Collective Modes of Molecular Fragments

Let us first consider the M + = (A B) system, consisting of an acidic (A) and basic (B) pair of reactants. As explicitly shown elsewhere [9,15,20,25], the presence of the other reactant modifies the respective blocks of the hardness matrix, due to relaxational contributions. As we shall demonstrate in the next section, the relaxed hardness matrix of Eq. (la) corresponds to the collective relaxational modes Ntet = Nt, j/rd = t 1 J/t, where the transformation matrix t is defined by the relaxational matrices T(A B) and T,B A) (Eqs. (39) and (42)). This transformation and the eigenvectors of the diagonal blocks t/A, a and 

Obviously, one may also probe M+ via the test charge displacements of AIM in one reactant, say on atom a in A. Such a forced, localized displacement A/Va = 1 creates, via the minimum energy criterion for the assumed charge separation between the reactants, the collective charge displacement on both 

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