Subject: Re: CCL:Orbital energies for 1st row transition metals.

From: Victor Lua~na <[email-masked]>
Date: Wed, 17 Oct 2001 14:12:53 +0200 (METDST)

> Date: Tue, 16 Oct 2001 18:08:26 -0700
> From: Laurence Lavelle <[email-masked]>
> Subject: CCL: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.

Laurence,

   Most probably the ground state of Cr^{-1} will close the 4s shell and
maintain the highest spin in the 3d half filled shell:

      K(2)L(8)3S(2)3P(6)4S(2)3D(5) 6S

Non-relativistic restricted Hartree-Fock energy for this configuration is
-1043.337094 hartree (*) compared to -1043.356371 hartree of the neutral Cr
ground state. Cr^{-1} appears to be unstable according to these energies.
Expect quite significant correlation effects though.

May be you are interested in the orbital energies. In the neutral Cr atom
e(4s) = -0.22205 hartree and e(3d) = -0.37360 hartree. In the Cr^{-1}
ground state e(4s) = -0.01664 hartree and e(3d) = -0.21310 hartree. It can
be noticed that Cr^{-1}-e(4s) predicts the wrong sign for the energy of
the Cr^{-1} -> Cr and Cr-e(4s) is even worse. The orbital reorganization
is so significant that the frozen orbital model assumed by the Koopman's
rule is of no use in this case. 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.

(*) RHF calculations using a large STO basis set by Koga et al
    Phys. Rev. A. 47, 4510-4512 (1993)
    Check http://www.unb.ca/chem/ajit/  for the bases and other references.

                             Regards,
                                      Victor Lua~na
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From: "Dr. Richard L. Wood" <[email-masked]>
Date: Wed, 17 Oct 2001 09:07:38 -0400

Victor Lua~na wrote:

> I would say that this example has a low

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.

Richard

--
Richard L. Wood, Ph. D.
Physical/Computational Chemist
Post-doctoral Associate
Department of Food Science
120 Stocking Hall
Cornell University, Ithaca, NY 14853