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This article is divided into two main parts: (1) The theoretical part contains a new derivation of the topological matrix D (M. Baer and A. Alijah, Chem. Phys. Lett., 2000, 319, 489) which is based, solely, on the spatial dependent electronic manifold. This derivation enables more intimate relations between the adiabatic and the diabatic frameworks as is discussed in detail in the manuscript. (2) The numerical part is also divided into two parts: (a) In the first part we extend our previousdoi:10.1039/b313883f pmid:15471354 fatcat:fr4wgryvhbfvpimpnqkkym2jne