From chemistry-request@server.ccl.net Tue Feb 29 22:11:35 2000 Received: from mail2.panix.com (mail2.panix.com [166.84.0.213]) by server.ccl.net (8.8.7/8.8.7) with ESMTP id WAA31955 for ; Tue, 29 Feb 2000 22:11:35 -0500 From: kynn@panix.com Received: from panix3.panix.com (panix3.panix.com [166.84.0.228]) by mail2.panix.com (Postfix) with ESMTP id 4FA80156C9; Tue, 29 Feb 2000 22:10:55 -0500 (EST) Received: (from kynn@localhost) by panix3.panix.com (8.8.8/8.7.1/PanixN1.0) id WAA20609; Tue, 29 Feb 2000 22:10:55 -0500 (EST) Date: Tue, 29 Feb 2000 22:10:55 -0500 (EST) Message-Id: <200003010310.WAA20609@panix3.panix.com> X-Authentication-Warning: panix3.panix.com: kynn set sender to kynn@panix.com using -f To: CHEMISTRY@ccl.net Subject: Yet another WHAM question... Dear CCL'ers: There's a line in Kumar et al.'s paper [1] on the WHAM method that makes no sense to me. It concerns the histogram's required dimensionality. Kumar considers a modified Hamiltonian of the form L ___ \ H = / \lambda_i V_i = V_0 + S --- i=0 That is, the Hamiltonian is a linear combination of L+1 terms with coefficients \lambda_i. Moreover, \lambda_0 is assumed to be identically 1, and the corresponding term V_0 to represent the unmodified Hamiltonian. The remaining terms V_i are restraining potentials, with coupling parameters \lambda_i. (I denote the sum of these last L terms by S; hence the potential energy becomes V_0 + S.) Furthermore, the authors assume that we are interested in determining the density of states as a function of a reaction coordinate \xi. In the appendix to the paper (p. 1020), they write: "When the restraining potential is a function of the coordinate \xi only the dimensionality of the histogram reduces from L + 2 to 2..." It's the "L + 2" that makes no sense to me. I don't see why, in this situation, the dimensionality of the histogram needs to be any larger than 3, even when L > 1. At most we need to histogram the values of V_0, S, and \xi. (If S is entirely a function of \xi, then, as the authors say, we can get away with only two dimensions, namely V_0 and \xi.) To histogram the values of each of the restraining potentials only increases the amount of data that must be collected without providing any obvious benefit (only the sum of these values enters in the WHAM equations). Besides, the restraining potentials are presumably of little intrinsic interest, since they are merely a technical trick to bias the sampling. If all this is true, what's the rationale for histogramming the values of the V_i (0 < i <= L)? Regards, Kynn Jones [1] Kumar, S. et al., J. Comp. Chem. 13(8):1011-1021, 1992