111 publications from this institution
We have recently introduced a model of the dispersion interaction based on the position-dependent dipole moment of the exchange hole [J. Chem. Phys. 122, 154104 (2005)]. The original derivation, involving simple dipole-induced-dipole electrostatics, was somewhat heuristic, however, and lacking in rigor. Here we present a much more satisfying derivation founded on second-order perturbation theory in the closure approximation and a semiclassical evaluation of the relevant interaction integrals. Expressions for C6, C8, and C10 dispersion coefficients are obtained in a remarkably straightforward manner. Their values agree very well with ab initio reference data on dispersion coefficients between the atoms H, He, Ne, Ar, Kr, and Xe. We also highlight the importance of the exchange-hole contribution to the dispersion coefficients, especially to C6.
We present a new coordinate-space model of spherically averaged exchange-hole functions in inhomogeneous systems that depends on local values of the density and its gradient and Laplacian, and also the kinetic energy density. Our model is completely nonempirical, incorporates the uniform-density electron gas and hydrogenic atom limits, and yields the proper 1/r asymptotic exchange potential in finite systems. Comparisons of model exchange energies, holes, and potentials with exact Hartree-Fock results in selected atoms are very encouraging.
We introduce in this work a new approach to the identification of localized electronic groups in atomic and molecular systems. Our approach is based on local behavior of the Hartree–Fock parallel-spin pair probability and is completely independent of unitary orbital transformations. We derive a simple ‘‘electron localization function’’ (ELF) which easily reveals atomic shell structure and core, binding, and lone electron pairs in simple molecular systems as well.
In two recent papers [A. D. Becke, J. Chem. Phys. 156, 214101 (2022) and 157, 234102 (2022)] we compared two Kohn-Sham density functionals based on physical modelling 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 GMTKN55 chemical database of Goerigk, Grimme, and coworkers [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 (DH) density functional with the lowest GMTKN55 "WTMAD2" error yet seen for a DH functional. We call it "DH23".
A completely numerical method for the computation of Hartree–Fock–Slater wave functions in diatomic systems has been previously reported and applied to the calculation of dissociation energies for selected first-row molecules. The previous results were obtained using spin-restricted orbitals. In this note, the results of new, fully spin-unrestricted calculations are presented.
A simple formalism for the evaluation of 〈S2〉 in terms of the two-particle density matrix is presented. The implementation of the formalism in the restricted open-shell Hartree–Fock (ROHF), unrestricted HF (UHF) and density functional (DFT) based theories is discussed. Rules governing the nonzero S2 matrix elements in the UHF based methods are presented. Further examples are given of 〈S2〉 in several atomic and radical systems from very simple density functional models.
Bonds between, and to, transition-metal atoms often involve strong electron correlation which cannot be handled by conventional density-functional-theory approximations. The recent “B13” functional of Becke [J. Chem. Phys. 138, 074109 (2013) and J. Chem. Phys. 138, 161101 (2013)] models dynamic, static, and strong correlation in an exact-exchange-based framework. We test B13 on bond energies of transition-metal diatomics in this work, with promising results.
We test an exchange-correlation functional with explicit dependence on kinetic-energy density as well as the density, its gradient, and its Laplacian, on the Gaussian-2 thermochemical data base. With a small degree of exact-exchange mixing, we find average errors with respect to experiment of order 2 kcal/mol, 0.15 eV, and 2 kcal/mol, respectively, for atomization energies, ionization potentials, and proton affinities. © 1994 John Wiley & Sons, Inc.
First singlet (S1) excitations are of primary importance in the photoluminescence spectra of organic chromophores. However, due to the multi-determinantal nature of the singlet excited states, standard Kohn-Sham density-functional theory (DFT) is not applicable. While linear-response time-dependent DFT is the method of choice for the computation of excitation energies, it fails severely for excitations with charge-transfer character. Becke’s recent virial exciton model [A. D. Becke, J. Chem. Phys. 148, 044112 (2018)] offers a promising solution to employ standard DFT for calculation of the S1 excitation energy in molecular systems. Here, it is shown that the virial exciton model is free of charge-transfer error. It is equally reliable for S1 excitations with significant charge-transfer character as for other classes of transitions.
Despite the remarkable thermochemical accuracy of Kohn–Sham density-functional theories with gradient corrections for exchange-correlation [see, for example, A. D. Becke, J. Chem. Phys. 96, 2155 (1992)], we believe that further improvements are unlikely unless exact-exchange information is considered. Arguments to support this view are presented, and a semiempirical exchange-correlation functional containing local-spin-density, gradient, and exact-exchange terms is tested on 56 atomization energies, 42 ionization potentials, 8 proton affinities, and 10 total atomic energies of first- and second-row systems. This functional performs significantly better than previous functionals with gradient corrections only, and fits experimental atomization energies with an impressively small average absolute deviation of 2.4 kcal/mol.
Meta-generalized-gradient approximations (meta-GGAs) in density-functional theory are exchange-correlation functionals whose integrands depend on local density, density gradient, and also the kinetic-energy density. It has been pointed out by Johnson et al. [Chem. Phys. Lett. 394, 334 (2004)] that meta-GGA potential energy curves in dispersion-bound complexes are susceptible to spurious oscillations unless very large integration grids are used. This grid sensitivity originates from the saddle-point region of the density near the intermonomer midpoint. Various dimensionless ratios involving the kinetic-energy density, found in typical meta-GGAs, may be ill-behaved in this region. Grid sensitivity thus arises if the midpoint region is sampled by too sparse a grid. For most meta-GGAs, standard grids do not suffice. Care must be taken to avoid this problem when using, or constructing, meta-GGAs.
A completely numerical method is presented for the calculation of Hartree–Fock–Slater wave functions in diatomic systems. The method is numerical in the sense that no LCAO basis sets are employed. Muffin tin or other cellular approximations are also avoided. All molecular functions are defined on a two-dimensional discrete mesh in prolate spheroidal coordinate space. The method is mathematically very simple, and numerical accuracy is easily controlled by changing the number of mesh points. Calculations on the molecules B2, C2, N2, CO, O2, and F2 are reported, and we compare dissociation energies, bond lengths, vibrational frequencies, and charge moments with recent LCAO results and with experiment. These calculations indicate that the method works very nicely for the molecules considered, and also that the Hartree–Fock–Slater theory describes molecular systems remarkably well.
The exchange-hole dipole moment (XDM) dispersion model of Becke and Johnson combined with the PW86 exchange GGA and the PBE correlation GGA comprise a nonempirical (almost) density functional for covalent and noncovalent chemistry. Only two fit parameters are required in the dispersion damping part. We have fit these two parameters to a comprehensive test set of 65 intermolecular complexes spanning three orders of magnitude in binding energy strength (from the He dimer to the hydrogen bonded uracil dimer) with uniform quality over the entire set. The fit parameters are clearly universal and transferable. Our current efforts are concentrated on obtaining forces and optimized geometries from this functional
