A general treatment of internal rotation is given for molecules whose moments of inertia for over-all rotation are independent of internal rotational coordinates. Tables are presented for the various thermodynamic functions which are accurate for molecules with one internal rotation and for the potential energy (V/2) (1 — cos nφ). The tables are shown to be a good approximation for molecules with several internal rotational coordinates, provided the potential energy can be expressed as a sum of terms of this type. Methods are suggested for treating problems where cross terms involving more than one internal coordinate are present in the potential energy. The energy level expressions are developed for the more general case with the potential energy expressed by a Fourier series. Although a few specific cases were worked out with different shape potential barriers, it appears that the simple form assumed above will be satisfactory for many purposes.
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.
The microwave spectrum and structure of sulfur tetrafluoride has been determined. One FSF angle is 101°33′±30′, the opposite FSF angle is 186°56′±30′. The bond length for the nearly linear bonds is 1.646 A±0.003 A; for the other pair it is 1.545 A±0.003 A. The dipole moment was determined from the Stark effect to be 0.632±0.003 debye.
The J = 1 to J = 2 and J = 2 to J = 3 transitions for CH3NO2 and CD3NO2 have been assigned for several internal rotational states. The best values of the rotational constants B and C were found to be 10 542.7 and 5876.7 Mc/sec for CH3NO2 and 8697.1 and 5254.3 Mc/sec for CD3NO2. The rotational constant for the NO2 group about the symmetry axis is 13 277.5 Mc/sec. These constants are determined assuming no inertial defect, slightly different values are calculated if other assumptions are made. Some of the assigned lines are a very sensitive function of the low barrier to internal rotation. The barrier term V6 was determined to be 6.03±0.03 calories/mole for CH3NO2 and 5.19±0.03 calories/mole for CD3NO2. The term V12 is less than 0.05 calorie/mole. The dipole moment of CH3NO2 is 3.46±0.02 Debye units.
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