# Perturbational Molecular Orbital Theory - How to derive the results?

I am reading Albright's Orbital Interactions in chemistry. The qualitatively perturbational treatment of molecular orbitals seem to be a central tool used throughout the book. I've referred to the Appendix for a thorough derivation of the theory. However, I got stuck at equation 22(a). I don't understand how it follows from everything that is spelled out before it.

• For those interested, eq 22(a) is $$[(e^\circ+\tilde{H})-e_i(1+\tilde{S})]T_i=0$$ – Andrew Dec 24 '19 at 20:49