Subject: ADF/G92 binding energies SUMMARY

From: [email-masked] (Stephan Irle)
Date: Thu, 20 Jul 1995 20:05:16 +0100 (MESZ)

Dear Netters,

two days ago i posted a (in fact very faint-hearted)
message to CCL claiming to have detected a difference
of about 70 kcal/mol in the binding energy of the
hydrogen molecule (that makes up nearly 70% of the
experimental and routinely calculated binding energy).

===============================================
This was only due to my poor ability of reading
    program manuals and NOT DUE TO ADF!
===============================================

Thanks to all who made me reading the manual!
One mail needed only a single sentence to clear
all confusion:

> So the reason for difference between ADF and Gaussian (or DMol) is the:
>
> =====================================================================
>  DIFFERENT DEFFINITION OF ATOMIC reference energies in ADF program
> ======================================================================

Namely, the ADF binding energy is apparently calculated
with respect to spin 'restricted' atoms. This term does
not have the same meaning in DFT calculations (with ADF)
than for Hartree-Fock ROHF calculations and must not be
confused:

> A restricted DFT calculation (with ADF) on an Hydrogen
> atom will put 0.5 electron in spin-up and 0.5 in
> spin-down, or more precisely: the charge density is
> not spin-polarized.

A rather new definition for somebody coming from
LCAO-MO in his (or her) head, isn't it?

Therefore, the self-interaction between these two
times two half electrons has to be subtracted from
the molecular energy to correct the molecular binding
energy in order to compare w.r.t. ''atomic energies''
and not w.r.t. ''arbitrarily introduced fragment
energies''.

> In the large-distance dissociation limit the same
> aspect produces the zero-value limit: an offset
> w.r.t. the correct value of precisely two times
> the difference between a restricted and an
> unrestricted atom.

The binding energies at the X-Alpha/DZP-optimized
geometry now read:
             ADF: -83.2 kcal/mol
             G92: -84.8 kcal/mol
which is a fairly good agreement considering the
small basis sets of only DZP quality in both cases.
Please note that i refer to alpha=0.7 and not
2/3; therefore the bond distance is shorter
(better compared to 0.741 A from experiment or
QCISD) by about 0.014 A than from pure Slater
exchange.

One last suggestion for a discussion: Within
ADF (and probably also within other DFT programs)
the initial density is guessed from SPHERICAL
SYMMETRIC atoms. It is well known that atoms
in molecules are quite deformed and NOT SPHERICAL
SYMMETRIC. E.g. Fluorine in the F2 molecule has
valence orbital occupations of Px**2 Py**2 Pz**1
if z is the bond axis. Boron orbital occupations
in B2 are Px**0 Py**0 Pz**1. These values stem
from a least squares fit of the promolecular to
the molecular electron density w.r.t. orbital
occupations and orientations (W. H. E. Schwarz,
K. Ruedenberg, L. Mensching, JACS 111 (1989),
6926):

   \deltaIQ = \delta\int dr^3 *
  [\rho(r) - \sum_a \rho_a(r;D_ij^a)]^2
            = 0

where IQ="integrated squared difference density",
     \rho(r)=molecular electron density,
     \rho_a(r;D_ij^a)=atomic electron density
                      from their atomic density
                      matrix.
 
The atomic density matrices D^a can be expressed
with the help of diagonal matrices W^a which specify
the orbital occupations and U^a which specify the
orbital's shape (d,f orbitals) and orientations as:

              D^a = U^a * W^a * U^a+

Therefore the atomic valence state in the molecule
is uniquely defined and free from an arbitrary
guess.

They are transferable among molecules with
similar bond partners (e.g. Fluorine bonded
to Carbon as well as Boron triply bonded to
Carbon or Nitrogen: Their shape is always
spherical oblate vertically to the bond axis,
Carbon in pi-conjugated systems is always oblate
in the bond plane, etc ...).

Now two questions: Would it make sense to use
this information for the startup density (so
to say as convergence acceleration)? And second:
This would require the use of 'unrestricted'
fragments in ADF which are presently (ADF 1.1.3)
not allowed. Another ADF user pointed out that
this feature would be nice, e.g.
> in the case of CH3* (where * is a unpaired
> electron) reacting with H* you would like
> to start the computation of CH4 with the
> unrestricted density of CH3*, but you cannot.
Probably there are more ADF users who have similar
problems and would like the implementation of
'unrestricted' fragments?

Again, thanks to all

Stephan Irle

[email-masked]
 http://www.itc.univie.ac.at/~stephan/
 voice:+43/1/40480-679