Comparison of classical, new corrected-classical, and semiclassical IR spectra of non-rotating H 2 O with quantum calculations Alexey L. Kaledin * , Xinchuan Huang, Joel M. Bowman Department of Chemistry and Cherry L. Emerson Center for Scientific Computing, Emory University, 1515 Dickey Drive, Atlanta, GA 30322, USA Received 10 November 2003; in final form 3 December 2003 Published online: Abstract Model infrared spectra for non-rotating H 2 O are calculated at 0 K, based on exact quantum, standard classical and semiclassical calculations. An accurate potential energy surface is used along with a realistic dipole function. An analysis of the classical and quantum spectrum in the harmonic approximation is presented at 0 K. This clearly reveals that the magnitude of the classical intensities is essentially arbitrary, depending on the total energy. Thus, the intensity of classical harmonic spectrum disagrees with the corresponding quantum one. A very simple correction to the classical spectrum is suggested that largely restores agreement with the harmonic quantum spectrum. A second, more general classical correction is also suggested, which, however, requires knowledge of the normal modes. Ó 2003 Published by Elsevier B.V. 1. Introduction The classical Molecular Dynamics approach to the calculation of infrared spectra [1] is well-known and widespread, especially in applications to large systems and/or condensed phases, where quantum approaches are prohibitively difficult to implement. The expression for the IR spectrum of a system in thermal equilibrium in particular is given both classi- cally and quantum mechanically (in first-order pertur- bation theory in the field-matter interaction) by [2] I ðxÞ¼ Re p Z 1 0 dt e ixt hdðtÞ dð0Þi; ð1:1Þ where hdðtÞ dð0Þi is the average of the dipole auto- correlation function. Usually this averaging refers to a canonical distribution; however, it can also refer to a microcanonical average. This kind of averaging is the one of interest here. There have been several suggestions made in the literature to correct the classical IR spectrum for a canonical distribution by noting the differences between the classical and quantum spectra in the (double) har- monic approximation. For an oscillator of frequency x the correction factor of interest here is given by the ratio of the quantum and classical harmonic vibrational partition functions [1], Q CM ðT Þ¼ k B T  hx ; ð1:2aÞ Q QM ðT Þ¼ 1   exp    hx k B T  1 : ð1:2bÞ Obviously, this correction factor applies to a thermal averaged spectrum. It is also worth noting that the derivation of it assumes a linear approximation to the dipole moment function. Here, we consider two corrections to the classical spectrum that are still based on the harmonic normal mode model; however, for a microcanonical ensemble, and where we consider a more general form for the di- pole moment. We also present a numerical comparison of the model IR spectrum using exact quantum, several semiclassical and classical methods. We begin with brief description of these methods followed by results. * Corresponding author. Fax: +1-4047276628. E-mail address: akaledin@uclink.berkeley.edu (A.L. Kaledin). 0009-2614/$ - see front matter Ó 2003 Published by Elsevier B.V. doi:10.1016/j.cplett.2003.12.013 Chemical Physics Letters 384 (2004) 80–85 www.elsevier.com/locate/cplett