Continuum Model of Water—An Erroneous Interpretation

Abstract

LETTERS TO THE EDITOR 567 water, and to be inconsistent with a continuum model for the liquid. 2-s The purpose of this note is to indicate that, on the contrary, Walrafen's data seems to be in very satisfactory agreement with the continuum model and, furthermore, that some difficulties apparently exist with his own assignment which might require further scrutiny. In his study of the stretching band of ordinary water, Walrafen found that band contour heights above 3460 cm-l increased in intensity with increasing temperature, while heights below this value responded oppositely. Furthermore, his Fig. 5 indicates that contour heights at 3200 cm-l decreased much more rapidly than flanking heights at 3300 and 3100 em-I. These findings are in excellent agreement with the continuum model of liquid water. 3 In terms of this model there is not just one VI and V3 mode for liquid water, but a continuum of VI and Va modes of varyingly distorted molecules (Vld and V3d modes). These originate from collisional interactions in the liquid. The water molecules are so distorted by collision that their Vld and V3d states are very nearly vibrational eigenstates of their individual OR bonds. 2 ,3 These states, particularly those of the Vld distribution, may be considered in Fermi resonance with the 2V2 continuum near 3250 em-I. In addition, they may also be involved in weak intermolecular coupling. In terms of this, the stretching band may be viewed as being a superposition of a continuum of bands, Jlld and V3d, intermolecularly coupled and in Fermi resonance with 2V2, Walrafen's findings are in good agreement with the above model, as seen by the following: when temperature is increased, the Vld and Vad continua shift to higher wavenumber. This is confirmed by the corresponding shift with temperature of the inter-and intramolecu-larly uncoupled JlOR of liquid water. 5 If we accept this displacement of the JlJd, Jlad distributions, we predict that contour heights to the high-frequency side of some particular wavenumber value should increase in intensity , while the opposite effect should be observed on the low-frequency side of this value. If this wavenumber value is 3460 em-I, we have agreement with Walrafen's findings. Furthermore, the more rapid decrease in contour height at 3200 cm-l reflects a decrease in Fermi resonance with temperature due to the increased separation with temperature of the Vld, 2V2 distributions. Walrafen's data are then not inconsistent with the continuum model nor with the 3250-cm-l band being 2V2 in resonance interaction with Jlld and V3d continua. Another indication of the consistency of the continuum model with Walrafen's data concerns the decomposition of the stretching band into components. Walrafen, with the aid of a computer, fit the Raman stretching band with a superposition of four Gaussian components. These same four components, with but small changes in frequency and half-widths, were found to give acceptable fits for the stretching band between 10° and 90°C. Walrafen assigned these components to stretching absorptions of non-hydrogen-bonded mono-meric water, at 3622 and 3535 cm-1 (both weak in intensity) and to stretching bands of lattice water molecules at 3435 and 3247 cm-1 (both intense). Although, at first sight, this decomposition seems reasonable, it is not the only one possible for the stretching region of liquid water. Another assignment leading to a better computer fit than that proposed by Walrafen is a continuum of Vld, V3d, and 2V2 bands, in Fermi resonance with each other and intermolecularly coupled. A continuum distribution can certainly give an excellent fit at all temperatures. The continuum model is then in excellent agreement with a decomposition of the stretching absorption into components. In conclusion, two serious difficulties inherent in Walrafen's own assignment may be noted. 3 (1) 2V2 has been clearly identified in spectra of many hydrates with hydrogen bonding close to that in liquid water.2 It generally appears near 3250 cm-l. It should certainly appear close to this value in liquid water. If so, we may expect Fermi resonance with it and the component at 3247 cm-l assigned by Walrafen to VI of lattice water molecules. This interaction would clearly introduce a fifth component into Walrafen's picture. (2) A second difficulty in Walrafen's assignment lies in its inability to properly predict the position of the uncoupled OR band of liquid water. Using Walrafen's Raman (or infrared predictions) at 30°C, one expects a strong uncoupled OR band to appear between the intense Raman components at 3425 and 3250 cm-I, i.e., near 3338 em-I; this band should be slightly asymmetric due to a super-position with the uncoupled OR of monomeric water. This band does not fall at 3338 em-I, but at 3439 cm-l at 27°C in the Raman 4 and at 3415 cm-l in the infrared spectrum,3 both near one of the four assigned stretching components of ordinary water. We also obtain the same inconsistent predictions by considering the intense components at 3425 and 3250 cm-l to represent continuum distributions. 3 The above indicates some difficulties in need of explanation before Walrafen's assignment can be fully accepted. The continuum model of water was previously thought to be supported by Raman data,l but the Downloaded 12 Apr 2011 to 139.222.113.146. Redistribution subject to AIP license or copyright; see http://jcp.aip.org/about/rights_and_permissions