Hello DavidF,
HF theory will to very poorly in describing the interaction between two methane molecules, due to its complete (aside from basic exchange) neglect of electron correlation, even for very accurate methods (eg. g3 composite methods), this is very difficult to correctly describe because it is so weak.
and what about the structure and symmetry of Methane molecule ? (I know that as far as structure is concerned, it's better to work with VSEPR)
David, HF theory is a mathematical construct which begins from a set of atomic coordinates and a basis set and calculates energy, the derivative of energy and attempts to optimize the molecular geometry by doing this. VSEPR is a nice way of visualizing molecular structure and remembering the
ideal way that atoms arrange themselves around a central atom, but is not a way of computing molecular structures. N2, being a relatively light molecule made up of relatively light atoms has no significant relativistic effects while computing its electronic structure. Relativistic effects manifest only when heavier, larger atoms are involved (eg 2nd row transition metals).
Also, HF theory generally in practice makes use of Gaussian-type orbitals, rather than Slater-type orbitals, due to vastly increased efficiency when computing electon-electron repulsion integrals, although slater-type orbitals can be used.
Try googling some of these terms and read course notes posted on the web and you will get the hang of things a bit more. Molecular structure is a very interesting, complex field and take a lot of time to understand (I still don't understand most of it)
Keep reading!
Best of luck,
sdm