Subject: Calculation on biradical

From: <[email-masked]>
Date: Wed, 16 Aug 1995 17:42:28 +0200 (MST)

Dear netters,

 At the moment I am doing ab initio calculations on 
1,5-Dehydronaphthalin, so it is supposed to be a biradical. It is an 
isomer to a ordinary closed-shell molecule which I am interested in. So 
to compare the energies of the molecules, I am interested in the 
singlet-groundstate of the biradical.
 But this doesn't seem to be a trivial problem. It was no problem at all 
to get the wavefunction for the triplet state. So I optimized the 
geometry for the triplet state and tried to get some singlet 
wavefunctions for this geometry.

 Here is what I got:

 1. UHF, 6-31G*, mult=3 : E=-382.059168, <S**2>=2.2470 (2.0346 after 
annihilation of first spin contaminant)

 2. UHF, 6-31G*, mult=1 : E=-381.906022, <S**2>=0.0000
 This result was the same as the result with RHF. Especially the spin 
desity was zero everywhere. So I thought that this wouldn't be a proper 
description of a biradical.

 3. UHF, 6-31G*, mult=1, GUESS=mix
 This calculation didn't converge at all.
 
 4. In fact I was able to get another singlet state wavefunction. The 
only way to get it was from a stability analysis and optimization from the 
wavefunction obtained with 2. The result was: E=-382.086893, 
<S**2>=2.2807 (8.1431 after annihilation of the first spin contaminant)
At least the spin density gave two unpaired electrons with different spin 
at the right carbons.

 Because dft is known to give lower spin contaminations, I tried it this way:

 5. UHF, 6-31G*/B3LYP, mult=3 : E=-384.510256, <S**2>=2.0136 (1.9996)
 
 6. UHF, 6-31G*/B3LYP, mult=1 : E=-384.484437, <S**2>=0.000
 Again the same result as with RHF, spin density zero everywhere.

 7. UHF, 6-31G*/B3LYP, mult=1, GUESS=mix : E=-384.518499, <S**2>=0.9392 
(0.1510 after annihilation) This calculation had no difficulties to converge.

 ROHF calculations for the singlet states always gave the same 
wavefunction as for RHF calculations.

 So there are a couple of questions:
 
 a) Why is it so difficult to get a UHF singlet wavefunktion for a normal 
biradical? 

 b) Can I rely on the energies obtained when the spin contamination is 
about 1.0 (Point 7.)? This is especially problematic because I want to 
compare it to the energiy of a closed-shell isomer. Since I got this 
results with 6-31G*/B3LYP it seems to be the best I can get...
Is a geometry optimization sensible in this case?

 c) What can I say about the wavefunction of point 4.? The spin 
contamination is about 2.3 before annihilation (not a very small value 
for a singlet ;-) and about 8.1 AFTER annihilation of the first spin 
contaminant. I have no idea what this should mean!

 d) Am I right when I think that the spin density of a system with to 
unpaired electrons in the sigma frame separated far enough from 
another should exhibit these two electrons at the carbons they are 
attached to?

e) Having all these problems in mind: Which way should I go to determine 
the energiy of the singlet ground state?

Sorry for this somewhat lengthy question, but I'll summarize the 
responses, when there is interest :-)

Bye, Thorsten 

/-----------------------------------------------------------------\
|                        Thorsten Koch                            |
| Institut fuer physikalische Chemie II der Universitaet zu Koeln |
|                    [email-masked]                       |
|                   Tel. +49 [0]221 470 4816                      |
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