Subject: SUMMARY: A problem with O(1D)

From: "Alexei Khalizov" <[email-masked]>
Date: Thu, 25 Jul 2002 18:17:09 -0400

This is a SUMMARY of the answers on my question about the calculation 
of the correct energy of singlet oxygen atom O(1D). I am very 
grateful for all responses I received, which helped to shed some 
light upon the problem.

In short words, the 1D state cannot be represented with a single 
determinant so there is no an easy way to get around it using DFT 
theory. MCSCF can solve the problem. Using MP2 with complex orbitals 
might be prominent as well. Composite model chemistry G3 or coupled 
clusters including triple and maybe quadruple excitations with 
sufficiently extended basis set may be of help. Since convergence of 
the inter-pair correlation energy with the size of basis set is slow, 
using a basis set extrapolation formula might be necessary in the 
latter case. Besides, most basis sets are optimised and contracted 
for the ground states of atoms, which leads to overestimation of 
their excitation energies. By now, I have tried G3 and CCSD(T)/aug-cc-
pVQZ, which resulted in 8.5 and 20.5 kJ/mol overestimation of the 
experimental value, respectively. In the latter case T1 value is 
small, 0.004. 

Regards,
Alexei

----------------------
Dear CCLers,

Does anyone know how to calculate correctly the energy of an oxygen 
atom in the singlet state O(1D)? I am having a problem of evaluating 
the singlet-triplet energy difference E(S-T) = E[O(1D)] - E[O(3P)] 
whose experimental value is 190 kJ/mol. Using DFT methods (B3LYP and 
PW91) with small basis sets (6-31G*) significantly overestimates this 
energy splitting, giving E(S-T) = 270-280 kJ/mol. Calculation at 
CCSD(T)/6-311+G(3df) level of theory leads to a better result, 
however, it is still far from being acceptable, E(S-T) = 214 kJ/mol. 
So far I have found that it is the energy of O(1D) that is incorrect 
while the energy of O(3P) is reproduced properly. What goes wrong? 
The wavefunction for O(1D) seems to be correct - population analysis 
shows that it is symmetrical (2Px alpha) (2Px beta) (2Py alpha) (2Py 
beta).  

Thank you in advance,
Alexei
----------------------
Dear Alexei,

You can try correlation consistent basis set, e.g. aug-cc-pVTZ,
which is better suited for electron correlation calculations than the
conventional Pople basis.

Best regards,
Victor.

Victor Anisimov,
Krakow, Poland.
----------------------
Hi Alexei,

I am not sure what the problem is but I'll give you my view anyway.

First of all your problem reminds me of the singlet-triplet splitting 
of methylene. This is a well know benchmark problem for post Hartree-
Fock treatments. One not only needs to recover a large fraction of 
the correlation energy to get it right but the basis set requirements 
for the 2 states are quite different as well. So as far as your 
CCSD(T) results are concerned the basis set might be the problem.

Second using DFT I don't think your 1D state can be represented as a
single Slater determinant. In that case you can still do DFT but you 
need special energy expressions (see e.g. the work of Filatov and 
Shaik, CPL 304 (1999) 429-437). Are you sure that your code supports 
such expressions?

Best wishes,

Huub

Huub van Dam                               E-mail: 
[email-masked]
CCLRC Daresbury Laboratory                  phone: +44-1925-603362
Daresbury, Warrington                         fax: +44-1925-603634
Cheshire, UK WA4 4AD
----------------------

Getting the 1D state for O requires a two-determinant
wave function, or alternatively using complex orbitals
for a single determinant. A single determinant RHF type
wave function is a mixture of the 1D and 1S states, which
is why you are getting a too high value. You can model
the 1D with a small MCSCF (many programs) or using complex
orbitals (Gaussian is the only one I know of). With the
latter, you can include correlation with MP2, but I don't
know any other methods/programs availabel. MP2, however, gives
a fairly decent description of the singlet-triplet energy
difference, but you are presumably after something more than
just this value(?).

 Frank

| Frank Jensen, Department of Chemistry          |
| University of Southern Denmark                 |
| Campusvej 55, DK-5230 Odense, Denmark          |
| FAX +45 66 15 87 80 , Voice +45 65 50 25 07    |
| http://www.sdu.dk/Nat/Chem/STAFF/sci/FrjE.html |
| http://bogense.chem.ou.dk/~frj        
----------------------
The S/T splitting is very hard to calculate, because the intrapair
correlation energy converges very slow with the basis set size.  Two
states of oxygen have different number of electron pairs (or beta
electrons, assuming each beta electron is paired with an alpha one).  
If you apply an empirical correction to account for this, as it is 
done in G3 theory [JCP, 109, 7764 (1998); I'm talking about the HLC 
correction, Eq. 6], your difference will drop by another 10 kJ/mol.  
Since the basis set used in G3 theory is slightly different (it 
includes core correlation functions, which your set is missing), the 
agreement between theory and experiment becomes OK.

To summarize:  nothing seems wrong with your calculations.  The 
computational models you are using can go only that far.

Vitaly Rassolov
Dept. of Chemistry and Biochemistry         (803) 777-7811
University of South Carolina            fax (803) 777-9521
631 Sumter St
Columbia, SC 29208
[email-masked]
----------------------
Hi Alexei,

as always, it might be either a correlation problem
or a basis set problem. Within CC theory, the size
of the largest T1 and T2 amplitudes is a qualitative
measure of the importance of correlation. When
both are smaller than maybe 0.05 CCSD(T) usually
gives very accurate energy differences. When one
of them (especially the largest T2-amplitude) is
larger than ~0.10, the quality may suffer visibly. In
the latter case inclusion of higher excitations is
helpful, e.g. CCSD(TQ). The size of the largest
T1-amplitude may depend on the choice of
reference function (UHF, ROHF, QRHF, ...).

The other part is basis sets, quite possibly more
important here. Most basis sets are optimized and
contracted for the ground states of atoms (3P for
O). Therefor the excitation energies from the ground
state to excited states are prone to be too large,
especially for small basis sets. The way out is to
use basis set extrapolation. It has been shown to
be reliable for many properties with the cc-basis
sets of Dunning and co-workers. A good formula
is found in Peterson, Woon, Dunning, J. Chem.
Phys. 100, 7410 ('94), equation 2.

Stefan
Dr. Stefan Fau                    
[email-masked] University of Florida
(352) 392-6714 Quantum Theory Project 2319 NPB #92,
P.O.Box 118435 Gainesville, FL 32611-8435
-------------------------
Dr. Alexei Khalizov
Department of Chemistry
McGill University,
801 Sherbrooke St. W.,
Montreal, Quebec, CANADA,
H3A 2K6

Phone: (514) 398-6920
Fax: (514) 398-2382