A simple method using the techniques of transformation theory for the generation of the matrix elements of unusual potential fUnctions for. one-dimensional quantum-mechanical problems is described. It is applicable both to functions which exist as a set of points, for example, a curve or table, as welJ as to those in explicit form. Some representative calculations have been made for anharmonic oscillators.

The microwave spectrum of tetrahydrofuran has been studied. Nine complete rotational spectra have been observed. These arise from the ground and eight excited states. All of these states are less than 200 cm−1 from the ground state. The rotational constants and dipole moments exhibit a strong nonlinear dependence on the quantum number of the excited state. Vibration–rotation interaction is strong and the spectra of the first four states deviate from that of rigid rotor spectra. These deviations permit the determination of two energy separations: Δ01 = 0.67 cm−1 and Δ23 = 1.5 cm−1. All of the results are interpreted in terms of a model of restricted pseudorotation with a potential function of [30(1-cos2φ) / 2] + [40(1-cos4φ) / 2] cm−1, where φ is the angle of pseudorotation. The dipole moment varies from 1.52 to 1.76 D depending upon the pseudorotation state. The details of this variation indicate that the twisted configuration is at lower energy than the bent configuration.

As a general introduction to a subsequent series of papers on pseudorotation and five-membered rings, the two-ring puckering modes of a five-membered ring are discussed in general terms. Five cases are separated depending upon the nature of the potential function for each mode. Correlation diagrams connecting the various cases are given. Consistent with our basic policy, we have gone directly from fundamental theory to an arithmetical development using large digital computers. The classical section of this development is outlined. The quantum-mechanical section is developed in the following paper.

Refinements in the experimental application of the energy-distribution-difference (EDD) method for resolving fine structure in ionization-efficiency curves are presented. These include data acquisition and computer-processing techniques by which first-differential EDD curves can be obtained with a good signal-to-noise ratio. Using these techniques, a study has been made of the fine structure observed in the first-differential EDD ionization-efficiency curves of C2H2+ and Xe+ near their thresholds. Distinct “steps” are resolved in the first-differential ionization-efficiency curve of C2H2+. The energy separations between these steps agree quite well with energy separations between vibrational levels of the C2H2+ ion determined by photoionization techniques. However, the relative cross sections for these processes determined by electron impact are drastically different from those reported for photoionization. Possible explanations for these differences are discussed. The electron-impact results for xenon indicate that a large portion of the cross section between the P3/22 and P1/22 states of Xe+ is due to autoionization from known Rydberg levels.

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