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At least to me, the contents of chapters 5 & 6 given here are representative of discussions on chemical bonding given in nearly all intro general & organic chem books, the statements in those chapters are mainly memorization (to me anyway). I basically don't find it rigorous enough, leads to more rather than less confusion and doesn't give any in depth discussion (similar to the way the quantum mechanics sections of those books are rote assertion ignoring all of the math).

I'm in the middle of a physics-based quantum mechanics course, so I'm developing the conceptual & mathematical tools to read a serious explanation of lewis bonding, polar-covalent bonding etc... but my book doesn't mention much in detail on this topic either, and apparently not even Pauling's QM book mentions much on the topics.

I'm really hoping somebody would have a quick look at the contents of chapters 5 & 6 of the first link & offer a recommendation of a rigorous reference or four on the contents of those chapters - I really can't face the headache I'll get reading chapters like those again due to all the confusion they lead to by dumbing it down, I need something more rigorous if such a thing exists, thanks a lot :)

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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 & 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.

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