Subject: Group theory

From: Xavier ASSFELD <[email-masked]>
Date: Thu, 25 Oct 2001 12:16:35 +0200

Dear collegues,

I have a problem with group theory.
When you consider two electrons in a two-fold degenerate level
(let say (e^2) configuration for a transition metal in a tetrahedral
surrounding (Td point group)) it is easy two find the multielectronic
symmetry with the symmetric and antisymmetric direct products.

There are 6 possible configurations for two electrons in 4 spinorbitals.
The spin multiplicity is either 1 or 3.
The direct product (E * E) reduce to A1 + A2 + E and it is not
straightforward
to assign the spin label, since one cannot have both spin multiplicities
for all spatial symmetry (1-A1, 3-A1, 1-A2, 3-A2, 1-E and 3-E give 16
states!)

However, with the symmetric and antisymmetric direct products is it very
simple :

symmetric direct product:
(E * E)+ = A1 + E which leads to 1-A1 and 1-E singlet electronic states
(antisymmetric spin function and symmetric space function).

antisymmetric direct product:
(E * E)- = A2 leading to 3-A2 triplet state (symmetric spin function and
antisymmetric space function).

Now my problem is : what about when you have three electrons in a
three-fold
degenerate level ? 
For example, (t2^3) configuration for Td point group. 

Thanks in advance.

-- 

                                      ...Xav

WARNING! NEW E-MAIL ADDRESS !
(u-nancy changed to uhp-nancy)

Ast. Pr. Xavier Assfeld             [email-masked]
Laboratoire de Chimie theorique     (T) 33 3 83 91 21 49
Universite Henri Poincare           (F) 33 3 83 91 25 30
F-54506 Nancy BP 239                http://www.lctn.uhp-nancy.fr

---

From: <[email-masked]>
Date: Thu, 25 Oct 2001 07:19:35 -0500 (CDT)

Dear Prof Assfeld:

   I have two papers on this subject, J. Chem. Phys. _45_, 2304 (1966) and
Intern. J. Quantum Chem. _8_, 267 (1974) looking at this problem from
different viewpoints.

The CRUNCH program suite, available for downloading at

http://phy-ggallup.unl.edu/crunch

has a module that makes calculations of this sort.

Regards,

On Thu, 25 Oct 2001, Xavier ASSFELD wrote:

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Gordon A. Gallup                          Dept. of Physics and Astronomy
University of Nebraska-Lincoln            Lincoln, NE 68588-0111
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