111 publications from this institution
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.
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.
Previous attempts to combine Hartree–Fock theory with local density-functional theory have been unsuccessful in applications to molecular bonding. We derive a new coupling of these two theories that maintains their simplicity and computational efficiency, and yet greatly improves their predictive power. Very encouraging results of tests on atomization energies, ionization potentials, and proton affinities are reported, and the potential for future development is discussed.
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.
Density-functional exchange–correlation approximations depending on spin densities and their gradients have proven remarkably accurate in recent thermochemical tests [e.g., A. D. Becke, J. Chem. Phys. 107, 8554 (1997)]. With the inherent limitations of first-order gradient corrections now in sight, however, we investigate here a class of inhomogeneity corrections based on a new second-order gradient parameter. The new parameter is logically motivated by previous work on Taylor expanded exchange hole densities, and generates exchange–correlation functionals more accurate than those containing first-order gradients only.
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.
An old and yet unsolved problem in density-functional theory is the strong dependence of degenerate open-shell atomic energies on the occupancy of the atomic orbitals. This arises from the fact that degenerate atomic orbitals of different ml do not have equivalent densities. Approximate density functionals therefore give energies depending strongly on which orbitals are occupied. This problem is solved in the present work by incorporating current density into the calculations using a current-density dependent functional previously published by the author.
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.
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.
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.”
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.
The application of conventional GGA and meta-GGA density functionals to van der Waals interactions is fraught with difficulties. Conventional functionals do not contain the physics of the dispersion interaction. To make matters worse, the exchange part alone can yield anything from severe overbinding to severe over-repulsion depending on the choice of functional. We have assessed a variety of exchange GGAs for their ability to reproduce exact Hartree-Fock repulsion energies in rare-gas systems, and we find that PW86 [ Phys. Rev. B 1986 , 33 , 8800 ] performs remarkably well. The addition of a dynamical correlation GGA and the nonempirical dispersion model of Becke and Johnson [ J. Chem. Phys. 2007 , 127 , 154108 ] to PW86 gives a simple GGA plus dispersion theory yielding excellent rare-gas interaction curves for pairs involving He through Kr, with only two adjustable parameters for damping of the dispersion terms.
Alkalides are crystalline salts in which the anion is a negatively charged alkali metal.
In previous work (J. Chem. Theory Comput. 2009, 5, 719), we assessed the performance of standard semilocal exchange-correlation density functionals plus the nonempirical dispersion model of Becke and Johnson (J. Chem. Phys. 2007, 127, 154108) on binding energy curves of rare-gas diatomics. The results were encouraging. In this work, we extend our study to 65 intermolecular complexes representing a wide variety of van der Waals interactions including dispersion, hydrogen bonding, electrostatic, and stacking. Comparisons are made with other density-functional methods for van der Waals interactions in the literature.
Previous work by the author on diatomic molecules and by others on polyatomic systems has revealed that Kohn–Sham density-functional theory with ‘‘gradient corrected’’ exchange-correlation approximations gives remarkably good molecular bond and atomization energies. In the present communication, we report the results of an extensive survey of density-functional atomization energies on the 55 molecules of the Gaussian-1 thermochemical data base of Pople and co-workers [J. Chem. Phys. 90, 5622 (1989); 93, 2537 (1990)]. These calculations have been performed by the fully numerical molecules (NUMOL) program of Becke and Dickson [J. Chem. Phys. 92, 3610 (1990)] and are therefore free of basis-set uncertainties. We find an average absolute error in the total atomization energies of our 55 test molecules of 3.7 kcal/mol, compared to 1.6 kcal/mol for the Gaussian-1 procedure and 1.2 kcal/mol for Gaussian-2.
