Subject: Summary: DFT functionals

From: [email-masked] (John Lohrenz)
Date: Wed, 3 May 1995 11:05:33 -0600 (MDT)

A week ago or so I posted a query about the reliability of functionals
in DFT. Thanks for all who responded. Although I didn't answer every
comment personally I appreciate the information. 
My personal feeling is, that there still is a lot of work left for the
evaluation of the different functionals. Second there is no! standard
functional although some seem to do better than other in general. I am
looking forward to see how the "mixed" or "hybrid" methods will do...
Furtheron it would be nice to see, what is a good choice for TM complexes
and properties.

Once again thanks to every single one.

John

===========================================================================
The original question:

Hi everone,

while browsing through the most recent summaries I noticed that someone
stated that BLYP (in his eyes) is the best combination of functionals.
I heard a lot of this kind of information. Other people favour the 
mixed HF-methods... There seems to be some confusion. I would like to 
hear, what experiences are there, concerning the quality of results
calculated with different combinations of functionals. Has somebody
systematically studied this? What about transition metal complexes?
Quality of geometries? Relative energies? Transition states? Bond energies?

I would like to summerize the responses. I think it should be of general
interest to a least have an idea of the quality of the applied functional.
I get the strange feeling that BLYP is becoming something like a standard
just because it is stated so in the G92/DFT manual.

John

And here the answers:
=============================================================================
Gabor I. Csonka ([email-masked]) wrote:

Hello John,

We recently published a paper on the First ECCC (ECCC1). It is the Paper 50.
As far as I know it was accepted for the final CD release. The details:

Title: The performance of Gradient Generalized Approximation DFT Methods with
Gaussian Basis Sets: Sulfur-containing Molecule

<b>G&aacute;bor I. Csonka, N. Anh and J. R&eacute;ffy</b><p>
<p>
Department of Inorganic Chemistry, Technical University of Budapest<p>
H-1521 Budapest, Hungary<p>
E-mail: [email-masked]<p>

The abstract:

The performance of Gradient Generalized Approximation Density Functional
Theory (GGA-DFT) methods with Gaussian basis sets are examined by studying 5
small molecules. Their geometries are optimized by HF, MP2 and DFT methods
to which we have applied four different DFT functionals. The gradual
improvements of basis sets gradually decrease the bond lengths and increase the
bond angles. Accidentally the HF/6-311G(d) results are close to the
experimental results while the improvement of the basis sets to 6-311G(2d,f)
decreased the agreement with  experimental observations. The inclusion of the
electron correlation effect increases the bond lengths considerably. The
various GGA-DFT results agree qualitatively with each other and with the MP2
results. Some functionals provide exaggerated effects and poor agreement with
experimental results while others yield reasonable correlation.

Conclusion:

The results show that various GGA-DFT methods introduce
different strength of electron correlation. It was found that the
correlation strengths increase in the following order: B3-P86, B3-LYP,
B-P86 and B-LYP.
In general the basis set dependence of the GGA-DFT methods is not larger than
that of the HF method for the present cases.

---------------------------------------
Comment: One can fine tune the approximate functionals by increasing or
decreasing the correlation effects. If  correlation effects are weak mixed
functionals from the above list will perform well. Otherwise you should apply
methods wich can reproduce the stronger correlation.

The paper contanis lot of figures.

You can find the paper on my web home page or on the ECCC1 hompage

-- 

Gabor I. Csonka		        Budapest University of Technology
Tel/FAX: (361) 463.18.35	Inorganic Chemistry Dept. Ch. Bldg
[email-masked] 		H-1111, Bp. Szent Gellert ter 4
http://www.fsz.bme.hu/bme/chemical/csonka.html

=============================================================================
Jan Hrusak ([email-masked]) wrote:

Hi John,

we are using DFT methods now for a good while comparing the results 
quite often to those obtained by sophisticated ab initio calculations 
like CCSD(T) (larger polarized basis sets). In the beginning I got the 
same impression You mentioned." B-LYP is a standard". Now after 
spending few CPU years on comparing the different  DFT and 
approximate DFT methods for neutral, cationic, anionic, organic and 
metalorganic systems I would be more carefull. There is nothing like 
a general standard method. 
For many cases I saw the B3LYP working in a excelent agreement with 
experiment and highly correlated ab initio methods for both structures and 
energies. Using ECP's we got also quite a lot very nice results even for 
heavy transition metal containing systems.
However, in other case this parametrized method fails and pure DFT 
proceed better. An (in my opinion) still unsolved problem are the open 
shell systems (often found with TM). Here DFT/HF methods give 
often unphysical results like wrong ground states, while pure DFT 
offer the qualiattive agreement with the experiment.

I would be interested to get the summary on Your request

Jan

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Dr. Jan Hrusak                               ###############################
J. Heyrovsky Institute of Physical Chemistry ## MEMOR ESTO CONGREGATIONIS ##
Academy of Sciences of the Czech Republic    ##   TVAE QVAM POSSEDISTI    ##
Dolejskova 3, CZ-182 23 Prague 8             ##         AB INITIO         ##
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                     E-Mail: [email-masked]
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=============================================================================
Jack A. Smith ([email-masked]) wrote

John:

   Warren Hehre's new book on "Practical Strategies for Electronic
Structure Calculations" (from Wavefunction, Inc) gives a presents a very
good comparison of the differents methods (AM1, HF, SVWN, BLYP, B3LYP, MP2)
and basis sets (STO-3G, 3-21G(*), 6-31G*, 6-311+G((2d,p)) for equilibrium
geometries, transition state structures, conformational energies, reaction
(thermodynamic) energies , activation (kinetic) barriers, dipole moments,
charges, etc.  He  discusses when correlation (MP2 or DFT) is important,
when geometries from lower-level theories are adequate, when basis set
choice is critical, the importance of posing problems as an anlogous series
of isodesmic reactions  where possible, etc.  I found the book very
informative.

   The book doesn't discuss any other energy functionals besides the 3
mentioned (nor any form of CI, CC theory, or MP beyond 2nd order).  It
doesn't cover any transition metal complexes.  It doesn't discuss any
"strategies" like G2 or CBS-4, but maybe "S5" (Spartan-5) is in the works?
;-)

- Jack

-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
  JACK A. SMITH                 ||
  Union Carbide Corp.           ||  Phone:    (304) 747-5797
  Catalyst Skill Center         ||  FAX:      (304) 747-5571
  P.O. Box 8361                 ||
  S. Charleston, WV  25303      ||  Internet: [email-masked]
-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=

=============================================================================
Andrew T. Pudzianowski ([email-masked]) wrote:

John - I have made a fairly thorough comparison of the B-LYP combin-
ation with the Becke3-LYP (B3-LYP) combo, where the B3 exchange 
functional has a Hartree-Fock component. This was done with the
6-311++G(d,p) basis and compared with MP2/6-311++G(d,p) results for
the same systems, which were 10 ionic H-bonded binary systems, i.e.,
10 ion/molecule systems of which 5 were cationic and 5 were anionic.
Two examples are CH3NH3+/NH3 and HCOO-(formate)/H2O.
    The B3-LYP results are tangibly closer than B-LYP to the MP2
values. To make things simpler I'll quote you root mean square dev-
iations from MP2 for complexation energies at 0 K (delta E0), comp-
lexation enthalpies at 298.15 K (delta H), acceptor-hydrogen distances
(A--H) and acceptor-donor center distances (A--D) for the fully optim-
ized H-bonded complexes. For delta H I also have rms deviations from
experimental gas-phase values. Energies are in kcal/mol, distances in
Angstroms.

            (delta E0)rms    (delta H)rms(MP2)   (delta H)rms(exp)
B-LYP           0.92                1.06               1.92
B3-LYP          0.69                0.73               1.65
MP2             ----                ----               1.21

             (A--H)rms           (A--D)rms
B-LYP           0.034               0.026 
B3-LYP          0.019               0.014

Remember, these are rms deviations of the specified results from the
the corresponding MP2 values for all ten systems except in the compar-
ison with experimental enthalpies, where the deviations are with res-
pect to the experimental quantities.
   I think you'll agree that B3-LYP does a better job on ionic H-bonded
systems. I'm busy writing all this stuff up and with luck it will
appear in print towards the end of the year.
                            Best wishes,
                           Andy Pudzianowski
***********************************************************************
Andrew T. Pudzianowski,Ph.D.       
Bristol-Myers Squibb PRI      
Box 4000                  *   "There are two ways to do things.
Princeton NJ 08543-4000   *    There's the scientific way, and               
(609) 252-4248            *    there's the disgusting way."
(609) 252-5747: fax       *          
[email-masked]      *        "Beakman's World", 1994
***********************************************************************

=============================================================================
Benny Johnson ([email-masked]) wrote:

Dear Dr. Lohrenz,

For a systematic study of DFT geometries, vibrational frequencies, dipole
moments and atomization energies by different combinations of functionals see 

B.G. Johnson, P.M.W. Gill and J.A. Pople, J. Chem. Phys. 98, 5612 (1994).

Qualitatively, it was found that Becke gradient-corrected exchange +
a correlation functional (either local or gradient corrected) gave the
best results, with B-LYP giving the best performance out of the set of 6
functionals studied.

A later paper examined open-shell H abstraction barrier heights with even
more combinations of functionals, including GGA's:

B.G. Johnson, C.A. Gonzalez, P.M.W. Gill and J.A. Pople,
  Chem. Phys. Lett. 221, 100 (1994).

Here it was found that none of the functionals gave acceptable results.
However, the performance of the various gradient-corrected functional pairs
on this particular problem was similar, e.g. the GGA91-GGA91 results were
not too different from the B-LYP results.  Other studies have found similar
results as to the quality of functionals.  There are definitely some
functionals that are much better than others -- generally these involve
gradient corrections.  However, there currently does not seem to be a single
combination of functionals which is demonstrably superior to all others on
a wide range of chemical problems.  B-LYP is one of the leaders, but by no
means does it always perform well.  This, plus the fact that there is no real
way to systematically improve the quality of a density functional (as
contrasted with usual ab initio theories, where one can e.g. keep going to 
larger and larger CI expansions) makes systematic validation studies of DFT
methods critically important.

Cheers,
Benny Johnson
Q-Chem, Inc.
317 Whipple St.
Pittsburgh, PA  15218

=============================================================================
Scott E. Boesch ([email-masked]) wrote:

Dr. Lohrenz,
	
	I noticed your message on CCL and I would refer you to a
	paper that is currently in press for the Journal of Physical 
	Chemistry.
	S.E. Boesch and R.A. Wheeler ; Jouranl of Physical Chemistry; 1995.
	I will send you a preprint as soon as I receive them.   It
	is supposed to be published in May.
	The title of the paper is 'Pi-Donor Substituent Effects on
	Calculated Structures and Vibrational Frequencies of p-Benzoquinone,
	p-Fluoranil, and p-Chloranil'

	We did geometry optimizations and frequency calculations
	on the three molecules mentioned above.
	For, p-benzoquinone we did optimizations using every possible
	combination of exchange and correlation functionals available
	in G92/DFT . (Of course, we did not include all of that in
	the paper.)
	
	For p-benzoquinone, we found that the hybrid Hartree-Fock/Density
	Functional methods ( B3P86 and B3LYP) gave the best geometries,
	almost within experimental error of electron diffraction structures.
	The pure density functional method that gave the best structures
	was the local density functional method, SVWN, which uses  
	Slater's exchange functional and the correlation functional of
	Vosko, Wilk, and Nusair.

	I would be happy to send you a preprint as soon as they are
	available.  Also, if you want information regarding the
	different combinations of functionals that we did not put
	in the paper, I could provide that.

	If you have any questions, feel free to email me at

	[email-masked]  

	Scott E. Boesch
	Department of Chemistry @ Biochemistry
	University of Oklahoma
	Norman, OK 73019

=============================================================================
Joe Durant ([email-masked]) wrote:

Hi John!

First off, I am interested in a summary of the responses you get.

On to the meat of the matter.  I have been focussing on calculation of
transition states, and have been comparing various DFT functionals to
a set of transition states which I believe have been well
characterized by more traditional methods (see J. Chem. Phys. 98,
8031o 1993 for the full list).  The transition states include things
like H + H2 -> H2 + H, F + H2 -> HF + H, O + HCl -> OH + Cl; I feel
fairly comfortable that the energies, frequencies and geometries are
not too far off reality.

I have looked at these transition states using G92/DFT with the BLYP,
B3LYP, B3P86 and BHandHLYP functionals.  First off, BLYP fails
miserably.  O + HCl -> OH + Cl has a 8.5 kcal/mole barrier.  BLYP
predicts that the surface is completely attractive, although there is
an inflection point at about the right geometry for the transition
state.  It also fails to find the barrier in the F + H2 -> HF + H
system.  I gave up on it at that point.  The B3xx functionals fared
somewhat better, but they both systematically underpredicted the
barriers for reactions (average underprediction of 5+ kcal/mole for
B3P86, and 4+ kcal/mole for B3LYP, with average deviations of about 2
kcal/mole in each case).  B3LYP failed to find the F + H2 -> HF + H
transition state.

BHandHLYP wins my vote for the best functional.  It underpredicted
barriers by less than 1 kcal/mole, with an average deviation of about
2 kcal/mole.  (I suspect that this performance is comparable to that
for the G2 data set).  Geometries are generally good to < 0.05 A and <
4 degrees.  Frequencies aren't as good, with errors of the order of
300 cm-1 being common.

I have quoted performances using "about" and "order of" because I have
done calculations using 6-31G*, 6-311G**, 6-311++G** and
6-311G(3df,2p) basis sets.  I don't find any systematic trends...
bigger basis sets don't seem to offer better performance (although I
am settling on 6-311G** as a "standard").

One other note:  Gaussian noted that BHandHLYP as implemented in
G92/DFT is a different functional than that proposed by Becke.  But it
works.

Joe

-- 

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=============================================================================
John M. McKelvey ([email-masked]) wrote:

I prefer Beck3LYP....It gives very good geometries, which seem more accurate
than from BLYP, at least for my applications.  In general Gaussian, Inc.,
prefers Becke3LYP, overall.

Regards,

John

-- 

John M. McKelvey			email: [email-masked]
Computational Science Laboratory	phone: (716) 477-3335
2nd Floor, Bldg 83, RL
Eastman Kodak Company			
Rochester, NY 14650-2216

--

=============================================================================
Max Muir ([email-masked])  wrote:

Dear Dr. Lohrenz,

you may care to look at "A study of some organic reactions using density functional
theory" Jon Baker, Max Muir, and Jan Andzelm, J. Chem. Phys. 102(5), 1995. We studied
twelve reactions (6 radical and 6 closed shell) with BIOSYM's TurboDFT at the 6-31G*
level.

Regards,

Max Muir
=============================================================================
end
-- 
=========================================================================
Dr. John Lohrenz
Dept. of Chemistry                         Phone: (403) 220 3232
University of Calgary                      FAX:   (403) 289 9488
2500 University Drive, N.W.
Calgary, Alberta, T2N 1N4            email: [email-masked]
Canada
=========================================================================