A symmetrical top molecule is one in which two of the main. moments of inertia are equal. The energy levels of the asymmetric rotor cannot be represented by an explicit formula analogous to that for the symmetric top. To obtain the energy levels of the asymmetric rotor, we need to solve the wave equation.
for 2:; electronic states the total eigenfunction has the symmetry of the rotational eigenfunction, and the levels of even J. A generally satisfactory description that takes into account the slight deviation from harmonicity is the Morse function (9) for the potential energy. If the electric field is parallel to the electric vector of the microwave radiation, the quantum number M does not change.
In the non-degenerate case, the wave functions of the asymmetric rotor belong to the representations of Group v. UsU9.lly all electron spins are paired and the nuclear spins are coupled to the rotation of the molecule.
LINE SHAPF.8 AND INTENSITIES
The total absorption coefficient of the transition in the absence of a field is often desired. The modulation of absorption lines by the Stark effect was first presented by Hughes and Wilson (22). A third factor is the effect of uncertainty in time on the energy levels of molecules.
Figures 5 and 6 represent schematic diagrams of the square wave generator and its power supply. Therefore, the bandwidth of the amplifier is determined by the cut-off of the low-pass filter. Finally, the klystron's tendency to drift will put a practical limit on the sweep rate.
One or the other of these gauges will usually be resonant at the frequency of the line being studied. By tuning the receiver, you can always superimpose one of the "pips" on the suction line.
THE DETERMINATION OF THE STRUCTURE OF ISOCYANIC ACID IN THE VAPOR PHASE
They also showed that many of the reactions of cyanic acid can be interpreted in terms of addition to the double bond in the species HN:CO. Linhard and Betz finally concluded that the chemistry of isocyanic acid in solution could be explained on the basis of the structure HNCO alone. The calculation of the structure of HNCO was greatly facilitated and improved by the infrared data communicated to us by L,H.
On the basis of this work, the analysis of the microwave data we obtained for isocyanic acid was carried out for a model with the sequence of atoms H-N-C-0. After the exchange had taken place, the excess water was distilled from the sample tube and. Two of the lines have been tentatively identified as arising from rotational transitions in molecules possessing a vibrational quantum of excitation to vibrational v modes.
Angle 8 is itself a function of parameters which is too complicated to present explicitly. The numerical values for oc:.B are such that the effect of the two bending N-C-0. Consequently, the percent error in the distance will be half the percent error in the measurement of 11 - I.
This is due to the interaction of the electric quadrupole moment in the nitrogen nucleus with the molecular electric field. Receiver frequency readings and relative intensities for the three components of the triplet are recorded in Table VIII. The quadrupole interaction energy for each of the energy levels involved in this transition is reduced to that of the limiting symmetric top.
To fit the theoretical pattern to the observed separation of the two strongest lines in the multiplet, F = 1. Recent microwave studies of linear acetylenes show a marked shortening of C-C single bonds adjacent to triple bonds. Some of this material was converted to CF3CCD by condensing several cubic centimeters of steam.
Lines with the same J and different K values should appear with slightly different frequencies, but is not resolved. This results in a broadening of the lines and limits the accuracy of the frequency measurements.
ELECTRIC DIPOLE MOMENTS FROM STARK EFFECT MEASUREMENTS
Detailed studies of the Stark effect on the rotational energy levels of molecules as a function of the applied electric field lead to a determination of their electric dipole moments. These dipole moments are somewhat more important than those determined by the usual method of measuring the dielectric constant as a function of temperature. During the structural determinations of HNCO and CF3CCH, it was important to resolve the second-order Stark structure of the spectrum.
The displacement of the absorption line is taken as the average of the displacements caused by the top and bottom of the square wave. A determination of the distance in the waveguide can be made by direct measurement of the electrode thickness and internal dimensions of the waveguide. The narrow dimension of the waveguide is claimed by the manufacturer to vary no more than 0.001 inch from 0.400 inch.
Shulman (46) has considered errors arising from inhomogeneities in the electric field due to curvature near the edges of the electrode. At the time the data were collected, all frequencies were reduced to values of AVM', the displacement of the Mth Stark component, and all voltage measurements were reduced to the corresponding field strengths in the waveguide and recorded as the square of the field strength in . The perpendicular component of the dipole moment in deuteroisocyanic acid contributes twice as much to the Stark effect.
Calculation of the direction cosine matrix elements requires the asymmetric rotor eigenfunctions for the states involved. Instead of measuring the shifts for different values of the quantum number M, one can just as well measure the difference in the shifts for different values of M. The quoted error is the sum of the precision error of the particular measurement and the systematic errors.
Error in the displacement due to error in the measurement of the undisplaced frequency of the absorption line, ::!: O.l per cent. The precision error is taken as the average deviation from the mean divided by the square root of the number of measurements. It soon became clear that problems with handling the HF and monitoring the pressure dictated extensive modifications to the apparatus.
Change the mass of A to A1, allowing no change other than the change in zero-point vibration, resulting in a small change in all effective distances. The conservation of linear quantity requires that this expression also holds for the vibrating molecule. Let .a I be the difference between I measured for the original molecule and I for the original if it has the zero-point amplitude of the substituted molecule.
The moment of inertia, I', of the new molecule about x', the new center of mass, is equal to the moment of inertia of the new molecule about the old center of mass minus (M + £1 m) .a x • 2. In the OCS case, neglecting the fourth term in the parenthesis would result in an error of only 0.0003 ~ at the distance of the sulfur atom from the center of mass.
CROSS SECTION OF CELL
THEORETICAL
INCREASING FREQUENCY-
ENERGY LEVELS
4 FCF
Groetzinger (1) claims that the thermal conductivity of a dielectric material increases by as much as 70 percent when it is made into an electret. He suggests that the inhomogeneous fields used partially split a mixture such as beeswax into components with different dielectric constants and thermal conductivities. I propose that the application of the thermodynamic equations to a system in an electric field will show an insignificant degree of sorting for components whose dielectric constants are reasonably different for fields achievable in such experiments.
The non-existence of HOON (2) in the vapor phase, even at low temperatures, casts some doubt on the keto-enol tautomerism proposed by Werner (3) to explain the fact that the liquid obtained by depolymerizing cyanuric acid polymerizes. to a mixture of cyamelide and cyanuric acid, where cyamelide is the main product (60%) at 0°C, and. The dipole moment component along the major axis with the least moment of inertia for HNCO and HNCS was measured (4.5). I propose that the additional charge separation in HNCS can be viewed as arising from the predominance of one formal resonant structure over the other, while in HNCO the contributions of such structures cancel each other out.
A recent structure determination for OCSe (6) by microwave spectroscopy gives the probable error in the bond distances as 0.0001 Z. This figure was obtained from the consistency of the OC and CSe distances calculated from moment of inertia measurements for two separate pairs of molecules containing isotopes. Formyl chloride base has often been proposed as an intermediate in various reactions involving mixtures of CO and HCl.
3• At low temperatures, there may be a small concentration of HCOCl in equilibrium with CO and HCl. One can test this hypothesis by putting pure CO and HCl. observed to give no absorption below 100 kmc) in a waveguide and search for absorption lines from the asymmetric rotor HCOCl. 3 and HF to test for the existence of nuoboric acid, HBF4, in the vapor phase.
Microwave studies of the symmetrical top CF3-C:C-CH3 would be interesting because of its almost completely unhindered rotation around the figure axis of the CF. The highly efficient drying agents P2o5 and Mg(c104)2 would not be satisfactory for this purpose, as P. Measurements of the nitrogen quadrupole coupling constant would probably allow a choice between structures A and B.
