Page 138 - Strategies and Applications in Quantum Chemistry From Molecular Astrophysics to Molecular Engineer

MOLECULAR ORBITAL ELECTRONEGATIVITY AS ELECTRON CHEMICAL POTENTIAL 123

with

where is the eigenvector matrix of in the original non-orthogonal basis.
With this notation, eqn 22 becomes

where

is a matrix formed by the diagonal elements of the matrices:

Equations 26 form a linear system which can be solved without any difficulty. Let us
first of all divide eqn 26 by and pass to the limit, so as to work directly in terms
of partial derivatives. Let us then define the matrix:

With this notation, we can write the very simple expression:

For the off-diagonal part of P we have:

with the matrices W and X defined by eqns 28 and 29, respectively. If we next define
a set of matrices with elements

we can finally write