Chemical bonding descriptors based on electron density inhomogeneity measure: a comparison with ELI-D

The electron localizability indicator (ELI-D) is suitable to describe certain aspects of the bonding situation of molecules and solids. ELI-D is based on integrals of electron pair density over very small regions. Recently proposed functional C _p , derived from the electron population in regions of fixed amount of electron density inhomogeneity, is based on the same approach as ELI-D, that is, ω-restricted space partitioning. The electron density inhomogeneity is given by the distance of electron density values to the averaged density within chosen region. Thus, in contrast to ELI-D, C _p is a single-electron property. The distance measure depends on a parameter that can be optimized in such way that C _p mimics the topology of the ELI-D distribution for atoms. Such an optimization was performed for the atoms Li to Xe. The optimal parameter p = 0.6 yields the functional C _0.6 that was exemplary applied to a few chosen molecules. In case of molecules the topology of the inner shell and lone-pair regions as given by C _0.6 is comparable with that of the ELI-D representation. However, in the bonding region between the atoms the topology of C _0.6 is dominated by the low density gradient close to the bond critical point. This may result in rather different topologies when comparing C _0.6 and ELI-D.     

Electronic structures of 4d transition metal monoxides by density functional theory

Bond distances, dissociation energies, ionization potentials and electron affinities of 4d transition metal monoxides from YO to CdO and their positive and negative ions were studied by use of density functional methods B3LYP, BLYP, B3PW91, BPW91, B3P86, BP86, SVWN, MPW1PW91 and PBE1PBE. It was found that calculated properties are highly dependent on the functionals employed, especially for dissociation energy. For most neutral species, pure density functionals BLYP, BPW91 and BP86 have good performance in predicting dissociation energy than hybrid density functionals B3LYP, B3PW91 and B3P86. In addition, BLYP gives the largest bond distance compared with other density functional methods, while SVWN gives shortest bond distance, largest dissociation energy and electron affinity. For the ground state, the spin multiplicity of the charged species can be obtained by ± 1 of their corresponding neutral species.     

A density functional for the correlation energy,deduced in the framework of the correlation factor approach

An approximate density functional is deduced from a wave function within the correlation factor method. The new functional does not include terms depending on the gradient of the density, but shows the simplicity of local density functionals without spin polarization. However, it includes correctly the inhomogeneity effects and, also, the nonlocal nature of an electronic system. The approach adopted here stresses the goodness of the expression taken by Colle and Salvetti for building a correlation factor and, at the same time, allows us to gain light on the nature of the deficiencies of those functionals obtained, up to now, from the perspective of the Hohenberg and Kohn theorem.     

Electron-density topology in molecular systems: paired and unpaired densities

This work studies the partitioning of the electron density into two contributions which are interpreted as the paired and the effectively unpaired electron densities. The topological features of each density field as well as of the total density are described localizing the corresponding critical points in simple selected molecules (local formalism). The results show that unpaired electron-density concentrations occur out of the topological bonding regions whereas the paired electron densities present accumulations inside those regions. A comparison of these results with those arising from population analysis techniques (nonlocal or integrated formalisms) is reported.     

Kinetic energy density study of some representative semilocal kinetic energy functionals

There is a number of explicit kinetic energy density functionals for noninteracting electron systems that are obtained in terms of the electron density and its derivatives. These semilocal functionals have been widely used in the literature. In this work, we present a comparative study of the kinetic energy density of these semilocal functionals, stressing the importance of the local behavior to assess the quality of the functionals. We propose a quality factor that measures the local differences between the usual orbital-based kinetic energy density distributions and the approximated ones, allowing us to ensure if the good results obtained for the total kinetic energies with these semilocal functionals are due to their correct local performance or to error cancellations. We have also included contributions coming from the Laplacian of the electron density to work with an infinite set of kinetic energy densities. For all but one of the functionals, we have found that their success in the evaluation of the total kinetic energy is due to global error cancellations, whereas the local behavior of their kinetic energy density becomes worse than that corresponding to the Thomas-Fermi functional.     

Fuzzy fragment selection strategies,basis set dependence and HF–DFT comparisons in the applications of the ADMA method of macromolecular quantum chemistry

The Adjustable Density Matrix Assembler (ADMA) method is examined in this paper. This method approximates (first order) density matrices by taking only those interactions into account which are present between fragments separated by a preset distance parameter (d). The accuracy of this approximation is tested using different basis sets, distance parameters and exchange‐correlation functionals. As an illustration of the applications of the method, the electron density of the hemoglobin molecule is presented in its oxy, deoxy and carbon‐monoxy form. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

Regional self-interaction correction of density functional theory

We propose a new simple scheme for self-interaction correction (SIC) of exchange functionals in the density functional theory. In the new scheme, exchange energies are corrected by substituting exchange self-interactions for exchange functionals in regions of self-interaction. To classify the regions of self-interaction, we take advantage of the property of the total kinetic energy density approaching the Weizs?cker density in the case of electrons in isolated orbitals. The scheme differs from conventional SIC methods in that it produces optimized molecular structures. Applying the scheme to the calculation of reaction energy barriers showed that it provides a clear improvement in cases where the barriers are underestimated by conventional "pure" functionals. In particular, we found that this scheme even reproduces a transition state that is not given by pure functionals.     

About the difference between density functionals defined by energy criterion and density functionals defined by density criterion: Exchange functionals

The difference between density functionals defined by energy criterion and density functionals defined by density criterion is studied for the exchange functional. It is shown that Slater potentials are exact exchange potentials in the sense that they yield the Hartree–Fock electron density if all operators are given by local expressions. © 2016 Wiley Periodicals, Inc.     

Generalized nonlocal kinetic energy density functionals based on the von Weizsäcker functional

We generalize the ideas behind the procedure for the construction of kinetic energy density functionals with a nonlocal term based on the structure of the von Weizs?cker functional, and present several types of nonlocal terms. In all cases, the functionals are constructed such that they reproduce the linear response function of the homogeneous electron gas. These functionals are designed by rewriting the von Weizs?cker functional with the help of a parameter β that determines the power of the electron density in the expression, a strategy we have previously used in the generalization of Thomas-Fermi nonlocal functionals. Benchmark calculations in localized systems have been performed with these functionals to test both their relative errors and the quality of their local behavior. We have obtained competitive results when compared to semilocal and previous nonlocal functionals, the generalized nonlocal von Weizs?cker functionals giving very good results for the total kinetic energies and improving the local behavior of the kinetic energy density. In addition, all the functionals discussed in this paper, when using an adequate reference density, can be evaluated as a single integral in momentum space, resulting in a quasilinear scaling for the computational cost.     

Standard grids for high‐precision integration of modern density functionals: SG‐2 and SG‐3

Density‐functional approximations developed in the past decade necessitate the use of quadrature grids that are far more dense than those required to integrate older generations of functionals. This category of difficult‐to‐integrate functionals includes meta‐generalized gradient approximations, which depend on orbital gradients and/or the Laplacian of the density, as well as functionals based on B97 and the popular “Minnesota” class of functionals, each of which contain complicated and/or oscillatory expressions for the exchange inhomogeneity factor. Following a strategy introduced previously by Gill and co‐workers to develop the relatively sparse “SG‐0” and “SG‐1” standard quadrature grids, we introduce two higher‐quality grids that we designate SG‐2 and SG‐3, obtained by systematically “pruning” medium‐ and high‐quality atom‐centered grids. The pruning procedure affords computational speedups approaching a factor of two for hybrid functionals applied to systems of atoms, without significant loss of accuracy. The grid dependence of several popular density functionals is characterized for various properties. © 2017 Wiley Periodicals, Inc.     

Performance of the density matrix functional theory in the quantum theory of atoms in molecules

The generalization to arbitrary molecular geometries of the energetic partitioning provided by the atomic virial theorem of the quantum theory of atoms in molecules (QTAIM) leads to an exact and chemically intuitive energy partitioning scheme, the interacting quantum atoms (IQA) approach, that depends on the availability of second-order reduced density matrices (2-RDMs). This work explores the performance of this approach in particular and of the QTAIM in general with approximate 2-RDMs obtained from the density matrix functional theory (DMFT), which rests on the natural expansion (natural orbitals and their corresponding occupation numbers) of the first-order reduced density matrix (1-RDM). A number of these functionals have been implemented in the promolden code and used to perform QTAIM and IQA analyses on several representative molecules and model chemical reactions. Total energies, covalent intra- and interbasin exchange-correlation interactions, as well as localization and delocalization indices have been determined with these functionals from 1-RDMs obtained at different levels of theory. Results are compared to the values computed from the exact 2-RDMs, whenever possible.     

On the accuracy of DFT methods in reproducing ligand substitution energies for transition metal complexes in solution: the role of dispersive interactions

The performance of a series of density functionals when tested on the prediction of the phosphane substitution energy of transition metal complexes is evaluated. The complexes Fe-BDA and Ru-COD (BDA=benzylideneacetone, COD=cyclooctadiene) serve as reference systems, and calculated values are compared with the experimental values in THF as obtained from calorimetry. Results clearly indicate that functionals specifically developed to include dispersion interactions usually outperform other functionals when BDA or COD substitution is considered. However, when phosphanes of different sizes are compared, functionals including dispersion interactions, at odd with experimental evidence, predict that larger phosphanes bind more strongly than smaller phosphanes, while functionals not including dispersion interaction reproduce the experimental trends with reasonable accuracy. In case of the DFT-D functionals, inclusion of a cut-off distance on the dispersive term resolves this issue, and results in a rather robust behavior whatever ligand substitution reaction is considered.     

Wigner molecules: the strong-correlation limit of the three-electron harmonium

At the strong-correlation limit, electronic states of the three-electron harmonium atom are described by asymptotically exact wave functions given by products of distinct Slater determinants and a common Gaussian factor that involves interelectron distances and the center-of-mass position. The Slater determinants specify the angular dependence and the permutational symmetry of the wave functions. As the confinement strength becomes infinitesimally small, the states of different spin multiplicities become degenerate, their limiting energy reflecting harmonic vibrations of the electrons about their equilibrium positions. The corresponding electron densities are given by products of angular factors and a Gaussian function centered at the radius proportional to the interelectron distance at equilibrium. Thanks to the availability of both the energy and the electron density, the strong-correlation limit of the three-electron harmonium is well suited for testing of density functionals.     

Simple tests for density functional methods

The performance of the currently used generalized gradient approximation density functionals is analyzed using several simple, yet critical requirements. We analyze the effects of the self-interaction error, the inclusion of the exact exchange, and the parameter settings used in the popular three-parameter hybrid density functionals. The results show that the elimination of the self-interaction error from the current density functionals lead to very poor results for H₂. The inclusion of the exact exchange does not significantly influence the self-interaction corrected results. The variation of the A, B, and C parameters of a hybrid DFT method influences the H(SINGLE BOND)H equilibrium bond length through a very simple linear equation, and it is possible to reproduce the experimental H(SINGLE BOND)H distance with appropriate selection of these parameters, although an infinite number of solutions exists. Similar results were obtained for the total energy and the electron density along the internuclear axis. The analysis of the exact KS potential at the bond critical point of the dissociating H₂ molecule shows that, for this property, the second order Moller–Plesset perturbation theory yields a better potential than the density functionals studied in this article. © 1997 John Wiley & Sons, Inc. J Comput Chem 18 : 1534–1545, 1997     

Systematic formulations for electronegativity and hardness and their atomic scales within density functional softness theory

A unified Mulliken valence with Parr ground‐state electronegativity picture is presented. It provides a useful analytical tool on which the absolute hardness as well ionization potential and electron affinity functionals are based. For all these chemical reactivity indices, systematic approximate density functionals are formulated within density functional softness theory and are applied to atomic systems. For the absolute hardness, a special relationship with the new electronegativity ansatz and a particular atomic trend paralleling the absolute electron affinity are established that should complement and augment the earlier finite‐difference energetic approach. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2006     

Binding energy curves from nonempirical density functionals II. van der Waals bonds in rare-gas and alkaline-earth diatomics

Binding energy curves have been calculated for the ground-state rare-gas diatomics Ne(2) and Ar(2) and for the alkaline-earth diatomic Be(2) using the nonempirical density functionals from the first three rungs of a ladder of approximations: the local spin density (LSD) approximation, the Perdew-Burke-Ernzerhof (PBE) generalized gradient approximation (GGA), and the Tao-Perdew-Staroverov-Scuseria (TPSS) meta-GGA. Binding energy curves in reasonable agreement with those constructed from experiment are found from PBE and TPSS, which incorporate inhomogeneity corrections that satisfy the Lieb-Oxford bound and so describe the short-range part of the van der Waals interaction. At large internuclear separation, these functionals produce an exponentially decaying attraction in place of the correct long-range -C(6)/R(6). Basis-set and exchange-only effects are also discussed.