Approximate molecular orbital theory: the ese MO formalism. I. General theory and notation

A new formalism for simplified molecular orbital calculations is elucidated. The focus of the formalism is the production of a good approximation to the LCAO SCF F matrix of Roothaan's equations, and preoccupation with approximations to individual molecular integrals is avoided. The great majority of multicentre two-electron integrals of the exact formalism are found to be largely inconsequential to the attainment of a good approximation to the F matrix.