Is there an equation, similar to the Rydberg formula, for calculating the energies of molecular orbitals?

For example, with the Rydberg formula, I can work out that the energy of a $1s$ orbital in hydrogen is $-13.6\ \mathrm{eV}$. Is there any way that I can calculate (or approximate) the energies of the bonding and anti-bonding orbitals in $\ce{H2}$?

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    $\begingroup$ It doesn't exist. Hydrogen atom can be solved exactly, multielectron systems can't. $\endgroup$ – Ivan Neretin Nov 18 '16 at 14:10
  • $\begingroup$ Ok, thanks! I believe multi electron systems can be approximated by calculating Zeff (for example with Slater's rules) - are there any things like this for the MOs? $\endgroup$ – user1150512 Nov 18 '16 at 14:13
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    $\begingroup$ Well, for conjugated systems you can use the Hückel method for getting relative energies, but that's about it. Since this was tagged as computational chemistry: it's very easy to use computational chemistry to predict MO energies. $\endgroup$ – DSVA Nov 18 '16 at 14:26
  • $\begingroup$ How would you go about doing it computationally? Are there any free software packages which are able to do it? Thank you. $\endgroup$ – user1150512 Nov 18 '16 at 14:37
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    $\begingroup$ I recommend Psi4. You can use Avogadro to help write input files and look at results. $\endgroup$ – pentavalentcarbon Nov 19 '16 at 16:53

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