From chemistry-request@www.ccl.net Thu Mar 11 04:20:32 1999 Received: from ccl.net (atlantis.ccl.net [192.148.249.4]) by www.ccl.net (8.8.3/8.8.6/OSC/CCL 1.0) with ESMTP id EAA26048 Thu, 11 Mar 1999 04:20:32 -0500 (EST) Received: from oxmail.ox.ac.uk (oxmail1.ox.ac.uk [129.67.1.1]) by ccl.net (8.8.6/8.8.6/OSC 1.1) with ESMTP id EAA10896 for ; Thu, 11 Mar 1999 04:20:29 -0500 (EST) Received: from ermine.ox.ac.uk ([163.1.2.13]) by oxmail.ox.ac.uk with esmtp (Exim 2.10 #1) id 10L1dX-0001M1-00; Thu, 11 Mar 1999 09:20:15 +0000 Received: from oums0054 (helo=localhost) by ermine.ox.ac.uk with local-smtp (Exim 2.12 #1) id 10L1dX-0000d9-00; Thu, 11 Mar 1999 09:20:15 +0000 Date: Thu, 11 Mar 1999 09:20:15 +0000 (GMT) From: "Ivan I. Oleinik" To: Fernando Vila cc: Computational Chemistry List Subject: Re: CCL:G:Damped Coulomb Potential Summary In-Reply-To: Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Fernando, Explicit calculation of matrix element of the 'dumped Coulomb potential' (error function/R) with gaussians is in the paper of G. Lippert, J. Hutter and M. Parrinello " A hybrid Gaussian and plain wave denisty functional scheme", Mol Phys 92 (1997) pp 477-487. They have error function in the local part of the pseudopotential. On page 481 they write: " erf(a|r-R|) V(r) = ------------- |r-R| can be regarded as the Coulomb potential originating from a Gaussian charge centered at R". Formula (34) immediately gives the answer. Ivan Oleinik ------------------------------------------------------------------------ Ivan I. Oleinik E-mail : ivan.oleinik@materials.ox.ac.uk Department of Materials University of Oxford Parks Road Oxford OX1 3PH Tel : +44 (0)1865 283325 United Kingdom Fax : +44 (0)1865 273764 ------------------------------------------------------------------------ > ------------------------------------------------------------------------ > > On Wed, 10 Mar 1999, Fernando Vila wrote: > Dear Fellows; > > I would like to thank all the people that replied to me request. Right > after I sent my e-mail to the list I decided to give it a new try. At the > very beginning of my equations I found an error that was complicating > everything. After I fixed that the integrals turned out to be > embarrassingly easy, easier than those including only the Coulomb > potential. The references you sent will be useful to double check my > results. > > My original question was: > > Dear Fellows, > > For the past weeks I have been trying to calculate the matrix elements > for a damped Coulomb potential to no avail. The potential has the form: > > erf(a|r-R|) > V(r) = ------------- > |r-R| > > where r and R are position vectors and erf(t) is the error function: > > 2 t > erf(t) = -------- int exp(-x^2) dx. > PI^(1/2) 0 > > The matrix elements then are of the form: > > erf(a|r-R|) gij > = int gi V(r) gj dr = int ----------------- dr > |r-R| > > Here gi are spherical Gaussians and gij is the resulting Gaussian from the > Gaussian Product Theorem. > > I have tried using techniques similar to those used for the calculation of > the pure Coulomb potential (based on Fourier or Laplace transforms) but > the usual cancellation is not complete. > > Any pointers to papers, books or web pages are welcome.. The complete > solution is also very much welcome.. :-) > > Thanks to all in advance, Fer. > > Here is a summary of the replies I received: > > ========================================================================== > From: koelmel > > Hi, > > Lecture Notes in Chemistry, vol. 48, authored by C. Pisani, R. Dovesi > and C. Roetti, titled > "Hartree-Fock Ab Initio Treatment of Crystalline Systems" > (1988, springer) > > may be a useful reference. What you're looking for is mentioned > on page 60. > > One way is to convert 1/r into an integral using the Laplace transform > trick, then change the order of integration, I think. > > Hope this helps somewhat > > Cheers, > Christoph > > ========================================================================== > From: Frank Jensen > > Try looking up some of Peter Gill's work in > recent years. They have played with screened > Coulomb potentials. > Frank > > > ========================================================================== > From: Norge Cruz Hernandez > > Hi , > > Try to see : > > S. Obara and A. Saika. > J. Chem. Phys. 84(7), 3963 > > best regard > Norge > > ========================================================================== > From: "Jeremy P. Dombroski" > > Dear Fernando: > > This is work that myself, Professor Peter Gill and Dr Ross Adamson have > spent considerable time on (in particular, the latter). We have recently > published an article in J. Comp. Chem. and if you contact Ross at > ross@theor.ch.cam.ac.uk he may provide you with a preprint should the > article not yet be in print. > > Q-Chem 1.2 performs O(N) damped Coulomb SCF calculations, including > energies, optimizations and frequencies using what we have called the > CASE approximation where we replace all occurrences of the Coulomb > operator with the so-called Damped Coulomb potential. > > May I ask where your research interest lies in this damped Coulomb > potential? > > Regards, > Jeremy Dombroski > > > ========================================================================== > From: "Jan H. Jensen" > > Hello, > I believe Peter Gill at Cambridge has worked on something quite > similar. I don't have any references on hand. > > Best regards, > > Jan Jensen > > ******************************************************************************* > Fernando D. Vila > Department of Chemistry Voice (412)624-8691 > University of Pittsburgh Fax (412)624-8552 > Box 90 Chevron Science Center E-mail fer@theory6.chem.pitt.edu > Pittsburgh, PA 15260, USA WWW http://www.pitt.edu/~fer > ******************************************************************************* > > > > -------This is added Automatically by the Software-------- > -- Original Sender Envelope Address: chemistry-request@www.ccl.net > -- Original Sender From: Address: fer@theory6.chem.pitt.edu > CHEMISTRY@www.ccl.net: Everybody | CHEMISTRY-REQUEST@www.ccl.net: Coordinator > MAILSERV@www.ccl.net: HELP CHEMISTRY or HELP SEARCH | Gopher: www.ccl.net 73 > Anon. ftp: www.ccl.net | CHEMISTRY-SEARCH@www.ccl.net -- archive search > Web: http://www.ccl.net/chemistry.html > >