The Pure Rotational Spectrum of Solvated HCl: Solute-Bath Interaction Strength and Dynamics Bret N. Flanders, Xiaoming Shang, and Norbert F. Scherer* ,† Department of Chemistry, the James Franck Institute, and the Institute for Biophysical Dynamics, UniVersity of Chicago, 5735 S. Ellis AVe. Chicago, Illinois 60637 Daniel Grischkowsky School of Electrical and Computer Engineering and Center for Laser and Photonics Research, Oklahoma State UniVersity, Stillwater, Oklahoma 74078 ReceiVed: June 18, 1999; In Final Form: August 5, 1999 A combination of pulsed THz transmission and FTIR spectroscopy was employed to measure the normalized frequency dependent absorption coefficient of HCl in spherical, dipolar, and linear solvents (CCl 4 , CHCl 3 , and alkanes, respectively) in the 0-350 cm -1 portion of the far-infrared spectral region. The analysis applied to the measured spectra describes the interaction between the quantum mechanical rigid rotator motion of HCl and the solvent through explicit consideration of the anisotropic potential between HCl and the bath. Nominally, the theory requires two adjustable parameters to fit the solvated HCl absorbance spectra. However, a compilation of experimental results for HCl dissolved in various solvents of high symmetry reveals a quadratic dependence of one parameter, the mean square field of the bath, on solvent polarizability. It is shown that dipole-induced dipole (DID) interactions account for the observed quadratic form. This observation introduces a constraint that reduces the number of adjustable parameters so that unique values for the second fitting parameter, the exponential decay rate of the anisotropic potential time correlation function, may be extracted from the measured absorbance curves. The analysis of HCl-alkane solution spectra reveals a more subtle aspect of this dependence. Only a very weak polarizability dependence was found for solvents of large aspect ratio such as the alkanes. This difference indicates that the molecular polarizability density, not simply the molecular polarizability, dictates the strength of the solvent mean square field. Last, a simple scheme for classifying nonpolar solvents based on DID interactions between the solute and the bath is established. I. Introduction Steady-state spectroscopic and structural investigations of liquids serve as an introduction to the difficult task of acquiring detailed knowledge of how solvents interact with reactants. 1,2 Such knowledge is important because during a chemical reaction the solvent strongly influences the possible reaction pathways. 3-7 Quantitative understanding of this influence would significantly impact our ability to predict chemical 8 and biological 9 reactivity in liquids. After a century of work to understand the details of condensed phase dynamics, 10-14 much more work is needed to connect the developing understanding of “homogeneous” con- densed-phase environments to even more complex biological issues. Steady-state 15-19 and time-resolved far-infrared (FIR) stud- ies 20-22 of condensed phase dynamics are two general experi- mental approaches that are being developed to study chemical reactions in liquids. Both have significant merits. Time-resolved spectroscopy allows processes to be studied in “real time” and, thereby, helps to discriminate between the many different dynamical contributions to a time-averaged spectrum. Optical pump-far-infrared-probe spectroscopy methods are, in principle, sensitive to reaction-induced solvent motion (e.g., rotational and translational) in the vicinity of the chromophore. The time- resolved monitoring of this solvent reorganization is essentially a study of linear response theory. 23 However, measuring time- resolved far-infrared spectra of reactive solutions is technically quite demanding. Furthermore, few analytical methods for reliable interpretation of the time-resolved data have been developed. 24 Both of these challenges currently impede the progress of such studies of condensed phase reaction dynamics. However, the identification of reliable analysis methods for studies of transient spectra is logically developed through analysis of steady-state spectra. That is, for cases in which linear response theory and the fluctuation-dissipation theorem are valid, the equilibrium time-correlation function (or spectral density) corresponding to an experimental observable is con- nected to the nonequilibrium time-correlation function. 25,26 In such cases, knowledge of the equilibrated solute-solvent system can be directly related to understanding nonequilibrium spectra. Investigations of gaseous systems often yield extremely detailed descriptions of the processes that occur in the molecular samples. A recent pulsed terahertz study of gaseous methyl chloride presents data so rich in spectral structure that an anomalous absorption around 1THz can be conclusively as- signed to tunneling of the halide atom through the molecule. 27,28 The detailed analysis of condensed phase systems is more problematic because the magnitude and frequency of fluctuating intermolecular interactions characteristic of the liquid state “wash out” most spectroscopic information; rotational fine * Corresponding author, E-mail: nscherer@rainbow.uchicago.edu. † National Science Foundation National Young Investigator. 10054 J. Phys. Chem. A 1999, 103, 10054-10064 10.1021/jp992036n CCC: $18.00 © 1999 American Chemical Society Published on Web 11/20/1999