ADF/G92 binding energies SUMMARY



 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
 -Stephan-Irle--stephan "at@at"
 itc.univie.ac.at---------------------------------------
  http://www.itc.univie.ac.at/~stephan/
  voice:+43/1/40480-679