111 publications from this institution
In an earlier paper [A. D. Becke, J. Chem. Phys. 96, 2155 (1992)], Kohn–Sham density-functional calculations of the total atomization energies of the 55 molecules of the Gaussian-1 database of Pople and co-workers [J. Chem. Phys. 90, 5622 (1989); 93, 2537 (1990)] were reported. We found that the local-spin-density exchange-correlation approximation with a ‘‘gradient correction’’ for exchange gave an average deviation from experiment of only 3.7 kcal/mol. In the present work we assess the role of gradient corrections for dynamical correlation, and we enlarge our earlier survey to include 42 atomic and molecular ionization potentials and 8 proton affinities as well. We conclude that gradient corrections for correlation do not improve atomization energies, but are vitally important in electron nonconserving processes such as ionization.
Kohn–Sham density-functional theory (DFT), the predominant framework for electronic structure computations in chemistry today, has undergone considerable evolution in the past few decades. The earliest DFT approximations were based on uniform electron gas models completely free of empirical parameters. Tremendous improvements were made by incorporating density gradients and a small number of parameters, typically one or two, obtained from fits to atomic data. Incorporation of exact exchange and fitting to molecular data, such as experimental heats of formation, allowed even further improvements. This, however, opened a Pandora’s Box of fitting possibilities, given the limitless choices of chemical reactions that can be fit. The result is a recent explosion of DFT approximations empirically fit to hundreds, or thousands, of chemical reference data. These fitted density functionals may contain several dozen empirical parameters. What has been lost in this fitting trend is physical modeling based on theory. In this work, we present a density functional comprising our best efforts to model exchange–correlation in DFT using good theory. We compare its performance to that of heavily fit density functionals using the GMTKN55 chemical reference data of Goerigk and co-workers [Phys. Chem. Chem. Phys. 19, 32184 (2017)]. Our density-functional theory, using only a handful of physically motivated pre-factors, competes with the best heavily fit Kohn–Sham functionals in the literature.
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.
We examine and compare two previously introduced functions of the one-particle density matrix that are suitable to represent its off-diagonal structure in a condensed form and that have illustrative connections to the nature of the chemical bond. One of them, the Localized-Orbital Locator (LOL) [J. Molec. Struct. (THEOCHEM) 527, 51 (2000)], is based only on the noninteracting kinetic-energy density τ and the charge density ρ at a point, and gives an intuitive measure of the relative speed of electrons in its vicinity. Alternatively, LOL focuses on regions that are dominated by single localized orbitals. The other one, the Parity Function P [J. Chem. Phys. 105, 11134 (1996)], is a section through the Wigner phase-space function at zero momentum, and contains information about the phase of the interference of atomiclike orbital contributions from bound centers. In this paper, we discuss the way in which these functions condense information in the density matrix, and illustrate on a variety of examples of unusual chemical bonds how they can help to understand the nature of “covalence.”
In previous work, Kannemann and Becke [ J. Chem. Theory Comput. 5, 719 (2009) and J. Chem. Theory Comput. 6, 1081 (2010) ] have demonstrated that the generalized gradient approximations (GGAs) of Perdew and Wang for exchange [Phys. Rev. B 33, 8800 (1986)] and Perdew, Burke, and Ernzerhof for correlation [Phys. Rev. Lett. 77, 3865 (1996)] , plus the dispersion density functional of Becke and Johnson [J. Chem. Phys. 127, 154108 (2007)] , comprise a nonempirical density-functional theory of high accuracy for thermochemistry and van der Waals complexes. The theory is nonempirical except for two universal cutoff parameters in the dispersion energy. Our calculations so far have been grid-based and have employed the local density approximation (LDA) for the orbitals. In this work, we employ orbitals from self-consistent GGA calculations using Gaussian basis sets. The results, on a benchmark set of 65 van der Waals complexes, are similar to our grid-based post-LDA results. This work sets the stage for van der Waals force computations and geometry optimizations.
Vertical single-particle excitations from closed-shell ground states are complicated by the fact that the singlet open-shell states are, even in the first approximation, two-determinantal. Thus two-electron integrals come into play and standard time-independent DFT (density-functional theory) does not apply. In this work, we use the “adiabatic connection” to analyse the role of the two-electron integrals, obtaining a time-independent DFT approach to excitation-energy calculations that is new and simple. A non-empirical modeling of the method works as well as the popular TD-B3LYP time-dependent approach to excited states, and can be made even simpler by introducing one reasonable semi-empirical parameter.
We have developed a completely numerical scheme for solution of Poisson’s equation in multicenter systems. We are thus able to numerically calculate the Coulomb potential of arbitrary charge distributions in polyatomic molecules. The method is based on a decomposition of the multicenter Poisson problem into independent single-center problems, each of which is solvable in standard spherical coordinates. In combination with our multicenter numerical integration scheme reported previously, completely numerical evaluation of arbitrary two-electron Coulomb integrals is possible. Test calculations on the classic two-electron Coulomb and exchange integrals of H2 and the Coulomb interaction energies of several model polyatomic systems indicate that the scheme is both practical and accurate.
The energy surfaces of the ground and low-lying excited states of ethylene are challenging tests of multi-reference electronic structure methods. A variety of multi-reference wavefunction theories have been applied to this problem and the ensuing photochemistry has been well studied. Density-functional methods, however, have been less successful. In this work, the ‘B13’ strong-correlation density functional is used to generate multi-reference orbitals for the computation of the three lowest-lying singlet states. We explore the states and energies as a function of torsion angle, and as a function of the pyramidalisation angle with respect to the twisted orthogonal structure. The former features an avoided crossing at the orthogonal structure; the latter a Cs slice through a conical intersection. Both features are well reproduced by our B13 method.
Local density-functional exchange-correlation approximations perform remarkably well in simulating nondynamical or “left-right” correlation in molecular bonds. Yet, they do so in a haphazard and unintentional way. In this work we carefully examine the nature of left-right correlation in multicenter systems and suggest a new nondynamical correlation model of post-Hartree–Fock style. The conventional approach to nondynamical correlation is based on the mixing of nearly degenerate states in electronic configuration space. Our approach, on the other hand, is based entirely in real space and uses a single determinant only.
