F. Lattanzi

Rotational analysis of the v 2 + v 6 ±1, v 5 ∓1 + v 6 ∓1 and v 5 ∓1 + v 6 ±1 interacting infrared bands of methyl bromide

The rotational analysis of the infrared absorption spectrum of CH3 79Br and CH3 81Br between 2150 and 2510 cm-1 was performed on a Fourier transform spectrum with a resolution of 0·007 cm-1. The bands v 2 + v 6(E) and v 5 + v 6(A 1 + A 2 + E) occur in this region, giving rise to several perturbations as in the corresponding system of methyl chloride [3]. Forbidden transitions, observed in correspondence of the level crossing of the x-y Coriolis coupling between v 2 + v 6 and v 5 + v 6(E), enabled us to estimate the value of A″ - 225D″K at 5·16186 cm-1 for CH3 79Br and 5·16173 cm-1 for CH3 81Br. The parallel system of v 5 + v 6 exhibits a perpendicular structure, and an l-type resonance couples those levels of the parallel and perpendicular components of v 5 + v 6 involved in transitions from the K″ = 0 levels of the ground state. The QQ 0 branches of the A 2 component of v 5 + v 6, made active by this resonance, are observed for both isotopic species.

Vibrational symmetry classification and torsional tunneling splitting patterns in G6(EM), G12, and G36(EM) molecules

It is shown that the torsional splitting patterns in methanol-like molecules, with the excitation of small amplitude vibrational modes in the methyl group, are determined by mechanisms that can be formulated in an almost identical fashion to that for ethane-like molecules. This is achieved by treating ethane-like molecules by the internal axis method (IAM) and methanol-like molecules by the principal axis method (PAM) or rho-axis method (RAM). Using the extended molecular groups G6(EM) or C6v(M) for methanol and G36(EM) for ethane, vibrations perpendicular to the internal rotation axis are conveniently described by modes of higher degeneracy (E for methanol and Gs for ethane) in the absence of coupling of top and frame. Head–tail coupling operators, except the cos-type barrier terms, lower the degeneracy, causing vibrational splittings. Coupled vibrational pairs with torsional splitting patterns that we call ‘regular’ (pure A1, A2 pairs for methanol and pure E1d, E2d pairs for ethane) or ‘inverted’ (pure B1, B2 pairs for methanol and pure E1s, E2s pairs for ethane) can be formed as limit cases. Actual splitting patterns occur between the above limits, and are basically determined by torsional Coriolis coupling, which can tune more or less to resonance pairs of uncoupled basis levels linked by specific head-tail coupling operators. The inversion of torsional splitting patterns, observed in perpendicular vibrational modes of the methyl group of methanol, can be predicted by these theoretical considerations. Similar considerations apply to molecules of G12 symmetry.It is shown that the torsional splitting patterns in methanol-like molecules, with the excitation of small amplitude vibrational modes in the methyl group, are determined by mechanisms that can be formulated in an almost identical fashion to that for ethane-like molecules. This is achieved by treating ethane-like molecules by the internal axis method (IAM) and methanol-like molecules by the principal axis method (PAM) or rho-axis method (RAM). Using the extended molecular groups G6(EM) or C6v(M) for methanol and G36(EM) for ethane, vibrations perpendicular to the internal rotation axis are conveniently described by modes of higher degeneracy (E for methanol and Gs for ethane) in the absence of coupling of top and frame. Head–tail coupling operators, except the cos-type barrier terms, lower the degeneracy, causing vibrational splittings. Coupled vibrational pairs with torsional splitting patterns that we call ‘regular’ (pure A1, A2 pairs for methanol and pure E1d, E2d pairs for ethane) or ‘inverted’ (pure ...

The effect of phase conventions on vibration-rotation matrix elements

Abstract The transformation properties of vibrational and rotational basis operators and functions under symmetry operations and time reversal are investigated, with emphasis on their dependence on normal coordinate orientation and phase conventions. The effect of phase conventions on the values of the off-diagonal vibration-rotation matrix elements is examined, and it is shown that if the molecular symmetry allows for an operation denoted R′ , consisting of either a reflection through a plane containing the angular momentum quantization z-axis or a rotation about a binary axis normal to z, all vibration-rotation matrix elements of axially symmetric and asymmetric rotor molecules can be made real by appropriate vibrational and rotational phase conventions, which are discussed and recommended. Therefore vibration-rotation matrix elements of these molecules can be made all real for all molecular symmetry groups, with the exception of the groups containing separably degenerate E-species, Ci, C1 (no symmetry), and C2, Cs, and C2h if the binary rotation axis is oriented along z and σh = σxy. It is shown that, with the same conventions which render all vibration-rotation matrix elements real, the matrix elements to be used in the calculation of electric dipole vibration-rotation intensities, when the M-degeneracy is not removed, are taken all real if R′ is a reflection plane and all imaginary if R′ is a binary rotation axis. Relative phases of rotational wavefunctions differing by the value of M have to be defined in order to determine the values of matrix elements with ΔM = ±1.

The ν6, ν8, 3ν4 + ν12 infrared system of Si2H6 under high resolution: rotational and torsional analysis

A Fourier transform infrared spectrum of disilane has been measured at a Doppler limited resolution, and analysed in the region of the ν6 and ν8 fundamentals, from about 800 to 1020cm−1. The torsional splittings are not resolved in the ν6 band, showing that the splittings in the ν6 = 1 state and in the ground state are almost identical. The torsional splittings in the reasonably unperturbed regions of the ν8 fundamental are about 0.0146cm−1, and a detailed rotation-torsion analysis shows that the intrinsic splittings in the ν8 = 1 state are smaller than in the ground state by this amount. An intrinsic torsional splitting about 0.0150 cm−1 is estimated in the vibrational ground state and in the ν6 = 1 state, and almost vanishing in the ν8 = 1 state (about 0.0004cm−1), with a barrier height around 407cm−1. This is in agreement with the expectation from theory. The ν8 band, beyond a moderate x, y-Coriolis coupling with ν6, is affected by several perturbations, also selective in the torsional components. The 3ν4 + v12 combination, with three quanta of the torsional mode excited and large torsional splittings, is the main perturber, causing both Fermi and Coriolis resonances in several regions of the spectrum. The vibrational origins of all four torsional components of 3ν4 + v12 were determined. Other perturbative effects are attributed to the systems 2ν3 + ν4, and ν4 + 249(E + A). The spectrum was numerically analysed, and the relevant vibration-rotation-torsion parameters were determined.

The infrared spectrum of C D from 1195cm 1 to 1335cm 1: rotational analysis of nu + nu a - 2 6 nd torsional splitting in the 4 11 2nu + nu state 4 11

The υ4 + υ11 (Eu) infrared band of C2D6 has been rotationally analysed under high resolution, between 1195 cm-1 and 1335 cm-1, taking into account the x,y Coriolis coupling with υ2 + υ4(A1u. The rotational structure is affected by strong l-type interactions, with both Δl = Δk = ±2 and Δl = plusmn;2, Δk = ±1. Torsional splittings are not resolved, as expected. Several Q branches of the hot band (2υ4 + υ11)- υ4 have been identified, and some of them occur as narrow features with unresolved J structure, due to the l-interaction mechanisms. The hot RQ1 and RQ2 are so sharp that the maxima of the torsional components can be resolved, and a splitting of about 0·015 cm-1is measured. This value, apparently too small, is in agreement with the fact that υ11 in 2υ4 + υ11 is not a pure E2d vibrational mode, due to the γ Coriolis coupling mechanisms in the CD3 deformation vibration–torsion system.

Vibrational spectra and force constants of symmetric tops: High-resolution spectra of H374Ge35Cl in the ν1ν4 region near 2100 cm−1

Abstract The gas-phase infrared spectrum of monoisotopic H 3 74 Ge 35 Cl has been studied in the ν 1 , ν 4 region near 2100 cm −1 with a resolution of 0.008 cm −1 . Rotational fine structure for Δ J = ±1 branches has been resolved for both fundamentals. ν 1 ( a 1 ), 2119.977 03(19) cm −1 ; and ν 4 ( e ), 2128.484 65(8) cm −1 are weakly coupled by Coriolis x,y resonance, Bξ 1,4 y 2.6 × 10 −3 cm −1 , and l -type resonance within ν 4 , q 4 (+) −8.4 × 10 −6 cm −1 , has been observed. An extended Fermi resonance with ν 5 ±1 + 2 ν 6 ±2 , which mainly affects the kl = −14 and −15 levels of ν 4 , has been detected and analyzed. In addition, several weak and local resonances perturb essentially every K subband of ν 4 and some of ν 1 , and a qualitative model is proposed to account for the features observed in the spectrum. Disregarding the transitions involved in local perturbations, the rms deviation of the fit to the remaining 2021 lines is σ = 1.34 × 10 −3 cm −1 .

Vibrational spectra and force constants of symmetric tops

The infrared spectrum of H3SiI in the 800–1050 cm-1 region has been recorded with a resolution of 0·04 cm-1 and rotationally analysed. Features related to the Fermi resonance between v 5 and v 3 + v 6 and to the Coriolis x, y resonance between v 2 and v 5 have been explained, and a set of vibration-rotation parameters for the three bands has been determined by least-squares calculations, σ(J, K) = 9·4 × 10-3 cm-1. The Fermi resonance matrix element |W 356| is found to be 3·7859(7) cm-1 and the vibrational frequencies are v 2 0 = 904·551(1), v 5 0 = 941·0746(8) and (v 3 + v 6)0 = 953·688(3) cm-1. The anharmonicity constant, x 36 = -1·745(9) cm-1, has been determined. Comparison is made with v 2/v 5/v 3 + v 6 of H3SiCl, H3SiBr and H3GeBr.

The high-resolution infrared spectrum of H3Si79Br from 2100 to 2330 cm-1. The v 1 and v 4 fundamentals

The Fourier transform infrared spectrum of monoisotopic H3 28Si79Br (fwhm ≈ 0·0035 cm-1) is investigated in the region of the v 1 and v 4 fundamental bands, from 2100 to 2330 cm-1. Anharmonic resonances involving v 4, v ±1 5 + 2v 0 6, v ∓1 5 + 2v ±2 6, v 2 + 2v ∓2 6 and 3v 3 + v 5 are observed, yielding information on this complex perpendicular polyad. The fundamental v 1 is anharmonically coupled to v 2 + 2v 0 6. Several strong vibration-rotation perturbations are also observed, especially in the low-K region, so that several anomalous patterns in the rotational structure of the spectrum are caused by different concomitant and even conflicting mechanisms. The determination of the values of vibration-rotation parameters requires different series of least squares iterative calculations based on different appropriate selections of the avcailable data. The total overall standard deviation σ (in units of 10-3 cm-1) of the fit of the observed wave-numbers of v 1, v 4 and perturber lines made detectable near re...

Phase conventions that render all matrix elements of the vibration-rotation Hamiltonian real

Rotational and vibrational operators of a molecule possessing an ℜ symmetry element, consisting of either a binary rotation axis normal to the angular momentum quantization z axis or of a reflection plane containing z, are classified according to the irreducible co-representations of the group (E, ℜ′, Θ, ℜ′Θ), Θ being the time-reversal operator. Using this classification, it is shown that the matrix elements of the vibration-rotation Hamiltonian, in the usual vibration-rotation basis, can be made all real for all classes of molecules possessing the ℜ′ symmetry element, by appropriate rotational and vibrational phase conventions, which are defined and recommended. With the same phase conventions that render the matrix elements of the vibration-rotation Hamiltonian all real, the matrix elements of the electric dipole vibration-rotation transition moment can be made all real if ℜ′ is a reflection plane, and all imaginary if ℜ′ is a binary rotation axis, by appropriate additional conventions about the relativ...

Vibrational spectra and force constants of symmetric tops: XXXIV. Rotational analysis of the v 2, v 5, v 3 + v 6 system near 850 cm-1 of the monoisotopic species H3 74Ge 79Br and H3 74Ge 81Br

The infrared spectra of the monoisotopic species H3 74Ge 79Br and H3 74Ge 81Br in the 750–1000 cm-1 region covering the vibrations v 2, v 5 and v 3 + v 6 have been recorded with a resolution of 0·0...