Second derivatives and chemical descriptors: advances and remarks

ROBERTO C. BOCHICCHIO; RAMÓN A. MIRANDA-QUINTANA; D. RIAL

San Crsitóbal

Congreso; 40TH QUITEL 2014; 2014

Universidad de San Francisco de Quito

The convex piece-wise linear dependence of the molecular energy with the number of particles and its based physico-chemical descriptors formulation [1] involves non integer electron number domains. The existence of descriptors defined as first derivatives of the energy and the electron density has been rigorously established from both, the conceptual DFT (Density Functional Theory) [2] and the recent Grand-canonical formulation [3,4]. The further and natural consideration of the higher order descriptors, i.e., those related to the second derivatives of the mentioned magnitudes, and the discontinuity of the first derivatives at the integer number of electrons induce a non linear dependence of these magnitudes even regarding the isolated piece-wise linear hypothesis for the electronic energy and then the onset of such dependence is due to the interaction with the environment [5]. The physical domains within a molecule thus considered may be regarded sensu strictu, as open quantum systems at equilibrium. So, the number of electrons is obtained by means of an average over the like GC ensemble configurations of integer N and N+1 particles and the fractional population can be fixed at N+ν; 0