From chemistry-request@www.ccl.net Sat Feb 27 19:36:17 1999 Received: from alchemy.chem.utoronto.ca (alchemy.chem.utoronto.ca [142.150.224.224]) by www.ccl.net (8.8.3/8.8.6/OSC/CCL 1.0) with ESMTP id TAA01013 Sat, 27 Feb 1999 19:36:16 -0500 (EST) Received: (from elewars@localhost) by alchemy.chem.utoronto.ca (8.9.3/8.9.3) id TAA25742 for chemistry@www.ccl.net; Sat, 27 Feb 1999 19:36:14 -0500 (EST) Date: Sat, 27 Feb 1999 19:36:14 -0500 (EST) From: "E. Lewars" Message-Id: <199902280036.TAA25742@alchemy.chem.utoronto.ca> To: chemistry@www.ccl.net Subject: IR INTENSITIES 1999 Feb 26 I have a question about calculating the relative intensities of IR vibrations. Let me say at the outset that my interest here is to *illustrate* in a simple way how intensities can be calc from the change in dipole moment accompanying the normal-mode vibration; I know there are sophisticated algorithms for calculating the intensity of IR bands. I just want to show how, in principle, one might get relative intensities in a conceptually simple way. The intensity of a normal-mode vibration is approximately I = k(dm/dq)**2 where k is a proportionality constant (we are interested in _relative_ intensities) m = dipole moment q = a geometric parameter like bond length Approximating the derivative as the ratio of finite increments enables us to readily calculate relative intensities for the single mode of diatomic molecules: I = k(delta m/delta q)**2 Thus for H-F and HCl, using HF/6-31G* calcs: H-F r(0.9109=r-equil), m = 1.9719 D; r(0.9209), m = 1.9897 I = k(0.0178/0.01)**2 = 3.17k H-Cl r(1.2662=r-equil), m = 1.5017 D; r(1.2762), m = 1.5081 I = k(0.0064/0.01)**2 = 0.41k Intensity ratio, I(HF)/I(HCl) = 3.17/0.41 = 7.7 A calc using Gaussian 98 gives an intensity ratio of 141.5/24.3 = 5.8 Fine. ------------- QUESTION: Suppose we have, say H2O, and want to calc the relative intensities of the asym and the sym stretching modes. In principle we can distort the geom a little (as for H-F and H-Cl, above) and calc the change in dipole moment, delta m. But what do we take as delta q when there is not just *one* simple geometric parameter like r=(H--X)? I suppose either q is composite, or the expression for I has several terms. O / \ H H Thanks E. Lewars ==================