*From*: stephan.irle "at@at" itc.univie.ac.at (Stephan Irle)*Organization*: Institute for Theoretical Chemistry, University of Vienna*Subject*: ADF/G92 binding energies SUMMARY*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 -Stephan-Irle--stephan "at@at" itc.univie.ac.at--------------------------------------- http://www.itc.univie.ac.at/~stephan/ voice:+43/1/40480-679