Volume 32, Issue 6, 01 June 1960

Comparison of n and s as Fall‐Off Parameters in the Slater and Rice‐Ramsperger‐Kassel Classical Theories of Unimolecular Reaction
View Description Hide DescriptionThe classical Rice‐Ramsperger‐Kassel integral for the unimolecular rate constant has been evaluated over a range of s values at the several values of b = 32, 36, 40 and 44. Equivalent values of s and of the Slater theory parameter n have been found by comparison of the shape of the fall‐off behavior predicted by both theories in the upper region of fall‐off. The equivalence diverges from the limiting relation n = 2s—1 even below n = 8. The findings are discussed briefly.

Electronic States of p‐Benzoquinone. V. Vibrational Analysis of the Vapor Absorption Spectrum around 4500‐A Region
View Description Hide DescriptionThe absorptionspectrum of p‐benzoquinone vapor in the region between 4080 and 5100 A was photographed and measured. Although the theoretical calculation as well as the experimental crystal spectrum indicate that two singlet‐singlet electronic transitions exist in this region, prominent vibrational structure of the vapor spectrum can be interpreted as caused by a single forbidden electronic transition. If we assume that the hydrogen vibrations are not effective as perturbing vibrations which make the forbidden electronic transitions allowed through the vibrational‐electronic interaction, this fact suggests the following two sets of assignments for the symmetries of the forbidden transition and the perturbing allowed transition: (1) the spectrum is a superposition of ^{1} A_{u} , ^{1} B _{2u }←^{1} A_{g} transitions perturbed by a ^{1} B _{2u }←^{1} A_{g} transition, (2) the spectrum is caused by a single ^{1} B _{1g }←^{1} A_{g} transition being allowed through vibrational‐electronic interaction with the allowed ^{1} B _{1u }←^{1} A_{g} transition. Vibrational structure alone cannot exclude the second possibility, but a discussion supporting the first assignment is given. This assignment (1) is in agreement with the theoretical calculation of the energy levels. Most prominent bands are assigned to particular vibronic transitions. Fundamental frequencies in the excited electronic state 436, 796, 1109, and 1220 cm^{—1} are obtained corresponding probably to the ground‐state values of 444, 770, 1144, and 1667 cm^{—1}.

Electronic States of p‐Benzoquinone. VI. Molecular Geometry in the Excited Electronic State of the 4500‐A Absorption System as Derived from the Franck‐Condon Principle
View Description Hide DescriptionThe method used for evaluating the Condon overlap integral associated with any vibronic band of an electronic absorption system of an XY_{2} molecule, as developed by J. B. Coon and his co‐workers, is applied to more complex molecules. Thus, some information about the geometry of the excited electronic state of a complex molecule may be determined if the geometry in the ground state, the intensities of vibronic bands of the associated electronic absorption system, and normal coordinates and frequencies in both electronic states are known. The method is applied to the 4500‐A absorption system of p‐benzoquinone. Since the normal coordinate treatment for this molecule is only qualitatively valid, especially in its excited state, the results are expected to be more or less qualitative. If we take the resulting change of bond angles into account, the ring‐bending frequency of species A_{u} in the excited electronic state is calculated to be 438 cm^{—1} by the method described in Part III of this series [T. Anno and A. Sadô, Bull. Chem. Soc. Japan 31, 728 (1958)].

Second Differences of Moments of Inertia in Structural Calculations: Application to Methyl‐Fluorosilane Molecules
View Description Hide DescriptionAn extension and application of the method recently proposed by Pierce for the location of ``near‐axis atoms'' from spectroscopically determined moments of inertia is made. Equations are derived which are required for the application of the method to asymmetric top molecules with C_{s} symmetry. The method is applied to the determination of silicon coordinates in the molecules CH_{3}SiH_{2}F and CH_{3}SiHF_{2}. The experimental results are combined with results of previous microwave investigations of these molecules in order to determine their structures. Addition of each fluorine atom lowers the SiC distance. The SiF distance is lowered on adding the second fluorine. In the case of CH_{3}SiHF_{2} the equilibrium conformation (staggered) is also determined.

Rotational Diffusion Constant of a Cylindrical Particle
View Description Hide DescriptionThe torque constant of a closed cylinder rotating in a viscous medium has been calculated for length (2a) over width (2b) ratios larger than 3.5 to within a first order in b/a. The analysis demonstrates how the contributions to the viscous dissipation tend to be underestimated in hydrodynamic considerations so that the geometrical values deduced from them come out too high. Experimental results for the torque on cylindrical rods and ellipsoids for a/b values from 3.5 to 30 are close to the theoretical results. For a/b>10 the difference is about 10%; for shorter molecules 20%. With the rotational diffusion constant given by 3kT (σ—γ)/8πηa ^{3}ω, where σ=log2a/b we obtain best fit with γ(σ>2)=1.57–7 (1/σ—0.28)^{2}±0.2^{5}. Experimental data for the rotational diffusion constant of a cylindrical virus (a/b=20) in water, obtained by O'Konski and Haltner agree with this result within 10%. The length of the protein fits within 3%.

Viscous Force Constant for a Closed Cylinder
View Description Hide DescriptionThe viscous force constant of a moving cylinder closed at the ends has been calculated including first‐order effects in width (2b)/length (2a). Experimental results, obtained for macroscopic models, are in essential agreement with this. For a/b>20 the discrepancy is about 8%, for shorter cylinders near 20%. With the force on a cylinder moving sideways given by F=8πηav/(σ—γ), where σ=log2a/b, it is found that γ(σ>2)=0.35–4(1/σ—0.43)^{2}±0.2^{5}. For a translation lengthwise, with F=4πηav/(σ—γ), the relation γ(σ>2)=1.30–8(1/σ—0.30)^{2}±0.2^{5} holds.

Analysis of the Nuclear Magnetic Resonance Spectrum of a Six‐Spin System of Monofluorobenzene
View Description Hide DescriptionThis paper is concerned with the general analysis of a six‐spin system belonging to the point group C _{2V }, using monofluorobenzene as an example. The apparatus used for the NMR measurements is the one constructed in this laboratory, operating at 27.030 Mc. The absorption lines calculated suggest the doublet structure of the spectrum, which is consistent with the observed spectrum. It was confirmed that this doublet structure is due to the spin‐spin couplings of the ring protons with fluorine. More precise comparison of the calculated results with the observed spectrum was made by integrating the intensities of the lines having a suitable line shape and width. It was noted that this procedure for constructing the absorptionspectrum from the calculated lines is useful in the discussion of the power of resolution of the apparatus and the type of line shape.

Principle of Corresponding States for Transport Properties
View Description Hide DescriptionThe principle of corresponding states can be demonstrated by use of the autocorrelation function expressions for the transport properties and the assumption that the intermolecular potential has the form u=εu ^{*}(r/σ). The result follows from the fact that both the canonical ensembledistribution function and the solution of the mechanical equations of motion may be written in reduced variables. One finds that η^{*}=ησ^{2}/m ^{½}ε^{½}, κ^{*}=κkε^{½}/m ^{½}σ^{ 2}, and D ^{*}=Dm ^{½}/ε^{½}σ are universal functions of T ^{*}=Tk/ε, P ^{*}=Pσ^{3}/ε, and in the quantum mechanical case ℏ ^{*}=ℏ/σm ^{½}ε^{½}.

Thermodynamic Inequalities for Elastic Solids
View Description Hide DescriptionA table of all the positive quantities among measurable coefficients is given for anisotropicelastic solids under the variation of only temperature and stress. Examples of inequality formulation are presented. Upper or lower limits containing only the Grüneisen's parameter and heat capacities are derived for adiabatic and isothermal compressibilities, thermal expansion, and thermal stress.

Perturbation Treatment of the Characteristic Vibrations of Polypeptide Chains in Various Configurations
View Description Hide DescriptionA perturbation treatment has been made of localized group vibrations of helical polymer chains. The amide I and II frequencies were derived in terms of adjacent group interactions as well as interchain and intrachain hydrogen bonding interactions. Frequency shifts caused by these interactions depend upon the configuration of polypeptide chains and also upon the chain packing in the crystalline region. Each characteristic vibration of the amide group gives rise to parallel and perpendicular bands. The parallel bands of the α helix of poly‐γ‐benzyl‐L‐glutamate were observed at 1650 cm^{—1} (amide I) and 1516 cm^{—1} (amide II) whereas the perpendicular bands were observed at 1652 cm^{—1} (amide I) and 1546 cm^{—1} (amide II). Both the parallel‐chain and antiparallel‐chain pleated sheets exhibit the perpendicular amide I band at ca 1630 cm^{—1}. A characteristic band of β configurations at ca 1690 cm^{—1} was assigned to the parallel amide I band of the antiparallel‐chain pleated sheet.

Nuclear Magnetic Shielding in Molecules: Hydrogen Molecule
View Description Hide DescriptionA method for calculating the nuclear magnetic shielding in molecules has been developed using valencebond or LCAO type molecular orbitals. The perturbation of the molecular wave function due to a steady magnetic field is derived by solving the first‐order perturbation equation. The method has been applied to the calculation of proton shielding in hydrogen molecule with the Wang function. The value of σ^{ p }=—0.55× 10^{—5} is in good agreement with the value of —0.56×10^{—5} derived by Ramsey from the experimental value of the spin‐rotational coupling constant in hydrogen molecule.

Theory of Electronic Excitation and Reorganization in the Formaldehyde Molecule
View Description Hide DescriptionThe use of a previously described iterative method of separated electron pairs is demonstrated by calculations on the formaldehyde molecule. Investigation is made, for example, of detailed changes in the polarity of sigma bonding electron wave functions in this molecule when a pi or lone‐pair electron is excited or ionized. The molecule is treated as a six‐electron problem (four electrons in the C=O bond plus two lone‐pair electrons on O); matrix elements involving the ``core'' are obtained by fitting experimental data. The use of Pariser‐type one‐center repulsion integrals is tested in conjunction with various sets of two‐center repulsion integrals. Although one combination gives reasonable results, none of the combinations is found to be entirely satisfactory, and a procedure is outlined from which could be obtained one‐center integrals approximately incorporating Arai‐Hurley type corrections. It is demonstrated (with reservations) that the constant sigma structure assumption, usually made in calculations of pi electron excitations and ionizations, is not always good with regard to wave functions, but that it may lead to only small errors in calculated energies.

Photolysis of Ammonia in a Solid Matrix at Low Temperatures
View Description Hide DescriptionSolid deposits of argon containing 0.3 mole % ammonia were irradiated at 4.2°K with light of wavelengths shorter than 2000 A. The emission of a hydrogen discharge with a LiF window and of a thin‐walled quartzmercury arc were used. The production of the unstable species NH and NH_{2} was observed by means of electronic absorption spectroscopy. Experiments using filters led to the conclusion that NH is produced by irradiation with light of wavelengths shorter than 1550 A. NH_{2} is produced by radiation above 1700 A and below 1550 A with comparable quantum efficiency. Warmup experiments show that NH_{2} disappears close to 20°K whereas NH is stable up to at least 36°K. Photolysis at 20°K is approximately five times less efficient than at 4.2°K. On certain assumptions a molar absorption coefficient of 40 000 is estimated for both NH and NH_{2} and the f values of the observed transitions of these molecules are estimated to be of the order of 10^{—3}.

Multiple Emission Spectra of Trivalent Europium in the Scheelite Structure
View Description Hide DescriptionSpectra resulting from emission from four electronic levels are observed for members of the series Ca_{1–2x }Na_{ x }Eu_{ x }WO_{4}. Their relative intensities are concentration dependent. Successively lower lying emission levels are quenched by what appear to be exchange interactions resulting from coupling between two or more neighboring Eu^{3+} ions.

Madelung Constant for K_{2}SO_{4}(II)
View Description Hide DescriptionThe Madelung constants of NaCl, CsCl, and K_{2}SO_{4} have been calculated with the aid of a digital computer.
The method of summing over neutral shells of atoms with each shell being composed of unit cells is used. This method allows the presence of surface dipole moments (de Boer effect) to be ignored. The results for K_{2}SO_{4} allow the calculation of the Madelung constant as a function of the charge on the oxygen (M _{δ}=6.922+0.36ε).

Relaxation of an Isolated Ensemble of Harmonic Oscillators
View Description Hide DescriptionThe collisional relaxation of an isolated ensemble of harmonic oscillators (at constant volume and energy) from initial nonequilibrium distributions is discussed in this paper. The ``transport equation'' for the relaxation process is derived and it is shown that it can be linearized even though the relaxation takes place via binary oscillator collisions. The final, stationary distribution is found to be a Boltzmann one with a temperature uniquely defined by the mean energy of the ensemble. The BoltzmannH function is obtained for this system of relaxing oscillators and it is shown that dH/dt<0 for all t. The time rate of change of the mean‐square deviation of the energy during the relaxation process is computed and is shown to be closely related to the time variation of the mean energy in the relaxation of an ensemble of harmonic oscillators in contact with a thermal reservoir.

Heterogeneous Nature of Reaction in Radiation‐Induced Solid‐State Polymerization of Acrylamide
View Description Hide DescriptionIt has been suggested that the radiation‐induced solid‐state polymerization of acrylamide is a heterogeneous reaction, that is, it goes by a two‐phase mechanism [G. Adler, J. Chem. Phys. 31, 848 (1959) and B. Baysal, G. Adler, D. Ballantine, and P. Colombo, J. Polymer Sci. (to be published)]. According to this concept, the reaction procedes at definite sites within the crystal. After the first few reaction steps, it forms regions of pure or nearly pure polymer imbedded in pure monomer. Further reaction would take place at the interface between the two. The polymer and monomer regions would remain segregated until the crystal is completely polymerized. It has been shown previously that the reaction can take place without the crystal breaking up. The alternative to this scheme seems to be that the reaction takes place within the crystal lattice and is directed by it. This requires a more homogeneous reaction mechanism. It seems feasible, in principle to distinguish between the two mechanisms by x‐ray diffraction. A single crystal technique that allows us to look at all the reflections simultaneously appeared to be most promising. It was therefore decided to run a series of rotation diagrams on a crystal in various stages of polymerization.

Relative Signs of Spin‐Spin Interactions in Nuclear Magnetic Resonance. II
View Description Hide DescriptionThe spectrum of the allyl group in allyl amine is discussed in detail. The interpretation of the spectra of 1‐butene and 3,3‐dimethyl‐1‐butene are also discussed. It is shown how the chemical shifts, spin‐spin interactions, and in particular the relative signs of the latter can be determined by numerical methods.
In all three molecules all spin‐spin interactions among the vinyl protons have the same sign. One of the three vinyl‐methylene interactions is found to have a different sign than the other two. This interaction has the same sign (and approximately the same magnitude) as the methyl‐methylene interaction in 1‐butene.

Electronic Structure and Spectrum of Acetanilide
View Description Hide DescriptionA molecular orbital calculation has been made for the π electronic structure of acetanilide and related compounds. The simple LCAO procedure, on which the calculation is based, was somewhat modified to allow for electron repulsion. The electronic behaviors of the acetanilide molecule are examined from the viewpoint of the interaction of the phenyl and acetyl groups through the nitrogen atom. From the calculated excitation energies,oscillator strengths, and charge distributions, the features of the observed ultraviolet absorption and other electronic phenomena can be satisfactorily explained. It is shown that the changes of the longer‐wavelength bands in passing from aniline to acetanilide may be interpreted in terms of two electronic effects: (1) a decrease in the tendency of the nonbonding electrons at the nitrogen atom to migrate into the benzene ring; (2) an extension of conjugation. The electronic properties in the ground state are shown to be explicable by taking account of the former effect.

Thermal Diffusion of Ternary Mixtures
View Description Hide DescriptionExperiments have been performed on ternary mixtures, consisting of two isotopes and a nonisotopic compound. It is found that the influence of the third compound on the separation of the isotopes cannot always be foreseen, the hardness (R_{T} value) being of extreme importance.