C. Di Lauro

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 ...

Remarks on the signs of g factors in atomic and molecular Zeeman spectroscopy

This paper draws attention to the advantages that would be obtained by adopting a new convention for the sign of g factors that would make the g factor for electron spin a negative quantity (g ≈ −2), rather than a positive quantity as generally adopted at present. The editors are aware that the proposal made in this paper concerning the conventional sign of the g factor for electron spin will be seen by some readers as controversial. We have nonetheless agreed to publish this paper in the hope that it will stimulate discussion. The editors would welcome comments on this proposal in the form of short papers, which they will then be happy to consider for publication together at a later date. Various magnetic moments, associated with rotational, vibrational, nuclear spin, electron orbital and electron spin angular momenta, can contribute to the Zeeman effect in atoms and molecules. They are considered in this paper in the context of the effective Hamiltonian where relativistic and other corrections as well as the effects of mixing with other electronic states are absorbed in appropriate g factors. In spherically symmetric systems, the magnetic dipole moment arising from a specific angular momentum can be written as the product of three factors: the nuclear or Bohr magneton (which is positive), the g factor (which may be positive or negative), and the corresponding angular momentum (which is a vector). A convention is discussed, in which the sign of the g factor is positive when the dipole moment is parallel to its angular momentum and negative when it is antiparallel. This would have the advantage that it could be applied consistently in any situation. Such a choice would require the g factors for the electron orbital and electron spin angular momenta to be negative. This concept can easily be extended to the case of a general molecule where the relation between the dipole and angular momentum vectors has tensorial character.

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.

DIMETHYLACETYLENE : THE THEORY REQUIRED TO ANALYSE THE INFRARED AND RAMAN PERPENDICULAR BANDS

Abstract In this paper we give a detailed account of the theory required to simulate and analyse the infrared and Raman perpendicular fundamental bands of the dimethylacetylene molecule at high resolution. A summary of this theory has appeared in a previous paper (P.R. Bunker, J.W.C. Johns, A.R.W. McKellar and C. di Lauro, J. Mol. Spectry. 162 (1993) 142) in which an analysis of the infrared methyl rocking fundamental band was given. As well as detailing the effect of various terms in the Hamiltonian we also discuss the Raman selection rules and show that the analysis of the ΔK = 2 component of the perpendicular fundamental bands will lead to a determination of the sign of the torsional barrier. The sign of the barrier (i.e. whether the minimum energy conformation is staggered or eclipsed) cannot be determined from the analysis of the infrared perpendicular bands.

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...

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...

Rotation–torsion analysis of the Si2H6 infrared fundamental ν9, perturbed by excited torsional levels of the vibrational ground state

The lowest infrared active perpendicular fundamental ν9 of disilane has been analysed on a Fourier transform spectrum between 320 and 430 cm−1, at the spectral resolution of 0.0012 cm−1. The rotation–torsion structure of this band is affected by x,y Coriolis interactions with excited torsional levels of the vibrational ground state, correlating with components of 3ν4 and 4ν4 in the high barrier limit. The interaction of ν9 and 4ν4, forbidden in the D3d symmetry limit, is allowed between components of E torsional symmetry under the G36(EM) extended molecular group, because of the large amplitude of the internal rotation motion. We could determine the values of the main vibration–rotation–torsion parameters of ν9, interaction parameters, and the vibrational wavenumbers of the four torsional components of 3ν4 and of the E3d component of 4ν4. The intrinsic torsional splitting of ν9 is found to be smaller than in the ground vibrational state by 0.0066 cm−1, in good agreement with our theoretical predictions. The possibility of observing the effects of D3d-forbidden interactions in the spectra of ethane-like molecules is also discussed.