Subject: Spin contamination, effect on energy and structure.

From: <[email-masked]>
Date: Mon, 14 Nov 1994 09:11:33 -0500 (EST)

Dear Netters,

I have a number of questions regarding the effects of spin 
contamination on total electronic energies and structures.  My 
understanding of spin contamination is that unrestricted Hartree-Fock 
(UHF) wave functions are not eigenfunctions of the total spin 
operator, so the electronic wave function of interest can be 
contaminated by functions corresponding to states of higher spin 
multiplicity.  This brings me to my questions:

1.  Given that, (a) we have performed an ab initio study on an open 
shell molecule using a single-determinant wave function (i.e., 
variational), (b) we have found its theoretical equilibrium geometry 
for the ground electronic state, and (c) have projected out ALL 
contaminating higher spin multiplicity states along the way to the 
minimum energy geometric configuration.  Will the total calculated 
electronic energy be the lowest possible calculated energy for the 
given basis set and Hamiltonian?

2.  What can be said about 1, above, regarding the total calculated 
electronic energy when a perturbation treatment to the configuration 
interaction is introduced, e.g., MP4(SDTQ)?

3.  What can be said regarding the total calculated electronic energy, 
if in the case of 2, above, condition (1c) is not fully met, i.e., 
some spin contamination remains while going to the optimum geometry.

4.  Given that different spin states correspond to different 
equilibrium geometries, is an optimized structure, which had 
significant spin contamination in its electronic wave function all the 
way down to its ÒminimumÓ energy geometrical configuration, some kind 
of mixture of structures involving the state of interest and the 
different contaminating higher spin multiplicity states?

5.  Regarding semiempirical calculations, in the paper of Novoa et 
al., Inorganica Chemica Acta, Vol. 198-200 (1992) 133, the heats of 
formation of some very large carbon clusters were calculated.  In 
their paper the authors state:  ÒFor an odd-membered linear C_n with 
13 <= n < 20, the AM1 calculations predict the triplet state to be 
more stable than the singlet, due mainly to the spin contamination of 
the UHF calculations.Ó  The calculated stabilities of these larger 
linear carbon clusters are not expected based on what is known for the 
smaller linear clusters where, for odd n (n > 1), the singlet states 
are more stable than the triplet states.  My question is this, is it 
possible that the authors are not correct regarding their reason for 
the for greater stabilities of the triplet states?  (It is not my 
intention to attack the above authors work.  I merely wish to evaluate 
the quoted heats of formation because I require some kind of estimate 
for the heats of formation for these species.)

Regards,

Ryan Bettens,
OSU Physics Department,
[email-masked]