David J. Tozer

DEVELOPMENT AND ASSESSMENT OF NEW EXCHANGE-CORRELATION FUNCTIONALS

We recently presented a new method for developing generalized gradient approximation (GGA) exchange-correlation energy functionals, using a least-squares procedure involving numerical exchange-correlation potentials and experimental energetics and nuclear gradients. In this paper we use the same method to develop a new GGA functional, denoted HCTH, based on an expansion recently suggested by Becke [J. Chem. Phys. 107, 8554 (1997)]. For our extensive training set, the new functional yields improved energetics compared to both the BLYP and B3LYP functionals [Phys. Rev. A 38, 3098 (1988); Phys. Rev. B 37, 785 (1988); J. Chem. Phys. 98, 5648 (1993); J. Phys. Chem. 98, 11623 (1994)]. The geometries of these systems, together with those of a set of transition metal compounds, are shown to be an improvement over the BLYP functional, while the reaction barriers for six hydrogen abstraction reactions are comparable to those of B3LYP. These improvements are achieved without introducing any fraction of exact orbital...

Improving virtual Kohn–Sham orbitals and eigenvalues: Application to excitation energies and static polarizabilities

Conventional continuum exchange-correlation functionals (e.g., local density approximation, generalized gradient approximation) offer a poor description of many response properties, such as static polarizabilities and single photon vertical excitation energies to Rydberg states. These deficiencies are related to errors in the virtual Kohn–Sham orbitals and eigenvalues, which arise due to a fundamental deficiency in the potentials of conventional continuum functionals. Namely, although these potentials approximately average over the exact integer discontinuity in energetically important regions, they fail to do so asymptotically, because they vanish. Our recent functional HCTH [J. Chem. Phys. 109, 6264 (1998)] was designed with this deficiency in mind, although its potential still fails to exhibit the appropriate asymptotic form. In this paper, we present a new procedure that explicitly corrects this asymptotic deficiency for any continuum functional. Self-consistent Kohn–Sham calculations are performed us...

Relationship between long-range charge-transfer excitation energy error and integer discontinuity in Kohn-Sham theory

Charge-transfer (CT) electronic excitation energies are known to be very poorly predicted by time-dependent density functional theory (TDDFT) using local exchange-correlation functionals. Insight into this observation is provided by a simple analysis of intermolecular CT excitations at infinite separation. It is argued that the first TDDFT CT excitation energy approximately underestimates the experimental excitation by the average of the integer discontinuities of the donor and acceptor molecules; errors are of the order of several electron volts.

Does density functional theory contribute to the understanding of excited states of unsaturated organic compounds

A comparative study has been performed on the electronic spectra of a number of unsaturated organic molecules, using on the one hand density functional linear response theory and on the other multiconfigurational second-order perturbation theory, in order to establish the accuracy that the density functional based methods can give for excitation energies and energy surfaces for excited states. The following molecules are included in the study: tetrazine; the five-membered ring systems cyclopentadiene, furan, pyrrole, and thiophene; acetone; and a dipeptide. The results show that DFT valence excited states have errors that vary between 0 and 1 eV, while Rydberg states are accurate to about 0.2eV in most cases. The use of an asymptotically corrected exchange-correlation potential was essential for the latter result. However, transitions which involve a considerable charge transfer have much larger errors. The results show in some cases a surprisingly strong interaction between valence and Rydberg excited st...

Hybrid exchange-correlation functional determined from thermochemical data and ab initio potentials.

Multiplicative potentials, appropriate for adding to the non-multiplicative fractional orbital exchange term in the Kohn–Sham equations, are determined from correlated ab initio electron densities. The potentials are examined graphically and are used in conjunction with conventional thermochemical data to determine a new hybrid exchange-correlation functional, denoted B97-2. Calculations using B97-2 are compared with those from (a) the B97-1 functional [J. Chem. Phys. 109, 6264 (1998)], which has the same functional form and fraction of orbital exchange, but was fitted to just thermochemical data; and (b) the widely used B3LYP functional [J. Chem. Phys. 98, 5648 (1993)]. B97-2 atomization energies are close to those from B97-1; total electronic energies and ionization potentials are less accurate, but remain an improvement over B3LYP. Molecular structures from all three functionals are comparable. Static isotropic polarizabilities improve from B3LYP to B97-1 to B97-2; the B97-2 functional underestimates e...

Assessment of a Coulomb-attenuated exchange–correlation energy functional

The recently proposed CAM-B3LYP exchange-correlation energy functional, based on a partitioning of the r operator in the exchange interaction into long- and short-range components, is assessed for the determination of molecular thermochemistry, structures, and second order response properties. Rydberg and charge transfer excitation energies and static electronic polarisabilities are notably improved over the standard B3LYP functional; classical reaction barriers also improve. Ionisation potentials, bond lengths, NMR shielding constants and indirect spin-spin coupling constants are comparable with the two functionals. CAM-B3LYP atomisation energies and diatomic harmonic vibrational wavenumbers are less accurate than those of B3LYP. Future research directions are outlined.

The exchange-correlation potential in Kohn–Sham nuclear magnetic resonance shielding calculations

A simple gradient correction to the local density approximation functional is proposed, which improves the structure of the exchange-correlation potential. The optimized generalized gradient approximation (GGA) functional provides uncoupled isotropic and anisotropic nuclear magnetic resonance shielding constants that are 2–3 times more accurate than those of commonly used GGAs, for a series of challenging molecules involving first- and second-row atoms; the results are competitive with those of ab initio wave function methods. A correlation is observed between the lowest occupied-virtual eigenvalue difference and the shielding accuracy. Magnetizabilities are also improved. The performance of the functional for structural and energetic predictions is investigated. These properties can be improved by relaxing the uniform electron gas condition, with no degradation in shielding quality. Atomization energies, ionization potentials, and molecular bond lengths are then comparable to those of other GGA functiona...

A semiempirical generalized gradient approximation exchange-correlation functional

We describe our attempts to improve upon the quality of the KT1 and KT2 generalized gradient approximation (GGA) exchange-correlation functionals [T. W. Keal and D. J. Tozer, J. Chem. Phys. 119, 3015 (2003)], through the introduction of additional gradient-corrected exchange and correlation terms. A GGA functional, denoted KT3, is presented, which maintains the high quality main-group nuclear magnetic resonance shielding constants obtained with KT1 and KT2; results are 2-3 times more accurate than conventional GGA and hybrid functionals. For the extensive range of systems considered in this study, KT3 also provides atomization energies, ionization potentials, electron affinities, proton affinities, bond angles, and electronic polarizabilities that are comparable to, or that surpass, those of the best present-day GGAs. Furthermore, it provides equilibrium molecular bond lengths and diatomic harmonic vibrational wave numbers that are as accurate as those from the best hybrid functionals. Further improvements are required in the description of classical chemical reaction barriers.

Excited state surfaces in density functional theory: A new twist on an old problem

Excited state surfaces in density functional theory and the problem of charge transfer are considered from an orbital overlap perspective. For common density functional approximations, the accuracy of the surface will not be uniform if the spatial overlap between the occupied and virtual orbitals involved in the excitation has a strong conformational dependence; the excited state surface will collapse toward the ground state in regions where the overlap is very low. This characteristic is used to predict and to provide insight into the breakdown of excited state surfaces in the classic push-pull 4-(dimethylamino)benzonitrile molecule, as a function of twist angle. The breakdown is eliminated using a Coulomb-attenuated functional. Analogous situations will arise in many molecules.

Influence of Triplet Instabilities in TDDFT.

Singlet and triplet vertical excitation energies from time-dependent density functional theory (TDDFT) can be affected in different ways by the inclusion of exact exchange in hybrid or Coulomb-attenuated/range-separated exchange-correlation functionals; in particular, triplet excitation energies can become significantly too low. To investigate these issues, the explicit dependence of excitation energies on exact exchange is quantified for four representative molecules, paying attention to the effect of constant, short-range, and long-range contributions. A stability analysis is used to verify that the problematic TDDFT triplet excitations can be understood in terms of the ground state triplet instability problem, and it is proposed that a Hartree-Fock stability analysis should be used to identify triplet excitations for which the presence of exact exchange in the TDDFT functional is undesirable. The use of the Tamm-Dancoff approximation (TDA) significantly improves the problematic triplet excitation energies, recovering the correct state ordering in benzoquinone; it also affects the corresponding singlet states, recovering the correct state ordering in naphthalene. The impressive performance of the TDA is maintained for a wide range of molecules across representative functionals.