Hyperhardness and hypersoftness of atoms and their ions.

Context: The theory of reactivity based on cDFT has been supplemented with the new method of calculating the atomic and local indices. With the use of previously derived relationship of the electron density gradient to the softness kernel and to the linear response function, we deliver theoretical analysis to obtain significant reactivity indices-the electron density derivatives: local softness and local hypersoftness together with the global hyperhardness index and the derivative of the global softness with respect to the number of electrons. The local derivatives have been applied in the calculation of responses of atoms to perturbation by an external potential by the alchemical approach.

Analytical approximation to the local softness and hypersoftness and to their applications as reactivity indicators.

Local density functional theory derivatives of the electron density have been calculated analytically for the set of canonical hydrogenic orbitals; original solutions have been obtained using the novel density gradient theorem. Results for the first and second derivatives of electron density over N (number of electrons) and over μ (chemical potential) have been demonstrated. Calculations of the state functions ΔN, ΔE, and Δμ disturbed by an external potential Δv(r) have been obtained via the concept of alchemical derivatives.

From the Electron Density Gradient to the Quantitative Reactivity Indicators: Local Softness and the Fukui Function.

Important reactivity measures such as the local softness, the Fukui function, and the global hardness have been calculated directly from first principles with the use of the electron density function, beyond the finite difference approximation. Our recently derived density gradient theorem and the principle of nearsightedness of the electronic matter have been instrumental in obtaining the original, albeit approximate, result on the local softness of an atom. By integration of the local softness (), we obtain the global softness and the Fukui function () = ()/.

The Connectivity Matrix: A Toolbox for Monitoring Bonded Atoms and Bonds.

The concept of a connectivity matrix, essential for the reaction fragility (RF) spectra technique for monitoring electron density evolution in a chemical reaction, has been supported with a novel formulation for the diagonal matrix elements; their direct link to the electron density function ρ() has been demonstrated. By combining the concept with the atomization energy of a system, the separation of the potential energy into atomic and/or bond contributions has been achieved. The energy derivative diagrams for atoms and bonds that are variable along a reaction path provide new insight into the reaction mechanism.

Bond Softening Indices Studied by the Fragility Spectra for Proton Migration in Formamide and Related Structures.

Computational scheme to obtain bond softening index λ, defined within the conceptual DFT, has been obtained with the use of the reaction fragility (RF) concept. Numerical results were obtained with the RF spectra for the proton transfer reaction in formamide molecule (HNCHO) and the water assisted proton migration in HNCHO·HO complex. Double proton transfer reaction in the formamide dimer, (HNCHO), and its analogues, (HNCHS) and (HNCHO)·(HNCHS), have also been studied.

Evolution of the atomic valence observed by the reaction fragility spectra on the reaction path.

The computational fragility spectra of atoms on the reaction path are presented for a selection of canonical processes represented by an amino group rotation around the (X)HC-NH(Y) bond (X = O, S; Y=H, CH). Calculated spectra are found to very accurately describe the variation of atomic valence. Significant linear correlation is also demonstrated between the Wiberg bond indices and the corresponding elements of the connectivity matrix, instrumental for calculation of the spectra.

Bond Fragility Spectra for the Double Proton-Transfer Reaction in the Formic Acid-Type Dimers.

The newly developed method of fragility spectra for observation of bond breaking and formation upon a reaction has been applied to the canonical reaction series of the double proton transfer (DPT). Formic acid and its thio-analogues HCXYH (X, Y = O, S) have been chosen for the analysis. Very accurate linear correlations have been determined between the nondiagonal elements of the connectivity matrix, essential for the method, and the Wiberg bond orders for the corresponding bonds.

Conceptual DFT analysis of the fragility spectra of atoms along the minimum energy reaction coordinate.

Theoretical justification has been provided to the method for monitoring the sequence of chemical bonds' rearrangement along a reaction path, by tracing the evolution of the diagonal elements of the Hessian matrix. Relations between the divergences of Hellman-Feynman forces and the energy and electron density derivatives have been demonstrated. By the proof presented on the grounds of the conceptual density functional theory formalism, the spectral amplitude observed on the atomic fragility spectra [L.

The reaction fragility spectrum.

We report an original method that provides a new insight into the reaction mechanism by direct observation of bond breaking and formation. Variations of the diagonal elements of the Hessian along the IRC are shown to reflect the anharmonic properties of the system that are induced by electron density modifications upon the reaction. This information is presented in the form of the reaction spectrum, demonstrating how particular atoms engage in the reorganization of bonds.

Atomic Resolution for the Energy Derivatives on the Reaction Path.

Definite algorithms for calculation of the atomic contributions to the reaction force Fξ and the reaction force constant kξ (the first and the second derivatives of the energy over the reaction path step) are presented. The electronic part in the atomic and group contributions has been separated, and this opened the way to identification of the reactive molecule fragments on the consecutive stages of the reaction path. Properties have been studied for the two canonical test reactions: CO + HF → HCOF and HONS → ONSH.

Variation of the electronic dipole polarizability on the reaction path.

The reaction force and the electronic flux, first proposed by Toro-Labbé et al. (J Phys Chem A 103:4398, 1999) have been expressed by the existing conceptual DFT apparatus. The critical points (extremes) of the chemical potential, global hardness and softness have been identified by means of the existing and computable energy derivatives: the Hellman-Feynman force, nuclear reactivity and nuclear stiffness.

Reactivity patterns of imidazole, oxazole, and thiazole as reflected by the polarization justified Fukui functions.

The concept of the polarization justified Fukui functions has been tested for the set of model molecules: imidazole, oxazole, and thiazole. Calculations of the Fukui functions have been based on the molecular polarizability analysis, which makes them a potentially more sensitive analytical tool as compared to the classical density functional theory proposals, typically built on electron density only. Three selected molecules show distinct differences in their reactivity patterns, despite very close geometry and electronic structure.

Polarization justified Fukui functions: the theory and applications for molecules.

The Fukui functions based on the computable local polarizability vector have been presented for a group of simple molecules. The necessary approximation for the density functional theory softness kernel has been supported by a theoretical analysis unifying and generalizing early concepts produced by the several authors. The exact relation between local polarizability vector and the derivative of the nonlocal part of the electronic potential over the electric field has been demonstrated.

Modeling the electron density kernels.

Existing approximation to the softness kernel, successfully explored in earlier work, has been extended; the normal Gauss distribution function has been used instead of the Dirac delta. The softness kernel becomes continuous functions in space and may be used to calculate the linear response function of the electron density. Three-dimensional visualization of the softness kernel and the linear response function are presented for a nitrogen atom as a working example.

Polarization justified Fukui functions.

New Fukui functions have been derived within the conceptual density functional theory by the analysis of the polarization effect of a system in static electric field. Resulting Fukui functions accurately reproduce the global softness and electronic dipolar polarizability; they meet the condition integral[f(r)/r]dr = -(partial differential mu/partial differential Z)(N) and lead to very reasonable values of the global hardness for atoms for the group of 29 main group elements. Computational clarity makes the new Fukui functions a promising tool in studies of molecular reactivity.

The amino group in adenine: MP2 and CCSD(T) complete basis set limit calculations of the planarization barrier and DFT/B3LYP study of the anharmonic frequencies of adenine.

The amino group in adenine plays a key role in formation of hydrogen bonds in nucleic acids and in other molecular systems. Thus, the structure of this group is of fundamental importance in the molecular recognition phenomena. Ab initio MP2 and density functional B3LYP methods with various basis sets have been used to calculate the optimized structure and the infrared spectrum of adenine (the N9-H tautomer).