111 publications from this institution
We have carried out completely numerical molecular-orbital calculations (i.e., no linear-combination-of-atomic-orbitals basis sets or cellular approximations) on 13 first- and second-row dimers from ${\mathrm{H}}_{2}$ to ${\mathrm{Cl}}_{2}$ in the local-density approximation. The resulting ground-state bond lengths, dissociation energies, and vibrational frequencies are reported and compared with experimental values.
In a recent paper [A. D. Becke, J. Chem. Phys. 156, 214101 (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. With only a handful of physically motivated pre-factors, our functionals matched, and even slightly exceeded, the performance of the best power-series functionals on the general main group thermochemistry, kinetics, and noncovalent interactions (GMTKN55) chemical database of Goerigk et al. [Phys. Chem. Chem. Phys. 19, 32184 (2017)]. This begs the question: how much can their performance be improved by adding power-series terms of our own? We address this question in the present work. First, we describe a series expansion variable that we believe contains more local physics than any other variable considered to date. Then we undertake modest, one-dimensional fits to the GMTKN55 data with our theory-based functional corrected by power-series exchange and dynamical correlation terms. We settle on 12 power-series terms (plus six parent terms) and achieve the lowest GMTKN55 “WTMAD2” error yet reported, by a substantial margin, for a hybrid Kohn–Sham density functional. The new functional is called “B22plus.”
We develop a coordinate-space model for dynamical correlations in an inhomogeneous electron gas. The model treats opposite-spin and same-spin pairs separately, and it also accounts properly for correlation contributions to the kinetic energy. Furthermore, it gives identically zero correlation energy in the case of one-electron systems. Applications to the uniform electron gas and to the atoms H through Ar are reported.
The calculation of molecular bond energies is a sensitive test of exchange-correlation approximations in density functional theory. The well known local density approximation (LDA) gives excellent bond lengths and vibrational frequencies, but seriously overestimates dissociation energies. Therefore, we have investigated the effect on bond energies of nonlocal corrections to the LDA exchange-correlation functional. We consider the nonlocal correction term of Langreth and Mehl, and also a new semiempirical exchange energy correction. Significant improvements over the LDA dissociation energies are obtained in calculations on first-, second-, and third-row homonuclear diatomic systems.
In recent work [A. D. Becke, J. Chem. Phys. 138, 074109 (2013)10.1063/1.4790598], a suite of density functionals for static, dynamical, and strong correlation was introduced. The strong-correlation part is intended to describe dissociating chemical systems using symmetry-restricted orbitals, and was calibrated on spin- and spatially-symmetrized open-shell atoms of the first and second rows. This Communication extends the calibration of our functionals to transition-metal atoms by including all open-shell atoms through the third row. We find that the theory works well for transition-metal atoms also. The new concomitant parametrization will be applied to problems of chemical interest in upcoming work.
A recently suggested procedure for the systematic optimization of gradient-corrected exchange-correlation functionals [A. D. Becke, J. Chem. Phys. 107, 8554 (1997)] has been applied to the extended G2 test set [L. A. Curtiss et al., J. Chem. Phys. 106, 1063 (1997)], which consists of the standard heats of formation of 148 molecules. The limit of reproduction of the experimental data in this test set is found to be 1.78 kcal/mol mean absolute error, with a maximum of 8.89 kcal/mol error for the ozone molecule. This compares rather well with previous results for G2 theory itself (1.58 and 8.2 kcal/mol, respectively). We show that fair stability can be obtained by our optimization procedure.
In two papers, Becke [J. Chem. Phys. 119, 2972 (2003) and J. Chem. Phys. 122, 064101 (2005)] introduced Kohn-Sham density-functional approximations for static and dynamical correlation to be partnered with 100 percent exactly computed exchange. Known as “B05,” this was the first non-local correlation model designed to work with the full non-locality of exact (or Hartree-Fock) exchange. Non-locality issues, often referred to as the “delocalization” problem, are among the most vexing problems in density-functional theory today. How much exact exchange should be used in a hybrid functional? What value of the range parameter should be used in a long-range corrected functional? Questions such as these abound, and the answers are system dependent. The physics of non-locality is built into the B05 functional in a natural way, and one wonders, therefore, if B05 might provide a mechanism to answer such questions. Here we explore a variational procedure, “B05min,” to do so. We compute dipole moments of 52 small molecules and find that B05min delivers better moments than parent hybrid and long-range corrected functionals. Furthermore, B05min provides a priori optimum exact-exchange mixing fractions and range parameters for the parent functionals, whose values agree with literature values fit to experimental data.
We have recently proposed a simple and systematic approach to the generation of exchange-correlation functionals in density-functional theory by linear least-squares fitting to accurate thermochemical reference data. In a series of four publications, new functionals with gradient corrections of first and also second order have been found in this way. In the present article we review and summarize our approach, highlighting the common threads and the most extensive fits from the heretofore published studies. © 1999 John Wiley & Sons, Inc. J Comput Chem 20: 63–69, 1999
Bonds and lone electron pairs can be made “visible” when the electron density distribution is used to calculate the electron localization function (ELF). This paper presents a computer-graphics image of ELF in colors which represent the extent of the localization (at the right a black-and-white picture of N2).
Abstract Recent X α calculations of bond energies and other related properties of first‐row diatomic molecules show very encouraging agreement with experiment. In the worst cases, however, the X α dissociation energies overestimate the experimental values by almost 2 eV. Therefore, we have examined several refinements of the X α theory and their effects on molecular bond lengths, bond energies, and vibrational frequencies. Among them, gradient corrections to the X α exchange energy and also some variations of the local spin‐density correlation energy approximation are considered. We find that a local exchange‐correlation functional with gradient corrections gives dissociation energies in significantly better agreement with experiment than the X α approximation.
Fully-numerical, non-basis-set molecular orbital calculations in coordinate space are reported for the first time on polyatomic systems. Self-consistent density-functional bond energy calculations have been performed on the ten-electron hydrides HF, H2O, NH3, and CH4, in addition to test calculations on the diatomics H2, N2, and F2, and the triatomic ion H+3. We find excellent precision for the present numerical algorithm, and very good agreement between the density-functional and experimental bond energies. Reliable basis-set-free quantum chemistry is now possible, at least in the density-functional theoretical framework.
It has been known for over twenty years that density functionals of the generalized-gradient approximation (GGA) type and exact-exchange-GGA hybrids with low exact-exchange mixing fraction yield enormous errors in the properties of charge-transfer (CT) complexes. Manifestations of this error have also plagued computations of CT excitation energies. GGAs transfer far too much charge in CT complexes. This error has therefore come to be called “delocalization” error. It remains, to this day, a vexing unsolved problem in density-functional theory (DFT). Here we report that a 100% exact-exchange-based density functional known as Becke’05 or “B05” [A. D. Becke, J. Chem. Phys. 119, 2972 (2003); 122, 064101 (2005)] predicts excellent charge transfers in classic CT complexes involving the electron donors NH3, C2H4, HCN, and C2H2 and electron acceptors F2 and Cl2. Our approach is variational, as in our recent “B05min” dipole moments paper [Dale et al., J. Chem. Phys. 147, 154103 (2017)]. Therefore B05 is not only an accurate DFT for thermochemistry but is promising as a solution to the delocalization problem as well.
A systematic procedure for refining gradient corrections in Kohn–Sham exchange-correlation functionals is presented. The procedure is based on least-squares fitting to accurate thermochemical data. In this first application of the method, we use the G2 test set of Pople and co-workers to generate what we believe to be an optimum GGA/exact-exchange density-functional theory (i.e., generalized gradient approximation with mixing of exactly computed exchange).
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.
Exchange holes in molecules can be delocalized over several centers, thus throwing into question their approximation by local density functionals. This work introduces a simple model which detects delocalization in molecules through a local variable related to kinetic energy density. A local exchange functional is derived that reproduces exact-exchange atomization energies of molecules with relatively low error. This has important implications for the simplification of “hybrid” density-functional theories which contain an exactly computed exchange term.
