Ni2+ has 6 valence electrons for it's 5 d orbitals. These electrons can either be in up/down spins in an orbital or two can go together as an up/down pair. Two cannot combine in the same orbital to form up/up or down/down pairs.
My job is to calculate the number of different pairings that can occur, and determine the sum of the spins in each pairing, (+1 = up spin, -1 = down spin.) as well as calculate the overall energy of the electron orbitals.
I have found the number of possible pairings that the electrons could have is 210, without violating any of the quantum rules. However, I can't seem to figure out how to calculate the sum of the spins or the overall energy. And was wondering if you guys could help. I'm rather apathetic, but I really don't want to resort to sketching out 210 combinations and counting the spins on each.
In order to calculate energy, each orbital (in which a maximum of two electrons can exist in) is labeled a relative energy level. the energies are 2,1,0,-1,-2. And to find the sum, one would (in a diagram) count up the number of electrons in each orbital and multiply them by the energy associated with that orbital.
I have calculated functions for determining these states for orbitals containing 1, 2, and 3 electrons, however I can't seem to find a clear pattern in the series' and have been unable to predict total spins and energies for 6 electrons.
Or if anyone knows the term symbols for nickel 2+ off hand, that would solve my problem immediately...
This is probably more of a programming problem than a straight math problem, but either way it is solving a system of variables.
None.