Partitioning of the Fukui Function Indices

The basic charge-response quantities of a given open molecular system M, the AIM FF indices, f, = cNJvN, can be partitioned into the respective collective mode contributions. In the reactive system M = (A IB ), one is also interested in the partitioning of the collective mode terms into the reactant contributions. 

Consider the general collective electron population displacements dp (p-modes)  

A straightforward chain-rule transformation of the AIM FF index f, gives  

It is also of interest to divide the w p) quantities of Eq. (199) into reactant contributions, defined by the corresponding partial summations over constituent atoms of each reactant  

The above partitioning applies when M in Mr = (r A B) changes the global number of electrons, d/V = d/VA + d/VB / 0. e.g., in catalytic system, when A = adsorbate, B = active site, and the reservoir r = surface reminder. When N is constrained in M = (A B), i.e., when d/VA = — dNB = NC1, the reactant FF indices are fixed (f ) —/a= 1 and (fA)/v=/e = — 1. For such N = const., internal CT processes, the AIM FF indices are replaced by the corresponding in situ indices. Their collective mode partitioning gives  

---