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.

The calculation of force constants and normal coordinates IV: XH4 and XH3 molecules

Normal coordinate calculations of XH4 and XH3 molecules are reviewed and discussed. It is shown that for most of these molecules the true values of the force constants in the most General Harmonic Force Field can be uniquely determined only by making use of vibration-rotation interaction constants. It is emphasized that without these extra data the GFF is not determined. The results are compared with various model force fields for these molecules.

Anharmonic force field of acetylene

The harmonic and anharmonic force field of acetylene has been determined in a least-squares calculation from recently determined data on the spectroscopic constants of various isotopic species (including the vibrational l-doubling constant). A general quadratic and cubic force field was used, but a constrained quartic force field containing only 8 of the 23 possible quartic constants. The results are discussed and compared with earlier work.

Analytical potentials for triatomic molecules IX. The prediction of anharmonic force constants from potential energy surfaces based on harmonic force fields and dissociation energies for SO2 and O3

Analytical potential energy functions which are valid at all dissociation limits have been derived for the ground states of SO2 and O3. The procedure involves minimizing the errors between the observed vibrational spectra and spectra calculated by a variational procedure. Good agreement is obtained between the observed and calculated spectra for both molecules. Comparisons are made between anharmonic force fields, previously determined from the spectral data, and the force fields obtained by differentiating the derived analytical functions at the equilibrium configurations.

A model for stretch-bend interactions in molecular force fields

Interaction force constants between bond-stretching and angle-bending co-ordinates in polyatomic molecules have been attributed, by some authors, to changes of hybridization due to orbital-following of the bending co-ordinate, and consequent changes of bond length due to the change of hybridization. A method is described for using this model quantitatively to reduce the number of independent force constants in the potential function of a polyatomic molecule, by relating stretch-bend interaction constants to the corresponding diagonal stretching constants. It is proposed to call this model the Hybrid Orbital Force Field. The model is applied to the tetrahedral four co-ordinated carbon atom (as in methane) and to the trigonal planar three coordinated carbon atom (as in formaldehyde).

Coriolis perturbations in the infrared spectrum of ethylene

Rotational structure has been resolved and analyzed in two of the infrared‐active perpendicular bands of C2H4 vapor: the Type b fundamental band, ν10, at 826 cm—1, and the Type c fundamental band, ν7, at 949 cm—1. Many of the individual PP and RR branch lines have been observed. The analysis has been confined to values of the quantum number K≥3, for which energy levels ethylene shows no detectable deviations from a symmetric‐top rotational structure. The analysis reveals a Coriolis interaction between ν7 and ν10, and between ν4 and ν10, and values of the Coriolis constants ζ7,10z and ζ4,10y are obtained; these are related to normal coordinate calculations for the appropriate symmetry species, and force constants are derived to fit the observed zeta constants. The band center of ν10 has been revised from the original figure of 810 cm—1 to the new value, 826 cm—1, and the inactive frequency ν4 is estimated to lie at 1023±3 cm—1, in good agreement with the previous estimate of 1027 cm—1. The change in the value of ν10 leads to a suggested change in the value of the Raman‐active fundamental ν6 from 1236 to 1222 cm—1. New combination bands have been observed at 2174 cm—1, assigned as ν3+ν10; and at 2252 cm—1, assigned as ν4+ν6; also rotational structure has been resolved and analyzed in the ν6+ν10 band at 2048 cm—1. The new data obtained for the C2H4 molecule are summarized in Table XII, with all of the other data presently available on the vibrational and rotational constants.

The calculation of accurate normal coordinates I: general theory, and application to methane

The calculation of accurate and reliable vibrational potential functions and normal co-ordinates is discussed, for such simple polyatomic molecules as it may be possible. Such calculations should be corrected for the effects of anharmonicity and of resonance interactions between the vibrational states, and should be fitted to all the available information on all isotopic species: particularly the vibrational frequencies, Coriolis zeta constants and centrifugal distortion constants. The difficulties of making these corrections, and of making use of the observed data are reviewed. A programme for the Ferranti Mercury Computer is described by means of which harmonic vibration frequencies and normal co-ordinate vectors, zeta factors and centrifugal distortion constants can be calculated, from a given force field and from given G-matrix elements, etc. The programme has been used on up to 5 × 5 secular equations for which a single calculation and output of results takes approximately l min; it can readily be extended to larger determinants. The best methods of using such a programme and the possibility of reversing the direction of calculation are discussed. The methods are applied to calculating the best possible vibrational potential function for the methane molecule, making use of all the observed data.

Analytical potentials for triatomic molecules from spectroscopic data V. Application to HOX (X=F, Cl, Br, I)

Analytical potential energy functions are reported for HOX (X=F, Cl, Br, I). The surface for HOF predicts two metastable minima as well as the equilibrium configuration. These correspond to HFO (bent) and OHF (linear). Ab initio calculations performed for the HOF surface confirm these predictions. Comparisons are drawn between the two sets of results, and a vibrational analysis is undertaken for the hydrogen bonded OHF species. For HOCl, one further minimum is predicted, corresponding to HClO (bent), the parameters for which compare favourably with those reported from ab initio studies. In contrast, only the equilibrium configurations are predicted to be stable for HOBr and HOI.

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.

Microwave spectrum of CHD2CN and CHD2NC, and the harmonic force field and rz structure of methyl cyanide and isocyanide

The microwave spectra of CHD2CN and CHD2NC have been measured from 18 to 40 GHz; about 20 type A and 30 type C transitions have been observed for each molecule. These have been fitted to a Hamiltonian using 3 rotational constants, and 5 quartic and 4 sextic distortion constants, in the IrS reduction of Watson [in “Vibrational spectra and structure” Vol. 6 (1977)]; the standard error of the fit is 26 kHz. For methyl cyanide the 5 quartic distortion constants have been used to further refine the recent harmonic force field of Duncan et al. [J. Mol. Spectrosc. 69, 123 (1978)], but the changes are small. Finally, for both molecules, the harmonic force field has been used to determine zero point average moments of inertia Iz from the ground state rotational constants for many isotopic species, and these have been used to determine an rz structure. The results are compared with rs structure calculations.

Rotational spectra induced by vibrations

Mizushima and Venkateswarlu showed in 1953 that certain molecules have the property that excited vibrational states may possess rotational spectra even when the rotational spectrum of the ground vibrational state is forbidden by symmetry. We call such a spectrum a vibrationally induced rotational spectrum, and have made a systematic examination of the point groups which permit such behaviour. We also give formulae for the approximate line frequencies and intensities in these spectra, and discuss some of the problems involved in observing them. The spectra can only arise from degenerate vibrational states, and are of three possible types: i) symmetric top perpendicular spectra, shown by molecules belonging to the point groups Dnh, Dn and Cnh, where n is odd; (ii) symmetric top parallel spectra, shown by molecules belonging to Dnd and S2n, where n is even; and (iii) spherical top spectra, shown by molecules belonging to T or Td. Excited vibrational states of polar molecules of point groups Cnv or Cn, where n is odd, may also possess vibrationally induced perpendicular components of type (i), in addition to their ordinary parallel spectra. In addition to the above limitations on the point groups there are, in general, limitations on the symmetry species of the degenerate vibrational states.

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.

The two-dimensional anharmonic oscillator II: the microwave spectrum of silyl isocyanate, SiH3NCO

The J + 1 ← J transitions (J = 2, 3, 4, 5, and 6) in the microwave spectrum of SiH3NCO have been assigned for the vibrational ground state and for the vibrational states v10 = 1, 2, and 3. The results for v10 = 0 confirm earlier work. The vibration-rotation constants show a remarkable variation with v10 and l10. To a large extent the anomalous behavior of these constants has been explained in terms of a strongly anharmonic potential function for the ν10 vibrational mode.