111 publications from this institution
We test an exchange-correlation functional with explicit dependence on kinetic-energy density as well as the density, its gradient, and its Laplacian, on the Gaussian-2 thermochemical data base. With a small degree of exact-exchange mixing, we find average errors with respect to experiment of order 2 kcal/mol, 0.15 eV, and 2 kcal/mol, respectively, for atomization energies, ionization potentials, and proton affinities. © 1994 John Wiley & Sons, Inc.
Meta-generalized-gradient approximations (meta-GGAs) in density-functional theory are exchange-correlation functionals whose integrands depend on local density, density gradient, and also the kinetic-energy density. It has been pointed out by Johnson et al. [Chem. Phys. Lett. 394, 334 (2004)] that meta-GGA potential energy curves in dispersion-bound complexes are susceptible to spurious oscillations unless very large integration grids are used. This grid sensitivity originates from the saddle-point region of the density near the intermonomer midpoint. Various dimensionless ratios involving the kinetic-energy density, found in typical meta-GGAs, may be ill-behaved in this region. Grid sensitivity thus arises if the midpoint region is sampled by too sparse a grid. For most meta-GGAs, standard grids do not suffice. Care must be taken to avoid this problem when using, or constructing, meta-GGAs.
Bonds and lone electron pairs can be made “visible” when the electron density distribution is used to calculate the electron localization function (ELF). This paper presents a computer-graphics image of ELF in colors which represent the extent of the localization (at the right a black-and-white picture of N2).
Abstract Recent X α calculations of bond energies and other related properties of first‐row diatomic molecules show very encouraging agreement with experiment. In the worst cases, however, the X α dissociation energies overestimate the experimental values by almost 2 eV. Therefore, we have examined several refinements of the X α theory and their effects on molecular bond lengths, bond energies, and vibrational frequencies. Among them, gradient corrections to the X α exchange energy and also some variations of the local spin‐density correlation energy approximation are considered. We find that a local exchange‐correlation functional with gradient corrections gives dissociation energies in significantly better agreement with experiment than the X α approximation.
We have recently proposed a simple and systematic approach to the generation of exchange-correlation functionals in density-functional theory by linear least-squares fitting to accurate thermochemical reference data. In a series of four publications, new functionals with gradient corrections of first and also second order have been found in this way. In the present article we review and summarize our approach, highlighting the common threads and the most extensive fits from the heretofore published studies. © 1999 John Wiley & Sons, Inc. J Comput Chem 20: 63–69, 1999
Fully-numerical, non-basis-set molecular orbital calculations in coordinate space are reported for the first time on polyatomic systems. Self-consistent density-functional bond energy calculations have been performed on the ten-electron hydrides HF, H2O, NH3, and CH4, in addition to test calculations on the diatomics H2, N2, and F2, and the triatomic ion H+3. We find excellent precision for the present numerical algorithm, and very good agreement between the density-functional and experimental bond energies. Reliable basis-set-free quantum chemistry is now possible, at least in the density-functional theoretical framework.
Piezochromic materials, whose luminescence responds to external pressure, have recently garnered much experimental attention. Computational modeling of piezochromism is of high theoretical interest, yet currently lacking. Herein, we present a computational effort to predict the piezochromism for a selection of molecular crystals. The current methodology employs a combination of dispersion-corrected solid-state and gas-phase density-functional theory and Becke’s virial exciton model. Our study finds that piezochromism is primarily driven by the modification of intermolecular interactions within the molecular crystal and can be understood from the perspectives of changing polarizability or bandgaps upon the application of mechanical pressure.
In two recent papers [A. D. Becke, J. Chem. Phys. 156, 214101 (2022) and 157, 234102 (2022)] we compared two Kohn-Sham density functionals based on physical modelling and theory with the best density-functional power-series fits in the literature. The best error statistics reported to date for a hybrid functional on the GMTKN55 chemical database of Goerigk, Grimme, and coworkers [Phys. Chem. Chem. Phys. 19, 32184 (2017)] were obtained. In the present work, additional second-order perturbation-theory terms are considered. The result is a 12-parameter double-hybrid (DH) density functional with the lowest GMTKN55 "WTMAD2" error yet seen for a DH functional. We call it "DH23".
We have recently introduced a model of the dispersion interaction based on the position-dependent dipole moment of the exchange hole [J. Chem. Phys. 122, 154104 (2005)]. The original derivation, involving simple dipole-induced-dipole electrostatics, was somewhat heuristic, however, and lacking in rigor. Here we present a much more satisfying derivation founded on second-order perturbation theory in the closure approximation and a semiclassical evaluation of the relevant interaction integrals. Expressions for C6, C8, and C10 dispersion coefficients are obtained in a remarkably straightforward manner. Their values agree very well with ab initio reference data on dispersion coefficients between the atoms H, He, Ne, Ar, Kr, and Xe. We also highlight the importance of the exchange-hole contribution to the dispersion coefficients, especially to C6.
In recent papers, Becke et al. [J. Chem. Phys. 158, 151103 (2023)] and then Becke [J. Chem. Phys. 159, 241101 (2023)] have developed a novel double hybrid density functional, “DH23,” whose terms are based on good local physics. Its 12 coefficients are trained on the GMTKN55 (general main-group thermochemistry, kinetics, and noncovalent interactions) chemical database of Goerigk et al. [Phys. Chem. Chem. Phys. 19, 32184 (2017)]. The lowest GMTKN55 “WTMAD2” error to date for any hybrid or double hybrid density functional was obtained (1.73 kcal/mol for the revDH23 variant). Here, we simplify DH23 by introducing a dispersion damping scheme involving atomic numbers only and one global parameter. The resulting new functional, “DH24,” performs as well as its predecessors.
A recent virial-theorem-based model of the singlet-triplet splitting in singly excited configurations [A. D. Becke, J. Chem. Phys. 148, 044112 (2018)] offers an accurate and economical tool for the computation of optical gaps in large molecules. Two single-determinant density-functional-theory calculations, one on the (closed-shell) ground state and another on the (restricted open-shell) HOMO → LUMO triplet excited state, followed by a simple two-electron integral evaluation, are all we need. Here the method is used to compute the optical gaps of trans-polyenes containing up to 60 carbon atoms, approaching the polyacetylene limit. Comparisons with previous computations, and experiment, are made. We also explore changes of the exact-exchange mixing fraction in the underlying density functional. Its effect on the optical gap, and also the exciton size, is enormous. Thus we face the vexing, often asked, question: how much exact exchange should be used?
We have performed finite-field calculations of the dipole polarizabilities and hyperpolarizabilities of some first-row compounds in the local spin-density approximation (LDA) at the basis-set limit using the numerical density-functional code NUMOL. We show that the calculations of Guan et al. [J. Chem. Phys. 1993, 98, 4753] on dipole moments and polarizabilities are well converged with their high-quality double-zeta basis set which includes field-induced polarization functions. However, hyperpolarizabilities are not similarly well converged. We provide reference values for first hyperpolarizabilities and estimated LDA values of some second hyperpolarizabilities.
Intermolecular interactions are of great importance in chemistry but are difficult to model accurately with computational methods. In particular, Hartree–Fock and standard density-functional approximations do not include the physics necessary to properly describe dispersion. These methods are sometimes corrected to account for dispersion by adding a pairwise C6∕R6 term, with C6 dispersion coefficients dependent on the atoms involved. We present a post-Hartree–Fock model in which C6 coefficients are generated by the instantaneous dipole moment of the exchange hole. This model relies on occupied orbitals only, and involves only one, universal, empirical parameter to limit the dispersion energy at small interatomic separations. The model is extensively tested on isotropic C6 coefficients of 178 intermolecular pairs. It is also applied to the calculation of the geometries and binding energies of 20 intermolecular complexes involving dispersion, dipole-induced dipole, dipole–dipole, and hydrogen-bonding interactions, with remarkably good results.
Abstract We examine the short‐range behavior of the spherically averaged Hartree–Fock exchange charge density by performing a simple Taylor expansion. On the basis of this expansion, a theoretical model is constructed that generates gradient correction terms to the local density approximation for the exchange energy of an inhomogeneous electron gas. In particular, we derive the X αβ exchange energy functional and a theoretical value for the parameter β. Our value for β agrees well with previous empirical estimates, and with empirical calculations in the present work.
The zeroth-order (uncorrelated) singlet-triplet energy difference in single-particle excited configurations is 2Kif, where Kif is the Coulomb self-energy of the product of the transition orbitals. Here we present a non-empirical, virial-theorem argument that the correlated singlet-triplet energy difference should be half of this, namely, Kif. This incredibly simple result gives vertical HOMO-LUMO excitation energies in small-molecule benchmarks as good as the popular TD-B3LYP time-dependent approach to excited states. For linear acenes and nonlinear polycyclic aromatic hydrocarbons, the performance is significantly better than TD-B3LYP. In addition to the virial theorem, the derivation borrows intuitive pair-density concepts from density-functional theory.
ADVERTISEMENT RETURN TO ISSUEPREVArticleNEXTTheoretical study on the relative strengths of the metal-hydrogen and metal-methyl bonds in complexes of middle to late transition metalsTom Ziegler, Vincenzo Tschinke, and Axel BeckeCite this: J. Am. Chem. Soc. 1987, 109, 5, 1351–1358Publication Date (Print):March 1, 1987Publication History Published online1 May 2002Published inissue 1 March 1987https://pubs.acs.org/doi/10.1021/ja00239a011https://doi.org/10.1021/ja00239a011research-articleACS PublicationsRequest reuse permissionsArticle Views463Altmetric-Citations124LEARN ABOUT THESE METRICSArticle Views are the COUNTER-compliant sum of full text article downloads since November 2008 (both PDF and HTML) across all institutions and individuals. These metrics are regularly updated to reflect usage leading up to the last few days.Citations are the number of other articles citing this article, calculated by Crossref and updated daily. Find more information about Crossref citation counts.The Altmetric Attention Score is a quantitative measure of the attention that a research article has received online. Clicking on the donut icon will load a page at altmetric.com with additional details about the score and the social media presence for the given article. Find more information on the Altmetric Attention Score and how the score is calculated. Share Add toView InAdd Full Text with ReferenceAdd Description ExportRISCitationCitation and abstractCitation and referencesMore Options Share onFacebookTwitterWechatLinked InRedditEmail Other access optionsGet e-Alertsclose Get e-Alerts
In previous work we have introduced exact-exchange-based density-functional models of dynamical, nondynamical, and dispersion correlations. We have not yet, however, been able to combine these models into a single energy functional. The problem is that interaction curves in van der Waals complexes are too repulsive. A simple solution is proposed in the present work resulting in an exact-exchange-based energy functional for all chemical interactions, from the weakest (dispersion) to the strongest (molecular bonds).
