Andrés Cedillo

REACTIVITY INDICES AND FLUCTUATION FORMULAS IN DENSITY FUNCTIONAL THEORY: ISOMORPHIC ENSEMBLES AND A NEW MEASURE OF LOCAL HARDNESS

Fluctuation formulas for the external potential v(r) are introduced in a modified Legendre‐transformed representation of the density functional theory of electronic structure (isomorphic ensemble). A new (nuclear/geometric) reactivity index h(r), having the same status as the electronic Fukui function in the canonical ensemble, is thereby identified, h(r)=(1/N)[δμ/δσ(r)]N,T=(1/kT) [〈μ⋅v(r)〉−〈μ〉〈v(r)〉], where μ is the electronic chemical potential, σ is the shape factor of the electron density distribution, N is the number of electrons, 〈...〉 denotes the ensemble average of a quantity, and 〈v(r)〉 is the ensemble averaged external potential. This new local quantity is shown to be an inverse of the local softness, and to provide a useful definition of a local hardness.

Fukui function from a gradient expansion formula, and estimate of hardness and covalent radius for an atom

The Fukui function for a neutral atom is expressed as its LDA approximation plus a one‐parameter gradient correction, and the resultant formula is numerically tested. Expressing hardness as a density functional involving this Fukui function, global hardness values are determined for several atoms. Estimates also are made of the covalent radii of neutral atoms. Calculated Fukui functions exhibit characteristics similar to those reported in the literature. Calculated hardnesses compare favorably with experimental values, and predicted covalent radii are in agreement with existing theoretical values and experimental data. No information other than the electron densities of the neutral species enter in the calculations. An exact nuclear cusp condition on the Fukui function is derived.

Atoms‐in‐molecules partitioning of a molecular density

An atoms-in-a-molecule partitioning procedure, based on the minimization of the molecular grand potential, is presented. The fragments in the molecule are obtained from a set of integral operators that project the total density into its components, with the sum of the fragment densities equal to the molecular density. The hard and soft acids and bases (HSAB) principle is analyzed generalizing a previous proof to the case where the external potentials change.

Chemical softness in model electronic systems: dependence on temperature and chemical potential

Abstract Discrete and continuous model systems are studied in order to understand the behavior of average softness, for equilibrium states in a grand canonical ensemble, when the bath parameters are changed. While the former model seems to be appropriate for describing an isolated system, the latter could take care of atoms in a molecular framework. Three, four, and five level discrete models, and quadratic- and exponential-type continuous models were chosen for studying the dependence of average number of particles, average softness, average electronic, and Helmholtz free energies on temperature and chemical potential. For the quadratic model, the zero temperature limit of the average softness is the absolute softness of density functional theory. In the other models it generally goes to zero at 0 K, but for some specific values of μ. The high temperature limit of it is zero in all the studied cases. When the average number of particles is an integer or half integer in the discrete model at low temperature, there are local extrema in equilibrium softnes and the maximum hardness principle is shown to be valid.

Self-consistent methods constrained to a fixed number of particles in a given fragment and its relation to the electronegativity equalization method

The variational procedure of the Hartree–Fock and Kohn–Sham methods can be modified by adding one or more constraints that fix the number of electrons in a given number of molecular fragments. The corresponding Euler–Lagrange equations lead to a modified Fock matrix, where the contribution from the constraints only depends on the overlap matrix, when using the Mulliken or Hirshfeld atoms-in-molecules method. For all compounds in the test set, the energy shows a quadratic dependence on the fixed charges. This behavior provides a procedure to obtain the atomic electronegativity and hardness parameters in the electronegativity equalization method.

Bond fukui indices: Comparison of frozen molecular orbital and finite differences through mulliken populations

Bond Fukui functions and matrices are introduced for ab initio levels of theory using a Mulliken atoms in molecules model. It is shown how these indices may be obtained from first‐order density matrix derivatives without need for going to second‐order density matrices as in a previous work. The importance of taking into account the nonorthogonality of the basis in ab initio calculations is shown, contrasting the present results with previous work based on Hückel theory. It is shown how the extension of Fukui functions to Fukui matrices allows getting more insight into the nature of bond Fukui functions. All presently introduced indices respect the necessary normalization conditions and include the classical single atom condensed Fukui functions.

Hückel‐type semiempirical implementation of a variational method for determining electronic band gaps

A previously derived [J. Chem. Phys. 103, 7645 (1995)] general variational principle, for determining the hardness (or band gap) of electronic systems, is applied to π‐electron systems by a straightforward simple parameterization of the hardness kernel. For conjugated polyenes and annulenes, the hardness (band gaps) are essentially the same as (although no identical with) those predicted by the Huckel method. In contrast with the Huckel method, one need not assume that the total electronic energy is a sum of one‐electron energies. Comparisons are made with Nalewajski’s Charge Sensitivity Analysis.

Performance of density functional theory methods to describe intramolecular hydrogen shifts

The performance of three exchange and correlation density functionals, LDA, BLYP and B3LYP, with four basis sets is tested in three intramolecular hydrogen shift reactions. The best reaction and activation energies come from the hybrid functional B3LYP with triple-ζ basis sets, when they are compared with high-level post-Hartree-Fock results from the literature. For a fixed molecular geometry, the electrophilic Fukui function is computed from a finite difference approximation. Fukui function shows a small dependence with both the exchange and correlation functional and the basis set. Evolution of the Fukui function along the reaction path describes important changes in the basic sites of the corresponding molecules. These results are in agreement with the chemical behavior of those species.

Stability of the different AlOOH phases under pressure

The pressure effects on three different AlOOH structures (α, γ, and δ phases) are systematically analyzed by density functional theory with different exchange and correlation energy functional approximations, namely two local, two generalized-gradient approximation (GGA), and two GGA for solids (GGAsol). Phase stability, compressibility and hydrogen bond evolution are studied in a range of pressures from 0 to 30 GPa. In general, the use of GGAsol functionals is mandatory in order to have the correct phase stability order, a good description of the hydrogen bonds, and a close agreement with the experimental lattice parameters at the various pressures. Pressure-induced hydrogen-bond symmetrization is found in γ and δ phases at high compression, while the hydrogen bonds in the α phase remain asymmetric. A detailed analysis of the uncertainties on the values of the bulk moduli and their pressure derivative at zero pressure deduced by fitting calculated or experimental (P,V) data is also presented.

Wave function instabilities in the cis-trans isomerization and singlet-triplet energy gaps in a push-pull compound

The energy barriers for the cis–trans isomerization are obtained for a sample of push–pull compounds. The appropriate trend in the values for the barriers is obtained after an instability treatment of the restricted Kohn–Sham solution. At the instability zone, some compounds exhibit a singlet open-shell configuration. The width of the instability region around the transition state is characterized in an asymmetric push–pull compound. These results show that the instabilities in the twisted configuration of double bonds are mainly related to spin symmetry effects rather than to the molecular symmetry. For the open-shell singlet, an ensemble model is used to compute the electronic properties. The singlet–triplet energy gap along the rotation coordinate is qualitatively described by the use of spin potential and hardness.