Subject: EXTENDED HUECKEL AND ORTHOGONALIZATION

From: "E. Lewars" <[email-masked]>
Date: Wed, 15 Oct 1997 10:23:18 -0400 (EDT)

Wed, 1997 Oct 15

>From E. Lewars
To:  CCL
Subj: Extended Huckel Method

Hello,

Regarding the extended Hueckel method as implemented by Roald Hoffmann:
I know that the overlap integrals are calculated and used to construct
the Fock matrix elements (which are proportional to these integrals in
the EHM).   My question is:
in Hoffmann's implementation are the overlap integrals used to calculate an
orthogonalizing matrix to convert (e.g. by Loewdin orthogonalization) the
matrix equation
                    FC = SCe
into standard eigenvalue form
                    F'C' = C'e   i.e   F' = C'eC'^-1

as in ab initio calculations,
        OR  is it simply pretended, as in simple Hueckel theory, that
                    S=I  ?

   I read Hoffmann's 1963 paper in J Chem Phys, but this point does not
seem to be explicity made clear.  Maybe I missed it.

        Thanks

         E. Lewars
=============

---

From: "J. Sichel" <[email-masked]>
Date: Wed, 15 Oct 1997 15:04:26 -0300 (ADT)

Yes, Hoffmann's EH method uses explicit Lowdin orthogonalization; I 
remember working through a copy of his computer code as a graduate 
student in 1964!

As for his 1963 JCP paper, he does say (p.1399) that "the complete set of 
Eq.(2) [the secular equations] is solved with _two_ matrix diagonalizations."
If S = 1 were assumed, only one diagonalization would be required.

John Sichel
Dept de chimie et biochimie
Universite de Moncton, NB, Canada