Subject: DFT is over !/? (expert opinion needed)

From: Artem Masunov <[email-masked]>
Date: Wed, 21 Mar 2001 21:50:30 -0500 (EST)

Dear CCLers,
 I just became aware of the recent paper by Clementi et al. (see
the relevant abstracts below).
 It seems to me that the quest for correlation functional is over:
Clementi just did it (without any density, but with 16
empirical parameters).
 He...He, water trimer, and atomization energies to +/- 0.05 kcal/mol
sound pretty convincing.
 What do you think?

Regards,
Artem

-- 

     __    ___________       [email-masked]; Tel 212-650-7792
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 /  ____  \ \  \ \  \ \  \ -------http://www.biosys.net/artem----------
/__/\ _/\ _\ \ _\ \ _\ \ _\ FORGIVE MY NONSENSE AS I ALSO FORGIVE THOSE
\ _\/  \/__/\ __/\ __/\ __/ WHO THINK THEY TALK SENSE  --  ROBERT FROST

---------- Forwarded message ----------

Revision and extension of the HF-CC method
Clementi E, Corongiu G
JOURNAL OF MOLECULAR STRUCTURE-THEOCHEM
493: 1-20 DEC 15 1999

Abstract:
The Hartree-Fock-correlation correction (HF-CC) molecular model is a
recent post-HF perturbation model which decomposes the correlation
correction into atomic and molecular components. In this work, the HF-CC
model is modified with attention to weak and very weak interactions, and
validated by computing the atomisation energy of 112 test molecules: 104
closed shell, from diatomic to naphthalene, and 8 radicals. The
atomisation energies, computed at six successive approximations by
optimising an increasing number of empirical parameters have mean
deviations of 13.82, 11.90, 6.32, 4.57, 0.54 and 0.05 kcal/mol,
respectively, relative to experiments. The method is successfully extended
to weak interactions testing the dimer and trimer of water and the
complexes H2O-X with X = Li+, Na+, K+, F-, Cl-. The feasibility to predict
very weak interactions is tested with computations of van der Waals
energies: at the computed minimum. He-2, Ne-2 and Ar-2 have inter nuclear
distances and interaction energies in agreement with laboratory data.
Finally, the total molecular binding energy is decomposed into computed
bond energies that are comparable to the available experimental bond
energies.

Soft Coulomb hole method applied to theoretical equilibrium geometries of
singlet diatomic molecules
A. Hernández-Laguna and L. Alfonso-Méndez
Estación Experimental del Zaidín (CSIC), C/Prof. Albareda 1, 18008
Granada, Spain
P. Otto
University Erlangen-Nürnberg, Egerlandstraße 3, D-91055 Erlangen, Germany

It has been demonstrated that the soft Coulomb hole method is a reliable
and efficient approach to calculate the electron correlation energy for
atoms and molecules. In this method the perturbation operator
–exp(–ar)/r12 is introduced, where  determines the size of the Coulomb
hole. The set of parameters for  has been redetermined to calculate
equilibrium bond distances. Calculations have been performed for 41 homo-
and heteronuclear singlet diatomic molecules and ions (X 1+), including
atoms of the second and third periods of the periodic table. The soft
Coulomb hole correlation energies are compared to the corresponding
empirical correlation energies. In general, calculated equilibrium bond
distances are in better agreement with the experimental values than
Hartree-Fock and Møller-Plesset-2 results. With respect to
Møller-Plesset-3, the soft Coulomb hole method gives slightly larger
values for the average deviations, except for the homonuclear series

Molecular correlation energy with the HF-CC method
Clementi E, Corongiu G
CHEMICAL PHYSICS LETTERS
282 (5-6): 335-346 JAN 23 1998

Abstract:
The 'HF-CC' model is extended from atomic to molecular systems. An
analysis of the total and binding energy components points out mechanisms
of molecular binding and a strategy to compute the latter via a
partitioning of the correlation energy into atomic and molecular
components. The HF-CC model is size consistent and basis set independent.
We considered 41 molecules at optimised geometry with basis sets near to
the Hartree-Fock limit. The average atomisation energy is 69.65% of the
experimental data (average error is 147.59 kcal/mol) from Hartree-Fock and
becomes 95.10%, 97.68%, and 99.52% (average errors become 31.79 kcal/mol,
10.54 kcal/mol, and 2.36 kcal/mol, respectively) for the HF-CC model with
either one parameter (for the H atom), or one parameter per each atomic
species, or one parameter per each class of an atomic species; the
Becke-Perdue BP-86 density functional yields 94.45% with an average error
of 20.43 kcal/mol.

HARTREE-FOCK SOFT COULOMB HOLE TO ESTIMATE CORRELATION ENERGIES IN ATOMS,
MOLECULES AND POLYMERS
OTTO, P;REIF, H;HERNANDEZLAGUNA, A
THEOCHEM-JOURNAL OF MOLECULAR STRUCTURE
340: 51-62 SEP 20 1995

Abstract:
We have shown that the empirical correction introduced into the
Hartree-Fock method to calculate correlation energies for atoms and
therefore to remove the error caused by the so-called Coulomb hole can be
extended from atoms to molecules and polymers. A reformulation was
required of the necessary parameter representation. The reparametrization
has been performed staying as close as possible to the original
expressions for atoms reported by Chakravorty and Clementi (S.J.
Chakravorty and E. Clementi, Phys. Rev. A, 39 (1989) 2290). In addition to
their work, where the correlation energy has been calculated with the
self-consistent Hartree-Fock wavefunction and the correction integrals, we
have performed investigations, including the perturbation operator in the
Fock operator, so that the total energy also contains the correlation
energy. The applications of this approach to atoms and molecules show that
the total electron correlation energies and ionization potentials
calculated as differences of total energies can be obtained very
satisfactorily. On the basis of the reported calculations it turns out
that one obtains better agreement with reference values of more
sophisticated calculations when the correction integrals are used to build
up the Fock matrix. Furthermore we have found that the magnitude of the
correlation energy depends only weakly on the size of the basis sets,
which makes this empirical method very attractive for its application to
large molecular and polymeric systems.

COULOMB-HOLE-HARTREE-FOCK FUNCTIONAL FOR MOLECULAR-SYSTEMS
CLEMENTI E, HOFMANN DWM
THEOCHEM-JOURNAL OF MOLECULAR STRUCTURE
330: 17-31 JAN 10 1995

Abstract:
We have extended to molecules a density functional previously parametrized
for atomic computations. The Coulomb-hole-Hartree-Fock functional,
introduced by Clementi in 1963, estimated the dynamic correlation energy
by the computation of a Hartree-Fock type single-determinant wavefunction,
where the Hartree-Fock potential was augmented with an effective potential
term, related to a hard Coulomb hole enclosing each electron. The method
was later revised by S. Chakravorty and E. Clementi, Phys, Rev. A, 38
(1989) 2290, so that a Yukawa-type soft Coulomb hole replaced the previous
hard hole. Atomic correlation energies, computed for atoms with Z = 2 to
54, as well as for a number of excited states, validated the method. In
this work we have parametrized for molecules a function which controls the
width of the soft Coulomb hole by fitting the first and second atomic
ionization potentials of atoms with 1 less than or equal to Z less than or
equal to 18 and the binding energies of a few diatomic molecules. The
parametrization was successfully validated by computing the dissociation
energy for a number of molecules. A few-determinant version of the
Coulomb-Hartree-Fock method (CHF-N) necessary to account for the
non-dynamic correlation correction and to ensure proper dissociation
products, is briefly discussed with reference to a previous proposal by
G.C. Lie and E. Clementi, J. Chem. Phys., 60 (1974) 1275 and 60 (1974)
1288.

EXTENSION OF THE COULOMB-HOLE-HARTREE-FOCK THEORY TO MOLECULES
DEWINDT L, HOFMAN DWM, PISANI L, CLEMENTI E
INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY
53 (2): 131-147 JAN 15 1995

Abstract:
The Coulomb-Hole-Hartree-Fock method introduced by E. Clementi in the
early 1960s and reparametrized more recently by S. Chakraworty and E.
Clementi to compute the correlated electronic energy in atomic systems, is
here extended to compute molecules. The new parametrization is obtained
empirically by fitting first and second atomic ionization potentials from
He to Ca and a few diatomic molecules. The present formulation makes use
of either one or more determinants in order to ensure proper dissociation
products, following the early proposal of G. C. Lie and E. Clementi in the
context of density functional computations for molecular systems. The new
formulation is tested against the dissociation energies of a large number
of molecules and it is found satisfactory.

COULOMB-HOLE-HARTREE-FOCK FUNCTIONAL
CLEMENTI E, HOFMANN DWM
INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY
52 (4): 849-865 NOV 5 1994

Abstract:
We have extended to molecules a density functional previously parametrized
for atomic computations. The Coulomb-hole-Hartree-Fock functional,
introduced by Clementi in 1963, estimates the dynamical correlation energy
by the computations of a Hartree-Fock-type single-determinant wave
function, where the Hartree-Fock potential was augmented with an effective
potential term, related to a hard Coulomb hole enclosing each electron.
The method was later revisited by S. Chakravorty and E. Clementi [Phys.
Rev. A 39, 2290 (1989)], where a Yukawa-type soft Coulomb hole replaced
the previous hard hole; atomic correlation energies, computed for atoms
with Z = 2 to Z = 54 as well as for a number of excited states, validated
the method. In this article, we parametrized a function, which controls
the width of the soft Coulomb hole, by fitting the first and second atomic
ionization potentials of the atoms with 1 less-than-or-equal-to Z
less-than-or-equal-to 18. The parametrization has been preliminarily
validated by computing the dissociation energy for a number of molecules.
A few-determinant version of the Coulomb-hole-Hartree-Fock method,
necessary to account for the nondynamic correlation corrections, is
briefly discussed.

On Wed, 21 Mar 2001, Vitaly Rassolov wrote:

> Artem,
>
> The main stuff in JCP_corrop.pdf article.  There is a bit on problems of
> new operator in H2 molecule in the other article.  Peter Gill is working
> on a similar approach now, but as far as I know, his publications are
> still in the pipeline.
>
> Cheers,
> _______
>
> Vitaly Rassolov                      [email-masked]
> Chemistry Department                 tel. (847) 491-3423
> Northwestern University              fax  (847) 491-7713
>
> On Wed, 21 Mar 2001, Artem Masunov wrote:
>
> > Privet Vitaly!
> >  I was a little disappointed to learn that you terminated you project on
> > r12 operators. Did you ever publish the stuff presented at Sanibel 2 yrs
> > ago?
> >  If not, can you at least send me that abstract with the relevant
> > references (I am sure you searched for the refs)?
> >  I would greatly appreciate that.
> >
> > Artem
> >
> > --
> >
> >      __    ___________       [email-masked]; Tel 212-650-7792
> >     /  \  /  __   __  \     Computational Biophysical Chemistry Group
> >    /    \/\  \ \  \ \  \        Chemistry Dept, City College, CUNY
> >   /  /\  \ \  \ \  \ \  \    J-1325, Convent Ave, New York, NY 10031
> >  /  ____  \ \  \ \  \ \  \ -------http://www.biosys.net/artem----------
> > /__/\ _/\ _\ \ _\ \ _\ \ _\ FORGIVE MY NONSENSE AS I ALSO FORGIVE THOSE
> > \ _\/  \/__/\ __/\ __/\ __/ WHO THINK THEY TALK SENSE  --  ROBERT FROST
> >
> >
> >
>

-- 

     __    ___________       [email-masked]; Tel 212-650-7792
    /  \  /  __   __  \     Computational Biophysical Chemistry Group
   /    \/\  \ \  \ \  \        Chemistry Dept, City College, CUNY
  /  /\  \ \  \ \  \ \  \    J-1325, Convent Ave, New York, NY 10031
 /  ____  \ \  \ \  \ \  \ -------http://www.biosys.net/artem----------
/__/\ _/\ _\ \ _\ \ _\ \ _\ FORGIVE MY NONSENSE AS I ALSO FORGIVE THOSE
\ _\/  \/__/\ __/\ __/\ __/ WHO THINK THEY TALK SENSE  --  ROBERT FROST