Subject: SUMMARY:HF/DFT and dissociation

From: Leticia Gonzalez Herrero <[email-masked]>
Date: Tue, 13 Jun 2000 15:41:02 +0200 (CEST)

Dear CCl members,

Some days ago, I posted a question about HF and DFT suitable for
describing dissociation. Many many thanks to all who replied.  
Please find my original question and replies on the subject topic:

>If I want to describe the rupture of a covalent bond, it is known
>that RHF will lead to wrong dissociation energies while UHF will cure
>the energy problem but converges to an unphysical mixture of singlet
>and triplet states. Therefore, in general some other post-HF methods are
>used to describe dissociation.
>And what happens if I use DFT? Is DFT, restricted or unrestricted able to
>describe the dissocation of a covalent bond?

-----------------From Marcel Swart,
there is an interesting article by Baerends/Gritsenko about this
subject, where they prove that DFT does give the correct
dissociation. I think you could find it in: J.Phys.Chem.A, Vol
101(30), 1997, p. 5383-5403.

-----------------From Keith Refson, 
 > If I want to describe the rupture of a covalent bond, it is known
 > that RHF will lead to wrong dissociation energies while UHF will cure
 > the energy problem but converges to an unphysical mixture of singlet
 > and triplet states. Therefore, in general some other post-HF methods
 > are used to describe dissociation.

There's a nice discussion of this on p.60 of:

"Bonding and Structure of Molecules and Solids" by David Pettifor
(Oxford Science, ISBN 0-19-851786-6)

 > And what happens if I use DFT? Is DFT, restricted or unrestricted able
 > to describe the dissocation of a covalent bond?

Yes, at least LSDA gives the correct dissociation limit.  (LSDA is the
spin-polarized LDA -- "unrestricted" in chemistry terminology).

---------------From Stefan Grimme
For the dissociation of a covalent bond RDFT and UDFT will
give the same failures as HF because the ansatz is the
same in both methods (one-determinatal). However, in general
the spin-contamination problem at intermediate distances is
not so severe in DFT and the asymtotic energy with RDFT
is usually better than with RHF because of the inherent
self-interaction error of commonly used functionals
(from another point of view one can argue that the RHF error
for e.g. H2 at r=infinity is 0.5*(IP+EA) of the H-Atom,
a quantity which is much smaller in DFT).

-------------From Antonio M. Marquez 

Con DFT tienes el mismo problema. Al estar basado en un solo determinate
de Slater no describiras bien la disociacion y obtendras mezclas
singlete/triplete. Para u na descripcion correcta del problema necesitas
una funcion multiconfiguracional tip o CASSCF al menos. Si se trata de un
enlace covalente mas o menos normalito el calculo es sencillo. Si tienes
metales de transicion implicados se complica pues puedes tener varios
estados proximos en energia y cruces entre ellos en la superficie de
energia potencial.

------------From Klaus Stark

DFT based on a restricted determinant gives energies too high for large
bond distances, i.e. goes to an incorrect dissociation limit. UHF
references remedy for that. However, LDA/UHF dissociation energies might
be too large. Gradient corrected and hybrid methods follow the "true"
(e.g. CASSCF) potential curve much more closely. DFT methods based on UHF
references do not have a problem with spin contamination. Indeed there's a
paper by Pople, Gill and Handy showing that spin contamination is not well
defined in DFT (Int. J. Quantum Chem. 56 (1995) 303).

-----------------From  Reinaldo Pis Diez

Yes, you can use unrestricted dft in broken symmetry mode
to study dissociation of covalent bonds.
Broken symmetry is very important in such cases since it
is the only way to force different electronic configurations for the
isolated atoms, i.e, you can think of H2 dissociating into two H atoms,
one having an spin-up electron and the other having an spin-down one. If
you don't use broken symmetry the isolated atoms will be the same.
That can be accomplished by using guess(mix) in gaussian
98 and using the keywords modifystartpotential and fragoccupations if you
are dealing with adf99.

------------Richard P. Muller
> If I want to describe the rupture of a covalent bond, it is known
> that RHF will lead to wrong dissociation energies while UHF will cure
> the energy problem but converges to an unphysical mixture of singlet
> and triplet states. Therefore, in general some other post-HF methods are
> used to describe dissociation.

Correct, although you can also use a generalized valence bond
(essentially a two configuration MCSCF, but one that doesn't require
many additional 2e integrals beyond those required for HF) to get a
correct dissociation energy and proper spin states.

The Jaguar program suite (see http://www.schrodinger.com) has a nice GVB
implementation that I programmed a few years back.

> And what happens if I use DFT? Is DFT, restricted or unrestricted able
> to describe the dissocation of a covalent bond?

You can do either spin restricted or spin unrestricted DFT, although
unrestricted is more common. Jaguar has implementations of both. The
RDFT will give a better dissociation energy that RHF, but one that in
many cases will go to the wrong limit. UDFT is more reliable for broken
bonds.

It would probably be possible to do a hybrid GVB-DFT that would combine
the best elements of both theories, but I've never gotten around to
doing it. Jaguar has something like this (or at least it once did), but
it isn't quite what I had in mind.

-----------------From Sergio Emanuel Galembeck
    
The best methods to describe the rupture of a bond are
multireference methods, as CAS, because the problem
involves more then one  configuration. This is the reason why
DFT or other single-reference methods don't work well in
dissociation.

-------------Ernest Chamot :
As the atoms connected by a bond separate, the electrons that initially
formed that bond change from being paired to being independent: ie from
being a singlet to being two separated doublets, or a triplet.  And since
electron reorganization will take place much faster than atomic movement,
they can't be restricted to a specific multiplicity in the calculation of
the PES as you break the bond.  So the only choice, really, is some sort
of UHF calculation.  But as you point out, this leaves the calculation
open to spin contamination.  In the case of ab initio HF calculations,
this can be extreme, and give artificially high activation energies.  
You can monitor the spin contamination in your calculation by plotting
the <S**2> vs. atom separation.  There are some very nice illustrations
of this, and the resulting effect creating an artificial "activation"
energy for bond dissociation, in the figures in the paper by Chen and
Schlegel.  (It also interferes with convergence.):

 W. Chen & H. B. Schlegel, J. Chem. Phys. 101(7), 5957-68 (1994).

They studied various post-HF methods, and in particular the value of spin
projection to overcome this problem in MP calculations, for various H atom
dissociations.

The problem of spin contamination in UHF calculations is variable,
however.  In fact, for some calculations involving dissociation of 2 heavy
atoms (as usual, H seems to be a particularly difficult problem), plotting
<S**2> shows that spin contamination is minimal, and doesn't necessarily
create an artificial "transition state".  I have seen this with AM1 in
some of my own work, and there is also an instance shown in:

 J. Baker, M. Muir, & J. Andzelm, J. Chem. Phys., 102(5), 2063-79 (1995).

Of course, without correlation, HF methods (including AM1) systematically
underpredict the dissociation energies.  So you will want a correlated
method anyway, and the high level post-HF methods can be very compute
intensive.

Which brings us to the use of DFT, and I think you are on exactly the
right track:

>And what happens if I use DFT? Is DFT, restricted or unrestricted able to
>describe the dissocation of a covalent bond?

Several papers now have shown that DFT methods (unrestricted calculations)
seem to be much less prone to spin contamination than HF or post-HF
methods. Baker & Andzelm reported the advantage of BLYP and ACM in
minimizing spin contamination for a series of reactions, and observe,
"under the right circumstances DFT wave functions can exhibit minimal
contamination over an entire energy surface, including dissociation."  
Jungkamp and Seinfeld found B3LYP particularly effective in minimizing
spin contamination problems in calculating BDE's and transition state
barriers for a series of reactions:

 T. Jungkamp & J. Seinfeld, J. Chem. Phys., 107(5), 1513-21 (1997).

All three of these papers, though, show that there are tradeoffs in
accuracy of energies (overpredicting, underpredicting, difficulty
converging, etc.), however, so you may still prefer a high level post-HF
calculation with a large basis set. But in general, DFT looks like the
best way to go.

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  Dr. Leticia Gonzalez          	    Tel: ()49 30 838 520 97
  Freie Universitaet Berlin                 Fax: ()49 30 838 547 92 
  Institut fuer Chemie                      Room: 35.17 
  Takustrasse 3                          [email-masked]         
  D-14195 Berlin        http://userpage.chemie.fu-berlin.de/~leti
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