Subject: Summary: Off-diagonal elements of the CI matrix

From: "Gustavo Moura" <[email-masked]>
Date: Wed, 12 Aug 1998 15:07:42 -0400

Dear CCL readers,
	last week I sent a message to the CCL list asking how to calculate the
number of permutations necessary to obtain maximum coincidence between two
determinants. To my surprise I have received ONE answer. Probably my question
was not simple after all.
	Below you can find my original questions followed by the anser that I
have received. My thanks to Michael E. Beck for answering my question.

						Gustavo Moura
					     [email-masked]

My original question:

Dear CCL readers,
	I am writing a program to do CI calculations on some conjugated
molecules using semiempirical (PPP) parameters. Unfortunately, I am having
problems to calculate the off-diagonal elements of the CI matrix. In their book
Szabo e Ostlund show (tables 2.3 and 2.4) how to calculate these elements when
the determinants are in maximum coincidence. I am looking for references where
I
can find the answer to the following simple(?) question:

HOW TO CALCULATE THE NUMBER OF PERMUTATIONS NECESSARY TO OBTAIN MAXIMUM
COINCIDENCE BETWEEN THE DETERMINANTS?

In other words:

WHEN SHOULD I MULTIPLY THE EQUATIONS SHOWN IN THE BOOK BY -1?

	Thank you very much in advance. I will sumarize.
	Sincerely yours,

				Gustavo L.C. Moura
			    [email-masked]

The answer:

On Wed, 5 Aug 1998, Gustavo Moura wrote:

> Dear CCL readers,
> 	I am writing a program to do CI calculations on some conjugated
> molecules using semiempirical (PPP) parameters. Unfortunately, I am having
> problems to calculate the off-diagonal elements of the CI matrix. In their
book
> Szabo e Ostlund show (tables 2.3 and 2.4) how to calculate these elements
when
> the determinants are in maximum coincidence. I am looking for references
where
> I
  Dear Sir,

maybe this not quite the answer you are expecting, but from your letter i
suspect that your program is in a very early stage of development.

A very elegant way to set up the Hamiltonian in a basis of spin adapted
configurations (CCFs) is to use the graphical approach pioneered by Paldus
and Shavitt, GUGA. This approach also gives a very smooth way to construct
the configuration space.

GUGA seems to be applied mainly in ab initio theory, but personally i
think it's very well suited for semiempirics, too. Once you have got used
to the graphs, you'll love them, promise.

Coming back to your question: In GUGA problems like "maximal coincidence"
just do not arise.

sincerly

Michael E. Beck

___________________________________________________________________
  Dr. Michael E. Beck                  |  privat:
  Organisch--Chemisches Institut       |  Zschokkestr. 12a
  Theoretische Gruppe, Prof. W. Thiel  |  CH--8037 Zuerich
  Universitaet Zuerich                 |  +41-1-271 54 39
  Winterthurerstr. 190                 |___________________________
  CH--8057 Zuerich
  Tel.: +41-1-635-6117                  web : www.unizh.ch/~mbeck
  Fax.:           6836                  mail: [email-masked]
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