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Date: Fri, 09 Dec 1994 15:32:15 -0500 (EST)
Subject: Open shell hydrocarbons, AM1 ROHF versus UHF
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Dear Netters,

Thanks to those of you who responded to my last posting on the 14th of 
November regarding spin contamination.  Before summarizing these 
responses I would like to ask one further question which is related to 
my last question in the previous posting.  I will then compile all 
responses and post a summary.  My question concerns ROHF versus UHF 
calculations using the AM1 semiempirical model.  Is anybody aware of 
any published work which recommends the use of either in calculating 
heats of formation, specifically for hydrocarbon open shell species?

I have examined the original paper of Dewar, M.J.S.; Zoebisch, E.G.; 
Healy, E.F. and Stewart, J.J.P., J. Am. Chem. Soc., 107 (1985) 3902 
where AM1 was introduced.  In this work the heats of formation of 6 
hydrocarbon radicals (all doublets) where compared with the 
experimental values.  I could find no indication as to whether the 
reported calculations used the UHF or ROHF approaches.  This is 
important because the calculated heats for each approach produces 
significantly different results.  I consequently repeated the 
calculations on the 6 hydrocarbon radicals given in the above paper 
and found the following heats of formation (kcal mol^{-1}).  I also 
give the values of S^2 and the reported heats as well as the current 
experimental values (from J. Phys. Chem. Ref. Data, 17 (1988) Sup. 1) 
for comparison below.

           AM1           AM1    Reported
           UHF    S^2    ROHF      AM1     Exp.     Exp. - Calc.(ROHF)
CH3       29.95  0.7613  31.25    31.25   34.8(3)       3.6
C2H3      60.46  0.8589  64.78    64.78   63.4(10)     -1.4
C2H5      15.49  0.7619  18.14    15.48   28           10
CH2CHCH2  30.20  0.9300  38.58    38.58   39            0
(CH3)2CH   3.61  0.7622   6.80    10.07   22.3(6)      15.5
(CH3)3C   -6.14  0.7623  -2.66    -2.66   11.0(6)      13.7

For C2H5 the authors seem to have reported the UHF value.  I was not 
able to reproduce the reported result for (CH3)2CH with either the 
ROHF or the UHF result.  I was able to reproduce the calculated heat 
of formation for this species given by Dewar, M.J.S. and Thiel, W., J.
Am. Chem. Soc., 99 (1977) 4907, using the MNDO Hamiltonian.  In this 
earlier work the authors explicitly stated that they used ROHF heats 
of formation calculated with MNDO.  It is noted that for the remaining
species the reported AM1 heats of formation also appear to be the ROHF
values.  While agreement with the experimental values are not terrific
and appear particularly bad for the larger saturated hydrocarbon 
species, they are adequate for my purposes given that these errors can
be taken as typical for calculated heats of formation of analogous but
larger open shell hydrocarbon radicals.

Does anybody know of any further studies, using the AM1 Hamiltonian, 
on radicals where the calculated heats of formation have been compared
with experiment?  It seems to me, from the above table, that the UHF 
results are not useful in comparison with the ROHF results, and that 
the extent of spin contamination tends to increase with molecular size
and unsaturation, being close to 0.75 for the most saturated species. 
For instance, I repeated the calculation on triplet linear C19 given 
by Novoa et al., Inorganica Chemica Acta 198-200 (1992) 133, using UHF
and ROHF.  I obtained the same heat of formation as these authors with
no assumed symmetry in the linear chain and using the UHF AM1 
Hamiltonian.  However, I obtained an S^2 of 4.356 (should be 2) and a 
ROHF heat of formation of 678.72 kcal mol^{-1}, which is greater than 
the UHF value by 24.17 kcal mol^{-1}!  I would very much appreciate 
any helpful comments or literature references which deals with any of 
the above issues I've raised here about AM1 and its applicability of 
open shell systems.

Regards,

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