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

Abstract

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.

Relations among several nuclear and electronic density functional reactivity indexes

“…24 Before starting the evaluation of the Ϫ ͚ kϭ1 HCl, N 2 , F 2 , CO, BF, and LiF at the HF/6-31ϩϩG** are, in general, in good agreement with those reported in Table I. As already pointed out by Baekelandt 8 and Geerlings and coworkers, 9,10 NFF data can be related to the Berlin's function 8,13,14 to analyze bonding in molecules. Thus, in diatomic molecules a positive nucleophilic NFF is associated to an increasing bond length upon the addition of an electron, which increases the total electron density in antibonding regions.…”

“…͑7͒ and ͑15͒. 13 has been recently discussed 8,9,14 and new definitions of nuclear/geometric reactivity indexes have been also put forward. [15][16][17] These studies 8 -12,14 -17 have reinforced the idea that a complete representation of the total chemical response to a given perturbation must involve the analysis of both electronic and nuclear reactivity descriptors.…”

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

“…Examination of the Jahn-Teller distortion as an example of the usefulness of the electronic and nuclear Fukui functions have also been recently reported. 8 Ayers and Parr 33,45 have recently explicitly explored and derived some general principles for chemical reactivity based on a more complete variational scheme involving reactivity descriptors based on changes in the external potential. 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.…”

“…8 Ayers and Parr 33,45 have recently explicitly explored and derived some general principles for chemical reactivity based on a more complete variational scheme involving reactivity descriptors based on changes in the external potential. 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.…”

“…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,…”