From:	<BETTENS-0at0-MPS.OHIO-STATE.EDU>
Date:	Mon, 14 Nov 1994 09:11:33 -0500 (EST)
Subject:	Spin contamination, effect on energy and structure.

Dear Netters,

I have a number of questions regarding the effects of spin=20
contamination on total electronic energies and structures.  My=20
understanding of spin contamination is that unrestricted Hartree-Fock=
=20
(UHF) wave functions are not eigenfunctions of the total spin=20
operator, so the electronic wave function of interest can be=20
contaminated by functions corresponding to states of higher spin=20
multiplicity.  This brings me to my questions:

1.  Given that, (a) we have performed an ab initio study on an open=
=20
shell molecule using a single-determinant wave function (i.e.,=20
variational), (b) we have found its theoretical equilibrium geometry=
=20
for the ground electronic state, and (c) have projected out ALL=20
contaminating higher spin multiplicity states along the way to the=
=20
minimum energy geometric configuration.  Will the total calculated=
=20
electronic energy be the lowest possible calculated energy for the=
=20
given basis set and Hamiltonian?

2.  What can be said about 1, above, regarding the total calculated=
=20
electronic energy when a perturbation treatment to the configuration=
=20
interaction is introduced, e.g., MP4(SDTQ)?

3.  What can be said regarding the total calculated electronic energy=
,=20
if in the case of 2, above, condition (1c) is not fully met, i.e.,=
=20
some spin contamination remains while going to the optimum geometry.

4.  Given that different spin states correspond to different=20
equilibrium geometries, is an optimized structure, which had=20
significant spin contamination in its electronic wave function all th=
e=20
way down to its =D2minimum=D3 energy geometrical configuration, some =
kind=20
of mixture of structures involving the state of interest and the=20
different contaminating higher spin multiplicity states?

5.  Regarding semiempirical calculations, in the paper of Novoa et=
=20
al., Inorganica Chemica Acta, Vol. 198-200 (1992) 133, the heats of=
=20
formation of some very large carbon clusters were calculated.  In=
=20
their paper the authors state:  =D2For an odd-membered linear C_n wit=
h=20
13 <=3D n < 20, the AM1 calculations predict the triplet state to be=
=20
more stable than the singlet, due mainly to the spin contamination of=
=20
the UHF calculations.=D3  The calculated stabilities of these larger=
=20
linear carbon clusters are not expected based on what is known for th=
e=20
smaller linear clusters where, for odd n (n > 1), the singlet states=
=20
are more stable than the triplet states.  My question is this, is it=
=20
possible that the authors are not correct regarding their reason for=
=20
the for greater stabilities of the triplet states?  (It is not my=
=20
intention to attack the above authors work.  I merely wish to evaluat=
e=20
the quoted heats of formation because I require some kind of estimate=
=20
for the heats of formation for these species.)

Regards,

Ryan Bettens,
OSU Physics Department,
BETTENS "-at-" MPS.OHIO-STATE.edu



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