High sensitivity ICLAS of H2O in the region of the second decade (11 520-12 810 cm)

The high resolution absorption spectrum of the H₂¹⁸O isotopologue of water has been recorded by Intracavity Laser Absorption Spectroscopy (ICLAS) with a sensitivity on the order of α_min ∼ 10⁻⁹ cm⁻¹. The 11 520-12 810 cm⁻¹ spectral region corresponding to the 3ν + δ decade of vibrational states, was explored with an ICLAS spectrometer based on a Ti:Sapphire laser. It allowed detecting transitions with an intensity down to 10⁻²⁷ cm/molecule which is about 100 times lower than the weaker line intensities available in the literature, in particular in the HITRAN database.The rovibrational assignment was performed on the basis of the results of variational calculations and allowed for assigning 3659 lines to the H₂¹⁶O, H₂¹⁸O, H₂¹⁷O, HD¹⁶O and HD¹⁸O species, leaving only 1.7% unassigned transitions. A line list including 1712 transitions of H₂¹⁸O has been generated and assigned leading to the determination of 692 rovibrational energy levels belonging to a total of 16 vibrational states, 386 being newly observed. A deviation on the order of 25% has been evidenced for the average intensity values given by HITRAN and the results of variational calculations. Ninety two transitions of the HD¹⁸O isotopologue could also be assigned and the corresponding upper rovibrational levels are given.     

High sensitivity ICLAS of H2O in the 12,580-13,550 cm transparency window

High-sensitivity Intracavity Laser Absorption Spectroscopy (ICLAS) is used to measure the high resolution absorption spectrum of H₂¹⁸O between 12,580 and 13,550 cm⁻¹. This spectral region covers the 3v+δ polyad of very weak absorption. Four isotopologues of water (H₂¹⁸O, H₂¹⁶O, H₂¹⁷O, HD¹⁸O) are found to contribute to the observed spectrum. Spectrum analysis is performed with the aid of variational calculations and allowed for assigning 1126 lines belonging to H₂¹⁸O, while only 160 H₂¹⁸O lines are included in the HITRAN-2008 database. Altogether, 823 accurate energy levels of H₂¹⁸O are determined from transitions attributed to 26 upper vibrational states, 438 of them being reported for the first time. New information includes energy levels of four newly observed vibrational states of H₂¹⁸O: (2 4 0), (1 4 1), (0 4 2) and (2 3 1) at 13,167.718, 13,212.678, 13,403.71 and 15,073.975 cm⁻¹, respectively. H₂¹⁸O transitions involving highly excited bending states like (1 6 0), (0 6 1), (0 7 1), (1 7 0), (0 9 0) and even (0 10 0) have been identified as a result of an intensity borrowing from stronger bands via high-order resonance interactions. Thirty-six new energy levels of H₂¹⁷O, present with a 2% relative concentration in our sample, could be determined. The rotational structure of the (0 2 3) state of HD¹⁸O at 13,245.497 cm⁻¹ is also reported for the first time.     

D2O: ICLAS between 13 600 and 14 020 cm and normal mode labeling of the vibrational states

The high resolution absorption spectrum of dideuterated water, D₂¹⁶O, has been recorded by Intracavity Laser Absorption Spectroscopy (ICLAS) in the 13 600-14 020 cm⁻¹ spectral region which is the highest energy region reported so far for this water isotopologue. Because the HD¹⁶O absorption is stronger by three orders of magnitude in the region under study, it was necessary to use high deuterium enrichment in order to minimize the HD¹⁶O absorption lines overlapping the D₂¹⁶O spectrum. With the high sensitivity achieved (noise equivalent absorption α_min ∼10⁻⁹ cm⁻¹), transitions with line strengths on the order of 5 × 10⁻²⁸ cm molecule⁻¹ could be detected. The spectrum analysis, based on recent variational calculations has provided a set of 177 new rovibrational energy levels belonging to six vibrational states.The most complete set of 53 vibrational energy levels of D₂¹⁶O, including the three newly determined band origins, was constructed from an exhaustive review of the literature data. The fitting of the parameters of the vibrational effective Hamiltonian has allowed to reproduce the whole set of vibrational energies with an rms deviation of 0.055 cm⁻¹. This simple model gave consistent vibrational labels of the D₂¹⁶O states up to 18 000 cm⁻¹. Above 15 000 cm⁻¹, Fermi and Darling-Dennison resonance interaction were found to induce strong vibrational mixings of the wave functions in the normal mode basis, leading to ambiguous vibrational labeling.     

Analysis of the first triad of interacting states (0 2 0), (1 0 0), and (0 0 1) of D2O from hot emission spectra

The far-infrared and middle-infrared emission spectra of deuterated water vapour were measured at temperatures 1370, 1520, and 1940 K in the ranges 320-860 and 1750-3400 cm⁻¹. The measurements were performed in an alumina cell with an effective length of hot gas of about 50 cm. More than 3550 new measured lines for the D₂¹⁶O molecule corresponding to transitions from highly excited rotational levels of the (0 2 0), (1 0 0), and (0 0 1) vibrational states are reported. These new lines correspond to rotational states with higher values of the rotational quantum numbers compared to previously published determinations: J_max = 29 and K_a(max) = 22 for the (0 2 0) state, J_max = 29 and K_a(max) = 25 for the (1 0 0) state, and J_max = 30 and K_a(max) = 23 for the (0 0 1) state. The extended set of 1987 experimental rotational energy levels for the (0 2 0), (1 0 0), and (0 0 1) vibration states including all previously available data has been determined. For the data reduction we used the generating function model. The root mean square (RMS) deviation between observed and calculated values is 0.004 cm⁻¹ for 1952 rovibrational levels of all three vibration states. A comparison of the observed energy levels with the best available values from the literature and with the global predictions from molecular electronic potential energy surfaces of water isotopic species [H. Partridge, D.W. Schwenke, J. Chem. Phys. 106 (1997) 4618] is discussed. The latter confirms a good consistency of mass-dependent DBOC corrections in the PS potential function with new experimental rovibrational data.     

Assignment of surface IR absorption spectra observed in the oxidation reactions: 2H + H2O/Si(1 0 0) and H2O + H/Si(1 0 0)

Infrared reflection absorption spectroscopy that used buried metal layer substrates (BML-IRRAS) and density functional cluster calculations were employed to investigate the water related oxidation reactions of 2H + H₂O/Si(1 0 0)-(2 × 1), 2D + H₂O/Si(1 0 0)-(2 × 1), and H₂O + H/Si(1 0 0)-(2 × 1). In addition to the oxygen inserted coupled monohydrides, which were previously reported in the former reaction system, we report several other oxidized Si hydride species in our BML-IRRAS experiments. Three new pairs of vibrational bands are identified between 900 and 1000 cm⁻¹. These vibrational frequencies were calculated using Si9 and Si10 cluster models that included all possible structures from zero to five oxygen insertions into the top layer silicon atoms using a B3LYP gradient corrected density functional method with a polarized 6-31G** basis set for all atoms. The three pairs of vibrational modes are assigned to the scissoring modes of adjacent and isolated SiH₂ with zero, one, and two oxygen atoms inserted into the Si back bonds. All the other newly observed vibrational peaks related to Si oxidation are also assigned in this study. The Si-O stretching bands observed in the reaction 2D + H₂O/Si(1 0 0)-(2 × 1) show an isotope effect, which suggests that in the system 2H + H₂O/Si(1 0 0)-(2 × 1) also, hydrogen atom tunneling plays an important role for the insertion of oxygen atoms into Si back bonds that form oxidized adjacent dihydrides.     

Rotational levels of the (0 0 0) and (0 1 0) states of D2O from hot emission spectra in the 320-860 cm region

The far-infrared emission spectra of deuterated water vapour were measured at different temperatures (1370, 1520, and 1950 K) in the range 320-860 cm⁻¹ at a resolution of 0.0055 cm⁻¹. The measurements were performed in an alumina cell with an effective length of hot gas of about 50 cm. More than 1150 new measured lines for the D₂¹⁶O molecule corresponding to transitions between highly excited rotational levels of the (0 0 0) and (0 1 0) vibrational states are reported. These new lines correspond to rotational states with higher values of the rotational quantum numbers compared to previously published determinations: J_max=26 and for the (0 0 0) ← (0 0 0) band, J_max=25 and for the (0 1 0) ← (0 1 0) band, and J_max=26 and for the (0 1 0) ← (0 0 0) band. The estimated accuracy of the measured line positions is 0.0005 cm⁻¹. To our knowledge no experimentally measured rotational transitions for D₂¹⁶O within an excited vibrational state have been available in the literature so far. An extended set of experimental rotational energy levels for (0 0 0) and (0 1 0) vibration states including all previously available data has been determined. For the data reduction we used the generating function model. The root mean square (RMS) deviation between observed and calculated values is 0.0012 cm⁻¹ for 692 rotational levels of the (0 0 0) state and 0.0010 cm⁻¹ for 639 rotational levels of the (0 1 0) vibrational state. A comparison of the observed energy levels with the best available values from the literature and with the global predictions from molecular electronic potential energy surface [J. Chem. Phys. 106 (1997) 4618] for the (0 0 0) and (0 1 0) states is discussed.     

Cavity ring-down spectroscopy of H2O in the range 16 570-17 125 cm

Following previous investigations on H₂¹⁶O and H₂¹⁸O by cavity ring-down spectroscopy, this method has now been applied to investigate the energy region of the 5ν polyad in the absorption spectrum of H₂¹⁷O. In the range 16 570-17 125 cm⁻¹, the highest energy range investigated for the H₂¹⁷O isotopologue so far, 516 lines are attributed to H₂¹⁷O and assigned from a newly generated line list.     

Intracavity Laser Absorption Spectroscopy of D2O between 12 850 and 13 380 cm

The high resolution absorption spectrum of dideuterated water, D₂O, has been recorded by Intracavity Laser Absorption Spectroscopy (ICLAS) in the 12 850-13 380 cm⁻¹ spectral region which is the higher energy region reported so far for this water isotopologue. Very high deuterium enrichment was necessary to minimize the HDO absorption lines overlapping the D₂O spectrum. The achieved sensitivity (noise equivalent absorption α_min ∼ 10⁻⁹ cm⁻¹) allowed detecting transitions with line strengths on the order of 5 × 10⁻²⁸ cm/molecule. The spectrum analysis, based on recent variational calculations has provided a set of 422 new rovibrational energy levels belonging to 11 vibrational states, including rotational sublevels for four new vibrational states and one level of the (0 9 1) highly excited bending state. The very weak (1 0 4)-(0 0 0) band at 13 263.902 cm⁻¹, which is the highest D₂¹⁶O band currently observed, could be assigned despite the fact that the HDO absorption in the region is stronger by three orders of magnitude. The list of 996 D₂¹⁶O transitions is provided as Supplementary Material.     

Water vapour line assignments in the 9250-26 000 cm frequency range

Line parameters for water vapour in natural abundance have recently been determined for the 9250-13 000 cm⁻¹ region [M.-F. Mérienne, A. Jenouvrier, C. Hermans, A.C. Vandaele, M. Carleer, C. Clerbaux, P.-F. Coheur, R. Colin, S. Fally, M. Bach, J. Quant. Spectrosc. Radiat. Transfer 82 (2003) 99] and the 13 000-26 000 cm⁻¹ region [P.-F. Coheur, S. Fally, M. Carleer, C. Clerbaux, R. Colin, A. Jenouvrier, M.-F. Mérienne, C. Hermans, A.C. Vandaele, J. Quant. Spectrosc. Radiat. Transfer 74 (2002) 493] using a high-resolution Fourier-transform spectrometer with a long-path absorption cell. These spectra are analysed using several techniques including variational line lists and assignments made. In total, over 15 000 lines were assigned to transitions involving more than 150 exited vibrational states of H₂¹⁶O. Twelve new vibrational band origins are determined and estimates for a further 16 are presented.     

High sensitivity CW-cavity ring down spectroscopy of water in the region of the 1.5 μm atmospheric window

The absorption spectrum of natural water vapour around 1.5 μm has been recorded with a typical sensitivity of 5 × 10⁻¹⁰ cm⁻¹ by using a CW-cavity ring down spectroscopy set up based on fibred DFB lasers. A series of 31 DFB lasers has allowed a full coverage of the 6130.8-6748.5 cm⁻¹ (1.63-1.48 μm) region corresponding to the H transparency band of the atmosphere. The line parameters (wavenumber and intensity) of a total of 5190 lines, including 4247 lines of water vapor, were derived by a one by one fit of the lines to a Voigt profile. Different isotopologues of water (H₂¹⁶O, H₂¹⁸O, H₂¹⁷O, and HD¹⁶O) present in natural abundance in the sample contribute to the spectrum. For the main isotopologue, H₂¹⁶O, 2130 lines were measured with line intensities as weak as 10⁻²⁹ cm/molecule while only 926 lines (including a proportion of 30% inaccurate calculated lines) with a minimum intensity of 3 × 10⁻²⁷ cm/molecule are provided by the HITRAN and GEISA databases. Our comparison in the whole 5750-7965 cm⁻¹ region, has also evidenced that an error in the process of conversion of the intensity units from cm⁻²/atm to cm⁻¹/(molecule × cm⁻²) at 296 K, has led to H₂¹⁶O line intensities values listed in the HITRAN-2000 database, systematically 8 % below the original FTS values. The rovibrational assignment was performed on the basis of the ab initio calculations by Schwenke and Partridge with a subsequent refinement and validation using the Ritz combination principle together with all previously measured water transitions relevant to this study. This procedure allowed determining 172, 139, 71, and 115 new energy levels for the H₂¹⁶O, H₂¹⁸O, H₂¹⁷O, and HD¹⁶O isotopologues, respectively. The results are compared with the available databases and discussed in regard of previous investigations by Fourier transform spectroscopy. The spectrum analysis has showed that most of the transitions which cannot be assigned to water are very weak and are due to impurities such as carbon dioxide and ammonia, leaving only about 3% of the observed transitions unassigned. The interest of a detailed knowledge of water absorption for trace detectors developed in the 1.5 μm range is underlined: for instance HDO contributes significantly to the considered spectrum while no HDO line parameters are provided by the HITRAN database.     

Weak water absorption lines around 1.455 and 1.66 μm by CW-CRDS

The absorption spectra of water vapor near 1.455 and 1.66 μm have been recorded with a typical absorption sensitivity of 5 × 10⁻¹⁰ cm⁻¹ by using CW-cavity ring down spectroscopy. A series of 18 distributed feed-back (DFB) lasers was used as sources and allowed for the coverage of the 5911.0-5922.5, 5926-5941.8, 5957.0-6121.6, and 6745-7015.6 cm⁻¹ spectral regions. These regions extend to lower and higher energies our previous study of the water spectrum in the important 1.5 μm transparency window [P. Macko, D. Romanini, S.N. Mikhailenko, O.V. Naumenko, S. Kassi, A. Jenouvrier, Vl.G. Tyuterev, J. Mol. Spectrosc. 227 (2004) 90-108]. The line parameters were determined with the help of an interactive least squares multi-lines fitting program which uses a Voigt function as line profile. More than 1900 water lines with intensities ranging between 10⁻²⁸ and 5 × 10⁻²⁴ cm/molecule at 296 K were measured, about 690 of them being reported for the first time. The rovibrational assignment was performed on the basis of previously determined energy levels and of the results of the variational global calculations [H. Partridge, D.W. Schwenke, J. Chem. Phys. 106 (1997) 4618-4639]. The assignment results were validated by using the Ritz combination principle together with previously reported water transitions. Several new energy levels were determined for the H₂¹⁶O, H₂¹⁷O, and HD¹⁶O isotopologues. The retrieved line lists of the H₂¹⁶O, H₂¹⁷O, H₂¹⁸O, and HD¹⁶O isotopologues are compared with the available calculated and experimental (FTS) databases for water.     

High resolution analysis of the rotational levels of the (0 0 0), (0 1 0), (1 0 0), (0 0 1), (0 2 0), (1 1 0) and (0 1 1) vibrational states of SO2

A high resolution (0.0018 cm⁻¹) Fourier transform instrument has been used to record the spectrum of an enriched ³⁴S (95.3%) sample of sulfur dioxide. A thorough analysis of the ν₂, 2ν₂ − ν₂, ν₁, ν₁ + ν₂ − ν₂, ν₃, ν₂ + ν₃ − ν₂, ν₁ + ν₂ and ν₂ + ν₃ bands has been carried out leading to a large set of assigned lines. From these lines ground state combination differences were obtained and fit together with the existing microwave, millimeter, and terahertz rotational lines. An improved set of ground state rotational constants were obtained. Next, the upper state rotational levels were fit. For the (0 1 0), (1 1 0) and (0 1 1) states, a simple Watson-type Hamiltonian sufficed. However, it was necessary to include explicitly interacting terms in the Hamiltonian matrix in order to fit the rotational levels of the (0 2 0), (1 0 0) and (1 0 1) states to within their experimental accuracy. More explicitly, it was necessary to use a ΔK = 2 term to model the Fermi interaction between the (0 2 0) and (1 0 0) levels and a ΔK = 3 term to model the Coriolis interaction between the (1 0 0) and (0 0 1) levels. Precise Hamiltonian constants were derived for the (0 0 0), (0 1 0), (1 0 0), (0 0 1), (0 2 0), (1 1 0) and (0 1 1) vibrational states.     

Intracavity laser absorption spectroscopy of HDO between 11 645 and 12 330 cm

The weak absorption spectrum of monodeuterated water, HDO, has been recorded by intracavity laser absorption spectroscopy (ICLAS) between 11 645 and 12 330 cm⁻¹. This spectrum is dominated by the ν₂ + 3ν₃ band of HDO at 11969.76 cm⁻¹. A total of 497 energy levels belonging to 12 vibrational states were determined while only 140 levels were previously reported from a recent investigation by Fourier transform spectroscopy in the same spectral region. The rovibrational identification process of the 1378 lines assigned to the HDO isotopologue was mostly based on the results of the accurate variational calculations of Schwenke and Partridge. The overall agreement between these calculations and the observed spectrum is very good. However, strong discrepancies in the calculated line intensities were evidenced in a few cases corresponding to an intensity transfer to a dark state through local resonance interaction.     

The absorption spectrum of water between 13 540 and 14 070 cm: ICLAS detection of weak lines and a complete line list

The absorption spectrum of water vapor has been investigated by Intracavity Laser Absorption Spectroscopy (ICLAS) between 13 540 and 14 070 cm⁻¹. This spectrum is dominated by relatively strong transitions of the 4δ polyad of vibrational states. The achieved sensitivity - on the order of α_min ∼ 10⁻⁹ cm⁻¹ - has allowed one to newly measure 222 very weak transitions with intensities down to 5 × 10⁻²⁸ cm/molecule at 296 K. Fifty new or corrected H₂¹⁶O energy levels belonging to a total of 13 vibrational states could be determined from the rovibrational analysis based on variational calculations by Schwenke and Partridge. The previous investigations in the region by Fourier Transform Spectroscopy were critically evaluated and used to construct the best to date set of energy levels accessed by transitions in the considered region. All the rovibrational transitions reaching these upper energy levels and having intensities larger than 4.0 × 10⁻²⁸ cm/mol were calculated. In the resulting line list, the positions at the level of experimental accuracy were augmented with variational intensities leading to the most complete line list for water in normal isotopic abundance in the 13 500-14 100 cm⁻¹ region.     

High sensitivity ICLAS of D2O between 12 450 and 12 850 cm

The weak absorption spectrum of dideuterated water, D₂O, has been recorded between 12 450 and 12 850 cm⁻¹ by high sensitivity Intracavity Laser Absorption Spectroscopy (ICLAS). This spectral region corresponds to the (ν₁ + ν₂/2 + ν₃) = 5 polyad, dominated by the 4ν₁ + ν₃ band centered at 12 743.035 cm⁻¹. The achieved sensitivity has allowed for the detection of lines with a minimum intensity of 2 × 10⁻²⁸ cm/molecule i.e. typically two orders of magnitude lower than previous observations in the region considered. A total of 586 energy levels belonging to 11 vibrational states were determined. The rovibrational assignment process of 1025 lines ascribed to D₂O was based on new results of variational calculations by Shirin et al. [S.V. Shirin, N.F. Zobov, O.L. Polyansky, J. Quant. Spectrosc. Radiat. Transfer, in press, doi:10.1016/j.jqsrt.2007.07.010]. The overall agreement between these calculations and the observed spectrum is good both for the line positions and line intensities. The difficulties encountered while performing the rovibrational labeling and the assignment of the weakest transitions not included in Combination Differences relations, are discussed.     

HDO absorption spectrum above 11 500 cm: Assignment and dynamics

Assignment of an HDO line list extracted from a recently measured H₂O/HDO/D₂O Fourier transform absorption spectrum recorded in the 11 600-23 000 cm⁻¹ region by Bach et al. (M. Bach, S. Fally, P.-F. Coheur, M. Carleer, A. Jenouvrier, A.C. Vandaele, J. Mol. Spectrosc. 232 (2005) 341-350.) is presented. More than 94% of the 3256 lines are given quantum number assignments and ascribed to line absorption by HDO; most of the remaining lines are actually due to D₂O. High accuracy variational predictions of line positions and intensities are used for the spectral assignment process. Assignments to the ν₁ + 5ν₃, 2ν₂ + 5ν₃, ν₁ + ν₂ + 3ν₃ and ν₁ + 6ν₃ bands are presented for the first time. Comparisons are made with published ICLAS spectra covering the same spectral region and suggestions made for its recalibration. The results are used to illustrate the dynamical behaviour of highly excited vibrational states of HDO and to discuss previous vibrational assignments to high lying rotation-vibration states of this system.     

The rotationally-resolved absorption spectrum of formaldehyde from 6547 to 6804 cm

The room temperature absorption spectrum of formaldehyde, H₂CO, from 6547 to 6804 cm⁻¹ (1527-1470 nm) is reported with a spectral resolution of 0.001 cm⁻¹. The spectrum was measured using cavity-enhanced absorption spectroscopy (CEAS) and absorption cross-sections were calculated after calibrating the system using known absorption lines of H₂O and CO₂. Several vibrational combination bands occur in this region and give rise to a congested spectrum with over 8000 lines observed. Pressure broadening coefficients in N₂, O₂, and H₂CO are reported for an absorption line at 6780.871 cm⁻¹, and in N₂ for an absorption line at 6684.053 cm⁻¹.     

Intracavity laser absorption spectroscopy of D2O between 11 400 and 11 900 cm

The weak absorption spectrum of dideuterated water, D₂O, has been recorded by Intracavity Laser Absorption Spectroscopy (ICLAS) between 11 400 and 11 900 cm⁻¹. This spectrum is dominated by the 3ν₁ + ν₂ + ν₃ and the ν₁ + ν₂ + 3ν₃ centered at 11 500.25 and 11 816.64 cm⁻¹, respectively. A total of 530 energy levels belonging to eight vibrational states were determined. The rovibrational assignment process of the 840 lines attributed to D₂O was mostly based on the results of new variational calculations consisting in a refinement of the potential energy surface of Shirin et al. [J. Chem. Phys., 120 (2004) 206] on the basis of recent experimental observations, and a dipole moment surface from Schwenke and Partridge [J. Chem. Phys. 113 (2000) 6592]. The overall agreement between these calculations and the observed spectrum is very good both for the line positions and the line intensities.     

ICLAS of weak transitions of water between 11 300 and 12 850 cm: Comparison with FTS databases

Very weak water vapor absorption lines have been investigated by intracavity laser absorption spectroscopy (ICLAS) in the 11 335-11 947 and 12 336-12 843 cm⁻¹ spectral regions dominated by the ν₁ + 3ν₂ + ν₃ and ν₂ + 3ν₃ bands, respectively. A detectivity on the order of α_min ∼ 10⁻⁹ cm⁻¹ was achieved with an ICLAS spectrometer based on a Ti: Sapphire laser. It allowed detecting transitions with an intensity down to 5 × 10⁻²⁸ cm/molecule which is about 10 times lower than the weakest line intensities previously detected in the considered region. A line list corresponding to 1281 transitions with intensity lower than 5 × 10⁻²⁶ cm/molecule has been generated. A detailed comparison with the line lists provided by the HITRAN database and by recent investigations by Fourier transform spectroscopy associated with very long multi pass cell is presented. The rovibrational assignment performed on the basis of the ab initio calculations of Schwenke and Partridge, has allowed for determining 176 new energy levels belonging to a total of 16 vibrational states.     

Line broadening and shift coefficients of acetylene at 1550 nm

Pressure broadening and shift coefficients have been measured for the ν₁ + ν₃ band of acetylene, C₂H₂, broadened by N₂, H₂, D₂, air, and the noble gases at 295 K. Coefficients are reported for lines between 6470 and 6612 cm⁻¹ (1512-1546 nm). The pressure broadening coefficients are in general agreement with those reported for other vibrational bands, indicating that they are insensitive to vibrational excitation. The pressure shift coefficients, by contrast, are found to differ substantially among vibrational bands.