Atomic electron affinities and the role of symmetry between electron addition and subtraction in a corrected Koopmans approach.

The essential aspects of zero-temperature grand-canonical ensemble density-functional theory are reviewed in the context of spin-density-functional theory and are used to highlight the assumption of symmetry between electron addition and subtraction that underlies the corrected Koopmans approach of Tozer and De Proft (TDP) for computing electron affinities. The issue of symmetry is then investigated in a systematic study of atomic electron affinities, comparing TDP affinities with those from a conventional Koopmans evaluation and electronic energy differences. Although it cannot compete with affinities determined from energy differences, the TDP expression yields results that are a significant improvement over those from the conventional Koopmans expression. Key insight into the results from both expressions is provided by an analysis of plots of the electronic energy as a function of the number of electrons, which highlight the extent of symmetry between addition and subtraction. The accuracy of the TDP affinities is closely related to the nature of the orbitals involved in the electron addition and subtraction, being particularly poor in cases where there is a change in principal quantum number, but relatively accurate within a single manifold of orbitals. The analysis is then extended to a consideration of the ground state Mulliken electronegativity and chemical hardness. The findings further emphasize the key role of symmetry in determining the quality of the results.

Non-perturbative calculation of molecular magnetic properties within current-density functional theory.

We present a novel implementation of Kohn-Sham density-functional theory utilizing London atomic orbitals as basis functions. External magnetic fields are treated non-perturbatively, which enable the study of both magnetic response properties and the effects of strong fields, using either standard density functionals or current-density functionals-the implementation is the first fully self-consistent implementation of the latter for molecules. Pilot applications are presented for the finite-field calculation of molecular magnetizabilities, hypermagnetizabilities, and nuclear magnetic resonance shielding constants, focusing on the impact of current-density functionals on the accuracy of the results. Existing current-density functionals based on the gauge-invariant vorticity are tested and found to be sensitive to numerical details of their implementation. Furthermore, when appropriately regularized, the resulting magnetic properties show no improvement over standard density-functional results. An advantage of the present implementation is the ability to apply density-functional theory to molecules in very strong magnetic fields, where the perturbative approach breaks down. Comparison with high accuracy full-configuration-interaction results show that the inadequacies of current-density approximations are exacerbated with increasing magnetic field strength. Standard density-functionals remain well behaved but fail to deliver high accuracy. The need for improved current-dependent density-functionals, and how they may be tested using the presented implementation, is discussed in light of our findings.

High accuracy ab initio studies of electron-densities for the ground state of Be-like atomic systems.

Benchmark results for electron densities in the ground states of Li(-), Be, C(2+), Ne(6+), and Ar(14+) have been generated from very accurate variational wave functions represented in terms of extensive basis sets of exponentially correlated Gaussian functions. For Ne(6+), and Ar(14+), the upper bounds to the energies improve over previous results known from the literature. For the remaining systems our bounds are from 0.1 to 1.1 µhartree higher than the most accurate ones. We present in graphical and, partially, numerical form results both for the radial electron densities and for the difference radial density distributions (DRD) (defined with respect to the Hartree-Fock radial density) that highlight the impact of correlation effects on electron densities. Next, we have employed these DRD distributions in studies of the performance of several broadly used orbital-based quantum-chemical methods in accounting for correlation effects on the density. Our computed benchmark densities for Be have been also applied for testing the possibility of using the mathematically strict result concerning exact atomic electron densities, obtained by Ahlrichs et al. [Phys. Rev. A 23, 2106 (1981)], for the determination of the reliability range of computed densities in the long-range asymptotic region. The results obtained for Be are encouraging.

Range-dependent adiabatic connections.

Recently, we have implemented a scheme for the calculation of the adiabatic connection linking the Kohn-Sham system to the physical, interacting system. This scheme uses a generalized Lieb functional, in which the electronic interaction strength is varied in a simple linear fashion, keeping the potential or the density fixed in the process. In the present work, we generalize this scheme further to accommodate arbitrary two-electron operators, allowing the calculation of adiabatic connections following alternative paths as outlined by Yang [J. Chem. Phys. 109, 10107 (1998)]. Specifically, we examine the error-function and Gaussian-attenuated error-function adiabatic connections. It is shown that while the error-function connection displays some promising features, making it amenable to the possible development of new exchange-correlation functionals by modeling the adiabatic connection integrand, the Gaussian-attenuated error-function connection is less promising. We explore the high-density and strong static correlation regimes for two-electron systems. Implications of this work for the utility of range-separated schemes are discussed.

Accurate calculation and modeling of the adiabatic connection in density functional theory.

Using a recently implemented technique for the calculation of the adiabatic connection (AC) of density functional theory (DFT) based on Lieb maximization with respect to the external potential, the AC is studied for atoms and molecules containing up to ten electrons: the helium isoelectronic series, the hydrogen molecule, the beryllium isoelectronic series, the neon atom, and the water molecule. The calculation of AC curves by Lieb maximization at various levels of electronic-structure theory is discussed. For each system, the AC curve is calculated using Hartree-Fock (HF) theory, second-order Moller-Plesset (MP2) theory, coupled-cluster singles-and-doubles (CCSD) theory, and coupled-cluster singles-doubles-perturbative-triples [CCSD(T)] theory, expanding the molecular orbitals and the effective external potential in large Gaussian basis sets. The HF AC curve includes a small correlation-energy contribution in the context of DFT, arising from orbital relaxation as the electron-electron interaction is switched on under the constraint that the wave function is always a single determinant. The MP2 and CCSD AC curves recover the bulk of the dynamical correlation energy and their shapes can be understood in terms of a simple energy model constructed from a consideration of the doubles-energy expression at different interaction strengths. Differentiation of this energy expression with respect to the interaction strength leads to a simple two-parameter doubles model (AC-D) for the AC integrand (and hence the correlation energy of DFT) as a function of the interaction strength. The structure of the triples-energy contribution is considered in a similar fashion, leading to a quadratic model for the triples correction to the AC curve (AC-T). From a consideration of the structure of a two-level configuration-interaction (CI) energy expression of the hydrogen molecule, a simple two-parameter CI model (AC-CI) is proposed to account for the effects of static correlation on the AC. When parametrized in terms of the same input data, the AC-CI model offers improved performance over the corresponding AC-D model, which is shown to be the lowest-order contribution to the AC-CI model. The utility of the accurately calculated AC curves for the analysis of standard density functionals is demonstrated for the BLYP exchange-correlation functional and the interaction-strength-interpolation (ISI) model AC integrand. From the results of this analysis, we investigate the performance of our proposed two-parameter AC-D and AC-CI models when a simple density functional for the AC at infinite interaction strength is employed in place of information at the fully interacting point. The resulting two-parameter correlation functionals offer a qualitatively correct behavior of the AC integrand with much improved accuracy over previous attempts. The AC integrands in the present work are recommended as a basis for further work, generating functionals that avoid spurious error cancellations between exchange and correlation energies and give good accuracy for the range of densities and types of correlation contained in the systems studied here.

The calculation of adiabatic-connection curves from full configuration-interaction densities: two-electron systems.

The Lieb formulation of density-functional theory is briefly reviewed and its straightforward generalization to arbitrary electron-electron interaction strengths discussed, leading to the introduction of density-fixed and potential-fixed adiabatic connections. An iterative scheme for the calculation of the Lieb functionals under the appropriate constraints is outlined following the direct optimization approach of Wu and Yang [J. Chem. Phys. 118, 2498 (2003)]. First- and second-order optimization schemes for the calculation of accurate adiabatic-connection integrands are investigated and compared; the latter is preferred both in terms of computational efficiency and accuracy. The scheme is applicable to systems of any number of electrons. However, to determine the accuracy that may be achieved, the present work focuses on two-electron systems for which a number of simplifications may be exploited. The procedure is applied to the helium isoelectronic series and the H(2) molecule. The resulting adiabatic-connection curves yield the full configuration-interaction exchange-correlation energies extrapolated to the basis-set limit. The relationship between the Kohn-Sham and natural orbitals as functions of the electron-electron interaction strength is explored in detail for H(2). The accuracy with which the exchange-correlation contributions to the modified local potential can be determined is discussed. The new accurate adiabatic-connection curves are then compared with some recently investigated approximate forms calculated using accurate full configuration-interaction input data. This study demonstrates that the adiabatic-connection integrand may be determined accurately and efficiently, providing important insights into the link between the Kohn-Sham and traditional quantum-chemical treatments of the exchange-correlation problem in electronic-structure theory.

Maps of current density using density-functional methods.

The performance of several density-functional theory (DFT) methods for the calculation of current densities induced by a uniform magnetic field is examined. Calculations are performed using the BLYP and KT3 generalized-gradient approximations, together with the B3LYP hybrid functional. For the latter, both conventional and optimized effective potential (OEP) approaches are used. Results are also determined from coupled-cluster singles-and-doubles (CCSD) electron densities by a DFT constrained search procedure using the approach of Wu and Yang (WY). The current densities are calculated within the CTOCD-DZ2 distributed origin approach. Comparisons are made with results from Hartree-Fock (HF) theory. Several small molecules for which correlation is known to be especially important in the calculation of magnetic response properties are considered-namely, O(3), CO, PN, and H(2)CO. As examples of aromatic and antiaromatic systems, benzene and planarized cyclooctatetraene molecules are considered, with specific attention paid to the ring current phenomenon and its Kohn-Sham orbital origin. Finally, the o-benzyne molecule is considered as a computationally challenging case. The HF and DFT induced current maps show qualitative differences, while among the DFT methods the maps show a similar qualitative structure. To assess quantitative differences in the calculated current densities with different methods, the maximal moduli of the induced current densities are compared and integration of the current densities to yield shielding constants is performed. In general, the maximal modulus is reduced in moving from HF to B3LYP and BLYP, and further reduced in moving to KT3, OEP(B3LYP), and WY(CCSD). The latter three methods offer the most accurate shielding constants in comparison with both experimental and ab initio data and hence the more reliable route to DFT calculation of induced current density in molecules.