Subject: Biorthogonalization.

From: "Iraj Daizadeh" <[email-masked]>
Date: Mon, 20 Apr 1998 15:06:35 -0700

Hello.

Biorthogonalization is a method by which two sets of molecular orbitals are
rotated to such an extent that these sets of molecular orbitals are not only
orthogonal within themselves but are also pairwise orthogonal to each other.
 That is, the overlap matrix over the two sets of molecular orbitals is
diagonal.

Currently, we are rotating these two sets of molecular orbitals by Prosser and
Hagstrom fortran code (qcpe255).

We are wondering if there are any other groups out there using a similar
technique and what success they had with this program or others.  As a
reminder, the biorthogonalization procedure is an unsymmetrical choleski
decomposition.

I will summarize (any or) all results.

Thanks.

Iraj.

-- 
Iraj Daizadeh
Department of Chemistry
University of California
One Shields Ave.
Davis, CA  95616-5295
Phone:  530.754.8695
Fax:    530.752.8995
email:  [email-masked]

---

From: Qiang Cui <[email-masked]>
Date: Mon, 20 Apr 1998 19:49:26 -0400 (EDT)

>  That is, the overlap matrix over the two sets of molecular orbitals is

	Well, ur description reminds me of the corresponding orbital
transformation technique, which has been used to calculate transition
properties between two states with different sets of M.O.s. One original
paper is the following: B. H. Lengsfield, III,  J. A. Jafri, 
D. H. Phillips, C. W. Bauschlicher, Jr. J.Chem.Phys. 74,6849-6856(1981).
The algorithm is implemented in GAMESS, for instance, to calculate
transition dipole moments and spin-orbit coupling etc.

	Another thing, which I might be confused about, is the definition
of biorthogonality. I thought that refers to the relationship between
the left (bra) and right (ket) eigenvectors of a non-hermitian operator,
for instance, the hamiltonian after the similarity transformation in the
EOM-CCSD theory : [exp(-T)Hexp(T)]. Here the bra and the ket are not necc.
orthogonal among themselves.

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