*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 Winterthurerstr. 190 |___________________________ CH--8057 Zuerich Tel.: +41-1-635-6117 web : www.unizh.ch/~mbeck Fax.: 6836 mail: mbeck # - at - # unizh.ch ___________________________________________________________________