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.