Axel D. Becke

Density‐functional thermochemistry. III. The role of exact exchange

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.

A new mixing of Hartree–Fock and local density‐functional theories

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 Simple Measure of Electron Localization in Atomic and Molecular-Systems

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.

A multicenter numerical integration scheme for polyatomic molecules

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.

Density‐functional thermochemistry. IV. A new dynamical correlation functional and implications for exact‐exchange mixing

A new dynamical correlation functional is constructed subject to a small number of simple, yet key, requirements not all satisfied by existing functionals in the literature. The new functional gives good atomic correlation energies, and, in conjunction with previous gradient‐corrected exchange functionals and exact‐exchange mixing, excellent thermochemistry in the G2 benchmarks of Pople and co‐workers.

Density-functional thermochemistry. I. The effect of the exchange-only gradient correction

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.

Density-functional thermochemistry. V. Systematic optimization of exchange-correlation functionals.

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).

Density‐functional thermochemistry. II. The effect of the Perdew–Wang generalized‐gradient correlation correction

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.

Density Functional Calculations of Molecular-Bond Energies

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.

Correlation energy of an inhomogeneous electron gas: A coordinate‐space model

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.