Subject: SUMMARY - MP2/UMP2 vs B3LYP/UB3LYP

From: Valentine Ananikov <[email-masked]>
Date: Fri, 26 May 2000 18:26:05 +0400

Dear CCl members,

Please find my original question and replies on the subject topic
below. To summarize, the following references were suggested:

1) Cramer, C. J.; Worthington, S. E., J.Phys.Chem. 1995, 99, 1462.
2) Lim, M. H.; Worthington, S. E.; Dulles, F. J.; Cramer, C. J. "Density Functional Calculations of Radicals and Diradicals" in Density-Functional Methods in Chemistry, ACS Symposium Series, Volume 629, Laird, B. B., Ross, R. B. Ziegler, T., Eds.; American Chemical Society: WashingtonDC, 1996; 402.
3) Worthington, S. E.; Cramer, C. J., J. Phys. Org. Chem. 1997, 10, 755.
4) Cramer, C. J.; Dulles, F. J.; Giesen, D. J.; Alml÷f, J., Chem. Phys. Lett. 1995, 245, 165.
5) Holger F. Bettinger,Paul von Rague Schleyer, Peter R. Schreiner, and Henry F. Schaefer III, J. Org.Chem. 1997, 62, 9267-9275.
6) Yaoming Xie, Peter R. Schreiner, Paul von Rague Schleyer, and Henry F. Schaefer III, J. Am.Chem.Soc. 1997, 119, 1370-1377.
7) Holger F. Bettinger, Peter R. Schreiner, Paul von Rague Schleyer, and Henry F. Schaefer III, J. Phys. Chem. 1996, 100, 16147-16154.
8) Peter R. Schreiner, William L. Karney, Paul von Rague Schleyer, Weston T. Borden, Tracy P. Hamilton, and Henry F. Schaefer III, J. Org. Chem. 1996, 61, 7030-7039.
9) Sulzbach, et al . JACS, 1997, 119, 5682.

and I really thank to Christopher Cramer, Alexander Bagatur'yants, 
Seiji Mori, Stefan Grimme, Xavier Assfeld and Peter Schreiner
for the contribution and helpful discussion.

regards, Valentin.

---------------
 Dear CCL,

I am a little surprised with the following problem and
would be grateful for helpful comments.

On a substituted carbene compound MP2/UMP2 optimization of
singlet and triplet states respectively leads to energy gap
of about 9 kcl/mol and low lying singlet state. However,
in the case of B3LYP/UB3LYP optimized structures triplet
state is more stable by approximately the same value.
Geometry parameters are also different. Unfortunately,
experimental data for this compound is not available.

Is this a known thing ? any precedents ?

Does anybody have an idea on the possible explanation and what
accuracy one would expect from MP2 and B3LYP calculated s/t gaps?

Thank you!

best regards,  Valentin.
---------------

+++++++++++++++
Dear Valentine,
to my experience, B3LYP is quite good for
S-T gaps if both states are single reference and
spin-contamination is not a problem. For CH2, B3LYP
gives a good value, a little bit too low for the triplet.
I think MP2 has problems here because it is known to be
more sensitive to the multi-reference character and 
small spin-contamination may also be a problem. I would
suggest to use MR-MP or MR-CI.
stefan
_________________________________________________________
Prof. Dr. Stefan Grimme
+++++++++++++++
 
+++++++++++++++
MP2 is a disaster for most carbenes, unless they are very stable
singlets.
The bottom line is that the singlets tend to be two-configurational
(e.g.,
psi = c1 * |...HOMO^2> + c2 * |...LUMO^2> where ... refers to double
occupation of all HF orbitals 1 to HOMO-1 and c1 > c2 but not
necessarily
by all that much) and the extent of the non-dynamical correlation is
such
that perturbation theory is not a good way to estimate the energy.

DFT tends to be MUCH more reliable, although it too ultimately fails if
c1
and c2 come closer to being equal.

There is a vast literature on this topic, particularly with the carbene
focus. My group has contributed a bit.

Cramer, C. J.; Worthington, S. E. "The Electronic Structures of
Aziridenium
and Cyclopropylidene. Hypovalent Atoms in Three-Membered Rings" J.
Phys.
Chem. 1995, 99, 1462.

and

Lim, M. H.; Worthington, S. E.; Dulles, F. J.; Cramer, C. J. "Density
Functional Calculations of Radicals and Diradicals" in
Density-Functional
Methods in Chemistry, ACS Symposium Series, Volume 629, Laird, B. B., 
Ross, R. B. Ziegler, T., Eds.; American Chemical Society: Washington
DC, 
1996; 402.

provide some discussion, and also point to other excellent references.

Chris Cramer
+++++++++++++++

+++++++++++++++
Dear Valentin,
This is a well-known problem, closely associated with the Kohn-Sham
formalism.
Relative stabilization of the singlet state in a carbenoid system is
due to
the (nondynamic!) correlation effect of the mixing between the ground
state
[sigma]2[pi]0 configuration and the doubly excited [sigma]0[pi]2
configuration. This mixing gives rise to some electron density transfer
to
the region of p[pi] orbital. However, one cannot reproduce this
electron
density pattern within the Kohn-Sham formalism simply because of
symmetry
restrictions. Even if the symmetry restrictions are removed, the
one-electron orbital mixing between the [sigma] and [pi] orbitals will
be
negligible.

Best regards,

Prof. Alexander Bagatur'yants
+++++++++++++++

+++++++++++++++
Hi,

have a look at :

1) Worthington, S. E.; Cramer, C. J. "Density Functional Calculations
of  
the Influence of Substitution on Singlet-Triplet Gaps in Carbenes and
Vinylidenes" J. Phys. Org. Chem. 1997, 10, 755.

2) Cramer, C. J.; Dulles, F. J.; Giesen, D. J.; Alml÷f, J. "Density 
Functional Theory: Excited States and Spin Annihilation" 
Chem. Phys. Lett. 1995, 245, 165.

hope this helps.

                                      ...Xav

Ast. Pr. Xavier Assfeld        
+++++++++++++++

+++++++++++++++
Hi Valentin,

you may take carbenes as prime examples for computing S/T-gaps - DFT is
clearly superior due to a better description of the singlet (not
necessarily for a good reason). Have a look at:

Carbenes: A Test Ground for Electronic Structure Methods. Holger F.
Bettinger, Peter R. Schreiner, Paul von Rague Schleyer, and Henry F.
Schaefer III; in "The Encyclopedia of Computational Chemistry" Paul v.
Ragué Schleyer, Norman L. Allinger, Tim Clark, Johann Gasteiger, Peter
A.
Kollman, Henry F. Schaefer III, and Peter R. Schreiner (Eds.), John
Wiley &
Sons Inc.; Chichester, 1998, 183-196.

Substituted Cyclopropylidenes and Cyclic Allenes. Holger F. Bettinger,
Paul
von Rague Schleyer, Peter R. Schreiner, and Henry F. Schaefer III J.
Org.
Chem. 1997, 62, 9267-9275.

The Naphthylcarbene Potential Energy Hypersurface. Yaoming Xie, Peter
R.
Schreiner, Paul von Rague Schleyer, and Henry F. Schaefer III J. Am.
Chem.
Soc. 1997, 119, 1370-1377.

The Ring Opening of Cycopropylidene and the Internal Rotation of
Allene.
Holger F. Bettinger, Peter R. Schreiner, Paul von Rague Schleyer, and
Henry
F. Schaefer III J. Phys. Chem. 1996, 100, 16147-16154.

Carbene Rearrangements Unsurpassed: The C7H6 Potential Energy Surface
Revealed. Peter R. Schreiner, William L. Karney, Paul von Rague
Schleyer,
Weston T. Borden, Tracy P. Hamilton, and Henry F. Schaefer III J. Org.
Chem. 1996, 61, 7030-7039.

Hope this provides some input - Peter

--
Prof. Dr. Peter R. Schreiner
+++++++++++++++

+++++++++++++++
Hi. Valentine:

...

You may find hints from a paper at Sulzbach, et al . JACS, 1997, 119,
5682.
With hyperconjugation of a p orbital
of substituents into  empty p orbital of singlet carbene, S/T gap is
smaller
or sometimes a singlet state could be
 more stable than the triplet.
 although that of methylene carbene is 9.0 kcal/mol experimentally
(triplet ground state).

And is <S**2> of UMP2 result of triplet carbene fine? Is that close to
0.75?
Sulzbach, et al .used BHandHLYP.

Hope it helps.
Seiji

**************************************************
   Seiji Mori, Ph.D. 
+++++++++++++++

====================================================================
                                             ,         ,      ,   ,
Valentine P. Ananikov                        |\\\\ ////|     /////|
NMR Group                                    | \\\|/// |    ///// |
ND Zelinsky Institute of Organic Chemistry   |  |~~~|  |   |~~~|  |
Leninsky Prospect 47                         |  |===|  |   |===|  |
Moscow  117913                               |  |   |  |   |   |  |
Russia                                       |  | A |  |   | Z |  |
                                              \ |   | /    |   | /
e-mail: [email-masked]                     \|===|/     |===|/
http://nmr.ioc.ac.ru/Staff/AnanikovVP/          '---'      '---'
  Fax +7 (095)1355328   Phone +7 (095)9383536
====================================================================