Robert Balawender

Atomic Fukui function indices and local softness ab initio

The complete and original calculation scheme beyond the finite difference approximation, for the atomic (and orbital) Fukui function (FF) indices is proposed. The method explores an expansion for derivatives of LCAO coefficients, ∂C/∂N=CU. The separation scheme for the U matrix has been elaborated at the ab initio level. Nucleophilic and electrophilic FF indices, as well as atomic softness, have been derived from the standard result of SCF HF ab initio calculations. The indices reproduce two effects; the change in orbital occupancy and the relaxation of the electronic system. The molecular hardness (softness) provided by this scheme explicitly includes these two effects.

Derivatives of Molecular Valence as a Measure of Aromaticity

Derivatives of the molecular valence have been calculated ab initio within the new non-finite-difference approach elaborated on earlier for the global hardness and the Fukui function indices. The group of 10 five-membered-ring molecules C4H4X has been chosen for a test, using the exaltation of the total magnetic susceptibility (Λ) as a reference measure of their aromaticity. An excellent correlation has been found between the molecular valence derivatives in the nucleophilic regime and the exaltation Λ, for both the aromatic and antiaromatic molecules. Calculation of the valence derivatives provides an absolute measure of aromatic character that is not directly dependent on the size of the molecule and does not require adopting any standard reference molecule.

Nuclear Fukui function from coupled perturbed Hartree–Fock equations

A calculation scheme of the nuclear Fukui function via a coupled perturbed Hartree–Fock approach is proposed avoiding the finite difference approach in DFT-based descriptors. Nucleophilic and electrophilic nuclear Fukui functions are compared with the numerical approximation for the nuclear Fukui function (FF) as the negative derivative of the chemical potential with respect to the atomic coordinates and as the derivative of the Helman–Feynman force with respect to the total number of electrons. The results for a set of diatomic molecules are shown. Analytical and numerical techniques do show a high correlation. Overall, values from both numerical methods are larger than those from the analytical one. The analytical results can be interpreted in terms of the character of the orbital involved during ionization or adding of electrons; the change in the equilibrium bond length upon ionization, which is positive for bonding orbitals and negative for antibinding orbitals is connected with the negative or posit...

Nuclear Fukui function and Berlin’s binding function: Prediction of the Jahn–Teller distortion

The properties of the derivative of the total binding function (the virial of the forces) with respect to the number of electrons and its decomposition at local and atomic level have been analyzed. At local level the binding function is expressed by the Berlin function fv(r) and the electronic Fukui function f(r). The atomic analog is expressed in terms of the nuclear Fukui function (FF) and the nuclear position vectors. A relationship between the local maps of fv(r)f(r), the nuclear FF vectors, and the Jahn–Teller distortion direction is discussed. It is predicted that upon ionization the symmetry of the nearest local stationary point for BH3 is C2v, for AH4 molecules (CH4 and SiH4) D2d, and for C3H6 C2v. For the benzene anion a D2h symmetry is predicted.

Revisiting the chemical reactivity indices as the state function derivatives. The role of classical chemical hardness

The chemical reactivity indices as the equilibrium state-function derivatives are revisited. They are obtained in terms of the central moments (fluctuation formulas). To analyze the role of the chemical hardness introduced by Pearson [J. Am. Chem. Soc. 105, 7512 (1983)], the relations between the derivatives up to the third-order and the central moments are obtained. As shown, the chemical hardness and the chemical potential are really the principal indices of the chemical reactivity theory. It is clear from the results presented here that the chemical hardness is not the derivative of the Mulliken chemical potential (this means also not the second derivative of the energy at zero-temperature limit). The conventional quadratic dependence of energy, observed at finite temperature, reduces to linear dependence on the electron number at zero-temperature limit. The chemical hardness plays a double role in the admixture of ionic states to the reference neutral state energy: it determines the amplitude of the admixture and regulates the damping of its thermal factor.

DFT-based chemical reactivity indices in the Hartree-Fock method. II. Fukui function, chemical potential, and hardness

A derivation of the density-functional-theory- (DFT) based reactivity indices in the ensemble unrestricted Hartree-Fock (eUHF) method is presented. The comparison between the properties of the reactivity indices evaluated in one and two sets of spin-orbital approach of the eUHF and hyper-unrestricted Hartree-Fock (UHF) methods are shown. All approaches give similar Fukui function irrespective of methodology used, but significantly differ for the global indices, containing important chemical information, and so their interpretation in terms of DFT- based indices can be questionable. The calculation scheme for the indices using the first- and second-order coupled perturbed eHF equations is proposed. A method for the identification of the spinorbitals involved in the change of the total number of electrons is included. The illustrative examples (water and hydrogen cyanide) show that the ground-state (GS) properties of the (Z +/- 1)-electron systems can be predicted from the GS properties of the Z-electron systems with an accuracy comparable with the UHF calculations. The relaxation effect, important for the HCN system in which a change in the symmetry of the highest-occupied spin-orbital occurs, is effectively predicted.

Density-functional theory-based chemical reactivity indices in the Hartree-Fock method. I. Unrestricted Hartree-Fock method for a noninteger number of electrons

Correct evaluation of the reactivity indices, such as chemical potential, hardness, and Fukui function demands for the extension of the formalism beyond the integer particle picture. An ensemble approach is used as an extension of the unrestricted Hartree-Fock (UHF) method for noninteger electron number systems. A prescription is given for the construction of an ensemble Fock operator for a system with partially filled spin-orbitals. The comparison between the ensemble HF method and the hyper-HF method in terms of density matrices and spin-orbitals is presented. The equivalence of the equiensemble case and the ensemble UHF case with unequal weight factors is shown.

Structure Investigations of Dichloroaluminum Benzoates: An Unprecedented Example of a Monomeric Aluminum Complex with a Chelating Carboxylate Ligand

Dichloroaluminum benzoate and its adducts with Lewis bases show a large structural variety from molecular complexes to ionic species as indicated by X-ray diffraction, spectroscopic studies, and quantum-chemical calculations.

Comment on Legendre-transform functionals for spin-density-functional theory [J. Chem. Phys. 124, 224108 (2006)]

In this Comment the authors propose an alternative formulation of the starting point to the analysis performed in the commented paper [P. W. Ayers and W. Yang, J. Chem. Phys.124, 224108 (2006)]. An important role of the z component of the vector of the total spin angular momentum operator for the considered many-electron system is indicated. The authors believe their approach to be mathematically cleaner and conceptually easier than the original treatment.

Testing exchange – correlation functionals at fractional electron numbers

Dependence of the ground-state energy and density on the fractional electron number should be linear, while that of the chemical potential and Fukui function should be constant within the region between integers. In practical calculations with commonly used approximate functionals, results deviate from these ideal conditions. Four indicators are defined here to measure such deviations: from the global and local linearity condition, and from the global and local constancy condition. These indicators are used to test the performance of DFT method with five exchange–correlation functionals, and also the Hartree–Fock method, on a set of high-symmetry atoms: He, Li, Be, Na, Mg. The rCAM-B3LYP functional, having all four indicators small, is found to be the best functional for fractional electron number applications.