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Elements of Bader’s theory of atoms in molecules are combined with density-functional theory to provide an electron-preceding perspective on the deformation of materials. From this perspective, a network of atoms is changed by moving the bonds that connect them; the nuclei then follow. The electronic stress tensor is the key to understanding this process. Eigenvectors of the electronic stress tensor at critical points of the electron density provide insight into the “normal electronic modes” that accompany structural dynamics and rearrangements. Eigenvectors of the second-derivative matrix of the electron density emerge as effective approximations to the eigenvectors of the stress tensor; this makes it possible to apply our results to experimentally and computationally determined electron densities. To demonstrate the usefulness of our analysis, we show that (a) the low-frequency modes of ice Ic can be predicted from the eigenvectors of the second-derivative matrix and (b) the eigenvectors of the second-derivative matrix are associated with the direction of structural change during the pressure-induced phase transition from ice XI to a ferroelectric ice VIII-like structure. We conclude that the eigenvectors of the second-derivative matrix of the electron density are the key ingredient for constructing a dynamical theory of atoms in molecules. [ABSTRACT FROM AUTHOR]

Higher-order global softnesses, local softnesses, and softness kernels are defined along with their hardness inverses. The local hardness equalization principle recently derived by the authors is extended to arbitrary order. The resulting hierarchy of equalization principles indicates that the electronegativity/chemical potential, local hardness, and local hyperhardnesses all are constant when evaluated for the ground-state electron density. The new equalization principles can be used to test whether a trial electron density is an accurate approximation to the true ground-state density and to discover molecules with desired reactive properties, as encapsulated by their chemical reactivity indicators. [ABSTRACT FROM AUTHOR]

A variational method for forcing the exchange-correlation potential in density-functional theory (DFT) to have the correct asymptotic decay is developed. The resulting exchange-correlation potentials are much improved while the total energies remain essentially the same, compared with conventional density-functional theory calculations. The highest occupied orbital energies from the asymptotically corrected exchange-correlation potentials are found to provide significantly more accurate approximations to the ionization potential (for a neutral molecule) and the electron affinity (for an anion) than those from conventional calculations, although the results are usually inferior to direct methods by computing energy differences. Extending recent results from exchange-only DFT, we show that exact exchange-correlation potential is nonuniform asymptotically. Correcting the asymptotic decay of approximate exchange-correlation potentials towards the exact functional form binds the highest occupied orbitals for atomic and molecular anions, which supports the use of DFT calculations for negatively charged molecular species. With this technique, even hybrid functionals have local exchange-correlation potentials, effectively removing the largest objection to including these functionals in the panoply of Kohn-Sham DFT methods. [ABSTRACT FROM AUTHOR]

Examines the axiomatic basis for the concept of an atom within a molecule. Difficulty in providing a satisfactory mathematical basis; Definition of transferability; Description of Hirshfeld atom in a molecule.

The hard/soft-acid/base (HSAB) principle indicates that hard acids prefer binding to hard bases (often forming bonds with substantial ionic character) while soft acids prefer binding to soft bases (often forming bonds with substantial covalent character). Though the HSAB principle is a foundational concept of the modern theory of acids and bases, the theoretical underpinnings of the HSAB principle remain murky. This paper examines the exchange reaction, wherein two molecules, one the product of reacting a hard acid and a soft base and the other the product of reacting a soft acid with a hard base, exchange substituents to form the preferred hard–hard and soft–soft product. A simple derivation shows that this reaction is exothermic, proving the validity of the HSAB principle. The analysis leads to the simple and conceptually appealing conclusion that the HSAB principle is a driven by simple electron transfer effects. [ABSTRACT FROM AUTHOR]

We develop a variational procedure for the iterative Hirshfeld (HI) partitioning scheme. The main practical advantage of having a variational framework is that it provides a formal and straightforward approach for imposing constraints (e.g., fixed charges on certain atoms or molecular fragments) when computing HI atoms and their properties. Unlike many other variants of the Hirshfeld partitioning scheme, HI charges do not arise naturally from the information-theoretic framework, but only as a reverse-engineered construction of the objective function. However, the procedure we use is quite general and could be applied to other problems as well. We also prove that there is always at least one solution to the HI equations, but we could not prove that its self-consistent equations would always converge for any given initial pro-atom charges. Our numerical assessment of the constrained iterative Hirshfeld method shows that it satisfies many desirable traits of atoms in molecules and has the potential to surpass existing approaches for adding constraints when computing atomic properties. [ABSTRACT FROM AUTHOR]

We present an improved electronic linear response model to incorporate polarization and charge-transfer effects in polarizable force fields. This model is a generalization of the Atom-Condensed Kohn-Sham Density Functional Theory (DFT), approximated to second order (ACKS2): it can now be defined with any underlying variational theory (next to KS-DFT) and it can include atomic multipoles and off-center basis functions. Parameters in this model are computed efficiently as expectation values of an electronic wavefunction, obviating the need for their calibration, regularization, and manual tuning. In the limit of a complete density and potential basis set in the ACKS2 model, the linear response properties of the underlying theory for a given molecular geometry are reproduced exactly. A numerical validation with a test set of 110 molecules shows that very accurate models can already be obtained with fluctuating charges and dipoles. These features greatly facilitate the development of polarizable force fields. [ABSTRACT FROM AUTHOR]

A new numerical integration procedure for exchange-correlation energies and potentials is proposed and “proof of principle” results are presented. The numerical integration grids are built from sparse-tensor product grids (constructed according to Smolyak’s prescription [Dokl. Akad. Nauk. 4, 240 (1963)] ) on the unit cube. The grid on the unit cube is then transformed to a grid over real space with respect to a weight function, which we choose to be the promolecular density. This produces a “whole molecule” grid, in contrast to conventional integration methods in density-functional theory, which use atom-in-molecule grids. The integration scheme was implemented in a modified version of the DEMON2K density-functional theory program, where it is used to evaluate integrals of the exchange-correlation energy density and the exchange-correlation potential. Ground-state energies and molecular geometries are accurately computed. The biggest advantages of the grid are its flexibility (it is easy to change the number and distribution of grid points) and its whole molecule nature. The latter feature is potentially helpful for basis-set-free computational algorithms. [ABSTRACT FROM AUTHOR]

The computational approach to the Hirshfeld [Theor. Chim. Acta 44, 129 (1977)] atom in a molecule is critically investigated, and several difficulties are highlighted. It is shown that these difficulties are mitigated by an alternative, iterative version, of the Hirshfeld partitioning procedure. The iterative scheme ensures that the Hirshfeld definition represents a mathematically proper information entropy, allows the Hirshfeld approach to be used for charged molecules, eliminates arbitrariness in the choice of the promolecule, and increases the magnitudes of the charges. The resulting “Hirshfeld-I charges” correlate well with electrostatic potential derived atomic charges. [ABSTRACT FROM AUTHOR]

Different procedures to obtain atom condensed Fukui functions are described. It is shown how the resulting values may differ depending on the exact approach to atom condensed Fukui functions. The condensed Fukui function can be computed using either the fragment of molecular response approach or the response of molecular fragment approach. The two approaches are nonequivalent; only the latter approach corresponds in general with a population difference expression. The Mulliken approach does not depend on the approach taken but has some computational drawbacks. The different resulting expressions are tested for a wide set of molecules. In practice one must make seemingly arbitrary choices about how to compute condensed Fukui functions, which suggests questioning the role of these indicators in conceptual density-functional theory. [ABSTRACT FROM AUTHOR]