FTIR spectrum of vinyl fluoride near 3.6 μm: rovibrational analysis of the ν4+ν7 band and modelling Coriolis resonances in a seven-level polyad

ABSTRACT

The Fourier transform infrared (FTIR) spectrum of vinyl fluoride, H₂C=CHF, has been widely investigated in the region of the ν₄+ν₇ combination band around 2800 cm^?1 at a resolution of 0.005 cm^?1. This vibration of A' symmetry gives rise to an a/b-hybrid band with a predominant a-type component. The rovibrational structure is strongly perturbed and the analysis has been rather complicated since this combination band is involved at least in a seven-level interacting polyad, including the ν₈+2ν₁₀, 2ν₈+ν₁₀, 2ν₇+ν₉, ν₇+ν₈+ν₁₂, ν₅+ν₉+ν₁₀ and ν₇+ν₁₀+ν₁₂ vibrational states. The study has been further complicated by the absence of transitions coming from the perturbers that were considered as dark states. The spectral analysis resulted in the identification of 936 transitions with J" ≤ 46 and K_a" ≤ 11, all belonging to the a-type component. Most of the assigned data have been fitted using the Watson's A-reduction Hamiltonian in the I^r representation and proper Coriolis perturbation operators. The model employed includes seven different resonances within a complex polyad resonant system and a set of spectroscopic constants for the ν₄+ν₇ combination band, for the dark states, and Coriolis coupling coefficients have been determined.     

Infrared spectrum of the Coriolis coupled vibrations ν5 and ν6 of hydrazoic acid

The infrared absorption spectrum of the ν₅ and ν₆ fundamentals of HN₃ has been measured with a resolution of 0.03 cm⁻¹. The spectrum has been analyzed taking into account the first- and second-order a-type Coriolis resonance between the two vibrations. Constraining the value for the ζ constant and the ground state parameters the analysis yields values for the rotational constants for both bands.     

High-resolution infrared spectroscopy of CH2D79Br: ro-vibrational analysis of the ν4 and ν8 fundamental bands

The high-resolution Fourier transform infrared spectrum of CH₂D⁷⁹Br has been recorded and analysed in the region of the ν₄ and ν₈ fundamentals located in the range 1125?1360 cm^?1. The strong ν₄ band, centred at 1225 cm^?1, shows an a/b-hybrid structure with predominant a-type character, whereas ν₈, at 1253 cm^?1, generates a c-type contour comparable in intensity to the b-type component of ν₄. The upper states of these fundamentals are coupled through a- and b-type Coriolis resonances; further complications in this band system arise from perturbations due to the ν₆ = 2 (1183 cm^?1) and ν₅ = ν₆ = 1 (1359 cm^?1) dark states. The former interacts with ν₈ = 1 by b-type Coriolis coupling, whereas the latter perturbs the ν₄ = 1 and ν₈ = 1 levels by anharmonic and a-type Coriolis resonances, respectively. Accurate upper state parameters and interaction terms have been determined for the tetrad system ν₄/ν₈/2ν₆/ν₅+ν₆ by also including in the dataset the assigned transitions of the 2ν₆?ν₆ and ν₅+ν₆?ν₆ hot bands obtained from previous analysis.     

Coriolis perturbations in the ν10, ν7, ν4, ν12 band system of trans-d2-ethylene

The effect of a-, b-, and c-axis Coriolis perturbations in the infrared spectrum of the band system ν₁₀, ν₇, ν₄, ν₁₂ of trans-d₂-ethylene has been studied at a resolution near 0.03 cm⁻¹. From a global analysis of this band system taking into account Coriolis resonances, spectroscopic constants for each of the vibrations are derived as well as second-order Coriolis interaction constants for ν₁₀ and ν₇.     

The infrared spectrum of carbon suboxide in the ν6 fundamental region: Experimental observation and semirigid bender analysis

The infrared spectrum of carbon suboxide, C₃O₂, was measured at high resolution in the region from 500 to 600 cm⁻¹. The spectrum was recorded with a Bomem interferometer at a resolution of about 0.004 cm⁻¹; after deconvolution a resolution of about 0.002 cm⁻¹ was attained. Seven bands were identified and assigned to rovibrational transitions of ¹²C₃¹⁶O₂. These consist of the ν₆ fundamental band and some of the hot bands associated with the ν₇, 2ν₇, and 3ν₇ states. The data obtained on the ν₆ + nν₇ states were used as input for a semirigid bender fit yielding the effective CCC bending potential energy function in the ν₆ state together with a number of related parameters. From the results of the present work together with the results of previous semirigid bender fits it was found that C₃O₂ is bent at equilibrium with an equilibrium CCC bond angle of 156° and a barrier to linearity of 28 cm⁻¹.     

High-resolution Fourier-transform infrared spectroscopy of the ν1 and ν8 fundamental bands of sulphur tetrafluoride (SF4)

The vibration-rotation spectra of the ν₁ and ν₈ fundamental bands of ³²SF₄ have been observed using Fourier-transform infrared spectroscopy. The band centre of the c-type ν₁ symmetric sulphur-equatorial-fluorine stretching vibration was observed at 891.6 cm^?1 and that for the b-type ν₈ asymmetric sulphur-equatorial-fluorine stretching vibration at 864.6 cm^?1. In total, 2044 rovibrational transitions have been assigned. Analysis of the spectra showed that the rotational states of the ν₁ = 1 and ν₈ = 1 upper vibrational levels are coupled by an a-type Coriolis interaction. This coupling has been treated both using perturbation theory and by the explicit inclusion of an appropriate Hamiltonian matrix element in a combined fit of the data for both bands. Spectroscopic parameters have been determined for the ground, ν₁ = 1 and ν₈ = 1 vibrational levels. Weaker transitions resulting from difference bands and the fundamental bands of the ³⁴SF₄ isotopomer have been identified but could not be assigned, because of the density of lines in the room-temperature spectrum. The possibility that discrepancies between the observed and predicted spectra of the ν₁ fundamental may result from either a Coriolis interaction with the states of another vibrational level, or the effects of intramolecular exchange of axial and equatorial fluorine atoms is considered. The discussion is supported by theoretical calculations which show that the likely path for intramolecular exchange is via a C _4v transition state.     

The Raman spectrum of C2D4 near 1000 cm−1: The Coriolis coupled ν3 and ν6 bands

The Raman spectrum of deuterated ethylene C₂D₄ has been investigated in the 1000-cm⁻¹ regions. The close-lying (16 cm⁻¹ apart) ν₃ and ν₆ bands are perturbed by a Coriolis interaction around the c axis with |ζ₃₆^c| = 0.39. This interaction distorts both the anisotropy and the trace spectra, which are presented as recorded in Aarhus and Madrid, showing also computer simulation of the contours. A least-squares refinement of around 300 transitions allows the determination of the ν₃ and ν₆ band origins and rotational constants.     

Classification of vibrational resonances in the energy spectrum of the formaldehyde molecule and Katz’s branch points

The Rayleigh–Schrödinger perturbation theory of high orders and the algebraic Padé–Hermite approximants are used to determine the singular points of a vibrational energy function of the formaldehyde molecule dependent on a complex perturbation parameter as on the argument. It is shown that the Fermi, Darling–Dennison, and other higher-order vibrational resonances are related to Katz’s points—common branch points on the complex plane of the energy of two vibrational states. Analysis of Katz’s points that connect different vibrational states allows one to reveal essential resonance perturbations, to introduce an additional classification for them, and to determine the polyad structure of an energy spectrum.     

High-resolution FTIR spectroscopy of HCFC-31 in the 950−1160 cm−1 region: rovibrational analysis and resonances in the ν4, ν9 and ν5+ν6 bands of CH235ClF

The FTIR spectrum of CH₂ClF (natural isotopic mixture) was investigated in the ν₄, ν₉ and ν₅+ν₆ band region between 950 and 1160 cm^?1 at the resolution of 0.004 cm^?1. The ν₄ and ν₅+ν₆ vibrations of A′ symmetry give rise to a/b hybrid bands with a predominant a-type component. The ν₉ vibration of A^″ symmetry, expected with a c-type band contour, shows an intense Coriolis-induced parallel component (ΔK_a = 0, ΔK_c = 0) derived from mixing with the v₄ = 1 vibrational state. The high-resolution spectra of ν₉ and ν₅+ν₆ have been analyzed for the first time, while the assignments of the ν₄ band, previously investigated, have been extended to higher J and K_a values in the b-type component. The spectral analysis resulted in the identification of 1508, 809 and 349 transitions for the ν₄, ν₉ and ν₅+ν₆ bands of CH₂³⁵ClF, respectively. Besides the strong first-order a- and b-type Coriolis resonances between ν₄ and ν₉, the ν₅+ν₆ vibration was found to interact through a c-type Coriolis with the ν₄ and 3ν₆. High-order anharmonic resonance (ΔK_a = ±2) between ν₄ and ν₅+ν₆ was also established. All the assigned data were simultaneously fitted using the Watson's A-reduction Hamiltonian in the I^r representation and the relevant perturbation operators. The model employed includes five types of resonances within the tetrad ν₄/ν₉/ν₅+ν₆/3ν₆. Α set of spectroscopic constants for ν₄, ν₉ and ν₅+ν₆ bands as well as parameters for the dark state 3ν₆ and seven coupling terms have been determined. The simulations performed in different spectral regions satisfactorily reproduce the experimental data.     

The ro-vibrational analysis of the v4 fundamental band of CF3Br from jet-cooled diode laser and FTIR spectra in the 8.3-μm region

The v₄ fundamental band of CF₃⁷⁹Br and CF₃⁸¹Br, present in natural isotopic abundance, was investigated in the 8.3-μm region by high-resolution infrared spectroscopic techniques. Tuneable diode laser spectra were recorded in the ranges 1202.5–1205.0 cm^?1, 1208.0–1210.1 cm^?1 and 1212.5–1214.5 cm^?1. The tuneable diode laser spectra were obtained at the reduced temperature of 200 K and in a free-jet expansion. The latter technique was used to reduce spectral congestion, achieving a rotational temperature of about 50 K, with a resolution up to 0.0008 cm^?1. A Fourier transform infrared spectrum covering the entire spectral region of the v₄ band, between 1190 and 1220 cm^?1, was recorded at 298 K with a resolution of 0.004 cm^?1. The experimental wavenumbers from the different spectroscopic techniques were combined to accomplish the complete ro-vibrational analysis of v₄. In total, 4651 transitions were assigned to CF₃⁷⁹Br, 4047 to CF₃⁸¹Br, with J″_max? = K″_max?=80; of these, 3171 for CF₃⁷⁹Br and 2755 for CF₃⁸¹Br are from diode laser measurements. The data of each isotopologue were analysed using the model Hamiltonian for a degenerate vibrational state of a molecule of C_3v symmetry. The v₄ band of both the isotopologues resulted essentially unperturbed, but the Δl = Δk = ±2 l-resonance was found to be active within the v₄ = 1 state. Precise values of the vibrational energy and of the ro-vibrational parameters of v₄ = 1 for CF₃⁷⁹Br and CF₃⁸¹Br were obtained. The bromine isotopic splitting amounts to 6.9 × 10^?3 cm^?1. In addition, the equilibrium geometry and the harmonic force field were calculated ab initio using the large-size basis set def2-QZVP in conjunction to the PBE0 functional.     

Analysis of the Coriolis interaction between ν6 and ν4 bands of ethylene-cis-d2(cis-C2H2D2) by high-resolution FTIR spectroscopy

The Fourier transform infrared (FTIR) spectrum of the ν₆ band of ethylene-cis-d₂(cis-C₂H₂D₂) was recorded with a unapodized resolution of 0.0063 cm^?1 in the 990–1100 cm^?1 region. A total of 609 transitions were assigned to this band centred at 1039.7682 ± 0.0003 cm^?1. The ν₆ band was found to be coupled to the ν₄ band by a-type Coriolis resonance. Both perturbed and unperturbed transitions were assigned and fitted to give eight rovibrational constants with high accuracy for the v₆ = 1 state with a standard deviation of 0.00097 cm^?1 using a Watson’s A-reduced Hamiltonian in the I^r representation. From a rovibrational analysis of the Coriolis interaction between the ν₆ band and non-infrared active ν₄ band of cis-C₂H₂D₂, the band centre of ν₄ at 984.9 ± 0.2 cm^?1 was derived. Furthermore, the second-order a-type Coriolis coupling constant between the two bands was obtained for the first time.     

H2-broadening,shifting and mixing coefficients of the doublets in the ν2 and ν4 bands of PH3 at room temperature

The broadening, shifting and mixing coefficients of the doublet spectral lines in the ν₂ and ν₄ bands of PH₃ perturbed by H₂ have been determined at room temperature. Indeed, the collisional spectroscopic parameters: intensities, line widths, line shifts and line mixing parameters, are all grouped together in the collisional relaxation matrix. To analyse the collisional process and physical effects on spectra of phosphine (PH₃), we have used the measurements carried out using a tunable diode-laser spectrometer in the ν₂ and ν₄ bands of PH₃ perturbed by hydrogen (H₂) at room temperature. The recorded spectra are fitted by the Voigt profile and the speed-dependent uncorrelated hard collision model of Rautian and Sobelman. These profiles are developed in the studies of isolated lines and are modified to account for the line mixing effects in the overlapping lines. The line widths, line shifts and line mixing parameters are given for six A₁ and A₂ doublet lines with quantum numbers K = 3n,?(n = 1,?2, …) and overlapped by collisional broadening at pressures of less than 50 mbar.     

The high-resolution infrared spectrum of Si2H6: rotation–torsion analysis of the ν5 and ν7 fundamentals,and torsional splittings in the degenerate vibrational states

The infrared active ν₇ and ν₅ fundamentals of disilane, coupled by an x,y Coriolis interaction, have been analysed on a Fourier transform spectrum between 2120 and 2225?cm^?1, at the Doppler limited spectral resolution. A Fermi resonance with 2ν ₂?+?ν₉ affects the Δ K?=?1 side of ν₇, and both ν₇ and ν₅ show the effects of several additional localized perturbations. Line splittings in the ν₅ transitions are not observed, showing that the torsional splitting in the ν₅ excited state and in the vibrational ground state are almost equal. The intrinsic torsional splitting of ν₇ is found to be smaller than in the ground vibrational state by 0.0085?cm^?1. This splitting value and those found for the other two infrared active degenerate fundamentals, ν₈ and ν₉, follow the trend expected from our theoretical predictions. Exploratory numerical calculations show that the decrease of the torsional splittings, observed in the fundamental degenerate vibrational states of disilane, can actually be accounted for by the head–tail and torsional Coriolis coupling of all the degenerate vibrational fundamentals, in several torsional states.     

Profile of the ν1 Raman Band of Pure CD4 and Its Mixtures with Ar and Kr in the Gas Phase

The ν₁ band profile of isotropic Raman spectrum of pure CD₄ and its mixtures with Ar and Kr is recorded in the temperature range 140–360 K at pressure of pure CD₄ ranging from 4 to 20 atm and at total pressure of gas mixtures in the interval 4–160 atm. The dependences of the band shape on temperature and density are analyzed. The coefficients of the CD₄ band broadening by Ar and Kr are determined, and the decisive role of vibrational contributions, in particular of the intramolecular energy transfer, is pointed out.     

Analysis of the ν 3, ν 6, ν7 + ν 8 Fermi and Coriolis interacting band system in methyl cyanide

A reinvestigation of the Fermi and Coriolis interacting band system ν ₃, ν ₆, ν ₇ + ν ₈ of methyl cyanide has been performed with a resolution better than 0·3 cm^-1. The observed J structure in some of the K sub-bands enables an unambiguous numbering of the sub-band Q branches to be made. The resulting assignment, which differs from Amat and Nielsen's previous assignment, is used to re-analyse the band system. A band contour has been calculated by computer simulation, including the effects of both the Fermi resonance of ν ₆ with ν ₇ + ν ₈ and the Coriolis resonance of ν ₆ with ν ₃; both the frequency and intensity perturbations which result have been accurately reproduced. The molecular parameters obtained from our analysis are summarized in table 2.     

Fourier transform infrared spectrum of carbon disulphide in the 4ν2 + ν3 band region near 3100 cm−1

Fourier transform spectra have been recorded for carbon disulphide CS₂ in the region of the 4ν₂ + ν₃ band near 3100 cm^?1. The data analysis has determined new molecular constants. Bands were also observed for the isotopomer ¹²C³²S³⁴S.     

Torsional tunneling splittings in the v4 = 1 excited torsional state of Si2H6: analysis of hot bands accompanying fundamental transitions in the high resolution infrared spectrum

The (ν₄?+?ν₆)???ν₄, (ν₄?+?ν₈)???ν₄ and (ν₄?+?ν₉)???ν₄ hot infrared systems of disilane (Si₂H₆) have been analysed at high resolution, and the values of the relative vibration–rotation–torsion parameters have been determined. The torsional splitting is about 0.500?cm^?1 in the ν₄ and ν₄?+?ν₆ states, and decreases strongly in the vibrationally degenerate upper states ν₄?+?ν₈ (about 0.0272?cm^?1 on average) and ν₄?+?ν₉ (about 0.3019?cm^?1), consistent with theoretical predictions. Comparison between the vibrational wavenumbers of cold transitions and hot transitions originating in the excited torsional state v₄?=?1 allows one to determine the change of the fundamental torsional frequency ν₄ caused by the excitation of small amplitude vibrations. A remarkable increase in ν₄ of about 8.599?cm^?1 is found in the v₉?=?1 state (E_1d SiH₃-rocking mode, asymmetric to inversion in the staggered geometry), and this corresponds to an increase in the torsional barrier height in this excited fundamental vibrational state by about 48.77?cm^?1. The mechanism responsible for the decrease of the torsional splittings in the degenerate vibrational states is briefly outlined by means of second-order perturbation theory, using torsion-hindered vibrational basis functions of E_1d and E_2d symmetries for the degenerate modes.