William D. Gwinn

Energy Levels and Thermodynamic Functions for Molecules with Internal Rotation I. Rigid Frame with Attached Tops

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.

Calculation of Matrix Elements for One‐Dimensional Quantum‐Mechanical Problems and the Application to Anharmonic Oscillators

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 well as to those in explicit form. Some representative calculations have been made for anharmonic oscillators.

Normal Coordinates: General Theory, Redundant Coordinates, and General Analysis Using Electronic Computers

A system of doing normal coordinate analysis is described which is better suited for use with electronic computers than are current methods. Mass‐weighted Cartesian coordinates are used, and rotation and translation are not separated until the matrix diagonalization procedure. The V matrix is generated numerically in a simple and accurate manner. Only one transformation is involved. The transformation which diagonalizes V is simply the transformation from Cartesian to normal coordinates. The problem of redundant coordinates does not exist in this proposed method, but the advantage of using linear potential constants in strained and constrained systems is retained.

Microwave Spectra, Dipole Moment, and Barrier to Internal Rotation of CH3NO2 and CD3NO2

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.

Microwave Spectrum, Vibration—Rotation Interaction, and Potential Function for the Ring‐Puckering Vibration of Trimethylene Sulfide

The microwave spectrum of the ground and first four excited states of the ring‐puckering mode of trimethylene sulfide has been observed and assigned. From an analysis of the perturbations to the rotational spectrum arising from the coupling of the internal angular momentum with the over‐all rotation of the molecule, the separation between the lowest two vibrational levels was determined to be 8229 Mc/sec. Three mixed vibration—rotation transitions have been observed, and give the more accurate value of 8232.5±0.4 Mc/sec (0.27461 cm−1) for this separation. From the vibration—rotation interaction and the relative intensities of certain lines, the potential function governing the vibration has been determined to be 7.0207Q4−87.7581Q2 cm−1, where Q is the coordinate describing the vibration. The height of the barrier to the planar configuration is 274.2±2 cm−1. The agreement between the far‐infrared spectrum that was calculated using this potential function derived from microwave data, and that which was rece...

Trimethylene Oxide. III. Far‐Infrared Spectrum and Double‐Minimum Vibration

The 0–1 transition of the out‐of‐plane bending vibration in trimethylene oxide has been observed at 53.4 cm−1. Previously reported bands by Lord and his co‐workers [J. Chem. Phys. 33, 294 (1960)] at 89.8, 105.2, 118.3, 128.9, 139.0, 147.6, 154.9, and 161.8 cm−1 have also been confirmed. In addition, six higher members of this series as well as three members of the Δv = 3 series have been observed. These transitions are readily interpreted in terms of the hot‐band series of a slightly perturbed quartic oscillator. A double‐minimum potential function of the form az4—bz2 predicted all the observed transitions to within experimental error (0.5 cm−1 or better). The central barrier in the potential‐energy function, while low, is finite and has a height of 15.3±0.5 cm−1. It had previously been concluded, from the variation of the rotational constants with vibrational state obtained from microwave spectroscopy that the potential energy contained a small barrier of the order of zero‐point energy at the planar conf...

Trimethylene Oxide. I. Microwave Spectrum, Dipole Moment, and Double Minimum Vibration

The microwave spectra of four isotopic species of trimethylene oxide have been investigated. Analysis of the spectra indicates that the four‐membered ring is essentially planar. From the intensity measurements of the rotational transitions and their vibrational satellites, it was concluded that the energy levels in the ring‐puckering vibration are single levels. The Stark effect also provided independent evidence that the ring is not highly puckered. The dipole moment of the molecule was found to lie solely on the C–O molecular axis. A value of 1.93±0.01 Debye was obtained. The existence of a small barrier in the potential function, however, was established by a detailed analysis of the observed vibration‐rotation interaction. Quantitative considerations have led to an accurate determination of the barrier height and the general shape of the potential function. The barrier restricting the ring‐puckering motion has been found to be 35±5 cm—1. The ground vibrational level is 8±4 cm—1 above the top of the ba...

Trimethylene Oxide. II. Structure, Vibration‐Rotation Interaction, and Origin of Potential Function for Ring‐Puckering Motion

In the previous paper of this series, the microwave spectra of four isotopic species of trimethylene oxide were investigated and the potential function for the puckering of the four‐membered ring was determined. Further analysis of the data has now enabled the molecular structure to be calculated. The structural parameters deduced from the rotational constants are: r(C–C) = 1.549±0.003 A, r(C–O) = 1.449±0.002 A, r(Cα–Hα) = 1.091±0.002 A, r(Cβ–Hβ) = 1.100±0.003 A, ∠Cα–Cβ–Cα = 84°33′±1′, ∠Cα–O–Cα = 91°59′±7′, ∠Cβ–Cα–O = 91°44′±3′, ∠Hα–Cα–Hα = 110°18′±10′, ∠Hβ–Cβ–Hβ = 110°44′±3′. The alphamethylene planes are slightly deflected towards the oxygen atom away from the bisectors of the ∠Cβ–Cα–Os. However, the actual angle of deflection is rather uncertain. Using these structural parameters, models have been constructed to calculate the vibration‐rotation interaction due to the ring‐puckering vibration. The experimentally observed rotational constant variations were found to be very well reproduced if the out‐of...

THE MICROWAVE SPECTRA, STRUCTURE, DIPOLE MOMENT, AND CHLORINE NUCLEAR QUADRUPOLE COUPLING CONSTANTS OF METHYLENE CHLORIDE

The microwave spectra of CH2Cl235, CH2Cl35Cl37, CH2Cl237, CDHCl235, CDHCl35Cl37, CD2Cl235, and CD2Cl35Cl37 have been examined and effective moments of inertia have been determined for these seven isotopic species. From these data the effective bond distances and angles were determined as C–Cl distance=1.7724±0.0005A, Cl–C–Cl angle=111°47′±1′, C–H distance=1.068±0.005A (average of all species), or 1.082A (extrapolated to infinite hydrogen mass), and H–C–H angle=112°0′±20′ (average of all species) or 112°58′ (extrapolated to infinite hydrogen mass). The best value for the dipole moment of methylene chloride was found from the Stark splitting to be 1.62±0.02×10−18 esu. The chlorine nuclear quadrupole coupling constants were also determined and their relationship to the structure is discussed.

Ring Puckering in Five‐Membered Rings. II. The Microwave Spectrum, Dipole Moment, and Barrier to Pseudorotation in Tetrahydrofuran

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.