Summary: Off-diagonal elements of the CI matrix

From: "Gustavo Moura" <gustavo # - at - # hathi.chem.pitt.edu>
Subject: Summary: Off-diagonal elements of the CI matrix
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
 					     gustavo # - at - # hathi.chem.pitt.edu
 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
 			    gustavo # - at - # hathi.chem.pitt.edu
 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
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   Tel.: +41-1-635-6117                  web : www.unizh.ch/~mbeck
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