CCL: ab initio and DFT

 Sent to CCL by: Pierre Archirel [pierre.archirel~!~lcp.u-psud.fr]
 Dear collegues,
Ab initio and DFT methods can be nicely differentiated with the following statement: 
 1- in ab initio we correlate the wave-function
 2- in DFT we correlate the hamiltonian
 This can be seen as follows:
 E_exact=<Psi_exact, H_exact Psi_exact>  (no doubt about it...)
Now if Psi_D is a simple determinant, it can be transformed to the exact wave function: 
 Psi_exact=U Psi_D and you get:
 E_exact=<U Psi_D, H_exact U Psi_D>=<Psi_D, H_mod Psi_D>
 with H_mod=aU H_exact U
 This means that the exact energy can be obtained with a simple determinant
 and a modified hamiltonian. DFT is looking for this new hamiltonian.
Note that this is also the spirit of semi-empirical theories, who also postulate 
 that the wave-function is a simple determinant, and parametrise H, so as
 to get the exact energy.
 DFT and semi-empirical methods both correlate the hamiltonian.
 Best wishes,
 P.A.
 __________________________________________________________
 Pierre Archirel
 Groupe de Chimie Théorique
 Laboratoire de Chimie Physique      Tel: 01 69 15 63 86
 Bat 349                             Fax: 01 69 15 61 88
 91405 Orsay Cedex
 France                   pierre.archirel-x-lcp.u-psud.fr
 __________________________________________________________