Alan G. Robiette

The anharmonic force field and equilibrium structure of methane

The anharmonic force field of methane has been refined to fit spectroscopic data from the isotopic species 12CH4, 13CH4, 12CH4, 12CH3D, 12CHD3 and 12CH2D2. Six of the thirteen cubic force constants have been determined experimentally, the remaining cubic constants being fixed at values derived from ab initio calculations. The quartic force field is very crude, in that only frrrr has been refined. It is concluded however that the cubic and quartic force fields, even though they are subject to limitations, provide a considerable improvement in the experimental determination of the r e structure and the quadratic force field. The equilibrium bond length is found to be r e(CH) = 1·0858 ± 0·001 A.

On the relationship of normal modes to local modes in molecular vibrations

A simple model for the effective vibrational hamiltonian of the XH stretching vibrations in H2O, NH3 and CH4 is considered, based on a morse potential function for the bond stretches plus potential and kinetic energy coupling between pairs of bond oscillators. It is shown that this model can be set up as a matrix in local mode basis functions, or as a matrix in normal mode basis functions, leading to identical results. The energy levels obtained exhibit normal mode patterns at low vibrational excitation, and local mode patterns at high excitation. When the hamiltonian is set up in the normal mode basis it is shown that Darling-Dennison resonances must be included, and simple relations are found to exist between the xrs , gtt , and Krrss anharmonic constants (where the Darling-Dennison coefficients are denoted K) due to their contributions from morse anharmonicity in the bond stretches. The importance of the Darling-Dennison resonances is stressed. The relationship of the two alternative representations of...

Rotational energy level structure in the local mode limit

The nature of the rotational energy level structure of the stretching vibrational states in XY2, XY3, and XY4 molecules (belonging to the C2v, C3v, and Td point groups, respectively) has been investigated in a local mode limit with no kinetic or potential energy copling between the bond oscillators and with the fundamental stretching frequencies much larger than the bending frequencies. The Coriolis effects between the rotational levels in the stretching vibrational states disappear in this limiting case, but the H22 resonance terms are seen to be important owing to the multiple vibrational degeneracies. Simple relationships are obtained between the coefficients of the vibrationally diagonal and off‐diagonal H22 terms and consequently the number of independent molecular parameters is reduced. The model is compared with experimental data for XHn hydrides, and particularly in the molecules with a heavy central mass the major contribution to the H22 coefficients is well explained.

Simultaneous analysis of the ν1, ν4, 2ν2, ν2 + ν5, and 2ν5 infrared bands of 12CH3F

Abstract The Fourier-transform spectrum of CH3F from 2800 to 3100 cm−1, obtained by Guelachvili in Orsay at a resolution of about 0.003 cm−1, was analyzed. The effective Hamiltonian used contained all symmetry allowed interactions up to second order in the Amat-Nielsen classification, together with selected third-order terms, amongst the set of nine vibrational basis functions represented by the states ν1(A1), ν4(E), 2ν2(A1), ν2 + ν5(E), 2ν50(A1), and 2ν5±2(E). A number of strong Fermi and Coriolis resonances are involved. The vibrational Hamiltonian matrix was not factorized beyond the requirements of symmetry. A total of 59 molecular parameters were refined in a simultaneous least-squares analysis to over 1500 upper-state energy levels for J ≤ 20 with a standard deviation of 0.013 cm−1. Although the standard deviation remains an order of magnitude greater than the precision of the measurements, this work breaks new ground in the simultaneous analysis of interacting symmetric top vibrational levels, in terms of the number of interacting vibrational states and the number of parameters in the Hamiltonian.

Electron diffraction study of large amplitude vibrations in H3SiNCO and H3SiNCS

Abstract The molecular dimensions of silyl isocyanate and isothiocyanate have been determined in the vapor phase by the sector-microphotometer method of electron diffraction. The large amplitude SiNC deformation are analysed in terms of possible potential functions.

Analysis of the v 3 and v 1 infra-red bands of SiH4

The high-resolution infra-red spectrum of SiH4 in the region 2101 cm-1 to 2265 cm-1 has been analysed. Most of the lines observed have been assigned to transitions of the v 3 and v 1 bands of the abundant isotopic species 28SiH4. The v 1 band is formally forbidden in the infra-red, but a vibration-rotation interaction between v 1 and v 3 lends intensity to the v 1 transitions. The spectrum has been fitted by diagonalizing the v 3 = 1 and v 1 = 1 hamiltonians coupled by the vibration-rotation interaction term. 500 transitions have been fitted with an overall standard deviation of 0·007 cm-1, using only 15 adjustable parameters (ten in the v 3 = 1 hamiltonian, four in the v 1 = 1 hamiltonian, and one interaction coefficient). The calculated intensities are also in good agreement with experiment. Transitions of the other isotopic species 29SiH4 and 30SiH4 have also been observed, but these spectra have not been analysed in detail.

Spectral intensities in the ν3 bands of 12CH4 and 13CH4

Abstract Relative and absolute line intensities for the ν 3 bands of the 12 C and 13 C isotopic varieties of methane have been measured using a tunable difference-frequency laser spectrometer. From these data the integrated band strength of 13 CH 4 is calculated to be 0.983 ± 0.007 that of 12 CH 4 , with the uncertainty representing three standard deviations. The absolute ν 3 bandstrength for 12 CH 4 is 266.1 ± 3.0 cm −2 atm −1 at 294.7 K where the errors are dominated by the pressure measurement. This band strength corresponds to an effective transition moment 〈μ 3 〉 = 0.0534(3)D for 12 CH 4 from which the ν 4 band dipole moment and the Herman-Wallis F factor can be estimated using a recent force field model for methane.

Extended measurement and analysis of the ν3 infrared band of methane

Abstract Previous Doppler-limited measurements of the allowed lines in the ν 3 infrared band of 12 CH 4 , recorded using a stabilized difference-frequency tunable infrared laser system, have been extended to P (17), Q (17), and R (19). The data have been analyzed by diagonalization of an effective Hamiltonian for the v 3 = 1 state, in which many higher-order terms (including tensor operators of up to eighth rank) have been added to the usual fourth-order expansion. These extra terms are necessary to reproduce the experimental splitting patterns and in particular to fit an unusual inversion of the ordering of the tetrahedral levels for R = J − 1 around J = 14 in the upper state. The standard deviation of the fit to 440 assigned transitions is 0.0056 cm −1 , and the calculated intensities are also in good agreement with experiment.

The two-dimensional anharmonic oscillator: 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.

The infra-red spectra of silyl fluoride and silyl fluoride-d3

Infra-red spectra have been recorded for silyl fluoride and silyl fluoride-d 3 at a resolution of circa 0·3 cm-1. Rotational structure has been observed for parallel fundamentals in both molecules, and for all perpendicular fundamentals. In both SiH3F and SiD3F the A 1 and E species deformation modes interact strongly via a Coriolis perturbation; this has been analysed, and the band origin of v 5 for SiH3F is reassigned. A hybrid-orbital force field based on the experimental data is also reported.