Inter-Reactant Coupling Modes

The IDM of Sect. 5.1 are defined as the eigenvectors of the block-diagonal hardness matrices  

Their eigenvectors, which we call the inter-reactant modes (IRM), provide yet another collective charge displacement reference frame, which can be used to describe the CT processes (internal or external) in a general reactive system 

Let us examine the above eigenvalue problem in more detail. We explicitly separate the reactant components (X = A, B) in the representative eigenvector ( 2fy)t = = ( Wi, ) also, to simplify notation, we denote A = Ay-r 

Multiplying the first of Eqs. (220) from the left by 7B A and inverting the transformed equation yields the expression for %lB in terms of 0eA  

Therefore, the HA and OlB components of are the eigenvectors of the (n x n)-A and [(m — n) x (m — n)]-B matrices, respectively, which exhibit the same eigenvalue, A2. Let us assume, e.g., that m 2n. Hence, the n eigenvectors aUA of A will combine with their n conjugates HB among the eigenvectors of B, 

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