Understanding LCAO Matrix Solutions for Molecules

[Astudious]

I would like to understand how LCAO may be used to construct the matrix to be solved for the molecular orbitals of two cases of molecules:

1) small molecules like H₃ (or H₃⁺, HF₂^-, H₂O, CH₄, etc.
2) groups or parts of molecules with delocalized pi-systems (including linear and cyclic hydrocarbons, crown ethers, carboxylate ions, etc.)

Huckel theory instruction is readily available, but it is only supposed to apply to the case of conjugated pi-systems in hydrocarbons, i.e. a special case of part 2 of what I'm looking for.

I wish to generalize this, to all very small molecules like the ones I listed, and also to delocalized pi-systems (within the framework of arbitrary larger molecules, which I presume need not be considered to affect that system much).

Can anyone suggest where I should read or look (Internet sources are welcome too) to find this explanation laid out?

 

[DrDu]

In general, this is a formidable task, and depends on the accuracy you want to achieve. A relatively simple method is extended Hueckel theory, see, e.g.
http://www.roaldhoffmann.com/sites/all/files/11s_1.pdf
There are also programs freely available, like
http://yaehmop.sourceforge.net/