111 publications from this institution
A novel density-functional approach provides accurate predictions for the colour zoning of ROY polymorphs and the fluorescence energies of a family of 9-acetylanthracene cocrystals.
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.
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.
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.
We describe a new algorithm for the generation of 3D grids for the numerical evaluation of multicenter molecular integrals in density functional theory. First, we use the nuclear weight functions method of Becke [A. D. Becke, J. Chem. Phys. 88, 2547 (1988)] to decompose a multicenter integral ∫F(r) dr into a sum of atomic-like single-center integrals. Then, we apply automatic numerical integration techniques to evaluate each of these atomic-like integrals, so that the total integral is approximated as ∫F(r) dr≊∑iωiF(ri). The set of abscissas ri and weights ωi constitutes the 3D grid. The 3D atomic-like integrals are arranged as three successive monodimensional integrals, each of which is computed according to a recently proposed monodimensional automatic numerical integration scheme which is able to determine how many points are needed to achieve a given accuracy. When this monodimensional algorithm is applied to 3D integration, the 3D grids obtained adapt themselves to the shape of the integrand F(r), and have more points in more difficult regions. The function F(r), which, upon numerical integration, yields the 3D grid, is called the generating function of the grid. We have used promolecule densities as generating functions, and have checked that grids generated from promolecule densities are also accurate for other integrands. Our scheme is very reliable in the sense that, given a relative tolerance ε, it generates 3D grids which are able to approximate multicenter integrals with relative errors smaller than ε for all the molecules tested in this work. Coarser or finer grids can be obtained using greater or smaller tolerances. For a series of 21 molecules, the average number of points per atom for ε=2.0⋅10−3, ε=2.0⋅10−4, ε=2.0⋅10−5, ε=2.0⋅10−6, and ε=2.0⋅10−7 is respectively 3141 (2.9⋅10−4), 10271 (2.4⋅10−5), 27184 (3.1⋅10−6), 72266 (1.9⋅10−7), and 164944 (5.2⋅10−9) (in parentheses are the maximum errors obtained when integrating the density). It is possible to reduce the number of points in the grid by taking advantage of molecular symmetry. It seems that our method achieves a given accuracy with fewer points than other recently proposed methods.
We have developed a fully numerical, basis-set-free algorithm for solution of the Schrödinger single-particle equation in polyatomic molecules. As a test of the algorithm, the Hartree–Fock energy of H+3 is computed and compared with previous momentum-space benchmarks. The present calculations are the first successful basis-set-free calculations in coordinate space on a polyatomic molecular system.
Since its formal inception in 1964–1965, Kohn-Sham density-functional theory (KS-DFT) has become the most popular electronic structure method in computational physics and chemistry. Its popularity stems from its beautifully simple conceptual framework and computational elegance. The rise of KS-DFT in chemical physics began in earnest in the mid 1980s, when crucial developments in its exchange-correlation term gave the theory predictive power competitive with well-developed wave-function methods. Today KS-DFT finds itself under increasing pressure to deliver higher and higher accuracy and to adapt to ever more challenging problems. If we are not mindful, however, these pressures may submerge the theory in the wave-function sea. KS-DFT might be lost. I am hopeful the Kohn-Sham philosophical, theoretical, and computational framework can be preserved. This Perspective outlines the history, basic concepts, and present status of KS-DFT in chemical physics, and offers suggestions for its future development.
We have compiled a benchmark set of mean ligand-removal enthalpies for 32 transition-metal complexes of relevance in organometallic and catalysis chemistry. Our recent exact-exchange-based density-functional model, DF07 ( J. Chem. Phys. 2007, 127 (12), 124108 ), is assessed on this benchmark set along with other representative GGA, meta-GGA, and hybrid functionals. DF07 performs remarkably well, despite its exact-exchange foundation, indicating that it properly describes nondynamical correlation in transition-metal–ligand bonds.
In this work, our exact-exchange-based static + dynamical correlation density functional [A. D. Becke, J. Chem. Phys. 122, 064101 (2005)]10.1063/1.1844493 is generalized to include “strong” correlation, i.e., accurate computations on dissociating chemical systems without breaking space or spin symmetries and without using multi-determinantal reference states. Also, we introduce a strong-correlation benchmark set composed of space- and spin-symmetrized open-shell atoms on which the generalized functional is tested. Initial results are very promising.
Real-space models of nondynamical correlation between electrons of opposite spin and of parallel spin in multicenter (molecular) systems are discussed. These models are designed to be partnered with Hartree–Fock or exact Kohn–Sham exchange. Thus the numerous and well-known problems of local density-functional exchange-correlation approximations, especially in stretched odd-electron systems, are circumvented.
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.
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?
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
Previous models for exchange (Becke and Roussel, Phys. Rev. A: 39, 3761 (1989)) and for correlation (Becke, J. Chem. Phys. 88, 1053 (1988)) are, in a simple and natural way, generalized to include explicit dependence on current density J. First-principles incorporation of J into exchange-correlation density functionals, as proposed here, is crucial for further progress in the study of magnetic effects in density-functional theory. Key words: density-functional theory, exchange-correlation functionals, current density.
A recent exact-exchange-based density-functional model of nondynamical and dynamical correlation [A.D. Becke, J. Chem. Phys. 122, 064101 (2005)] is tested on 70 barrier heights for a variety of reaction types: hydrogen transfer reactions, heavy-atom transfer reactions, nucleophilic substitutions, association reactions, and unimolecular rearrangements, including both even- and odd-electron systems. The mean absolute error with respect to accurate reference data is 1.4kcal∕mol. This is achieved without any refitting of the parameters of the model to the barrier height data.
In two recent papers [A. D. Becke, J. Chem. Phys. 156, 214101 (2022) and A. D. Becke, J. Chem. Phys. 157, 234102 (2022)], we compared two Kohn–Sham density functionals based on physical modeling 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 general main-group thermochemistry, kinetics, and noncovalent interactions (GMTKN55) chemical database of Goerigk et al. [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 density functional with the lowest GMTKN55 WTMAD2 “weighted total mean absolute deviation” error (1.76 kcal/mol) yet seen for any hybrid or double-hybrid density-functional approximation. We call it “DH23.”
