# Full Hamiltonians

Wikipedia distinguishes between the full "Molecular Hamiltonian" and the "Coulomb Hamiltonian" with which you solve the Schrodinger equation here: http://en.wikipedia.org/wiki/Molecular_Hamiltonian.

how is full molecular Hamiltonian written for a H nucleus and electron or H2 molecule?

DrClaude
Mentor
how is full molecular Hamiltonian written for a H nucleus and electron or H2 molecule?
You usually do not use the full molecular Hamiltonian, but add relativistic corrections, such as spin-orbit coupling, to the Coulomb Hamiltonian.

Actually, I'm not sure that would be such a thing as the "full" molecular Hamiltonian. You would use the Dirac instead of the Scrhödinger equation to get all relativistic effects to be taken into account.

If you see the Hamiltonian specified on page 3 here: http://www.phys.ubbcluj.ro/~vchis/cursuri/cspm/course2.pdf

What would I add to that to make it as exact as we know how to make it? That is, if relativistic corrections are reasonably easy to make. Spin-orbit coupling is a purely relativistic effect?

DrClaude
Mentor
$$\hat{H} = m_e c^2 + \frac{\hat{P}^2}{2m_e} + V(R) - \frac{\hat{P}^4}{8 m_e^3 c^2} + \frac{1}{2 m_e^2 c^2} \frac{1}{R} \frac{d V(R)}{dR} \hat{L} \cdot \hat{S} + \frac{\hbar^2}{8 m_e^2 c^2} \Delta V(R) + \ldots$$