James K. G. Watson

Determination of Centrifugal Distortion Coefficients of Asymmetric‐Top Molecules

The rotational Hamiltonian of an asymmetric‐top molecule in a given vibrational state, obtained by the usual vibrational perturbation treatment, contains more parameters than can be determined from the observed energy levels. This Hamiltonian is therefore transformed by means of a unitary transformation to a reduced Hamiltonian which is suitable for fitting to observed energies. The unitary transformation can be chosen so that the reduced Hamiltonian has the following properties: (i) It is totally symmetric in the point group D2, regardless of the symmetry of the molecule; (ii) It contains only (n+1) independent terms of total degree n in the components of the total angular momentum, for each even value of n; (iii) Its matrix elements in a symmetric‐top basis satisfy the selection rule ΔK=0, ±2. This paper is concerned mainly with the possibility of carrying out this reduction in general. However, the reduced Hamiltonian described above contains one less quartic coefficient than has been used previously, ...

Determination of Centrifugal Distortion Coefficients of Asymmetric‐Top Molecules. III. Sextic Coefficients

The rotational Hamiltonian of an asymmetric‐top molecule, containing terms up to sixth degree in the components of the total angular momentum, is transformed by a unitary transformation to a reduced Hamiltonian, so as to avoid the indeterminacies inherent in fitting the complete Hamiltonian to observed energy levels. Two methods of reduction are considered, one suitable for energy calculations by matrix diagonalization and the other for calculations by perturbation theory. The relations between the coefficients in the reduced Hamiltonians and those in the original Hamiltonian are given. Extension of the perturbation treatment to the first‐order contributions from the sextic terms and the second‐order contributions from the quartic terms yields explicit expressions for these contributions in terms of Rays function EJτ(κ) and its first and second derivatives with respect to the asymmetry parameter κ.

Determination of Centrifugal‐Distortion Coefficients of Asymmetric‐Top Molecules. II. Dreizler, Dendl, and Rudolph's Results

Dreizler, Dendl, and Rudolph used the method of least squares to fit the equation of Kivelson and Wilson, which gives the rotational energy levels of an asymmetric top with first‐order corrections for centrifugal distortion, to the observed rotational spectra of dimethyl sulfoxide and dimethyl sulfide. The normal equations obtained were found to be highly ill‐conditioned, so that the centrifugal coefficients, A1to A6, were essentially indeterminate. It is shown here that the form of this indeterminacy can be understood quantitatively on the basis of a previously published linear relation between the average values in Kivelson and Wilsons equation. Explicit expressions are presented for the first‐order centrifugal corrections to those energy levels that are given by linear or quadratic equations. These expressions suggest that there are no further linear relations of the above type.

Rotational dependence of the dipole moment of CH3D

Radio frequency modulated side bands of the C18O2 P (18) laser line were used to perform infrared–infrared double resonance between the first order Stark components of the ν6 rP (10,1) transition of CH3D. The dipole moment in the J=10, K=1 level in the ground state has been measured to be (1.03±0.1) ×10−3 D, which is very different from the previously reported values of around 5.65×10−3 D. This difference has been explained as due to rotational dependence of the dipole moment. Combining the present result with the previous molecular beam measurements by Wofsy, Muenter, and Klemperer, we have obtained the rotational dependence of the dipole moment derived from Stark measurements in the form μStark(J,K) =∓{ (5.657±0.004)−(0.0427±0.0009) J (J+1) +(0.0696±0.0026) K2}×10−3 D. The upper sign would be consistent with ab initio calculations of the signs of the dipole derivatives. A theory was developed to calculate the above coefficients of J (J+1) and K2 for CH3D. It has been demonstrated that they can be comple...

Excitation of the E,F1Σ+g states of H2 by electron impact

Optical excitation functions produced by low‐energy electron impact excitation are reported for several rotational lines originating from the E,F1Σ+g and the H1Σ+g electronic states of neutral H2. The E1Σ+g→B1Σ+u, F1Σ+g→B1Σ+u, and H1Σ+g →B1Σ+u band systems are observed at an effective spectral slit width of ?2 A, over an electron energy range 0–300 eV. The observed transitions are identified as originating from v′=2,3,4 vibrational levels of the E state, the v′=5 level of the F state, and the v′=2 level of the H state. Absolute emission cross section measurements are obtained at 200 eV electron energy and 30 mtorr H2 gas pressure through direct comparison with the λ=4686 A (n=4→3) line of the He II spectrum. Analysis of the E→B (2,1) R0 rotational line intensity yields (1.0±0.3) ×10−18 cm2 as a lower‐limit estimate of the E1Σ+g direct cross section at 200 eV.

Perturbations in the 4ν3 level of the {\tf="PS7CD9"{\raise7pt\tilde \lower7ptA\clap}^\lower4pt{\hskip-.5pt1}\hskip-1ptA_u} state of acetylene, C2H2This article is part of a Special Issue on Spectroscopy at the University of New Brunswick in honour of Colan Linton and Ron Lees.

Perturbations in the K = 1 and 3 levels of the {\rm \tilde A}^\lower2pt{\rm 1} {\rm A}_{\rm u}, 4ν3 state of acetylene are explained as interactions with levels of the {\rm \tilde A}^\lower2pt{\rm 1} {\rm A}_{\rm u}, 31B4 (v3 = 1, v4 + v6 = 4) polyad. A satisfactory least-squares fit to the perturbed level structure has been obtained, treating the 4ν3 state as an asymmetric top perturbed by isolated K = 1 and 3 levels. Accurate deperturbed rotational constants for the interacting states are presented.