der Waals density functional: The simpler the better

We devise a nonlocal correlation energy functional that describes the entire range of dispersion interactions in a seamless fashion using only the electron density as input. The new functional is considerably simpler than its predecessors of a similar type. The functional has a tractable and robust analytic form that lends itself to efficient self-consistent implementation. When paired with an appropriate exchange functional, our nonlocal correlation model yields accurate interaction energies of weakly-bound complexes, not only near the energy minima but also far from equilibrium. Our model exhibits an outstanding precision at predicting equilibrium intermonomer separations in van der Waals complexes. It also gives accurate covalent bond lengths and atomization energies. Hence the functional proposed in this work is a computationally inexpensive electronic structure tool of broad applicability

Implementation and Assessment of a Simple Nonlocal van der Waals Density Functional

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.National Science Foundation (U.S.) (NSF CAREER Grant No. CHE-0547877)David & Lucile Packard Foundation (Fellowship

Exchange and correlation in molecular wire conductance: non-locality is the key

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.National Science Foundation (U.S.) (CAREER under Grant No. CHE-0547877)David & Lucile Packard Foundation (Fellowship

Generalized gradient approximation for solids and their surfaces

Successful modern generalized gradient approximations (GGA) are biased toward atomic energies. Restoration of the first-principles gradient expansion for the exchange energy over a wide range of density gradients eliminates this bias. We introduce PBEsol, a revised Perdew-Burke-Ernzerhof GGA that improves equilibrium properties for many densely-packed solids and their surfaces.Comment: 4pages, 2figures,2table

Dispersion interactions from a local polarizability model

A local approximation for dynamic polarizability leads to a nonlocal functional for the long-range dispersion interaction energy via an imaginary-frequency integral. We analyze several local polarizability approximations and argue that the form underlying the construction of our recent van der Waals functional [O. A. Vydrov and T. Van Voorhis, Phys. Rev. Lett. 103, 063004 (2009)] is particularly well physically justified. Using this improved formula, we compute dynamic dipole polarizabilities and van der Waals C_6 coefficients for a set of atoms and molecules. Good agreement with the benchmark values is obtained in most cases

Exchange and Correlation in Open Systems of Fluctuating Electron Number

While the exact total energy of a separated open system varies linearly as a function of average electron number between adjacent integers, the energy predicted by semi-local density functional approximations curves upward and the exact-exchange-only or Hartree-Fock energy downward. As a result, semi-local density functionals fail for separated open systems of fluctuating electron number, as in stretched molecular ions A$_2^{+}$ and in solid transition metal oxides. We develop an exact-exchange theory and an exchange-hole sum rule that explain these failures and we propose a way to correct them via a local hybrid functional.Comment: 4 pages, 2 figure

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.Comment: 32 pages, single pdf fil

Software for the frontiers of quantum chemistry:An overview of developments in the Q-Chem 5 package

This article summarizes technical advances contained in the fifth major release of the Q-Chem quantum chemistry program package, covering developments since 2015. A comprehensive library of exchange–correlation functionals, along with a suite of correlated many-body methods, continues to be a hallmark of the Q-Chem software. The many-body methods include novel variants of both coupled-cluster and configuration-interaction approaches along with methods based on the algebraic diagrammatic construction and variational reduced density-matrix methods. Methods highlighted in Q-Chem 5 include a suite of tools for modeling core-level spectroscopy, methods for describing metastable resonances, methods for computing vibronic spectra, the nuclear–electronic orbital method, and several different energy decomposition analysis techniques. High-performance capabilities including multithreaded parallelism and support for calculations on graphics processing units are described. Q-Chem boasts a community of well over 100 active academic developers, and the continuing evolution of the software is supported by an “open teamware” model and an increasingly modular design

Correcting the self-interaction error of approximate density functionals

Common density functional approximations (DFAs) for the exchange-correlation energy suffer from self-interaction error (SIE), which is believed to be the cause of many of the failures of these approximations, such as poor description of charge transfer and transition states of chemical reactions. The standard self-interaction correction (SIC) of Perdew and Zunger (PZ) removes spurious self-interaction terms orbital-by-orbital. We implemented the Perdew–Zunger SIC self-consistently and carried out systematic tests of its performance. We found that PZ-SIC impairs the accuracy of semi-local functionals for equilibrium properties. PZ-SIC seems to overcorrect many-electron systems. We devised a modified version of the SIC, which is scaled down in many-electron regions. The scaled-down SIC has greatly improved performance for many molecular properties. Studies of fractionally-charged systems led to the new definition of "many-electron self-interaction error", which is a generalization of the one-electron concept. An " M -electron self-interaction-free" functional is one that produces a realistic linear variation of total energy with electron number N between the integers M -1 and M . Semi-local DFAs exhibit large many-electron SIE and therefore fail for systems with fractional average electron number. PZ-SIC and its scaled-down variants are one-electron SIE-free. PZ-SIC is often nearly many-electron SIE-free, but this property is lost in the scaled-down SIC. Another consequence of the SIE is incorrect asymptotic behavior of the exchange-correlation potential in semi-local DFAs. PZ-SIC recovers the exact asymptote, but its scaled-down version does not. An efficient method to impose the exact asymptote in a hybrid functional is to introduce range separation into the exchange component and replace the long-range portion of the approximate exchange by the Hartree-Fock counterpart. We show that this long-range correction works particularly well in combination with the short-range variant of the Perdew, Burke, and Ernzerhof (PBE) exchange functional. This long-range-corrected hybrid, denoted LC-ωPBE, is remarkably accurate for a broad range of molecular properties, such as thermo-chemistry, barrier heights of chemical reactions, bond lengths, and most notably, description of processes involving long-range charge transfer. Although LC-ωPBE is not exactly one-electron SIE-free, it can be nearly many-electron SIE-free in many cases

Benchmark assessment of the accuracy of several van der Waals density functionals

The nonlocal correlation functional VV10, developed recently in our group, describes the whole range of dispersion interactions in a seamless and general fashion using only the electron density as input. The VV10 functional has a simple analytic form that can be adjusted for pairing with the exchange functional of choice. In this paper, we use several benchmark data sets of weakly interacting molecular complexes to test the accuracy of two VV10 variants, differing in their treatment of the exchange component. For the sake of comparison, several other density functionals suitable for noncovalent interactions were also tested against the same benchmarks. We find that the “default’’ version of VV10 with semilocal exchange gives very accurate geometries and binding energies for most van der Waals complexes but systematically overbinds hydrogen-bonded complexes. The alternative variant of VV10 with long-range corrected hybrid exchange performs exceptionally well for all types of weak bonding sampled in this study, including hydrogen bonds.David & Lucile Packard FoundationNational Science Foundation (U.S.) (CHE-1058219