Orbital of Hydrogen molecule does anybody here know an analytical approximation of the bonding hydrogen orbital MOLECULE?
I am looking for a good approximation to this orbital, that might be in some textbooks to get an impression how this whole concept of bonding antibonding works?
 A: The approximation that we all started out learning is the linear combination of atomic orbitals (LCAO) approach. The molecular wavefunction, $\Psi$, can be expressed as a sum of some set of basis functions:
$$ \Psi(\vec{r}) = \sum_n f_n(\vec{r}) $$
and a convenient set of basis functions is the atomic orbitals of hydrogen. As a starting point we could take just the two $1s$ orbitals of the hydrogen atoms, $\psi_a$ and $\psi_b$, and write the lowest energy molecular orbital as:
$$ \Psi \approx \frac{1}{\sqrt{2}} \left( \psi_a + \psi_b \right) $$
This gives you the bonding orbital, and the anti-bonding orbital is the difference of the atomic orbitals:
$$ \Psi^* \approx \frac{1}{\sqrt{2}} \left( \psi_a - \psi_b \right) $$
The approximation is too crude to be of use in comparing calculations with experiment, but it's a good way to play with the ideas involved. You'll find many articles on the web explaining how to calculate the energies of these orbitals. A quick Google found this one, which looks a good introduction, or you'll find a description in any introductory QM textbook. My copy of Atkins Molecular Quantum Mechanics treats the LCAO calculation for hydrogen in chapter 9 (though I think it's chapter 8 in the latest edition).
