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1 Jun 1960

Volume 32, Issue 6, pp. 1599-1894

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Comparison of n and s as Fall‐Off Parameters in the Slater and Rice‐Ramsperger‐Kassel Classical Theories of Unimolecular Reaction

E. W. Schlag, B. S. Rabinovitch, and F. W. Schneider

J. Chem. Phys. 32, 1599 (1960); http://dx.doi.org/10.1063/1.1730990 (3 pages) | Cited 6 times

Online Publication Date: 29 July 2004

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The 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

Tosinobu Anno and Akira Sadô

J. Chem. Phys. 32, 1602 (1960); http://dx.doi.org/10.1063/1.1730991 (9 pages) | Cited 9 times

Online Publication Date: 29 July 2004

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The absorption spectrum 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 1Au, 1B2u←1Ag transitions perturbed by a 1B2u←1Ag transition, (2) the spectrum is caused by a single 1B1g←1Ag transition being allowed through vibrational‐electronic interaction with the allowed 1B1u←1Ag 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

Tosinobu Anno and Akira Sadô

J. Chem. Phys. 32, 1611 (1960); http://dx.doi.org/10.1063/1.1730992 (9 pages) | Cited 11 times

Online Publication Date: 29 July 2004

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The method used for evaluating the Condon overlap integral associated with any vibronic band of an electronic absorption system of an XY2 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 Au 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

Lawrence C. Krisher and Louis Pierce

J. Chem. Phys. 32, 1619 (1960); http://dx.doi.org/10.1063/1.1730993 (7 pages) | Cited 20 times

Online Publication Date: 29 July 2004

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An 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 Cs symmetry. The method is applied to the determination of silicon coordinates in the molecules CH3SiH2F and CH3SiHF2. 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 CH3SiHF2 the equilibrium conformation (staggered) is also determined.

Rotational Diffusion Constant of a Cylindrical Particle

S. Broersma

J. Chem. Phys. 32, 1626 (1960); http://dx.doi.org/10.1063/1.1730994 (6 pages) | Cited 245 times

Online Publication Date: 29 July 2004

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The 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)/8πηa3ω, where σ=log2a/b we obtain best fit with γ(σ>2)=1.57–7 (1/σ—0.28)2±0.25. 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

S. Broersma

J. Chem. Phys. 32, 1632 (1960); http://dx.doi.org/10.1063/1.1730995 (4 pages) | Cited 102 times

Online Publication Date: 29 July 2004

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The 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±0.25. For a translation lengthwise, with F=4πηav/(σ—γ), the relation γ(σ>2)=1.30–8(1/σ—0.30)2±0.25 holds.

Analysis of the Nuclear Magnetic Resonance Spectrum of a Six‐Spin System of Monofluorobenzene

Shizuo Fujiwara and Hiroshi Shimizu

J. Chem. Phys. 32, 1636 (1960); http://dx.doi.org/10.1063/1.1730996 (7 pages) | Cited 11 times

Online Publication Date: 29 July 2004

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This paper is concerned with the general analysis of a six‐spin system belonging to the point group C2V, 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 absorption spectrum 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

Eugene Helfand and Stuart A. Rice

J. Chem. Phys. 32, 1642 (1960); http://dx.doi.org/10.1063/1.1730997 (3 pages) | Cited 40 times

Online Publication Date: 29 July 2004

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The 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 ensemble distribution function and the solution of the mechanical equations of motion may be written in reduced variables. One finds that η*=ησ2/m☒ϵ☒, κ*=κkϵ☒/m☒σ 2, and D*=Dm☒/ϵ☒σ are universal functions of T*=Tk/ϵ, P*=Pσ3/ϵ, and in the quantum mechanical case ℏ*=ℏ/σm☒ϵ☒.

Thermodynamic Inequalities for Elastic Solids

James C. M. Li and Hsiao S. Kiang

J. Chem. Phys. 32, 1644 (1960); http://dx.doi.org/10.1063/1.1730998 (3 pages) | Cited 1 time

Online Publication Date: 29 July 2004

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A table of all the positive quantities among measurable coefficients is given for anisotropic elastic 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

Tatsuo Miyazawa

J. Chem. Phys. 32, 1647 (1960); http://dx.doi.org/10.1063/1.1730999 (6 pages) | Cited 147 times

Online Publication Date: 29 July 2004

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A 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

S. K. Sinha and A. Mukherji

J. Chem. Phys. 32, 1652 (1960); http://dx.doi.org/10.1063/1.1731000 (5 pages) | Cited 9 times

Online Publication Date: 29 July 2004

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A 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 σp=—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

Joe M. Parks and Robert G. Parr

J. Chem. Phys. 32, 1657 (1960); http://dx.doi.org/10.1063/1.1731001 (25 pages) | Cited 44 times

Online Publication Date: 29 July 2004

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The 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

O. Schnepp and K. Dressler

J. Chem. Phys. 32, 1682 (1960); http://dx.doi.org/10.1063/1.1731002 (5 pages) | Cited 9 times

Online Publication Date: 29 July 2004

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Solid 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 quartz mercury arc were used. The production of the unstable species NH and NH2 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. NH2 is produced by radiation above 1700 A and below 1550 A with comparable quantum efficiency. Warmup experiments show that NH2 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 NH2 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

L. G. Van Uitert and R. R. Soden

J. Chem. Phys. 32, 1687 (1960); http://dx.doi.org/10.1063/1.1731003 (3 pages) | Cited 13 times

Online Publication Date: 29 July 2004

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Spectra resulting from emission from four electronic levels are observed for members of the series Ca1–2xNaxEuxWO4. 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 Eu3+ ions.

Madelung Constant for K2SO4(II)

Robert H. Wood

J. Chem. Phys. 32, 1690 (1960); http://dx.doi.org/10.1063/1.1731004 (3 pages) | Cited 15 times

Online Publication Date: 29 July 2004

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The Madelung constants of NaCl, CsCl, and K2SO4 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 K2SO4 allow the calculation of the Madelung constant as a function of the charge on the oxygen (Mδ=6.922+0.36ϵ).

Relaxation of an Isolated Ensemble of Harmonic Oscillators

Kurt E. Shuler

J. Chem. Phys. 32, 1692 (1960); http://dx.doi.org/10.1063/1.1731005 (6 pages) | Cited 35 times

Online Publication Date: 29 July 2004

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The 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 Boltzmann H 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

George Adler and Walter Reams

J. Chem. Phys. 32, 1698 (1960); http://dx.doi.org/10.1063/1.1731006 (3 pages) | Cited 18 times

Online Publication Date: 29 July 2004

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It 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

S. Alexander

J. Chem. Phys. 32, 1700 (1960); http://dx.doi.org/10.1063/1.1731007 (6 pages) | Cited 18 times

Online Publication Date: 29 July 2004

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The 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

Hiroaki Baba and Satoshi Suzuki

J. Chem. Phys. 32, 1706 (1960); http://dx.doi.org/10.1063/1.1731008 (8 pages) | Cited 5 times

Online Publication Date: 29 July 2004

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A 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

A. E. de Vries and M. F. Laranjeira

J. Chem. Phys. 32, 1714 (1960); http://dx.doi.org/10.1063/1.1731009 (3 pages) | Cited 2 times

Online Publication Date: 29 July 2004

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Experiments 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 (RT value) being of extreme importance.

Experimental Oscillator Strengths of CH and NH

R. G. Bennett and F. W. Dalby

J. Chem. Phys. 32, 1716 (1960); http://dx.doi.org/10.1063/1.1731010 (4 pages) | Cited 43 times

Online Publication Date: 29 July 2004

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The radiative lifetimes of the A 2Δ and B 2Σ states of CH and the A 2II state of NH have been measured to be (5.6±0.6) 10—7, (1.0±0.4) 10—6, and (4.25±0.6) 10—7 sec, respectively. The oscillator strengths of the respective ground‐state transitions were then calculated to be (4.9±0.5) 10—3, (1.2±0.4) 10—3, and (8.0±1.1) 10—3.

Transferability of Urey‐Bradley Force Constants. III. The Vinylidene Halides

James R. Scherer and John Overend

J. Chem. Phys. 32, 1720 (1960); http://dx.doi.org/10.1063/1.1731011 (14 pages) | Cited 13 times

Online Publication Date: 29 July 2004

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Force constants have been calculated by a least‐squares method for vinylidene bromide and vinylidene fluoride using complete deuterium isotopic data and a Urey‐Bradley potential function. The results of this work show that the ``C☒C stretching'' and ``CH2 scissors'' modes are not pure vibrations but exhibit appreciable coupling between C☒C stretching and CH2 bending coordinates. Further, the molecules within the vinylidene‐halide series do not seem to have constant normal coordinates and hence the frequency differences are not entirely associated with changes in the force field. It follows that in molecules of this type, it is dangerous to infer changes in bond strength from observed frequency shifts except with the aid of a complete normal‐coordinate analysis.

Effect of Pressure on Color Centers in Ag+‐Doped Alkali Halides

R. A. Eppler and H. G. Drickamer

J. Chem. Phys. 32, 1734 (1960); http://dx.doi.org/10.1063/1.1731012 (5 pages) | Cited 9 times

Online Publication Date: 29 July 2004

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The effect of pressure on various color centers in silver‐doped alkali halides has been studied. The crystals include NaCl (two concentrations), KCl, and KBr. The resulting shifts are used to confirm the assignments of some peaks, and, in certain cases, to decide among conflicting interpretations.

Method for Calculating Average Molecular Weights and Molecular Weight Distributions of Polymeric Materials from Sedimentation Equilibrium Experiments

Hiroshi Fujita

J. Chem. Phys. 32, 1739 (1960); http://dx.doi.org/10.1063/1.1731013 (4 pages) | Cited 2 times

Online Publication Date: 29 July 2004

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A method is proposed for the determination of average molecular weights and molecular weight distributions of polymeric materials from sedimentation equilibrium experiments in theta solvents. The data required are the refractive index gradients at the center of the ultracentrifuge cell as a function of a parameter λ = (1—vρ0) (r22—r12)ω2/2RT; here v is the partial specific volume of the polymer solute in the given solvent, ρ0 is the density of the solvent, ω is the rotor speed, r1 and r2 are the radial distances from the rotor axis to the meniscus and the bottom of the cell, respectively, T is the absolute temperature, and R is the gas constant. The most important feature of the proposed method is that it allows calculation of the number‐average molecular weight. The desired distribution of molecular weights of a given sample can be obtained by solving an integral equation of the Fredholm type.

Charge Transfer Mechanism of Reaction of Conjugated Molecules

Kenichi Fukui, Keiji Morokuma, Teijiro Yonezawa, and Chikayoshi Nagata

J. Chem. Phys. 32, 1743 (1960); http://dx.doi.org/10.1063/1.1731014 (5 pages) | Cited 1 time

Online Publication Date: 29 July 2004

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Mathematical interrelations are found between the superdelocalizability and the Z value, i.e., two of the reactivity indexes of conjugated molecules. MO theoretical discussions on the mechanism of aromatic substitution are also made.
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