Publications

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 double-hybrid density functional based on good local physics with outstanding performance on the GMTKN55 database

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".

Numerical Hartree–Fock–Slater calculations on diatomic molecules: Addendum

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.

Density-functional thermochemistry.

Evaluation of 〈<i>S</i>2〉 in restricted, unrestricted Hartree–Fock, and density functional based theories

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.

Quantum Chemical Methods for Modeling Covalent Modification of Biological Thiols

Targeted covalent inhibitor drugs require computational methods that go beyond simple molecular-mechanical force fields in order to model the chemical reactions that occur when they bind to their targets. Here, several semi-empirical and density-functional theory (DFT) methods are assessed for their ability to describe the potential energy surface and reaction energies of the covalent modification of a thiol by an electrophile. Functionals such as PBE and B3LYP fail to predict a stable enolate intermediate. This is largely due to delocalization error, which spuriously stabilizes the pre-reaction complex, in which excess electron density is transferred from the thiolate to the electrophile. Functionals with a high-exact exchange component, range-separated DFT functionals, and variationally-optimized exact exchange (i.e., the LC-B05minV functional) correct this issue to various degrees. The large gradient behaviour of the exchange enhancement factor is also found to significantly affect the results, leading to the improved performance of PBE0. While ωB97X-D and M06-2X were easonably accurate, no method provided quantitative accuracy for all three electrophiles, making this a very strenuous test of functional performance. Additionally, one drawback of M06-2X was that MD simulations using this functional were only stable if a fine integration grid was used. The low-cost semi-empirical methods, PM3, AM1, and PM7, provide a qualitatively correct description of the reaction mechanism, although the energetics are not quantitatively reliable. As a proof of concept, the potential of mean force for the addition of methylthiolate to MVK was calculated using QM/MM MD in an explicit polarizable aqueous solvent.

Communication: DFT treatment of strong correlation in 3d transition-metal diatomics

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.

A note on least squares fitting with normalization parameters

A density-functional study of van der Waals forces: rare gas diatomics

Thermochemical tests of a kinetic-energy dependent exchange-correlation approximation

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.

Communication: Becke’s virial exciton model gives accurate charge-transfer excitation energies

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.

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.

Strong Correlation in Density-Functional Theory

Oscillations in meta-generalized-gradient approximation potential energy surfaces for dispersion-bound complexes

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.

Density Functional Calculations of Molecular Bond Energies

Foreword

Numerical Hartree–Fock–Slater calculations on diatomic molecules

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.

A Nonempirical density functional for covalent and noncovalent chemistry

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