Summary: Orbital energies for 1st row transition metals.

 My original emails are first. Responses follow.
 Thanks to all.
 Laurence Lavelle
 
 Date: Thu, 18 Oct 2001 13:53:16 -0700
 To: CCL <chemistry %-% at %-% ccl.net>
 From: Laurence Lavelle <lavelle %-% at %-% mbi.ucla.edu>
 Subject: Orbital energies for 1st row transition metals.
I'm still getting a number of responses (thanks), but before I get anymore reprimands for covering this topic in a first year course let me clarify. While discussing the ground state for Cr [Ar]3d^5 4s^1 and Cr^+1 [Ar]3d^5 there was general discussion about the relative filling of orbitals for ground state anions. In the past I have not discussed electronic configurations for negatively charged transition metals, hence my question below.
So far I don't yet have a quantitative answer. My qualitative answer is that the orbital occupancy will depend on the relative energy difference between the degenerate 3d and the 4s orbitals and the spin pairing energy. 
 Discussion welcome,
 Laurence Lavelle
 
 Date: Tue, 16 Oct 2001 18:08:26 -0700
 To: CCL <chemistry %-% at %-% ccl.net>
 From: Laurence Lavelle <lavelle %-% at %-% mbi.ucla.edu>
 Subject: Orbital energies for 1st row transition metals.
 The following question relates to a first year chemistry course that I teach.
 Cr ground state is [Ar]3d^5 4s^1
 What would be the ground state for Cr^-1 ?
Explain the e- configuration and estimate the relative energy difference between Cr and Cr^-1. 
 Discussion and comments welcome.
 Best,
 Laurence Lavelle
 
 
 To: Laurence Lavelle <lavelle %-% at %-% mbi.ucla.edu>
 Subject: Re: CCL:Orbital energies for 1st row transition metals.
 X-mailer: FoxMail 3.0 beta 1 [cn]
I think the ground state should be [Ar]3d^5 4s^2 for Cr^-1. As we know, 3d^5 is half-filled and the energy will be lower. 
 
 To: Laurence Lavelle <lavelle %-% at %-% mbi.ucla.edu>
 Subject: Re: CCL:Orbital energies for 1st row transition metals.
 This is an interesting question, but I would not give it to first year
 students. Already the ground state of neutral Cr can not be explained
 using the orbital approximation. A numerical treatment including electron
 correlation is needed to account for it, since the total energy of the
 atom is relevant not the sum of orbital energies.  What kind of answer do
 you expect from first year students? That the electron enters 4s because
 of greater penetration of s- compared to d-electrons? I guess that
 everything depends on electron correlation again. I don't think that
 subtle details can be estimated easily and I would not ask first year
 students to solve problems they can not possibly answer.
 
 
 To: Laurence Lavelle <lavelle %-% at %-% mbi.ucla.edu>
 Subject: Re: CCL:Orbital energies for 1st row transition metals.
 Hello,
 For (french) first year students, the only answer is :
 due to Hund's rule, I would propose that the electronic
 configuration of Cr{-1} anion is [Ar]3d^5 4s^2.
 First year students just know Slater rules to estimate
 the electronic energy.
 Thus:
 E(Cr)= E(Ar) + 5*E(3d) + E(4s Cr)
 E(Cr-) = E(Ar) + 5*E(3d) + 2*E(4s Cr-)
 E(Cr-) - E(Cr) = 2*E(4s Cr-) - E(4s Cr)
 E(4s Cr) = -0.5*(2.95*2.95)/(3.8*3.8) u.a.
 E(4s Cr-) = -0.5*(2.6*2.6)/(3.8*3.8) u.a
 where 3.8 is the value of n* for n=4
 2.95 is the value of Z* for the 4s electron of Cr
 2.6 is the value of Z* for one 4s electron of Cr-
 Z*(4s Cr) = Z - 2*1 - 8*1 - 13*0.85 = 2.95
 Z*(4s Cr-) = Z - 2*1 - 8*1 - 13*0.85 -0.35 = 2.6
 because the electrons are put together in "groups"
 1rst grp : 1s
 2nd grp : 2s2p
 3rd grp : 3s3p
 4th grp : 3d
 5th grp : 4s4p
 ...
 I think that is not useful to develop further here.
 I was just wondering if Cr{-1} anion exists experimentaly?
 I just demonstrate that Slater rules predict it to be more
 stable than Cr atom, but I am not very confident with that
 type of calculation for transition metal elements.
 Hope this helps.
 
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 Subject: CCL:Orbital energies for 1st row transition metals.
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 > I would say that this example has a low
 > pedagogical value for a first year course except if you want to show the
 > limitations of Koopman's theorem.
 Hi all-
 I wasn't aware that first year chemistry students were being taught about
 Koopman's
 theorem.  I have taught several first year chem classes and never seen it
 mentioned once.
 In fact, my own exposure to it didn't occur until I was a graduate student.