G. Pierre

Vibration-rotation energies of harmonic and combination levels in tetrahedral XY4 molecules: Theory and extrapolation method

Abstract This paper presents a general method for studying overtones and combination bands of tetrahedral XY4 molecules. Making full use of group theory, the matrix representation of the Hamiltonian restricted to any set of vibrational sublevels is easily derived from a basis of rovibrational matrices. Explicit expressions for the reduced matrix elements are developed for all the operators of any order occurring in states for which Σs vs ≤ 2, including any interaction type. The parameters introduced are directly the Hamiltonian expansion coefficients and consequently have the same physical significance in any vibrational state. The treatment of overtones and combination bands for which the corresponding fundamentals are analyzed is considered in detail. In this case, the parameters of the ground and fundamental states remain fixed and only a few new parameters occurring specifically in the studied state need to be determined. In this way, the convergence of least-squares fits is greatly improved. The example of methane is used to illustrate the efficiency of this method suitable for the direct determination of potential constants.

Rotational analysis of vibrational polyads in tetrahedral molecules: Simultaneous analysis of the pentad energy levels of 12CH4

Abstract A theoretical model for the rovibrational analysis of clustered vibrational states for tetrahedral molecules is presented. The results of a comprehensive study of the five bands ν1, ν3, 2ν2, ν2 + ν4, and 2ν4 of 12CH4 are reported. The Hamiltonian has been developed to the third order in the Amat-Nielsen classification. Twenty-two parameters related to the ground state and the dyad ν 2 ν 4 have been transferred unchanged and 52 new parameters have been adjusted to fit experimental data, mainly interferometric ir data in the region 2250–3250 cm−1. The analysis has been realized through J′ = 18 involving 1919 observed upper-state energies. The overall standard deviation of the fit is 0.022 cm−1. A prediction of upper-state energies for the five bands has been carried out through J′ = 20. The model reproduces qualitatively and quantitatively the rotational fine structure of the upper levels in the full range of J′ values including level crossings (J′ ≥ 12), for the first time. The problem of higher excited vibrational states in methane is briefly discussed.

Parameters of reduced Hamiltonian and invariant parameters of interacting E and F2 fundamentals of tetrahedral molecules: ν2 and ν4 bands of 12CH4 and 28SiH4

Abstract The problem of unambiguous processing of experimental data for interacting doubly and triply degenerate states of tetrahedral molecules is studied on the basis of 85 fits of ν2 and ν4 spectra of 12CH4 and 28SiH4. The formalism of irreducible tensors of the paper by J. P. Champion and G. Pierre [J. Mol. Spectrosc. 79, 255–280 (1980)] is used. The behavior of correlated parameters of the Hamiltonian expansion is examined first by series of actual fits of experimental data. It is shown that any of the q2J2- or q2J3-type parameters of the ν 2 ν 4 dyad may be given positive or negative or zero values without deterioration of the quality of fits. The other parameters move along trajectories which are described by PTZ equations [V. I. Perevalov, Vl. G. Tyuterev, and B. I. Zhilinskii, Chem. Phys. Lett. 104, 455–461 (1984)] with an accuracy of better than 5% (in the case of CH4). The experimental values of PTZ coefficients are determined. The nonlinear trajectories relating the isolated state and the interacting state models are presented as well. In order to achieve unambiguous fits the properties of the reduced Hamiltonian are studied in detail considering the influence of removing various terms from the Hamiltonian on the correlation matrix and on the standard deviation of fits σ. Twenty parameters of the reduced Hamiltonian are determined which reproduce 698 energy levels of ν 2 ν 4 of CH4 up to J = 20 with the experimental accuracy = 0.003 cm−1. Invariant q2J2-type parameters are introduced, and their values are determined for ν 2 ν 4 of 12CH4 and 28SiH4. Attention is paid to the fact that the latter approach would enable one to determine an unambiguous physically meaningful set of spectroscopic parameters and simultaneously achieve the absolute minimum of σfit.

The region of the 3ν3 band of methane

Abstract The spectrum of methane near 9000 cm −1 , the region of the 3 ν 3 band, has been recorded at Meudon Observatory with a Fourier transform spectrometer under high resolution. Intensity measurements at two different temperatures, 149 and 295 K, have allowed us to identify two new vibration bands by determining the lower-state quantum numbers J of the transitions. About 100 lines are now assigned in this range, including P and Q branches. Furthermore, the first detailed rotational analysis of the 3 ν 3 band has been made; nine parameters of the band have been determined. The standard deviation of the differences between observed and computed wavenumbers for 45 lines of the 3 ν 3 band is only 0.045 cm −1 . It is found that the observed 45 lines of the 3 ν 3 band correspond to the sublevel l 3 = 3 and C v = F 2 .

Fourth-order invariant parameters for F2 isolated fundamental states of tetrahedral molecules: The study of the ν4 band of 12CH4

Abstract The ambiguity of effective Hamiltonians for triply degenerate F 2 states of tetrahedral molecules is studied on the basis of a set of 70 fits of experimental data for ν 4 of 12 CH 4 . The formalism of irreducible tensors of the paper by J. P. Champion and G. Pierre [ J. Mol. Spectrosc. 79 , 255–280 (1980)] is used. It is shown that, in agreement with recent theoretical propositions [V. I. Perevalov, Vl. G. Tyuterev, and B. I. Zhilinskii, Dokl. Acad. Nauk SSSR 263 , 868–872 (1982)], any of q 2 J 4 diagnonal coupling parameters may be changed significantly without noticeable variation in the quality of fits; reduced Hamiltonians having fewer numbers of adjusted parameters are first applied to describe the ν 4 energy levels of methane. With good accuracy, the behavior of fitted q 2 J 4 parameters obey linear equations derived in the referred paper. A new set of q 2 J 4 -type diagonal coupling parameters [ w 1 , w 2 , w 3 ; ϱ] for triply degenerate F 2 fundamental states is suggested. Parameters w i are invariant under unitary transformations and can be used to refine molecular force field: their values are determined for ν 4 of 12 CH 4 .

Rotational analysis of vibrational polyads in tetrahedral molecules: line parameters of the infrared spectrum of 12CH4 in the range 2250-3260 cm−1 ― theory versus experiment

Abstract Experimental and theoretical line parameters of the infrared spectrum of 12 CH 4 in the range 2250–3260 cm −1 covering the pentad ν 1 , ν 3 , 2 ν 2 , ν 2 + ν 4 , and 2 ν 4 are reported. The individual line strengths are reproduced with a relative precision of 12% comparable to the experimental accuracy. In all, 6499 transitions have been calculated in the spectral region 2250–3260 cm −1 . Their intensities range from 2.5 to 213 000 × 10 −24 cm/molecule. Virtually all the absorptions of 12 CH 4 in this range are satisfactorily reproduced.

Microwave fourier transform spectroscopy of pure rotational ν4 ↔ ν4 transitions and reanalysis of the ν2ν4 dyad of methane-d4

Abstract Pure rotational transitions of a spherical top in a degenerate vibrational state have been observed directly for the first time with the help of pulsed microwave Fourier transform (MWFT) spectroscopy. Twelve rotational transitions in the v 4 = 1 vibrational excited state of CD 4 have been identified. The theoretical basis for the transition moments has been developed and the line strengths of the rotational transitions have been estimated. The measured rotational transition frequencies have been included in a reanalysis of the data from a previously recorded high-resolution FTIR spectrum of the ν 2 and ν 4 bands. The v 4 = 1 state of CD 4 is strongly coupled to the v 2 = 1 state by Coriolis interaction. Thirty molecular parameters of the ν 2 ν 4 dyad have been fitted finally from the combined microwave and infrared data. The microwave data are reproduced with a standard deviation of 42 kHz, and the infrared data with a standard deviation of 0.0002 cm −1 ; in each case, this is close to the estimated experimental prescision.

Vibration-rotation energies of harmonic and combination levels in tetrahedral XY4 molecules: Analysis of the 2ν2 and ν2 + ν4 bands of 12CH4

Abstract The theory and the extrapolation method described in the previous paper are used to analyze the v 2 = 2 and v 2 = v 4 = 1 levels of 12 CH 4 . In addition to the well-known parameters of the ground, v 2 = 1, and v 4 = 1 states, the computation of energy levels involves only 6 new parameters for 2 ν 2 and 13 for ν 2 + ν 4 up to the fourth order of approximation. These parameters have been determined from Raman and infrared data. Forty-four Raman lines observed by Berger in the region from 3060 to 3090 cm −1 have been assigned to the 2 ν 2 band. The standard deviation obtained by fitting 39 of these transitions with the 6 corresponding parameters is 0.025 cm −1 . The calculated frequencies of ν 2 + ν 4 are compared with moderate resolution ir spectra recorded in our laboratory and the recent spectra of Hunt et al. Totally polarized weak Raman lines observed by Berger in the region from 2850 to 2900 cm −1 have been assigned to the ν 2 + ν 4 band arising through a second-order Coriolis interaction with the ν 1 band. A project of a comprehensive treatment of the energy levels of methane between 2550 and 3650 cm −1 is discussed.

Microwave Fourier transform spectroscopy of rotational and rovibrational transitions in the ν2ν4 dyad of silane-28Si

Abstract Rotational and rovibrational transitions of silane- 28 Si in the ν 2 ν 4 dyad have been observed directly with a pulsed microwave Fourier transform spectrometer operating in the 8- to 18-GHz frequency range. Seventeen transitions of the types ν 4 ← ν 4 , ν 2 ← ν 2 , ν 2 ← ν 4 , and ν 4 ← ν 2 have been observed and assigned. The transitions are generally weaker than those of the vibrational ground state and weaker than the corresponding transitions of methane- d 4 . The observed microwave transitions have been analyzed in combination with previous high-resolution infrared measurements (G. Pierre, A. Valentin, and L. Henry, Canad. J. Phys. (1986), in press) in a least-squares fit of the vibration-rotation constants t s,s′ Ω (K,n Γ ) of the ν 2 ν 4 - dyad Hamiltonian.

Analysis of infrared and Raman spectra of 116SnH4 in the 1900 cm−1 region: Study of the 1000, 0010 interacting states

Abstract Monoisotopic stannane 116SnH4 has been investigated at room temperature in the 1775–2025 cm−1 region with the FTIR spectrometer at Giessen, Germany, with an effective resolution of nearly 3.8 × 10−3 cm−1, and in the 1906.0–1908.2 cm−1 region with the high-resolution stimulated Raman spectrometer at Dijon, France, with an effective resolution of 3.2 × 10−3 cm−1. Most observed transitions correspond to ν 1 ν 3 lines. For this dyad we have used a Hamiltonian developed to the fifth order to analyze the two spectra, for J values up to 14. The simultaneous analysis of infrared and Raman transitions enabled us to determine 4 parameters of ν1, 17 parameters of ν3, and 6 interaction parameters. The standard deviation was about 0.2 × 10−3 cm−1. For J values > 14 a perturbation appears because the third harmonic of the bending modes (ν2, ν4) is close to the stretching dyad ν 1 ν 3 . The interaction between the two polyads is too strong to be absorbed by the contact transformation. In order to be able to analyze the spectra for higher J values, the (1000, 0010, 0300, 0201, 0102, 0003) polyad interaction scheme must be considered.