111 publications from this institution
Current gradient-corrected density-functional approximations for the exchange energies of atomic and molecular systems fail to reproduce the correct 1/r asymptotic behavior of the exchange-energy density. Here we report a gradient-corrected exchange-energy functional with the proper asymptotic limit. Our functional, containing only one parameter, fits the exact Hartree-Fock exchange energies of a wide variety of atomic systems with remarkable accuracy, surpassing the performance of previous functionals containing two parameters or more.
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).
Density functional theory (DFT) is a (in principle exact) theory of electronic structure, based on the electron density distribution n(r), instead of the many-electron wave function Ψ(r1,r2,r3,...). Having been widely used for over 30 years by physicists working on the electronic structure of solids, surfaces, defects, etc., it has more recently also become popular with theoretical and computational chemists. The present article is directed at the chemical community. It aims to convey the basic concepts and breadth of applications: the current status and trends of approximation methods (local density and generalized gradient approximations, hybrid methods) and the new light which DFT has been shedding on important concepts like electronegativity, hardness, and chemical reactivity index.
A new dynamical correlation functional is constructed subject to a small number of simple, yet key, requirements not all satisfied by existing functionals in the literature. The new functional gives good atomic correlation energies, and, in conjunction with previous gradient-corrected exchange functionals and exact-exchange mixing, excellent thermochemistry in the G2 benchmarks of Pople and co-workers.
Becke and Johnson introduced an ad hoc definition of atomic volume [J. Chem. Phys. 124, 014204 (2006)] in order to obtain atom-in-molecule polarizabilities from free-atom polarizabilities in their nonempirical exchange-hole dipole moment model of dispersion interactions. Here we explore the dependence of Becke-Johnson atomic volumes on basis sets and density-functional approximations and provide reference data for all atoms H–Lr. A persuasive theoretical foundation for the Becke-Johnson definition is also provided.
In a recent paper, Becke et al. [J. Chem. Phys. 158, 151103 (2023)] presented a novel double hybrid density functional, “DH23,” whose terms are based on good physics. Its 12 coefficients were 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 (1.76 kcal/mol). Here, we make some revisions to DH23 and test its efficacy on reference data beyond GMTKN55, namely, organometallic reaction energies and barrier heights. The results confirm that DH23 is robust outside its training set. In the process, a slightly smaller GMTKN55 WTMAD2 of 1.73 kcal/mol is achieved.
A coordinate-space model of the exchange hole density, previously introduced by the author, is extrapolated to the case of very strongly inhomogeneous systems (i.e., large density gradients). As a result, we propose a new gradient-corrected exchange energy functional for application to atomic and molecular problems. The model provides theoretical estimates of the parameters in the functional, and these compare well with empirical values deduced from a least squares fit to exact atomic data.
The deficiency of conventional density-functional theory (DFT) in properly describing van der Waals (vdW) (especially dispersion-bound) complexes has been extensively addressed in the past decade. There are now several new methods published in the literature that are capable of accurately capturing weak dispersion interactions in complexes at equilibrium geometries. However, the performance of these new methods at non-equilibrium geometries remains to be assessed. We have previously published [F. O. Kannemann and A. D. Becke, J. Chem. Theory Comput. 6, 1081 (2010)10.1021/ct900699r; A. D. Becke, A. A. Arabi, and F. O. Kannemann, Can. J. Chem. 88, 1057 (2010)10.1139/V10-073] that the functional PW86+PBE+XDM for exchange + correlation + dispersion, respectively, is a highly accurate functional for general thermochemistry and vdW complexes at equilibrium geometries. Here, we show that this nonempirical, except for two parameters in the dispersion damping part, functional also performs well for vdW complexes at compressed and stretched intermonomer separations. The mean absolute relative error (MARE) is 9.4% overall for vdW complexes in the “S22×5” database incorporating compressed and stretched geometries [J. Rezac, K. E. Riley, and P. Hobza, J. Chem. Theory Comput. 7, 2427 (2011)10.1021/ct2002946]. Our largest MARE on the S22×5 database is 13.3% on the compressed geometry set.
Axel is interested in the development of new theoretical and computational methods for the electronic structure of atoms, molecules, and solids, with particular emphasis on the Density-Functional Theory (DFT) of electronic structure.
The optimized effective potential (OEP) for exchange was introduced some time ago by Sharp and Horton [Phys. Rev. 90, 317 (1953)] and by Talman and Shadwick [Phys. Rev. A 14, 36 (1976)]. The integral equation for the OEP is difficult to solve, however, and a variety of approximations have therefore been proposed. These are explicitly orbital dependent and require the same two-electron integrals as Hartree-Fock theory. We have found a remarkably simple approximate effective potential that closely resembles the Talman-Shadwick potential in atoms. It depends only on total densities and requires no two-electron integrals.
Bindungen und freie Elektronenpaare „sichtbar”︁ zu machen gelingt, wenn die Elektronendichteverteilung zur Berechnung der Elektronenlokalisierungsfunktion (ELF) genutzt wird. Dieser Beitrag präsentiert eine computergraphische Darstellung von ELF (rechts z. B. von N 2 , hier allerdings nur schwarzweiß wiedergegeben), in der Farben das Ausmaß der Lokalisierung beschreiben. magnified image
Geometries of 61 small, neutral, singlet-ground-state molecules have been calculated using the local spin-density approximation (LSDA) density-functional theory. The computational method employed [A. D. Becke, Int. J. Quantum Chem. S 23, 599 (1989)] is free of conventional LCAO basis-set error. Errors due to basis-set truncation in previously published LSDA geometries are thus distinguished from errors purely due to the LSDA. It is found that the LSDA consistently overestimates bond lengths between hydrogens and main-group elements by 0.01–0.04 bohr, and usually underestimates bond lengths between nonhydrogens by less than 0.05 bohr. The tabulated geometries should be useful in calibrating basis sets and in developing beyond-LSDA exchange-correlation functionals.
In a recent paper [H. L. Schmider and A. D. Becke, J. Chem. Phys. 108, 9624 (1998)], we applied a systematic method for the determination of exchange-correlation functionals within the generalized gradient approximation (GGA) to the extended G2 test set of standard heats of formation of Curtiss et al. [J. Chem. Phys. 106, 1063 (1997)]. In the present work, we apply a similar methodology that goes beyond the GGA by taking second-order gradients and the (noninteracting) kinetic-energy density into account. The resulting improvement in the reproduction of thermochemical data brings us very close to the quality of G2 theory itself. Our lowest mean absolute error for standard heats of formation, 1.60 kcal/mol, is only marginally greater than the G2 value (1.58 kcal/mol). The corresponding largest deviation is 9.97 kcal/mol, as compared to 8.2 kcal/mol for G2 theory.
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.
