Subject: Summary: High level for TMs

From: Per-Ola Norrby <[email-masked]>
Date: Mon, 11 Feb 2002 08:34:32 +0100

Dear CCLers,

	I've now had some responses to my question about high level
calculations on transition metals.  Not unexpectedly, if you need
accuracy, you pay for it...

	Several answers led to further corresponendence, but I'm
only summarizing the original answers here.  Many thanks to:

Frank Jensen
N.O.J. Malcolm
Stefan Grimme
Markus Reiher
Max C. Holthausen
Luigi Cavallo

	To summarize, we still have no good alternative to DFT for
medium size systems (>10 atoms), and it cannot be a priori trusted
for all transition metals.  Most responders agree that we can still
trust DFT for geometries, and then use better methods for single
point energies.  There is some verification for this statement;
for example, I've seen a chapter by Diedenhofen, Wagener, and Frenking
in "Computational Organometallic Chemistry" (Ed: Tom Cundari).
However, I'd want to see more before I believe it's valid for all
TMs.  Thanks also to Max C. Holthausen for a book reference
(see below); comparing to good experimental gas phase data is still
the best way to validate our methods...

	For near degenerate systems, CC or similar alternatives is
not the answer, especially not with small bases.  In my own case,
I'll try to go the way of CASSCF and CASPT2 (thanks to Björn Roos
for getting me started on this), but it is not the final answer.
I'm still looking for a method that can give me trustworthy relative
energies of different spin states for complexes with 10-20 atoms
(a full coordination shell around a TM), preferably in solvent.
Tweaking the DFT for each system might be the answer, but I still
need accurate data for coordinatively saturated TMs to apply this
method.  Maybe Max is right, that you can do this for coordinatively
unsaturated systems and then use the modified DFT for larger
complexes?  I'll try.

	Thanks to all who responded,

	Per-Ola

------------Original message-------------------------------------

	I'd like to get some opinions on high level calculations on 
first row transition metal complexes, in particular for complexes 
with near-degenerate states.  Furthermore, I'm interested in 
complexes used for homogeneous catalysis, so even very smal models 
frequently have 10-20 heavy atoms and as many hydrogens in addition 
to the metal.

	I've used various types of DFT, both pure and hybrid, for 
these types of systems for several years now.  However, I've seen 
several indications recently that the relative energies of different 
spin surfaces can be wrong by up to 100 kJ/mol.  This is, of course, 
unacceptable.  I very much like the pragmatic fix proposed by Reiher 
et al, Theor. Chem. Acc. 107 (2001) 48-55, where they reparameterize 
the amount of exact exchange in B3LYP for organometallic complexes. 
However, having been burned once, I don't want to assume that one 
fixed parameterization is going to be valid for all first row 
transition metals.  Thus, to apply this approach I need very good 
reference data for some experimentally inaccessible complexes.  I'll 
have to obtain them computationally, but what level to use? 
Alternatively, I may not go for the modified DFT, but then I still 
need a theoretical level I can access, which will give me good 
relative energies (and the geometries, but maybe DFT can do this..?).

	So, what level can we trust for this?  CCSD(T) has been 
proposed, but it's expensive, and we all know that it requires a 
large basis set, certainly much better than the double-zeta valence 
that is often used.  And it is still only a perturbation method, so 
if the underlying HF is way off, no amount of perturbation will fix 
it.  However, I'd like to try it out if I can find a program that is 
reasonably efficient.  I've heard rumors of linear scaling CCSD(T) or 
equivalent methods, does anyone know of an available implementation 
that will allow a calculation with ca 500 basis functions?

	How about MC methods?  I'm trying out CASPT2, but what else is there?

	BTW, don't suggest any MP-method (MP2, LMP2,...).  I've tried 
them for a couple of test cases, and the errors are much larger than 
with DFT.

	As a side issue, any suggestions of what type of experimental 
data to compare to?  There are a couple of cases where population 
distributions among near-degenerate states can be measured, but this 
is not general enough, I also want to be able to predict cases where 
the energy difference is large.

	All the best

	Per-Ola
----------Response from Frank Jensen---------------------------
	Per-Ola,
	DALTON er maaske en mulighed for CC-beregninger. Den kan
koere integral-direkte beregninger, bl.a. paa linux maskiner.
Det er gratis, check ICC-hjemmesiden for en www-adresse.

	Frank
----------Response from N.O.J. Malcolm-------------------------
per-ola,

you might want to try something along the lines of an experiment we
tried (simply for first row TM excitation energies), very quick and
dirty.

see:

"A simple scaling for combining multiconfigurational wavefunctions with
density functionals"
Malcolm NOJ, McDouall JJW
CHEMICAL PHYSICS LETTERS
282 (2): 121-127 JAN 9 1998

noj
----------Response from Stefan Grimme--------------------------
Dear Per-Ola,
we have developed a simplified MR-MP2 scheme without CASSCF step
running in parallel on a cheap linux PC-cluster. We are just testing
energetics of simple TM compounds. If you are interested I can provide
you with some numbers (we just started and are not so far yet). In principle
our implementation works for 500-800 basis functions.
Stefan Grimme
---(I asked for a reference on this, and got it, thank's Stefan)---
S. Grimme und M. Waletzke, Multi-reference M¯ller-Plesset
theory: computational strategies for large molecules, Phys. Chem. Chem.
Phys., 2, (2000), 2075-2081.
(its also available via our homepage)
However, this paper mainly deals with excited states and also
the parallel stuff is not described there.
----------Response from Markus Reiher--------------------------
Dear Per-Ola,

after I read your email postet at [email-masked]
I thought it might be useful to write you the latest
experiences with our reparametrized B3LYP functional.

My diploma student worked out how B3LYP* performs for the G2 test
set and for transition metal complexes of the first period.
It turned out that B3LYP* is as good as B3LYP for the
thermochemistry of the G2 test test. Furthermore, the
effects we found are transferable to other transition
metals. But there are some pathological cases, for which
the deficiencies which we detected are most prominent, which
means, that one must be very careful with DFT calculations.
These difficult cases are compounds with Mn, Fe, Co, Ni
in weak ligand fields. We prepared a second paper on this
which is submitted to JCP.

However, if states of different multiplicity are really close,
DFT will certainly not get things right. Therefore, we are
after these cases with multireference MP2 methods which are
capable of any electronic situation (CCSD(T) is too unreliable
as you often have multi-determinant ground states for transition
metal complexes).
Experimental data is hard to obtain and I believe that
highly accurate ab initio calculations done for a representative
of those molecules which shall be studied by DFT is the
best way to calibrate DFT.

Best regards

Markus
----------Response from Max C. Holthausen----------------------
Dear Per-Ola,

	you'll find an an excellent compilation of gas-phase ion data for small
TM systems in the book "Organometallic Ion Chemistry" edited by Ben
Freiser (Kluwer 1996) p284 ff.

	My two cent: The best you can probably do for this type of species is
full valence CAS-based MRCI (ACPF,AQCC). CASPT2 fails miserably in many
instances, and this is not only due to those 'intruder states' -
perturbation theory it is after all! MRCI has to be done with
substantially expanded basis sets in order to hope to predict meaningful
numbers (cc-pVT/QZ on first row elements, for the 3d metals
Bauschlicher's or Pou-Amerigo's ANOs including the full set of
polarization functions - see the EMSL Web site, the latter is referred
to as ROOS augmented triple zeta ANO). For late 3d metals you would
often need to include 4p orbitals in the active space next to 3d and 4s
and the valence space of the organic moiety. If you can keep the active
space consistent (i.e. empty 4s is not flipping out and 4d is flipping
into the active space or something painstaking like that) you would need
to start with a small basis and active space and improving both up to
the point where the observable of interest (binding energy, say)
converges. If you do not show this convergence, your post-HF result is
no better than any B3LYP/TZ2P calculation! You would need to check all
potentially meaningful spin states (e.g. Fe(H2O)+ in quartet and sextet
multiplicity). For Cu you need to include relativistic effects - one can
hope it's sufficiently done including darwin and mass velocity terms
only. Geometries can probably done at B3LYP/TZP (ECP), also BP/TZP (ECP)
seems to work fine (the latter not for energies!) - but this is an issue
for benchmarking, too. Definitely, studies like those of Bauschlicher
(and Siegbahn for 4d species) some years back, but with larger basis
sets and large reference expansions for MRCI, would be very important to
provide a solid database for checking experimental data and to fit
functionals. But this is hard work for more than one brave theorist.

	What you're up to is something that interests me for quite a while now.
I do think that parametrizing DFT on small, coordinatively unsaturated
TM complexes can be very successful, but most certainly not simply by
modifying the exact exchange admixture in Gaussian's B3LYP, as has been
done by Hess's group. E.g., some years ago I have modified that
parameter to about 35% in order to better describe the whole set of
M-C2H4+ and MCH3+ binding energies for first row metals. Then, however,
I found M=CH2+ being described worse than with the original 20% and I
never published that. I remember a polish group presenting a poster at
the Paris DFT conference presenting a parameter of 30% HF admixture
obtained by parametrizing some organic systems. In several recent
studies Fritz Schaefer finds BHHLYP superior over B3LYP, if memory
serves me right. This is to say: the 15% Reiher et al are coming up with
might do a good job for their set of systems, certainly not for others.
A general improvement of functional performance can most likely not be
accomplished by such simple modifications, based on scarce data. Basis
set quality plays a significant role as well. The compensation of errors
by admixing more or less of the very diffuse HF exchange hole to some
functional flavor is not likely to solve funadmental problems for TMs!

	However, proper physics can probably be incorporated to some extent by
parametrizing a functional, fitting ALL PARTS contributing to the
exchange-correlation hole! As far as I know, this has not been done on
the basis of "hard" transition metal data (I would think of an expansion
of Handy's recent work as promising). The reason is that there is no
such thing as the G2 set for TM systems (save atomic energies, which are
precisely known, probably a good set to start with). Some geometrical
data would be needed as well. Just these days I am thinking of
restarting research along theses lines, as a new PhD student will enter
my little group - he said he wants to do some real calculations, not
that B3LYP/lanl2dz he has done before ... if I can catch his interest
the first step would be creation of MRCI binding energy tables. Maybe
you have vacant resources as well ...

	Best regards,
	Max
----------Response from Luigi Cavallo--------------------------
      Dear Per-Ola,

my compliments for your post. I think you dared to say something that a
lot of people thinks but usually are rather scary to say. Pure or hybrid
DFT is often used uncritically (and I am in the number), just because it
is a "standard" tool, and reviewers usually don't complain. Particularly
if you use B3LYP.

As for the case that "burned" you, I think you refer to the Mn-salen
stuff. Well, I think I could have been on your place, indeed. It was just
a lucky case that I used BP86, and that BP86 proved to be less wrong than
B3LYP (at a level higher of ccsd(t) BP86 could be even worse than B3LYP).

I do agree that ccsd(t) is not the optimal solution. Recently, I've done
quite a few of those calculations with roughly 250 basis functions, 35
atoms H included, closed shell. On the average, the single point took.....
10 days!   (G98 is the program) So, unless you have huge cpu-power and HD
(yes, with ccsd(t) scratch space is another big issue), ccsd(t) is not the
tool to make "ordinary" chemistry.

After that much cpu-time I feel unsatisfied for the reasons you wrote.
Relatively poor basis set, perturbative approach, etc etc.

The alternative is to make MC calculations, as you wrote, and MOLCAS
> from the group in Lund should perform nicely. But I don't have
any experience there.

I would appreciate if you could summarize the "best" answers you got.

All the best, and meet you soon at some congress,

luigi

-- 

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Per-Ola Norrby, Assoc. Professor, http://compchem.dfh.dk/PeO/
Technical University of Denmark, Dept. of Chem., Org. Chem.
Building 201, Kemitorvet, DK-2800 Kgs. Lyngby, Denmark
Email: [email-masked]  tel +45-45252123,  fax +45-45933968