From forster@computing.nibsc.ac.uk Wed Oct 21 06:50:55 1992 From: Mark Forster Date: Wed, 21 Oct 92 11:03:35 BST To: CHEMISTRY Subject: correlation_functions Subject: Correlation functions Dear Comp. Chemists. Does anyone want a chat about correlation functions? I'll do a net summary is there is any interest. The text book definition of the autocorrelation function g(tau) of a time dependent function a(t) is g(tau)=< a(0) * a(tau) > where < > implies an ensemble average, this should be independent of time origin t=0 for a stationary process (i.e. system at equilibrium). Problem 1. In a molecular dynamics or Monte Carlo simulation we do not have an ensemble of 10^23 molecules to average over, there is typically one solute molecule. So we replace the ensemble average with a time average. Question 1. What type of time average is best ? If there are N points on the MD run with indices 0,1,2..N-1 one type of averaging involves fixing the number of terms in the average to M (less than N) and use a 'sliding time origin' M-1 1: g(k) = SUM ( a(i) * a(i+k) ) /M i=0 This has the disadvantage of choosing a (somewhat) arbitrary M. A second averaging scheme would involve a single time origin and an average of the (k+1) points from 0..k i.e. k 2: g(k) = SUM ( a(0) * a(i) ) /k i=0 Any comments on your experience of computing time autocorrelation functions would be appreciated. Problem 2. It is often useful to use the normalised autocorrelation function g(tau)= < a(0)*a(tau)> / < a(0)*a(0) > Conventional wisdom has it that g(tau) is limited to the range 0..1. If a(t) is a function that monotonically increases with time then any a(tau)>a(0) and this implies g(tau)>1 ! Does this imply g(tau) is only limited to 0..1 for a stationary process ? Might one find in MD that g(tau) can, at some points, adopt a value greater than 1? It's nice to be able to chat to you! Any and all comments gratefully received. Mark.Forster forster@comp.nibsc.ac.uk National Institute for Biological Standards and Control, Blanche Lane, South Mimms, Herts., EN6 3QG, UK. TEL (0707) 54753 FAX (0707) 46730 ps. sending message to CHEMISTRY%ccl.net@uk.ac.nsfnet-relay From forster@computing.nibsc.ac.uk Wed Oct 21 07:06:20 1992 From: Mark Forster Date: Wed, 21 Oct 92 11:01:30 BST To: CHEMISTRY , Functions@computing.nibsc.ac.uk Subject: Correlation Subject: Correlation functions Dear Comp. Chemists. Does anyone want a chat about correlation functions? I'll do a net summary is there is any interest. The text book definition of the autocorrelation function g(tau) of a time dependent function a(t) is g(tau)=< a(0) * a(tau) > where < > implies an ensemble average, this should be independent of time origin t=0 for a stationary process (i.e. system at equilibrium). Problem 1. In a molecular dynamics or Monte Carlo simulation we do not have an ensemble of 10^23 molecules to average over, there is typically one solute molecule. So we replace the ensemble average with a time average. Question 1. What type of time average is best ? If there are N points on the MD run with indices 0,1,2..N-1 one type of averaging involves fixing the number of terms in the average to M (less than N) and use a 'sliding time origin' M-1 1: g(k) = SUM ( a(i) * a(i+k) ) /M i=0 This has the disadvantage of choosing a (somewhat) arbitrary M. A second averaging scheme would involve a single time origin and an average of the (k+1) points from 0..k i.e. k 2: g(k) = SUM ( a(0) * a(i) ) /k i=0 Any comments on your experience of computing time autocorrelation functions would be appreciated. Problem 2. It is often useful to use the normalised autocorrelation function g(tau)= < a(0)*a(tau)> / < a(0)*a(0) > Conventional wisdom has it that g(tau) is limited to the range 0..1. If a(t) is a function that monotonically increases with time then any a(tau)>a(0) and this implies g(tau)>1 ! Does this imply g(tau) is only limited to 0..1 for a stationary process ? Might one find in MD that g(tau) can, at some points, adopt a value greater than 1? It's nice to be able to chat to you! Any and all comments gratefully received. Mark.Forster forster@comp.nibsc.ac.uk National Institute for Biological Standards and Control, Blanche Lane, South Mimms, Herts., EN6 3QG, UK. TEL (0707) 54753 FAX (0707) 46730 ps. sending message to CHEMISTRY%ccl.net@uk.ac.nsfnet-relay From ravishan@swan.wesleyan.edu Wed Oct 21 06:01:34 1992 Date: Wed, 21 Oct 92 10:01:34 -0400 From: G. Ravishanker To: forster@computing.nibsc.ac.uk Subject: correlation_functions Mark >> The text book definition of the autocorrelation function g(tau) >> of a time dependent function a(t) is >> g(tau)=< a(0) * a(tau) > >> where < > implies an ensemble average, this should be independent >> of time origin t=0 for a stationary process >> (i.e. system at equilibrium). I think a more general definition would be : g(tau) = < (a(0) - avg) * (a(tau) - avg) > N-tau or g(tau) =( SUM ( a(i) - avg) * (a(i+tau) - avg) ) / (N-tau) i=0 And for the normalized autocorrelation function, it should be: G(tau) = g(tau) / g(0) >> Question 1. What type of time average is best ? >> If there are N points on the MD run with indices 0,1,2..N-1 >> one type of averaging involves fixing the number >> of terms in the average to M (less than N) and use a 'sliding time >> origin' M-1 >> 1: g(k) = SUM ( a(i) * a(i+k) ) /M i=0 >> This has the disadvantage of choosing a (somewhat) arbitrary M. This I feel is the best way to do the computation. However, use the general formula above with the average included in the expression. You are correct in that the choice of M is arbitrary. Though theoretically one can go upto a lag of N-1, you will have only a pair of points to go into the expression, seriously undermining the conclusions due to lack of statistics. We stop at N/2, since we feel, beyond that the number of points one has will introduce serious statistical errors. >> A second averaging scheme would involve a single time origin and >> an average of the (k+1) points from 0..k i.e. k >> 2: g(k) = SUM ( a(0) * a(i) ) /k i=0 If I understand this expression correctly, g(0) = a(0) * a(0) / 0 {????} I think the denominator should be k+1. g(1) = ( a(0) * a(0) + a(0) * a(1)) / 1 (or 2) g(2) = ( a(0) * a(0) + a(0) * a(1) + a(0) * a(2) ) / 2 (or 3) etc. The problem with this is, g(tau) is supposed to measure correlations arising from data that are at lag tau. In these expressions, there are mixed lags in a single expression. >> Problem 2. It is often useful to use the normalised autocorrelation >> function >> g(tau)= < a(0)*a(tau)> / < a(0)*a(0) > >> Conventional wisdom has it that g(tau) is limited to >> the range 0..1. >> If a(t) is a function that monotonically increases with time >> then any a(tau)>a(0) and this implies g(tau)>1 ! I think these conclusions are derived based on the expression for autocorrelation functions not including the averages. If you use the general expression provided above, you can see how the range of the function is limited to 0..1. Hope this helps. **************************************************************************** * Ganesan Ravishanker Ph: (203) 347-8544 Ext. 3110 * * Coordinator of Scientific Computing, Fax:(203) 344-7960 * * Adjunct Associate Professor(Dept. of Chem.) * * Wesleyan University * * Middletown, CT 06457. * **************************************************************************** From scsupham@reading.ac.uk Wed Oct 21 11:49:18 1992 From: scsupham@reading.ac.uk Date: Wed, 21 Oct 92 16:46:03 BST To: CHEMISTRY@oscsunb.ccl.net Subject: Transition Metal Calculations Hi, Having recently joined this list I would like to ask about available programs that perform geometry optimisation on systems including 2nd row transition metals. I realise an ab initio packake would handle this but the systems are large and would require too much cpu time. I suppose I'm looking at semi-empirical programs ? Thanks for any help. john upham John Upham, School of Chemistry, University of Reading, Berks., RG6 2AD, UK. Email: scsupham%susssys1.rdg.ac.uk@uk.ac (BITnet), scsupham@rdg.susssys1 (Janet)Voice: +44 734 875123 x7441 (day), Fax: +44 734 311610 From E.A.Moore@open.ac.uk Wed Oct 21 17:38:22 1992 Date: Wed, 21 Oct 1992 16:38:22 +0100 From: E.A.Moore@open.ac.uk To: CHEMISTRY Subject: Surface charges for ionic solids Dear netters, Does anyone have a reference to calculations of the charge on the surface ions in ionic solids in particular Mg on the surface of MgCl2? Elaine A. Moore P.S. Please keep this list going. It is very useful to one-person groups like myself who cannot get to conferences. From scsupham@reading.ac.uk Wed Oct 21 13:06:11 1992 From: scsupham@reading.ac.uk Date: Wed, 21 Oct 92 16:50:02 BST To: CHEMISTRY@oscsunb.ccl.net Subject: Local Density Methods ? Hi, What are users recommendations for carrying out local density calculations for geometry optimisation ? What are the opinions of the DMol program as marketed by Biosym ? How would results expect to differ from say an X alpha program ? Thanks for any help ? john upham John Upham, School of Chemistry, University of Reading, Berks., RG6 2AD, UK. Email: scsupham%susssys1.rdg.ac.uk@uk.ac (BITnet), scsupham@rdg.susssys1 (Janet)Voice: +44 734 875123 x7441 (day), Fax: +44 734 311610 From MARYJO@northeastern.edu Wed Oct 21 07:59:00 1992 Date: Wed, 21 Oct 1992 12:59 EST From: MARYJO@northeastern.edu Subject: aromatic heterocycles To: chemistry@ccl.net Hello. I've see some discourse recently pertaining to ab initio calculations on conjugated heterocycles. I would like to ask the experts on these molecules: What level of ab initio calculation is needed to get good accuracy on such properties as dipole moment and quadrupole moment? (We are interested in such aromatic heterocycles as pyridine and pyrazine; this is an aside to one of our projects on transition metal complexes with these types of molecules as ligands.) Thanks very much, Mary Jo Ondrechen From schw0531@compszrz.zrz.tu-berlin.de Thu Oct 22 01:11:19 1992 Date: Thu, 22 Oct 92 00:11:19 +0100 From: Prof. Dr. Helmut Schwarz To: MARYJO@northeastern.edu, chemistry@ccl.net Subject: Re: aromatic heterocycles What level of ab initio calculation is needed to get good accuracy on such properties as dipole moment and quadrupole moment? (We are interested in such aromatic heterocycles as pyridine and pyrazine; this is an aside to one of our projects on transition metal complexes with these types of molecules as ligands.) Thanks very much, Mary Jo Ondrechen according to this i think, that more then the inclusion of correlation energy the use of moderate basis sets is required. I would recommend at least 6-31G** basis. The problem is, that for the correct geometry description of such systems according to our tests the MP2 geometry optimization is needed. This would be of course impossible (and by the way not sufficient) for the handling with those systems together with some transition metals. Depending on the metal used and !!!! on the coordinative satturation!!! for neutral systems some times the effective core potentials with DZP basis sets at the SCF level gives suprisingly good geometries. A single point calculation at correlated level produce fairly reasonable energetics. Jan Hrusak TU BERLIN schw0531@compszrz.zrz.tu-berlin.de From AHOLDER@VAX1.UMKC.EDU Sun Oct 21 17:09:41 1992 Date: 21 Oct 1992 22:09:41 -0500 (CDT) From: Andy Holder Subject: Aromatic heterocycles To: CHEMISTRY@ccl.net Question on aromatic heterocycles: On the subject of ways to treat these "big" molecules, you knew I'd have to point out that the semiempirical methods do a generally good job. These structures can then be used with higher level ab initio methods without reoptimizing. I did a little work on this (hate to toot my own horn, but its all I can find quickly): M. J. S. Dewar, A. J. Holder, Heterocyc. 28, 1135 (1989). It really works! Enjoy... Andy =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-= DR. ANDREW HOLDER Assistant Professor of Computational/Organic Chemistry Department of Chemistry || BITNET Addr: AHOLDER@UMKCVAX1 University of Missouri - Kansas City || Internet Addr: aholder@vax1.umkc.edu Spencer Chemistry, Room 315 || Phone Number: (816) 235-2293 Kansas City, Missouri 64110 || FAX Number: (816) 235-1717 =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=