The Raman spectra and cross-sections of H2O, D2O, and HDO in the OH/OD stretching regions

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Abstract

We report the OH and OD stretching regions of the vapor phase Raman spectra of H2O, and of a D2O/HDO mixture, at room temperature. Also, the corresponding spectrum of H2O at ∼2000 K in a methane/air flame is reported. These spectra are interpreted in terms of transition moments of the molecular polarizability, based on high-level ab initio calculations of the polarizability surface, and on variational wavefunctions considering the rotational–vibrational coupling in full. As a byproduct of this analysis several tables have been compiled including scattering strengths and assignments for individual rotational transitions of the three species. From these tables the Raman spectra in the OH/OD stretching regions can be simulated over the range of temperatures up to 2000 K for H2O, and up to 300 K for D2O and HDO.

Introduction

In previous works we have reported the vapor phase Raman spectra of H2O, and of mixtures of D2O and HDO, at room temperature, in the regions of the rotational spectrum [1] and of the ν2 bending band [2]. These spectra were interpreted in terms of transition moments of a high-level ab initio molecular polarizability, employing variational rotational–vibrational wavefunctions considering the rotational–vibrational coupling in full. As a result several tables were compiled with absolute scattering strengths for individual rovibrational transitions of the three species, aimed to be valid up to 2000 K for H2O, and up to 300 K for D2O and HDO.

In this paper we deal with the spectral region of the OH/OD stretching bands ν1 and ν3 of H2O, D2O, and HDO, along with the bending overtone 2ν2. The Raman spectrum of the ν1 and ν3 bands of H2O was reported and analysed previously by Murphy [3]. Absolute cross-sections for individual lines were reported by Avila et al. [4]. High-resolution nonlinear Raman spectra have been published too for the narrow spectral regions of the Q branches of ν1 of H2O [5], [6], [7], D2O, and HDO [7]. Other regions of the Raman spectra of D2O and HDO have not been reported before, as far as we are aware.

With respect to our previous work on ν1 and ν3 of H2O [4] we have improved substantially both the quality of the experimental spectrum and the level of theory to calculate the scattering cross-sections of the individual rovibrational lines: in [4] we used rovibrational wavefunctions from an effective Watson-type Hamiltonian [8], [9] for the triad of interacting states (0 2 0), (1 0 0), and (0 0 1), along with vibrational transition moments of the molecular polarizability, 〈1 0 0∣α∣0 0 0〉 and 〈0 0 1∣α∣0 0 0〉, that were fitted to reproduce the profile of the experimental spectrum. As a result, the reported line strengths could simulate the Raman spectrum of H2O at 400 K or less, and, with some caution, at higher temperatures. However, several lines showed differences between observed and calculated intensities [4], even at room temperature.

In the present work, we use improved rovibrational wavefunctions obtained variationally from a Hamiltonian in Radau coordinates [10], accounting for the coupling between the rotation of the molecule and the internal motions as described by a high-quality potential surface [11]. These wavefunctions, jointly with a high-level ab initio, wavelength-dependent molecular polarizability surface, yield transition moments accurate enough to reproduce all the experimental data of the molecular polarizability of the water molecule available to date: (i) rotational Raman spectra of H2O, D2O, and HDO [1], (ii) rotational–vibrational Raman spectra of the ν2 band of H2O, D2O, and HDO [2], (iii) rotational–vibrational Raman spectra of the 2ν2 and ν1/ν3 bands of H2O, D2O, and HDO, as reported here, (iv) absolute value of the mean polarizability (obtained from the molar refractivity [12]), and (v) depolarization ratio of the rotational Raman spectrum of H2O [13]. The wavefunctions and polarizability surface referred above can be used with reasonable confidence to simulate any region of the Raman spectrum of water vapor in the spectral range 0 < ν < 5000 cm−1 up to ∼2000 K, the temperature of hydrocarbon/air combustion flames [14].

Section snippets

Experimental

Two types of measurements have been carried out: from static samples at room temperature, and from combustion flames. The Raman spectra of static H2O, and that of a D2O/HDO mixture, have been recorded at room temperature using the low stray light sampling chamber and the high-sensitivity spectrometer described elsewhere in detail [1], [15]. The spectra were excited with up to 6 W of linearly polarized radiation at 514.5 nm, provided by an Ar+ laser beam sharply focused onto the scattering region

Theory

The conventions on axes orientation, vibrational coordinates, and symmetry notation employed here are the same as in our previous works [1], [2], [4]. The details about the variational calculation of the rovibrational wavefunctions from a Hamiltonian in Radau coordinates have been given in [2], and those of the ab initio (CCSD), wavelength-dependent, polarizability surface in [1], [2].

In summary, the rovibrational wavefunctions will be denoted by|V,J,τ,m=v|vJ=0k=-JJCvkVJτ|J,k,m,where ∣J, k, m

Raman spectra

The Raman spectrum of H2O between 3100 and 4300 cm−1, calculated from the variational wavefunctions and ab initio polarizability surface as described above, is shown in Fig. 1, along with the experimental spectrum. Calculated and experimental spectra have been scaled for easier comparison, and spectral peaks have been numbered as references to be used below.

The corresponding spectra of D2O and HDO, between 2300 and 3300 cm−1, calculated with the same procedure and polarizability surface as H2O,

Acknowledgments

This work was supported by the Spanish DGES, research project PB97-1203. We are indebted to the Centro de Supercomputación de Galicia (CESGA), for the use of extensive computation time.

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