Ok, so I have a rather tricky problem in my inorganic chemistry class, involving quantum spins of electrons, which essentially reduces down to computing aspects of a series. 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.

Ok, so I have a rather tricky problem in my inorganic chemistry class, involving quantum spins of electrons, which essentially reduces down to computing aspects of a series.
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.

[sup]3[/sup]F[sub]4[/sub]

³F₄

I totally forgot all my chemistry, but can't you use Combinations/permutations in some way? That was my initial thought upon reading this thread but I could be wrong.

I totally forgot all my chemistry, but can't you use Combinations/permutations in some way? That was my initial thought upon reading this thread but I could be wrong.

:| I'm going to have to learn shit like this.. :(

I'm going to have to learn shit like this..

Oh well. I eventually gave up trying to figure out an equation for the sequence, and simply wrote everything out by hand... Only to realize after handing it in that I had used the wrong Tanabe-Sugano diagram, and all was lost.

Oh well. I eventually gave up trying to figure out an equation for the sequence, and simply wrote everything out by hand...
Only to realize after handing it in that I had used the wrong Tanabe-Sugano diagram, and all was lost.

A little bit more, and I could have a serious chance at solving this. Wait for DTBK to get on :P.

A little bit more, and I could have a serious chance at solving this. Wait for DTBK to get on .

[color=#b5b5ff]I don't think I have any understanding of the chemistry side of this... -Six electrons in the set of five d-orbitals would, by Hund's Rule, first occupy each orbital once, resulting in five distinct combinations of one electron in each orbital, plus the remaining electron in the m=-2,-1,0,1, or 2 orbital. Ideally, it would occupy the orbital with the least energy (m=-2). You're going to have to explain the chemistry of this to me. And don't say "5 d orbitals".. it made me immediately think 5d[sup]6[/sup] :P [QUOTE]Or if anyone knows the term symbols for nickel 2+ off hand, that would solve my problem immediately...[/QUOTE] Ni[sup]2+[/sup] = [Ar]4s[sup]2[/sup]3d[sup]6[/sup] = 1s[sup]2[/sup]2s[sup]2[/sup]2p[sup]6[/sup]3s[sup]2[/sup]3p[sup]6[/sup]4s[sup]2[/sup]3d[sup]6[/sup] I guess if you're just calculating all possibilities of electrons spread over the six d-orbitals regardless of optimization.. it's just a bitchload of numerical statistics, which I hate.[/color]

Huston, we have a winner. :dontgetit:

Huston, we have a winner.