Coriolis interactions about x-y axes in symmetric tops

Selection rules and matrix elements are derived for Coriolis interactions between vibrational levels due to rotation about (x, y) axes in symmetric top molecules. The theory is developed in detail for the case of interaction between an A1 and an E species vibrational level in a C3v molecule; perturbations to both the positions and the intensities of the rovibration transitions in the spectrum are considered. A computer program has been written which calculates exactly the perturbed spectrum of two interacting rovibration bands according to this model, the results being presented directly by a graph plotter connected to the computer. This has been used to interpret perturbations observed in two pairs of interacting fundamentals in the spectrum of CH3F (ν2 - ν5 and ν3 - ν6) and one pair in CD3Cl (ν2 - ν5). The resulting analysis of the observed spectrum leads to new values for some vibration-rotation interaction constants and also leads to a unique determination of the sign relationship between the dipole moment derivatives in each pair of interacting normal vibrations. These sign relations are summarized in Figs. 8, 12, and 15.

Vibrational intensities VI: ethylene and its deutero-isotopes

Absolute intensity measurements have been made on the fundamental vibrations of ethylene and four of its deuteroisotopes. The bands were pressure broadened with nitrogen at 50 atmos, and the intensities were determined by the method of Wilson and Wells except that the observed optical density was integrated against logv rather than v. Normal coordinates have been calculated, and the intensities have been interpreted in terms of quantities (∂p/∂Si) giving the change in dipole moment with respect to each internal symmetry coordinate. Data from the different isotopic species have been used to eliminate ambiguities in the interpretation. Effective bond moments are calculated for each symmetry coordinate.

A refined quartic forcefield for acetylene: accurate calculation of the vibrational spectrum

It is now possible to calculate the nine-dimensional rovibrational wavefunctions of sequentially bonded four-atom molecules variationally without dynamical approximation. In the case of HCCH, the simplest such molecule, many hundreds of rovibrational (J = 0, 1, 2) levels can be converged to better than 1.5 cm −1. Variational calculations of this kind are used here systematically to refine the well-known quartic valence-coordinate forcefleld of Strey and Mills [J.Mol. Spectrosc.59, 103-115 (1976)] against experimental term values up to three C-H stretch quanta for the principal and two deuterated isotopomers, yielding a new surface that reproduces the energies of all the known Σ, Π, and Δ states of these species up to the energy of two C-H stretch quanta with an rms error of 3 cm−1 . The refined forcefield is used to study the resonances associated with the accidental degeneracies (ν2 + ν4 + ν5, ν3) and (ν2 + 2ν5, ν1) in the principal isotopomer, leading to a clarification of the assignment of she experimentally detected states in the 2ν3 and 3ν3, polyads, and to the finding that vibrational Coriolis (kinetic energy) terms, rather than quartic anharmonicities in the potential, are the primary cause of the resonant interactions. Using a new cubic ab initio electric dipole field to calculate IR absorption coefficients, 24 undetected Σ and Π states of 1H12C12C1H and 5 undetected Σ states of D12C12CD are identified as candidates for experimental study, and their calculated energies and assignments are given.

Vibration–rotation variational calculations: precise results on HCN up to 25 000 cm−1

Variation calculations of the vibration–rotation energy levels of many isotopomers of HCN are reported, for J=0, 1, and 2, extending up to approximately 8 quanta of each of the stretching vibrations and 14 quanta of the bending mode. The force field, which is represented as a polynomial expansion in Morse coordinates for the bond stretches and even powers of the angle bend, has been refined by least squares to fit simultaneously all observed data on the Σ and Π state vibrational energies, and the Σ state rotational constants, for both HCN and DCN. The observed vibrational energies are fitted to roughly ±0.5 cm−1, and the rotational constants to roughly ±0.0001 cm−1. The force field has been used to predict the vibration rotation spectra of many isotopomers of HCN up to 25 000 cm−1. The results are consistent with the axis‐switching assignments of some weak overtone bands reported recently by Jonas, Yang, and Wodtke, and they also fit and provide the assignment for recent observations by Romanini and Lehmann of very weak absorption bands above 20 000 cm−1.

Local modes and x,K relations for ethene and propadiene

The results recently obtained by Mills and Robiette on local-mode effects in H2O, NH3 and CH4 type molecules are extended to ethene (C2H4) and propadiene (C3H4) type molecules. General relations among the anharmonic xrs constants and the Darling-Dennison Krrss constants for the stretching vibrations are derived, called “x,K relations”, which allow local-mode effects to be generated by adding the appropriate anharmonic and Darling-Dennison constants to the familiar normal-mode model of molecular vibrations. The general utility of x,K relations is discussed, and the results are reviewed for the molecular types for which they have so far been derived.

Selection rules for rovibronic transitions in symmetric top molecules

A simple diagrammatic rule is presented for determining the rotational selection rules governing transitions between any pair of vibronic states in electric dipole spectra of symmetric top molecules. The rule is useful in cases where degenerate vibronic levels with first-order Coriolis splittings occur, because it gives immediately the selection rule for the (+l) and (-l) components in any degenerate state. The rule is also helpful in determining the symmetry species and the effective zeta constants in overtone and combination levels involving degenerate vibrations. Particular attention is devoted to the conventions concerning the signs of zeta constants.

Vibrational intensities VII: ethane and ethane-d6

Absolute intensity measurements have been made on the fundamental vibrations of C2H6 and C2D6, using the extrapolation method of Wilson and Wells and using nitrogen at pressures up to 50 atmospheres to broaden the bands. The absorption coefficient was integrated against the logarithm of the frequency. Normal coordinates were calculated from the potential function of Hansen and Dennison, and were used to interpret the results in terms of quantities (∂p/∂Si) giving the change of dipole moment with respect to the symmetry coordinates Si. Consistency of data between the isotopes was used both to eliminate ambiguities in the interpretation, and as a criterion in separating overlapping pairs of absorption bands. The results have been interpreted in terms of bond effective moments.

Excited vibrational state microwave spectra, structure, and force-field of trifluorosilane

The J = 2−1 microwave spectrum of six isotopic species of HSiF3 has been observed and assigned in excited states of five of the six fundamental vibrations. The assignment is based on relative intensities, double resonance experiments, and trial anharmonic force constant calculations. Analysis of the spectra leads to experimental values for five of the constants, all three l-doubling constants qt, one Fermi resonance constant φ233, and one zeta constant. The harmonic force field has been refined to all the available data on vibration wavenumbers, centrifugal distortion constants, and zeta constants. The cubic anharmonic force field has been refined to the data on and qt constants, using two models: a valence force model with two cubic force constants for SiH and SiF stretching, and a more sophisticated model. With the help of these calculations, the following equilibrium structure has been determined: re(SiH) = 1.4468(±5) Å, re(SiF) = 1.5624(±1) Å, HSiF = 110.64(±3)°,

Vibrational intensities VIII: CH3- and CD3- chloride, bromide and iodide

Absolute intensity measurements have been made on the fundamental vibrations of methyl chloride, bromide, and iodide, and their fully deuterated derivatives, by integrating the optical density over the absorption bands. The bands were fully pressure broadened by using up to 80 atmos of foreign gas. Band separations were made graphically. The results are analyzed in terms of the dipole moment derivatives with respect to symmetry coordinates in the molecule, (∂p/∂Si). The data on the different isotopic species are shown to yield consistent results, and this requirement of consistency has also been used as an aid in the analysis. In the E‐class vibrations the signs of the dipole moment derivatives have been determined unambiguously by assuming the permanent dipole to be directed CH3+☒X—.

C–H local modes in cyclobutene. II. Laser photoacoustic studies 10 000–17 000 cm−1. Vibrational structure and C–H local mode dynamics

In part I of this study [Baggott, Clase, and Mills, Spectrochim. Acta Part A 42, 319 (1986)] we presented FTIR spectra of gas phase cyclobutene and modeled the v=1–3 stretching states of both olefinic and methylenic C–H bonds in terms of a local mode model. In this paper we present some improvements to our original model and make use of recently derived ‘‘x,K relations’’ to find the equivalent normal mode descriptions. The use of both the local mode and normal mode approaches to modeling the vibrational structure is described in some detail. We present evidence for Fermi resonance interactions between the methylenic C–H stretch overtones and ring C–C stretch vibrations, revealed in laser photoacoustic spectra in the v=4–6 region. An approximate model vibrational Hamiltonian is proposed to explain the observed structure and is used to calculate the dynamics of the C–H stretch local mode decay resulting from interaction with lower frequency ring modes. The implications of our experimental and theoretical studies for mode‐selective photochemistry are discussed briefly.

C---H local modes in cyclobutene, part I: FTIR studies, 600 to 10000 cm–1

The vibrational structure of C---H stretching states in gas-phase cyclobutene was studied using FTIR spectroscopy in the range 700–9000 cm−1. The structure was modelled using two effective vibrational Hamiltonians, one for each type of C---H bond present, consisting of local mode basis functions subject to coupling with symmetrically equivalent bonds and to Fermi resonances with suitable low frequency vibrations. Best-fit model parameters were determined using least-squares routines and the model predictions are compared to the observed band positions and intensities. Some discussion is given of the relevance of the observed couplings to intramolecular vibrational redistribution (IVR) which results in the observation of statistical behaviour in cyclobutene isomerization induced by excitation of C---H stretching overtones in the visible region.

Second order Coriolis resonance in the v2, v5 Raman bands of CH3F

The vibration-rotation Raman spectrum of the ν2 and ν5 fundamentals of CH3F is reported, from 1320 to 1640 cm−1, with a resolution of about 0.3 cm−1. The Coriolis resonance between the two bands leads to many perturbation-allowed transitions. Where the resonance is still sufficiently weak that the quantum number K′ retains its meaning, perturbation-allowed transitions are observed for all values of ΔK from +4 to −4; in regions of strong resonance, however, we can only say that the observed transitions obey the selection rule Δ(k−l) = 0 or ±3. The spectrum has been analyzed by band contour simulation using a computer program based on exact diagonalization of the Hamiltonian within the ν2, ν5 vibrational levels, and improved vibration-rotation constants for these bands are reported. The relative magnitudes and relative sings of polarizability derivatives involved in these vibrations are also reported.

Coriolis perturbations in the infrared spectrum of diborane

High‐resolution infrared spectra of B2H6 vapor are reported. The sample was prepared from the naturally occurring 11B☒10B isotopic mixture. The rotational structure of the infrared bands has been analysed for Coriolis perturbations due to rotation about the axis of least moment of inertia (the B⋅⋅⋅B axis). The following results have been obtained: (a) interaction between the Type A fundamental ν18 and the inactive fundamental ν5 has been observed, thus confirming the assignment of ν5 at 833 cm—1, giving ∣ ζ5,18Z ∣=0.55±0.05; (b) interaction observed between the Type A combination band (ν10+ν12) at 1283 cm—1 and the inactive combination (ν10+ν7) gives an estimate of the unobserved fundamental ν7 as 850±30 cm—1, and an estimate of ∣ ζ7,12Z ∣=0.6±0.1; (c) the absence of any observed perturbation of the Type C fundamental ν14 at 973 cm—1, suggests, by negative arguments, that either the unobserved fundamental ν9 does not lie in the frequency range 900 to 1100 cm—1, or ∣ ζ9,14Z ∣<0.2. The assignment of the unobserved fundamental vibrations of diborane is discussed in the light of this evidence.

Internal rotation in dimethylacetylene

The vibrational spectrum of dimethyl acetylene has been remeasured with better resolving power than hitherto, and the rotational fine structure of some perpendicular type bands has been partly analyzed. The energy levels of a molecule of this kind in which internal rotation of methyl groups may arise have been re-examined theoretically and the rotational structure of the absorption bands has been more clearly defined than previously. The experimental results are consistent with the assumption of unrestricted internal rotation of the methyl groups, and the Coriolis factors $\zeta _{i}$ for several vibrations have been determined.

Vibrational intensities in methane

The absorption intensities of the two infra-red active vibrations in methane have been obtained from a perturbation calculation on the equilibrium wave functions derived in the preceding paper. The perturbation field is the change in the potential field due to the nuclei which results from moving the nuclei in the vibrational coordinate concerned, and a simplified form of second order perturbation theory, developed by Pople and Schofield, is used for the calculation. The main approximation involved is the neglect of f and higher harmonics in the spherical harmonic expansion of the nuclear field. The resulting dipole moment derivatives are approximately three times larger than the experimental values, but they show qualitative features and sign relationships which are significant.