Elsevier

Chemical Physics

Volume 356, Issues 1–3, 17 February 2009, Pages 131-146
Chemical Physics

Global analysis of the high resolution infrared spectrum of methane 12CH4 in the region from 0 to 4800 cm−1

This paper is dedicated to Prof. W. Kutzelnigg in honor of his 75th birthday.
https://doi.org/10.1016/j.chemphys.2008.10.019Get rights and content

Abstract

We report the global analysis of methane (12CH4) lines from high resolution rovibrational spectra including accurate line positions and intensities in the region 0–4800 cm−1. This covers four polyads: The Ground State Monad (rotational levels), the Dyad (940–1850 cm−1, 2 vibrational levels, 2 sublevels), the Pentad (2150–3350 cm−1, 5 vibrational levels, 9 sublevels) and the Octad (3550–4800 cm−1, 8 vibrational levels, 24 sublevels) and some of the associated hot bands (Pentad–Dyad and Octad–Dyad). New Fourier transform infrared (FTIR) spectra of the Pentad and Octad regions have been recorded with a very high resolution (better than 0.001 cm−1 instrumental bandwidth, unapodized) at 78 K using the Bruker IFS 125 HR Zürich prototype (ZP2001) spectrometer in combination with a long optical path collisional cooling system [S. Albert, S. Bauerecker, M. Quack, A. Steinlin, Mol. Phys. 105 (2007) 541]. Existing spectra previously recorded with the FTIR spectrometer at the National Solar Observatory on Kitt Peak in Arizona were remeasured selectively to provide new intensities and positions of weaker lines above 4400 cm−1. These were combined with previously reported absorption data from FTIR and laser absorption, as well as high-resolution stimulated Raman and microwave spectra. The effective hamiltonian was expanded up to order 6 for the Ground State, order 6 for the Dyad, order 5 for the Pentad and order 5 for the Octad. A total of 16,738 line positions were used in the least squares adjustment characterized by the following global root mean square deviations dRMS for line positions: 1.3 × 10−4 cm−1 for the Dyad, 6.0 × 10−4 cm−1 for the Pentad, and 3.5 × 10−3 cm−1 for the Octad. Absolute intensities were also analyzed for all the cold bands and some of the hot bands in the region under consideration and we obtained dRMS = 9.6% including 3262 experimental line intensities for the Octad. This analysis represents a large improvement over the previous one [J.-C. Hilico, O. Robert, M. Loëte, S. Toumi, A.S. Pine, L.R. Brown, J. Mol. Spectrosc. 208 (2001) 1] with dRMS = 0.041 cm−1 for positions and 15.6% for intensities in the Octad for a smaller data set. The new results are discussed as benchmarks in relation to accurate potential energy hypersurfaces and for atmospheric and planetary spectra.

Introduction

Methane (CH4) is the prototypical hydrocarbon, which is important in numerous fields of science. One may name here its fundamental role in the history of our understanding of three dimensional molecular structures and chemical bonding [1], [2], [3], leading today to the formulation of accurate potential energy hypersurfaces for molecular quantum dynamics [4], [5], [6], [7], [8], [9]. The methane molecule has been an important example for studies of time dependent intramolecular quantum wavepacket dynamics [10], [11] as well as an example for fully 9-dimensional calculations of time independent vibrational quantum eigenstates [12]. Methane has also been repeatedly used as testing ground for accurate ab initio electronic structure calculations [13], [14], [15]. CH4 has been a classic case for the study of nuclear spin symmetry conservation [16]. The subtle balance of electric dipole moments leading to the small electric dipole moment of methane isotopomers CH3D, CH2D2 and CHD3 has been a long standing problem [17], [18], [19], [20], [21], [22], [23] resolved only recently [4], [5], [17]. At the most fundamental level, the possible role of the parity violating electroweak interaction in relation to methane stereomutation has been discussed as well [24], [25], [26].

Towards more applied sciences, methane plays a crucial role in fields such as geosciences, reaction kinetics and combustion science, chemical technology of hydrogen generation, biotechnology, astrophysics, atmospheric and environmental science to name but a few. On Earth, CH4 is the main constituent of natural gas and excepting H2O it is the second most important greenhouse gas (after carbon dioxide) responsible for the present global warming, as established in Annex B of the Kyoto protocol and demonstrated by many studies [27]. CH4 is also an important constituent of various planetary atmospheres, like those of the Giant Planets (Jupiter [28], [29], Saturn [30], Uranus [31] and Neptune [32]), of Titan (Saturn’s main satellite) [33], [34], [35], [36], [37], Triton (Neptune’s main satellite) and Pluto [38]. It is even suspected to be present in Mars’ atmosphere [39]. It is also likely to be abundant in some of the newly-discovered extrasolar planets (the so-called “hot jupiters”) and brown dwarfs. As a matter of fact, the discovery of methane in the atmosphere of exoplanet HD 189733b has been reported very recently [40].

Since infrared spectroscopy is generally the best diagnostic tool to study CH4 in these environments, it appears essential to be able to model its absorption very precisely. This is true for the study of methane itself (i.e. its distribution, sources and sinks) but also for the determination of physical conditions, chemistry, optical properties and minor constituents of planetary atmospheres. A striking example is Titan which is presently studied by the Cassini–Huygens mission [33], [34], [35], [36], [37]. CH4 is present in significant amounts (a few %) on Titan at temperatures reaching around 80 K and thus the strong absorption bands make its atmosphere almost opaque, the ground being visible from space only through the methane transparency windows [36], [37]. A correct interpretation of Titan’s images, as well as the study of the many minor compounds responsible for its complex hydrocarbon chemistry, require first a global modeling of infrared absorption of CH4.

The vibrational spectroscopy of methane has been studied for a long time [41], [42], [43]. Due to the high-symmetry of the molecule and the related polyad structure of close lying levels [44] it is quite complex. Indeed, the four normal mode frequencies νi of CH4 exhibit an approximate relation of stretching and bending frequencies with ν1  ν3  2ν2  2ν4 resulting in vibrational levels being grouped into polyads with levels of similar energy. The number of interacting vibrational levels within each polyad increases rapidly with the polyad number, making the line-by-line assignment analysis more and more difficult when progressing toward the near infrared regions and above.

Fig. 1 shows a survey of the polyad energy level scheme for 12CH4 including a definition of the nomenclature. In the convention used here, the polyads Pn are simply numbered with increasing energy starting with n = 0 for the Monad, n = 1 for the Dyad etc. In this nomenclature the polyad number n gives roughly the number of CH-bending quanta with pure bending excitation and n/2 roughly the number of CH-stretching quanta with pure stretching excitation. In an alternative nomenclature in the literature one uses the polyad quantum number N = n/2, where one has then also polyads with half odd integer index [45]. Fig. 1 shows also the number of levels and sublevels within each polyad labeled with Greek prefix for the number of levels (Monad for 1, Dyad for 2 etc.). The number of levels is obtained from counting simply harmonic oscillator excitations with possible combinations of quanta in the modes. However, starting with the Pentad, these levels split into a larger number of vibrational sublevels of well defined symmetry species in the point group Td (A1, A2, E, F1, F2), 9 sublevels for the Pentad and 24 for the Octad, see Section 3.1 below). Finally one might also count the number of non-degenerate vibrational states by giving each sublevel a degeneracy corresponding to its species (1 for A, 2 for E and 3 for F). This would be relevant for the approximate average total vibrational density of states which is roughly the number of states in the polyad divided by the polyad width, by definition less than a bending quantum if the polyads are separated. This is relevant in statistical mechanics and kinetics. In many applications, however, the density of vibrational states of a given symmetry species including total parity are relevant [46], [47], [48].

The Ground State Monad of 12CH4 has been known for a long time from its centrifugal distortion spectrum in the microwave (Q branch) and THz (R branch) regions [49], [50], [51], [52], [53]. Intensities in the THz region have been recently reinvestigated [54]. The Dyad 1100–1800 cm−1 region is now also very well understood [55], [56], including line positions and intensities and also many studies concerning lineshapes, e.g. [57], [30]. The Pentad from 2300 to 3300 cm−1 region has been modeled with high accuracy by Hilico et al. [58]. The Octad from 3500 to 4700 cm−1 has been studied in a preliminary analysis [59]. Nevertheless, the modeling of this region, which is very important especially for planetary applications, has been insufficiently precise, with a global root mean square deviation dRMS for line positions of 0.041 cm−1, which is quite high considering the usual high resolution spectroscopic standards. Moreover, the strategy employed to interpret the complex near infrared spectrum of methane is to build upon the analysis and results of the low vibrational bands. For this we use retrieved constants of a successfully modeled lower polyad to predict the structure expected for the next higher set of states. Through successive analyses, we then construct a polyad ladder that will permit the very complex regions at shorter wavelengths to be understood. The 4800–6300 cm−1 region of the Tetradecad, also of primary importance for many applications, has been analyzed only partially up to now [60], and its detailed investigation awaits for a fully reliable hamiltonian parameter set for the polyads below it. Highly accurate cw-CRD (cavity ring down) supersonic jet spectra of the Icosad [61] around 7500 cm−1 exist already. Although some localized structure of prominent bands can be assigned, even a preliminary analysis will require considerable effort. Finally we should also mention that measured positions and intensities to up to 9200 cm−1 are available (i.e. through the Triacontad [62]).

Given the importance of the topic in relation to the questions mentioned above, it is the goal of the present work to provide a essentially definitive global analysis of the infrared spectrum of methane in the complete range from 0 to 4800 cm−1 covering all polyads up to and including the Octad. The basis for this analysis is provided by new highly accurate experimental results obtained from the Zürich prototype (ZP2001) Bruker IFS 125 HR spectrometer in combination with an enclosive flow cooling cell, providing reduced Doppler widths at 78 K. These new results provide about 1400 accurate line positions and are combined with various existing line positions (about 11,800 data) and intensities (almost 4000 lines). The highly accurate parameters of the effective hamiltonian resulting from a global least squares adjustment to the complete data set will provide benchmark data for full-dimensional quantum calculations [63], [64] improving finally potential energy hypersurfaces [9]. Furthermore, they can be used for reliable simulations of methane spectra under a variety of conditions ranging from planetary atmospheres to flames. In addition, they enable improved statistical mechanical partition function calculations in view of thermodynamical ideal gas properties [65] or for improved calculations of statistical kinetics [66], [67]. Finally, complete and reliable calculations of methane line intensities and frequencies based on the present work will improve the remote sensing of the terrestrial and planetary atmospheres.

The present work will also be a reliable starting point for tractable analysis of the 12CH4 Tetradecad and Icosad spectra. As mentioned above, highly accurate measurements exist already but with only very preliminary analyses [61], [68]. A preliminary account of parts of the present global analysis had been given in [69].

Section 2 describes the various experimental data sets used in the present study. Section 3 recalls the theoretical model used for methane. In Sections 4 Analysis of line positions, 5 Analysis of line intensities, we present the results of the new fits for line positions and intensities, respectively, and discuss them in Section 6.

Section snippets

Experimental data

Table 1 provides for convenience a summary of available spectroscopic data relevant for the present work on 12CH4. These include new experimental results based on the Zürich cooling cell-FTIR experiments [70]. We shall in the following describe the new measurements of the present work, as well as the other data used in the analysis, partly available from the literature cited. This will provide a concise summary of the complete database used. The line frequencies and intensities used in the

The polyads of methane

As all XY4 tetrahedral molecules, methane has four normal modes of vibration. They can be labeled by irreducible representations (irreps) of the Td point group, according to the symmetry of the associated normal coordinates. We have thus: ν1(A1), ν3(F2) (stretching modes), ν2(E) and ν4(F2) (bending modes). ν1(A1) is a non-degenerate oscillator, while ν2(E) is doubly degenerate and ν3(F2) and ν4(F2) are triply degenerate. The fundamental frequencies exhibit a simple approximate relation,ν1(A1)ν3

Analysis of line positions

H˜{GS}Octad, H{Dyad}Octad, H{Pentad}Octad and H{Octad}Octad were expanded up to order 6, 6, 5 and 5, respectively. In previous works, H{Pentad}Octad[58] and H{Octad}Octad[59] were expanded up to order 4 only, except in [44] in which order 5 was used for the Octad. Compared to [59], we thus used an effective hamiltonian with 94 additional parameters for the Pentad and 343 additional parameters for the Octad.

As already mentioned, we performed a simultaneous analysis of the Ground

Analysis of line intensities

Line intensities depend both on hamiltonian and dipole moment parameters. In particular, coupling parameters which induce level mixings have a large influence on intensities. Thus, the global line position fit presented above, since it has changed the effective hamiltonian parameter values, made it necessary to refit the effective dipole moment parameters. In principle, there exist several possible fit strategies when combining frequency and intensity data. In the first, one fits the line

Discussion

In Table 5, we give the positions of the vibrational levels for the Dyad, the Pentad and the Octad of 12CH4. They are obtained by calculating the J = 0 levels using the effective hamiltonian parameters obtained in the present study. The results are compared with the previous ones, published in Ref. [44] and with theoretical results [12], [63], [64]. In each case, the levels are identified by their main projection on the initial normal mode vibrational basis defined in Eq. (11) given as a

Conclusion

We have presented here new experimental results and a detailed reinvestigation of the available high-resolution spectroscopic data for methane 12CH4 in the 0–4800 cm−1 region, performing a global analysis of this whole region for line position and intensity (dipole moment) fits for all the cold bands under consideration as well as for some hot bands. All strong bands seem to be very well represented but further improvements might be needed to represent the weaker methane transitions in this

Acknowledgments

This work was supported financially by ETH Zürich, Schweizererischer Nationalfonds, the Conseil Régional de Bourgogne, the LEFE-CHAT National Program of the CNRS and by RFBR (Russia) through Grant 06-05-650100. We also wish to thank the SpecMo Research Group (CNRS GDR 3152). Part of the research at the Jet Propulsion Laboratory (JPL), California Institute of Technology was performed under contracts with the National Aeronautics and Space Administration. We enjoyed discussions with Hans

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