David M. Dennison

The Methyl Alcohol Molecule and Its Microwave Spectrum

The theory of hindered rotation in methyl alcohol developed by Burkhard and Dennison has been extended to include the second‐order Stark effect as well as a detailed discussion of K‐type doubling. It has been applied to an interpretation of the microwave spectrum of normal methanol and of two isotopic molecules, C13H3O16H and C12H3O18H3 recently measured by Hughes, Good, and Coles. A very convincing fit between the predicted and observed lines is obtained which serves to determine many of the molecular constants, as well as providing a substantial number of self‐consistency checks.The height of the potential barrier (on the assumption of a sinusoidal potential) is found to be 374.8 cm−1. The CH distance in the methyl group cannot be obtained with any accuracy from the present data but is consistent with the CH distance in methane, namely, 1.093A, and has been taken to have this value. The remaining dimensions are, however, well determined and are: OH distance=0.937A, CO distance=1.434A, COH angle=105°56′,...

The Potential Constants of Ethane

The infrared and Raman data of light and heavy ethane (C2H6 and C2D6) have been reexamined for the purpose of determining as accurately as possible the potential constants of the ethane molecule. In order to fill in some of the gaps in the spectroscopic data, additional high resolution measurements have been made on the infrared spectrum of heavy ethane which have given more precise values for the active fundamental frequencies and zeta‐values. Resolution of the fine structure associated with the parallel band ν5* has given the value of the large moment of inertia of C2D6, thus completing the information required for the spectroscopic determination of the dimensions of ethane. The data yield, C–C distance=1.543A, C–H distance=1.102A, H–C–C angle=109°37′, and H–C–H angle=109°19′. The twenty‐two distinct potential constants compatible with the D3d symmetry of ethane have been determined through their relationships to the normal frequencies and zeta‐values of C2H6 and C2D6. The normal frequencies have been o...

Reflection and Transmission Interference Filters Part I. Theory

An interference filter of the reflection type consists in its simplest form of a perfectly reflecting mirror on which is placed a thin layer of a dielectric material. The outer surface of the dielectric is coated with a very thin metallic film. When properly constructed such a filter reflects 100 percent of radiation at the frequencies 2nν0, and 0 percent of radiation at the frequencies (2n + 1)ν0.A transmission filter consists of a thin dielectric layer, both sides of which are coated with very thin metallic films. A well made filter will transmit up to approximately 40 percent of the incident radiation at the frequencies nν0. The transmission bands can be made quite narrow, and the transmission between the maxima may be less than 1 percent although it does not fall to zero.The theory, which consists of a straightforward application of the Maxwell equations, is initially applied to a single metallic film backed by dielectric media. The reflection and transmission coefficients, as well as the phase shifts, are obtained and are given in terms of the thickness and the optical constants of the film.The reflection coefficient for the reflection filter is developed next and is expressed as a function of the properties of a single metallic film. The general formula is quite complicated but degenerates to a simple form when the wave-length becomes long (i.e. for the infra-red region). By using the filter at oblique incidence it is shown that polarized radiation may be produced.The transmission filter is studied and its properties may again be formulated in terms of the properties of a single metallic film. The values of the optical constants are deduced, which lead to the construction of an efficient transmission filter. Silver films have approximately these values in the visible region of the spectrum, but fail to possess them either in the ultraviolet or in the infra-red region. The theory shows that when the filter is tilted so that the angle of incidence is no longer normal, the transmission band shifts towards shorter wave-lengths, and splits into two bands, one of which is polarized parallel and the other perpendicular to the plane of incidence. This phenomenon is observed with experimental filters.

Hindered Rotation in Molecules with Relatively High Potential Barriers

The theory of hindered rotation has been applied to the type of asymmetric molecule in which the hindering barrier is high enough so that the hindered rotation splittings of the energy levels are small compared with the rotational energies but yet large enough to be observable in the microwave spectrum. The specific type of molecule considered consists of a rigid asymmetric component which may undergo a hindered rotation about the symmetry axis of a rigid symmetric component where the symmetric component is in addition assumed to have threefold symmetry and the asymmetric component at least a plane of symmetry containing the symmetry axis of the symmetric component. An example might be the acetaldehyde molecule, CH3CHO.In principle, the theory developed by Burkhard and Dennison can be used directly but in practice the method is difficult to apply to such a molecule since the matrix elements of the Hamiltonian used previously do not degenerate naturally or easily to those for the rigid asymmetric rotator i...

Analysis of the torsion-rotation spectra of the isotopic methanol molecules

Abstract The high resolution infrared spectra of CH3OH, CH3OD, CD3OH and CD3OD observed by D. R. Woods and C. W. Peters in the region from 400 to 900 cm−1 have been analyzed to obtain the molecular moments of inertia, the barrier height and the Kirtman perturbation constants. The first step consisted in identifying as many Q branch origins as possible. Between 25 and 40 origins were determined for each isotopic molecule with an accuracy of about 0.03 cm−1. These data were combined with Q branch origins found by R. M. Lees and J. G. Baker from their very accurate measurements of the microwave spectra of these molecules. A nonlinear least squares solution yielded values for the constants. With these constants the spectrum was recomputed and found to agree with the observed spectrum to the order of the experimental errors. In all, 176 data points were described by 40 constants-10 for each molecule. In the second phase of the work a tentative theory is proposed which relates the perturbation constants of the four isotopic molecules. This theory, which contains a number of approximations, involves only 21 constants. These were evaluated from a nonlinear least squares analysis and the spectrum was recomputed. The agreement with the observed spectrum is good, but not as good as in the former case. The barrier height V3 was found to decrease upon deuteration and a mechanism is suggested based upon the zero point vibrations of the atoms. The barrier potential is shown to be highly sinusoidal in form with V 6 V 3 = −0.0002 ± 0.0006 .

Vibration‐Hindered Rotation Interactions in Methyl Alcohol. The J=0→1 Transition

The hindered rotation fine structure of the J=0→1, K=0→0 transition which has been observed by Venkateswarlu, Edwards, and Gordy in normal methanol as well as in five additional isotopic species can be understood only qualitatively on the basis of earlier investigations of the theory of hindered rotation in methanol. It has been shown that the frequency separations between the various torsional transitions and the splitting of each of these can be explained quantitatively by including in the theory the effects of the vibration‐hindered rotation interactions during the rotation of the whole molecular framework in space. The effects of the asymmetry of the rigid hindered rotator, the Coriolis interactions, and the centrifugal distortion of the molecule are discussed separately. A frequency formula for the transition is derived which contains essentially only four new rotational constants. Three of these depend solely upon the known structure of the molecule and the elastic force constants and can therefore ...

Rotation spectrum of methyl alcohol

Abstract The rotation spectrum of methanol vapor has been measured from 50 to 457 cm −1 . Combining these data with the work of Borden and Barker provides an accurate map of the spectrum to 625 cm −1 together with some provisional observations between 695 and 860 cm −1 . The primary purpose of the theoretical discussion is to identify the observed lines and subsequently, through combination relations, to establish the rotational energy levels of the molecule. These levels may be labeled by the quantum number n , τ, K , and J . n corresponds roughly to a vibration in the hindering potential field and τ designates the three types of levels resulting from the threefold potential. J gives the total angular momentum and K its component along the molecular symmetry axis. The method of analysis consisted first in calculating the rotational levels using the barrier height and the moments of inertia established through earlier investigations of the microwave spectrum. The intensities of the lines occurring within the region of experimental observation were calculated. The resulting predicted spectrum when compared with the observed spectrum allowed a considerable number of identifications to be made but revealed deviations due to centrifugal force effects. These latter were then calculated and ultimately a very satisfactory fit was obtained. The rotational levels were then determined for n = 0, 1, 2, and 3 and for K = 0 through 10. The accuracy is estimated to be of the order of a few tenths of a wave per centimeter. The small discrepancies between these observed levels and the calculated levels (taking account of centrifugal distortion) are discussed and it is concluded that the hindering potential must be sinusoidal in form with an accuracy of better than one percent.

The Centrifugal Distortion of Axial Molecules

The theory of the semi‐rigid rotator developed by Wilson and Howard has been applied to the axial molecules YX3 and ZYX3. It is found that the change in rotational energy, δW, caused by the centrifugal distortion, can be expressed in terms of the quantum numbers J and K and as a function of the potential constants and the molecular dimensions. The formula is evaluated explicitly for NH3, and ND3, and for the former is, in cm—1: δWJKhC=−0.000625J2(J+1)2+0.000950K2J(J+1) +0.000799J(J+1)−0.000630K4−0.00189K2. The pure rotation lines of NH3 and of ND3 are calculated and compared with the observations of Wright and Randall, and of Barnes. The agreement is very satisfactory. The theory predicts that the rotation lines are multiple. The spacing of this fine structure was too small to be observable in the region mapped by Wright and Randall but should be possible to detect in the case of the higher members of the rotation series.We have also calculated the pure rotation spectrum of PH3 by using Howards approxima...

Reflection and Transmission Interference FiltersPart II. Experimental, Comparison with Theory, Results

Reflection and transmission filters have been constructed by the evaporation process, and their properties have been measured and shown to conform with the theory developed in Part I of this paper. A more extended set of curves of the reflection and transmission coefficients and the phase shift angles of a single metal film are given. From these curves, and from measurements made on the transmission filter, the optical constants of silver films are deduced and shown to be in agreement with other published data. A typical spectrogram of an infra-red reflection filter is also given, showing a minimum reflection coefficient of less than one percent at the odd overtones of the fundamental frequency.

A high-resolution study of the OH-stretch fundamental of methanol

Abstract The OH-stretch fundamental of CH 3 OH has been observed with 0.025 cm −1 resolution between 3430 and 3940 cm −1 and the resulting spectrum deconvoluted using the procedure of P. A. Jansson. Approximately 600 lines have been assigned to a total of 67 P - or R -branch series and some 30 excited state levels have been determined. Of these, 14 belong to the lowest torsional state with n = 0, 13 to n = 1 and 3 to n = 2. A nonlinear least-squares fit to these levels varying the major parameters used by Y. Y. Kwan and D. M. Dennison in their analysis of the normal state produces an rms deviation between observed and calculated levels of 0.51 cm −1 . Variation of all the parameters including those of the smaller Kirtman perturbation terms produces only a slight improvement in the fit. Both analyses yield a barrier height of 411 cm −1 in the excited vibrational state as compared to the normal state value of 373 cm −1 . A number of unexplained anomalies appear in the spectra including large and irregular changes in the coefficient of J 2 + J for different torsion-rotation states.