Notes on the Infra‐Red Spectrum and Molecular Structure of Ozone

The nature of the fine structure of the band at 14.2μ in the absorption spectrum of ozone has been determined with prism and grating spectrometers. These data, together with the fine structure of the 9.57μ band (previously resolved in the solar spectrum) render possible an unambiguous choice between the divergent views currently held with regard to the structure of the ozone molecule. It is concluded that the form of the isoceles triangle is acute, with the apex angle in the neighborhood of 34°.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/69777/2/JCPSA6-14-6-379-1.pd

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 obtained by addition of anharmonic corrections to the spectroscopically observed fundamental frequencies. These corrections were estimated by means of the known anharmonic corrections for methane and the conditions imposed by the Teller product rule. The fundamental frequencies and zeta‐values have been taken directly from the observed band centers and rotational spacings wherever possible. In the cases of resonance, the influence of the couplings were either calculated or estimated and the corresponding unperturbed values for the frequencies and zeta‐values selected. The potential function is determined first in terms of a set of simple symmetry coordinates, and then reexpressed in terms of valence coordinates to permit comparison of the valence force constants of ethane and methane.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/70194/2/JCPSA6-20-2-313-1.pd

Centrifugal Distortion Effects in Methyl Chloride

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/69820/2/JCPSA6-21-7-1293-1.pd

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 in the infinite barrier limit. In the present treatment a transformation is made on the Hamiltonian whereby this complication is avoided and the resulting calculations are greatly simplified.It is found that the spectrum is essentially that of the rigid rotator with the important exception that all the strong lines are split into two components. For the low J transitions specific formulas have been derived for these splittings which are relatively simple functions of the barrier height, the principal moments of inertia, and two additional parameters involving the molecular dimensions and the masses. The barrier height can thus be deduced from the observed splittings without the use of the somewhat cumbersome machinery needed in the general case.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/69966/2/JCPSA6-26-1-31-1.pd

The Potential Functions of the Methyl Halides

The problem of the potential functions of the methyl halides is re‐examined in an attempt to find a function which is both adequate and simple. A valence form of potential was tried which contained four constants: k1, the C☒H elongation; c, the C—X elongation; k2, the deformation of the H☒C☒H angle; and k3, the deformation of the X☒C☒H angle. It was found that this simple valence potential must be modified by the inclusion of a cross product term between the X—C distance and the X☒C☒H angle, thus introducing a fifth constant, k4.The constants k1 and k2 were determined from the methane frequencies (k1=4.88×105 and k2=0.443×105) and were taken to be the same for all the methyl halides. By adjusting the three remaining constants it was possible to predict eight quantities, the six fundamental frequencies and two of the fine structure spacings. The agreement with the observed values was satisfactory, the average deviation being less than 1 percent.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/70083/2/JCPSA6-7-7-522-1.pd

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 be calculated from a knowledge of the vibrational spectrum. Since this latter has never been analyzed in more than a rough way some small adjustments have been made in the indicated values of the elastic constants which are within the limits of uncertainty. This adjustment is made for the normal molecule after which the three rotational constants are calculated for the remaining isotopic species without further adjustment. The fourth constant in the frequency formula describes the dependence of the barrier height upon the normal coordinates and is the only constant which must be determined empirically for each isotopic species. It has thus been possible to predict the 30 observed separations and splittings with the aid of essentially only six empirical constants. The agreement with experiment is remarkably good with one possible exception where the theory predicts for the fully deuterated methanol a very large splitting of the normal state line whereas the line in question is observed to be single. It is not improbable, however, that the large splitting actually exists and that the second component lay too far away to be recognized.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/69972/2/JCPSA6-26-1-48-1.pd

Rotation spectrum of methyl alcohol

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, [tau], K, and J. n corresponds roughly to a vibration in the hindering potential field and [tau] 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.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/32473/1/0000558.pd

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

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 V6/V3 = -0.0002 +/- 0.0006.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/34201/1/0000490.pd

Phycomyces

This monographic review on a fungus is not addressed to mycologists. None of the authors has been trained or has otherwise acquired a general proficiency in mycology. They are motivated by a common interest in the performances of signal handling exhibited by the sense organs of all organisms and by the desire to attack these as yet totally obscure aspects of molecular biology by the study of a microorganism with certain desirable properties. The sporangiophore of the fungus Phycomyces is a gigantic, single-celled, erect, cylindrical, aerial hypha. It is sensitive to at least four distinct stimuli: light, gravity, stretch, and some unknown stimulus by which it avoids solid objects. These stimuli control a common output, the growth rate, producing either temporal changes in growth rate or tropic responses. We are interested in the output because it gives us information about the reception of the various signals. In the absence of external stimuli, the growth rate is controlled by internal signals keeping the network of biochemical processes in balance. The external stimuli interact with the internal signals. We wish to inquire into the early steps of this interaction. For light, for instance, the cell must have a receptor pigment as the first mediator. What kind of a molecule is this pigment? Which organelle contains it? What chemical reaction happens after a light quantum has been absorbed? And how is the information introduced by this primary photochemical event amplified in a controlled manner and processed in the next step? How do a few quanta or a few molecules trigger macroscopic responses? Will we find ourselves confronted with devices wholly distinct from anything now known in biology

Inversion-vibration and inversion-rotation interactions in the ammonia molecule

An attempt has been made to extend the theory of ammonia inversion in order to account for the dependence of the inversion splitting on the full set of vibrational and rotational quantum numbers. The potential energy of ammonia is approximated by a double minimum potential V([zeta]) plus the potential of a system of harmonic oscillators in the remaining five vibrational coordinates. V([zeta]) has been chosen to have the form V([zeta]) = -2F cos ([zeta]/L) + 2G cos (2[zeta]/L) in which [zeta] is an inversion coordinate and L a constant, ([zeta] | [less, double equals] [pi]L). The double minimum wave functions are computed numerically. Inversion-vibration interactions are obtained by developing the parameters F and G, which are regarded as mild functions of the five vibrational coordinates, in a Taylor expansion in the vibrational coordinates. With the exception of the state this potential accounts for the dependence of the inversion splittings on the vibrational quantum numbers of the two doubly degenerate modes [nu]2 and [nu]4 (eleven experimental data are fitted with four empirical interaction constants). However, the potential fails to describe completely the interaction between the inversion coordinate and the remaining nondegenerate vibrational coordinate associated with [nu]1. Since the task of diagonalizing the complete rotation-inversion Hamiltonian is complicated by the presence of several resonances, the rotation-inversion constants B- - B+ and C- - C+ are calculated only from the lowest order vibration-rotation-inversion Hamiltonian. The calculated constants for the pure inversion states n2 = 0, 1, 2, and 3 and the states n2 = 1 in combination with the remaining vibrational modes agree surprisingly well with the experimentally observed values.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/32326/1/0000396.pd