Nuclear Fukui function from coupled perturbed Hartree–Fock equations

Abstract

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 positive values of the left-hand-side nuclear FF, respectively. The nucleophilic nuclear FF is positive for all cases except CO indicating a systematical increase of the bond length after addition of an electron.

Higher order derivatives for nuclear indexes in the framework of density functional theory

“…[2][3][4][5][6][7][8] In this work we have derived some general relationships to the higher order derivative of the Hellmann-Feynmann forces at the nucleus with respect to the electron number at a constant external potential. It is worth mentioning that the above general and exact equations can be written in a more compact form as…”

“…[2][3][4][5][6][7][8] They are important in order to rationalize and to predict changes in chemical reactivity, selectivity, and activation of a given molecular system, within an ''electron-cloud preceding'' approach, as responses to exter-nal perturbations such as the presence of reagents or solvatation field effects. It is expected that these relationships can be useful expressions to build up a more complete reactivity picture based on global, local, and nonlocal electronic and nuclear indexes.…”

“…It is clear, however, that a complete representation of the total chemical response within a perturbation theory viewpoint, which introduce response functions and kernels of higher order, must involve not only electronic responses 8,43,44 but nuclear reactivity indexes. [2][3][4][5][6][7][8] Recently we have derived 9 some general relationships within the electronic nonlocal ͑pair-site͒ chemical reactivity formalism of DFT which complements the electronic formalism to higher order derivatives of Fukui functions. With the aim to extend these treatments to nuclear reactivity descriptors, in this work we have focused on the search of general relationships between higher order derivatives of a nuclear Fukui function with respect to the electron number at a constant external potential.…”

“…1 Within a chemical viewpoint, it is clear that electronic and nuclear reactivity indexes provide the formal basis for a deeper understanding of chemical reactivity and chemical reaction processes. [2][3][4][5][6][7][8][9] In this context, global, local, and nonlocal hierarchies of the electronic counterparts have been introduced in a theoretical framework based on Taylor expansions of the energy functionals within the four Legendre transformed ensembles formalism of DFT. [10][11][12][13] Global electronic response quantities, such as the electronic chemical potential , 14,15 the chemical hardness , 16 and the chemical softness S, 17 define global responses of the system to global perturbations as, for instance, changes with respect to the number of electrons N or with respect to the chemical potential at constant external potential, namely,…”

DFT energy derivatives and their renormalization in molecular vibrations

“…Independently, Berkowitz et al [4], Baekelandt [5], and Ordon and Komorowski [6] proved it to be equal to the derivative of the chemical potential (, or the negative of electronegativity, ) over the nuclear displacement; the numerical values thereof have also been ascribed [6]. Balawender and Geerlings [7] discerned the nucleophilic and electrophilic ⌽ i and provided a computational ab initio scheme for this quantity. The counterpart to the nuclear reactivity, the nuclear softness, was introduced by Cohen et al [2] as i ϭ (ѨF i /Ѩ) ; the numerical values were ascribed to it by De Proft et al [8].…”