111 publications from this institution
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.
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.
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.
Density-functional calculations on transition-metal atoms are problematic due to the numerous possible ways, having inequivalent densities, of occupying the d orbitals. The problem is compounded by the issue of real orbitals versus complex orbitals. In this work we systematize the application of density-functional theories to transition-metal atoms using a current-density-dependent functional. For all the single-determinantal angular momentum eigenstates of ground-state terms, we obtain near degeneracy for the energies as we should. Also, we find a simple rule for occupying the real d orbitals that reproduces the energies of the (complex) angular momentum eigenstate results. Thus the long-standing confusion over how to compute transition-metal atom reference energies is resolved.
In a previous work [J. Chem. Phys. 127, 124108 (2007)] we introduced an exact-exchange-based density-functional methodology incorporating dynamical, nondynamical, and dispersion correlations, called DF07. In this work, the performance of the DF07 method is assessed on a variety of thermochemical and kinetic benchmark data including ionization potentials, electron affinities, proton affinities, isomerization energies, bond dissociation enthalpies, and barrier heights of radical reactions. DF07 gives uniform accuracy over all our benchmark data without any refitting of parameters. The importance of the exact-exchange character of DF07 is highlighted through comparison with a three-parameter hybrid meta-generalized-gradient-approximation functional.
A review of the "local density" exchange-correlation approximation (LDA) in quantum chemistry is provided, with particular emphasis on the calculation of molecular bond energies, bond lengths, and vibrational frequencies. The LDA, surprisingly successful in itself, is improved even further by addition of so-called "gradient correction" terms, and following a very brief discussion of the history of gradient-corrected exchange-correlation approximations, recent work in this area is presented. Experience to date, and new results of the present work, indicate that beyond-LDA density functional theories yield molecular spectroscopic properties of near chemical accuracy, even in transition-metal systems, with minimal computational effort.
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.
We have previously demonstrated that the dipole moment of the exchange hole can be used to derive intermolecular C6 dispersion coefficients [J. Chem. Phys. 122, 154104 (2005)]. This was subsequently the basis for a novel post-Hartree-Fock model of intermolecular interactions [J. Chem. Phys. 123, 024101 (2005)]. In the present work, the model is extended to include higher-order dispersion coefficients C8 and C10. The extended model performs very well for prediction of intermonomer separations and binding energies of 45 van der Waals complexes. In particular, it performs twice as well as basis-set extrapolated MP2 theory for dispersion-bound complexes, with minimal computational cost.
We propose a simple scheme for decomposition of molecular functions into single-center components. The problem of three-dimensional integration in molecular systems thus reduces to a sum of one-center, atomic-like integrations which are treated using standard numerical techniques in spherical polar coordinates. The resulting method is tested on representative diatomic and polyatomic systems for which we obtain five- or six-figure accuracy using a few thousand integration points per atom.
In recent papers [A. D. Becke, J. Chem. Phys. 138, 074109 (2013)10.1063/1.4790598; A. D. Becke, J. Chem. Phys. 138, 161101 (2013)10.1063/1.4802982], a density functional for strong correlations in quantum chemistry was introduced. The functional is designed to capture molecular dissociation limits using symmetry-restricted orbitals. Here we demonstrate that the functional describes, with good accuracy, two-determinant multi-reference states. The examples of this work involve 50/50 mixing of symmetry-equivalent Slater determinants at avoided crossings. We employ exactly-computed exchange and fractional spin-orbital occupancies. The connection with dissociated systems and single-determinant reference states is explained.
We have recently introduced [J. Chem. Phys. 122, 154104 (2005)] a simple parameter-free model of the dispersion interaction based on the instantaneous in space, dipole moment of the exchange hole. The model generates remarkably accurate interatomic and intermolecular C6 dispersion coefficients, and geometries and binding energies of intermolecular complexes. The model involves, in its original form, occupied Hartree-Fock or Kohn-Sham orbitals. Here we present a density-functional reformulation depending only on total density, the gradient and Laplacian of the density, and the kinetic-energy density. This density-functional model performs as well as the explicitly orbital-dependent model, yet offers obvious computational advantages.
A density-functional approximation for the relativistic kinetic energy of a many-electron system is introduced, depending on the total particle density and the (nonrelativistic) kinetic energy density. The resulting scalar variational orbital equation is similar to Schrödinger’s nonrelativistic equation, but includes relativistic mass-velocity effects to all orders in p. We test the theory by computing relativistic orbitals in the uranium atom and comparing their energies and mean radii with Dirac and zeroth-order regular approximation results.
In recent publications [A. D. Becke and E. R. Johnson, J. Chem. Phys. 122, 154104 (2005); E. R. Johnson and A. D. Becke 123, 024101 (2005)] we have demonstrated that the position-dependent dipole moment of the exchange hole can be used to generate dispersion interactions between closed-shell systems. Remarkably accurate C6 coefficients and intermolecular potential-energy surfaces can be obtained from Hartree-Fock occupied orbitals and polarizability data alone. In the present work, our model is extended to predict C8 and C10 coefficients as well. These higher-order coefficients are obtained as easily as C6 and with comparable accuracy.
The exchange-only (uncorrelated) singlet-triplet energy difference in one-electron excited configurations is 2Kif, where Kif is the Coulomb self-energy of the product of the transition orbitals. A nonempirical, virial-theorem argument was presented by Becke [J. Chem. Phys. 148, 044112 (2018)] that the correlated singlet-triplet energy difference should be half of this, namely, Kif. This incredibly simple result gave HOMO-LUMO singlet excitation energies in small-molecule benchmark sets as good as the popular TD-B3LYP time-dependent approach to excited states. In a subsequent application to long-chain polyenes approaching the polyacetylene limit [A. D. Becke, J. Chem. Phys. 149, 081102 (2018)], we found a dramatic dependence of the optical gap on the amount of exact exchange in the density functionals used to generate the orbitals. Here, we assess the effect of the exact-exchange fraction in standard small-molecule tests. Also, we assess two basis-set extremes: the highly practical cc-pVDZ basis set and the higher-quality aug-cc-pVTZ.
A simple model is presented in which the instantaneous dipole moment of the exchange hole is used to generate a dispersion interaction between nonoverlapping systems. The model is easy to implement, requiring no electron correlation (in the usual sense) or time dependence, and has been tested on various atomic and molecular pairs. The resulting C6 dispersion coefficients are remarkably accurate.
