Quantum Valence Theory Reference
Your Essentials of Physical Chemistry seems to be heavy on the "essentials" and light on the "physical chemistry". A textbook used in a physical chemistry course (and not a "physical chemistry for __" course) is what you need. The second portion of the traditional physical chemistry sequence is devoted entirely to the implications of quantum mechanics in chemical bonding. Pauling's book on QM will not cover much modern bonding theory since that book predates most modern bonding theory. The applications of QM to chemical bonding in all but the simplest molecules require computer programs to slog through the maths, since multielectron wave functions suffer from the three(+) body problem and cannot be solved exactly.

For example, in Physical Chemistry by Peter Atkins and Julio De Paula (W. H. Freeman &amp; Company), Chapters 8 through 20 deal with chemical bonding and phenomena first with quantum mechanics and then with statistical mechanics. There are other physical chemistry texts out there as well. These texts will also cover the computational methods seeking to find 1) exact solutions to approximate multielectron wavefunctions (treating multielectron wavefunctions as linear combinations of single electron wavefunctions) and 2) approximate solutions to exact multielectron wavefunctions.