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1 Jun 1956

Volume 24, Issue 6, pp. 1119-1284

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Vibration—Rotation Interaction in Polyatomic Molecules. I. The Zeta Matrices

Janet Hawkins Meal and S. R. Polo

J. Chem. Phys. 24, 1119 (1956); http://dx.doi.org/10.1063/1.1742728 (7 pages) | Cited 94 times

Online Publication Date: 7 October 2004

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Some properties of the zeta matrices which simplify the analytical treatment of vibration‐rotation interaction are given. Methods of obtaining relationships among the zeta elements which depend only on the atomic masses and geometry of the molecule are outlined and some examples are discussed. Symmetry arguments are introduced to simplify the results further.

Vibration—Rotation Interaction in Polyatomic Molecules. II. The Determination of Coriolis Coupling Coefficients

Janet Hawkins Meal and S. R. Polo

J. Chem. Phys. 24, 1126 (1956); http://dx.doi.org/10.1063/1.1742729 (8 pages) | Cited 66 times

Online Publication Date: 7 October 2004

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A general method for the analytical treatment of vibration‐rotation interaction in polyatomic molecules is presented. The method is especially adapted to carry out the calculation of the Coriolis coupling coefficients along with the normal coordinate treatment in terms of any chosen set of internal coordinates. The relations existing among the ζ elements and the potential constants are established in a general and convenient form. Particular attention is given to symmetric top molecules, and the effect of vibration‐rotation interaction on band structure is discussed. Approximate methods for the calculation of zeta values are considered also.

Matrices D—1 and G—1 in the Theory of Molecular Vibrations

S. R. Polo

J. Chem. Phys. 24, 1133 (1956); http://dx.doi.org/10.1063/1.1742730 (6 pages) | Cited 48 times

Online Publication Date: 7 October 2004

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A vector method to determine the elements of the matrices D—1 and G—1, used in the vibrational analysis of polyatomic molecules is presented. Examples are given to illustrate the method.

Rotation‐Vibration Spectra of Deuterated Water Vapor

W. S. Benedict, N. Gailar, and Earle K. Plyler

J. Chem. Phys. 24, 1139 (1956); http://dx.doi.org/10.1063/1.1742731 (27 pages) | Cited 671 times

Online Publication Date: 7 October 2004

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Spectra of heavy water have been obtained under high resolution between 1.25—4.1μ (2400—8000 cm—1). Approximately 4500 lines have been measured, and the majority of them analyzed into ten bands of D2O and nine bands of HDO. The analysis is described in some detail, spectra of all bands are shown and a partial table of lines and a complete table of energy levels are presented. The vibration‐rotation constants are derived and compared with those of H2O.

On the Pi‐Electron Approximation and Its Possible Refinement

Peter G. Lykos and Robert G. Parr

J. Chem. Phys. 24, 1166 (1956); http://dx.doi.org/10.1063/1.1742733 (8 pages) | Cited 129 times

Online Publication Date: 7 October 2004

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See Also: Erratum

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The pi‐electron approximation is defined to be the approximation in which the following two restrictions are imposed upon the total approximate electronic wave functions for some group of molecular states:
(I) The wave function for each state satisfies the sigma‐pi separability conditions: (A) the wave function has the form Ψ = [(Σ) (II)], where (Σ) and (II) are antisymmetrized functions describing the so‐called sigma and pi electrons, respectively, and the outer brackets connote antisymmetrization with respect to sigma‐pi exchange; (B) each of (Σ), (II), and Ψ is normalized to unity; (C) each of (Σ), (II), and Ψ is well‐behaved.
(II) The sigma description is the same for all states.
Imposition of these restrictions is shown to be sufficient to validate the customary procedure in which the pi electrons in a molecule are treated apart from the rest.
A formula is given for the pi‐electron Hamiltonian to be used when the pi‐electron approximation is invoked. Present day pi‐electron theories are examined, and lines for carrying out improved calculations are suggested. An iterative procedure is proposed for treating both sigma and pi electrons wherein first a sigma function is assumed (which defines a ``core'' in the field of which the pi electrons move), then a pi function is computed (which defines a ``peel'' in the field of which the sigma electrons move), then a new sigma function is computed, and so on.
Certain generalizations of the quantum‐mechanical argument are made which give it wider applicability, and several illustrations are drawn from pi‐electron theory and elsewhere.

Temperature Dependence of the Viscosity of Liquids

E. J. Hellund

J. Chem. Phys. 24, 1173 (1956); http://dx.doi.org/10.1063/1.1742734 (2 pages)

Online Publication Date: 7 October 2004

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The consequences of the introduction of long‐range disorder into the theory of the liquid state are examined. Application is made to the analysis of viscosity.

Ionization and Dissociation of Nitrogen Trifluoride by Electron Impact

Robert M. Reese and Vernon H. Dibeler

J. Chem. Phys. 24, 1175 (1956); http://dx.doi.org/10.1063/1.1742735 (3 pages) | Cited 27 times

Online Publication Date: 7 October 2004

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A mass spectrometric study of nitrogen trifluoride provides data on the relative abundances and appearance potentials of the NF3+, NF2+, NF+, N+, F+, F—, and F2— ions. The heat of formation of the NF3 molecule is used to determine the probable processes of formation of the N+ and F+ ions and to calculate the ionization potentials of the NF and NF2 radicals.

Higher Order Rotation‐Vibration Energies of Polyatomic Molecules. I

Mark Goldsmith, Gilbert Amat, and Harald H. Nielsen

J. Chem. Phys. 24, 1178 (1956); http://dx.doi.org/10.1063/1.1742736 (5 pages) | Cited 56 times

Online Publication Date: 7 October 2004

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As a prerequisite for the evaluation of third‐ and fourth‐order perturbation energies of a rotating‐vibrating polyatomic molecule, we derive here an appropriate Schroedinger equation and give a preliminary discussion of a useful contact transformation of the Hamiltonian.

9.6‐Micron Band of Telluric Ozone and Its Rotational Analysis

L. D. Kaplan, M. V. Migeotte, and L. Neven

J. Chem. Phys. 24, 1183 (1956); http://dx.doi.org/10.1063/1.1742737 (4 pages) | Cited 6 times

Online Publication Date: 7 October 2004

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The 9.6‐micron band of atmospheric ozone has been investigated by means of high resolution measurements of the solar spectrum from the Jungfraujoch in Switzerland. A rotational analysis confirms its assignment as the v3 fundamental and results in the following values for the vibrational frequency and rotational constants:
math
The decrease of all three rotational constants relative to the ground‐state values suggests an appreciable Coriolis interaction with the v1 fundamental.

Infrared Absorption Anisotropy of Crystalline Iodoform

R. M. Hexter and H. Cheung

J. Chem. Phys. 24, 1186 (1956); http://dx.doi.org/10.1063/1.1742738 (10 pages) | Cited 9 times

Online Publication Date: 7 October 2004

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The polarized infrared spectrum of crystalline iodoform has been obtained using single crystals of thicknesses from 50 to 200 microns. Spectra were recorded with the crystals oriented with respect to the electric vector by an x‐ray diffraction type goniometer, and the anisotropy of the spectrum was studied carefully as a function of angle of orientation.
A complete assignment of all fundamentals was possible, including at least two of the lattice frequencies of the crystal. The anisotropic behavior of v1, the C☒H stretching fundamental, is such that it is possible to state that Pimentel's ``oriented gas model'' holds within well‐defined limits. It is demonstrated that a much better procedure of locating transition moment directions in crystals than the use of ``dichroic ratios'' is the complete goniometric study of the absorption anisotropy. Finally the ``threefold degenerate'' first overtone of v4, the C☒H bending mode, was split, and the intensity ratio of its members is reported.

Kinetics of Capillary Shear Degradation in Concentrated Polymer Solutions

A. B. Bestul

J. Chem. Phys. 24, 1196 (1956); http://dx.doi.org/10.1063/1.1742739 (6 pages) | Cited 13 times

Online Publication Date: 7 October 2004

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Intrinsic viscosities at successive stages of the process have been used to obtain the rates of mechanical shear degradation produced in concentrated solutions of polyisobutenes in cetane by capillary flow at several high rates of shear. Rates of degradation were obtained for several shearing temperatures, polymer concentrations, and initial molecular weights. Rate constants K are calculated on the basis that the process is a first‐order reaction with respect to the polymer molecular bonds. K is treated as an inverse exponential function of the reciprocal of the rate of shear energy application J. Plots of logK versus 1/J for all shearing temperatures and polymer concentrations reported can be represented by a single straight line. The behavior of these plots with changing temperature supports the idea that the degradation process is a predominately mechanically, rather than thermally, activated reaction. Their insensitivity to polymer concentration supports the assumption that the degradation reaction is of first order. The rate of variation of K with J decreases with increasing initial molecular weight. This fact indicates that as the initial molecular weight increases the polymer molecular entanglements become increasingly effective in localizing mechanically applied shearing energy into the polymer molecular bonds as temporarily stored potential energy, as would be expected.

Elastic and Inelastic Scattering of Low‐Velocity H— Ions in Hydrogen

E. E. Muschlitz, T. L. Bailey, and J. H. Simons

J. Chem. Phys. 24, 1202 (1956); http://dx.doi.org/10.1063/1.1742740 (8 pages) | Cited 23 times

Online Publication Date: 7 October 2004

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An improved apparatus for the production of beams of negative ions and the measurement of the elastic and inelastic scattering of negative ions in gases at low pressures in briefly described. The measured cross‐sections are given for the scattering of 4—400 ev H— ions in hydrogen. In the range 4—40 ev (1.1—1.8 A) the interaction potential derived from the elastic scattering is V (ev) = —4.64×10—32/r4 (r in cm) which is close to the theoretical polarization interaction. The inelastic scattering is presumed to be due to electron detachment. The inelastic cross section increases from 1 cm—1 at 7 ev to 8.7 cm—1 at 395 ev. Above 75 ev the measured elastic cross section increases with increasing ion energy. This is attributed to the appearance of inelastic collisions which result in electronic excitation of the hydrogen molecules.

Evaluation of Collision Integrals Occurring in Higher Approximations to Diffusion Coefficients

S. C. Saxena

J. Chem. Phys. 24, 1209 (1956); http://dx.doi.org/10.1063/1.1742741 (2 pages) | Cited 4 times

Online Publication Date: 7 October 2004

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Several Chapman and Cowling Collision integrals for the Lennard‐Jones 12:6 model have been evaluated over an extensive range of temperatures and utilized to calculate the second approximation to the thermal diffusion ratio for the case of argon‐helium gas pair.

Spectra and Quantum States of the Europic Ion in Crystals. I. Absorption Spectrum of Anhydrous Europic Chloride

Edward V. Sayre and Simon Freed

J. Chem. Phys. 24, 1211 (1956); http://dx.doi.org/10.1063/1.1742742 (2 pages) | Cited 17 times

Online Publication Date: 7 October 2004

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Anhydrous europic chloride and single crystals of europic chloride dissolved in a preponderant proportion of isomorphous lanthanum chloride could be prepared so that they were sufficiently free of europous chloride to permit the study of their absorption spectra down to 3900 A. The crystal structure of these preparations was proved to be UCl3 type through the use of a trace of praseodymium chloride as an internal indicator. Because this structure is so well substantiated and is free of the ambiguity inherent in the structure of hydrated salts, the spectrum of these crystals provides a secure basis for resolving the conflicting interpretations of earlier spectrum analyses. The polarized spectra indicate that lines in the yellow, green, and blue visible regions arise from upper states with J values of 0, 1, and 2 as proposed by Joos and Hellwege rather than J's of 0, 2, and 3 as proposed by Gobrecht.

Spectra and Quantum States of the Europic Ion in Crystals. II. Fluorescence and Absorption Spectra of Single Crystals of Europic Ethylsulfate Nonahydrate

Edward V. Sayre and Simon Freed

J. Chem. Phys. 24, 1213 (1956); http://dx.doi.org/10.1063/1.1742743 (7 pages) | Cited 42 times

Online Publication Date: 7 October 2004

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From the polarization properties of the fluorescence spectrum of single crystals of europic ethylsulfate nonahydrate it was possible to determine the multipole character of transitions, the energies and quantum nature of the seven levels of the ground state multiplet of the europic ion, and the group character of the sublevels into which these states are split by the crystal field. Such an analysis was made of all pure, uncoupled electronic transitions in the fluorescence spectrum. The analysis revealed that the rare earth ion is predominantly perturbed by a field of D3h symmetry, arising from the water molecules of hydration immediately surrounding it. Upon this field is superimposed a weaker one of lower symmetry, C3h, arising from the lattice as a whole. All transitions involving a change of J of one appeared as magnetic dipole radiation. All others appeared as forced electric dipole transitions, including one which would have been fully allowed as a magnetic dipole transition.
A similar analysis of the absorption spectrum in the near ultraviolet was only partially successful because of the superposition of the split levels of some of the upper states. It was in accord with the analysis of the fluorescence spectrum and from it was determined the multipole nature of the transitions and the quantum nature of some of the more isolated upper states.

Infrared Absorption Spectra of Complex Cobalt Compounds

Douglas G. Hill and Alexander F. Rosenberg

J. Chem. Phys. 24, 1219 (1956); http://dx.doi.org/10.1063/1.1742744 (13 pages) | Cited 9 times

Online Publication Date: 7 October 2004

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The infrared absorption spectra of finely powdered complex cobalt salts were obtained in the 2 to 15 micron region. Complexed ammonia shows four absorption bands, at approximately 3000, 1600, 1350, and 850 wave numbers. A possible assignment of three of these to N☒H vibrations and the lowest to a rocking vibration, as proposed by Mizushima, is discussed. In the trisethylenediamine and hexanitrito complexes a frequency similar to the rocking vibration persists, but other frequencies characteristic of the particular ligands appear instead of N☒H bands. A shift in the absorption maxima as the anions are changed shows that the fields of the anions are of importance. Fine structure observed in some of the strong absorption bands might be combinations with lattice vibrations.
A comparison of the absorption spectra of certain hexammines obtained from deposited pure powders and from pressed KBr plates shows differences in details, which may be interpreted as indicating dissociation of the cobalt salt in the pressed KBr plate and an essentially liquid structure for the latter.
The series of complex cobalt compounds whose infrared spectra were reported recently [D. G. Hill and A. F. Rosenberg, J. Chem. Phys. 22, 148 (1954)] has been extended to include a number of hexammines with various anions and several similar series of pentammines. A comparison has been made with a series of hexanitrito cobalt compounds and trisethylenediamine salts. The spectra of some of the compounds mentioned earlier have been remeasured and the range has been extended to the whole spectrum obtainable with a rocksalt prism. This has demonstrated greater complexity in the spectra than we had first imagined, but has led to a better understanding of them. Special care has been taken to insure the purity of all salts used.

Vibrational Spectra of Fluorinated Aromatics. XII. m‐Fluorochlorobenzene

F. W. Harris, N. A. Narasimham, and J. Rud Nielsen

J. Chem. Phys. 24, 1232 (1956); http://dx.doi.org/10.1063/1.1742745 (4 pages) | Cited 1 time

Online Publication Date: 7 October 2004

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The infrared absorption spectra of gaseous and liquid m‐fluorochlorobenzene have been obtained in the region 2—38μ with NaCl and CsBr prisms. The Raman spectrum of the liquid has been photographed with a 3‐prism glass spectrograph of linear dispersion 15 A/mm at 4358 A. A complete assignment of the fundamental vibrational frequencies is given, and the spectra are interpreted in detail.

Crystal Structure of Gadolinium Orthoferrite, GdFeO3

S. Geller

J. Chem. Phys. 24, 1236 (1956); http://dx.doi.org/10.1063/1.1742746 (4 pages) | Cited 193 times

Online Publication Date: 7 October 2004

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The crystal structure of gadolinium orthoferrite, GdFeO3, has been determined from single‐crystal x‐ray data. There are four GdFeO3 distorted perovskite units in the orthorhombic cell with lattice constants a=5.346, b=5.616, c=7.668, all ±0.004 A. The structure is solved on the basis that the most probable space group is D2h(16)— Pbnm. However, although the atomic coordinates lead to very good agreement between calculated and observed reflection amplitudes, there are at least very slight deviations from the centrosymmetric space group because the iron sublattices are imperfectly antiferromagnetic.

Magnetic Properties of a Gadolinium Orthoferrite, GdFeO3, Crystal

M. A. Gilleo

J. Chem. Phys. 24, 1239 (1956); http://dx.doi.org/10.1063/1.1742747 (5 pages) | Cited 22 times

Online Publication Date: 7 October 2004

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Gadolinium orthoferrite, GdFeO3, in single‐crystal form exhibits magnetization between temperatures of 78 and 295°K which consists of a field independent part σ0 and a field dependent part χH for fields above 6000 oersteds. The parasitic ferromagnetization σ0 amounts to about 1% of the σ(Fe) available and may be attributed to imperfectly compensated antiferromagnetism of the Fe3+ ion sublattice. The susceptibility χ appears to be made up of a paramagnetic contribution from the Gd3+ ion sublattice and a contribution from the antiferromagnetic Fe3+ ion sublattice influenced by interaction between the two sublattices. The anisotropy of σ0 and χ changes with temperature. The maximum σ0 and minimum χ do not coincide as they would if both took the direction of the antiferromagnetic axis of the Fe3+ ion sublattice.

``Donor‐Acceptor'' Complex Formation by High Polymers

D. F. Evans

J. Chem. Phys. 24, 1244 (1956); http://dx.doi.org/10.1063/1.1742748 (3 pages) | Cited 5 times

Online Publication Date: 7 October 2004

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The interaction of iodine with polystyrene and rubber has been studied spectrophotometrically. Characteristic ``charge‐transfer'' bands were observed, and interpreted quantitatively in terms of complex formation. The equilibrium constants and ``molar'' extinction coefficients of the polymer‐iodine complexes are similar to those for the iodine complexes of analogous simple aromatic and olefinic molecules. Approximately half of the iodine in solid solution in polystyrene seems to be involved in complex formation. Polystyrene is soluble in strong alcoholic solutions of silver perchlorate, and the absorption spectrum of the solution indicates complex formation.

Infrared Spectra and Molecular Constants of Gaseous Tritium Bromide and Tritium Chloride

Llewellyn H. Jones and Eugene S. Robinson

J. Chem. Phys. 24, 1246 (1956); http://dx.doi.org/10.1063/1.1742749 (4 pages) | Cited 2 times

Online Publication Date: 7 October 2004

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The infrared spectra of TCl35, TCl37, and TBr79,81 have been observed using a CaF2 prism. Throughout this paper the notation TBr79,81 indicates the natural isotopic mixture of Br79 and Br81, and lack of spectral resolution of the two isotopes. A least squares treatment of the data yielded the following molecular constants for TBr79,81, TCl35, and TCl37, respectively:
math

Determination of Accurate Water Vapor Calibration Points for Prism Spectrometers in the Region 1330—2100 cm—1

Llewellyn H. Jones

J. Chem. Phys. 24, 1250 (1956); http://dx.doi.org/10.1063/1.1742750 (3 pages) | Cited 4 times

Online Publication Date: 7 October 2004

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The spectrum of water vapor in the region 1330—2100 cm—1 has been observed with a CaF2 prism in a Perkin‐Elmer double‐pass spectrometer. A Friedel‐McKinney equation [D. S. McKinney and R. A. Friedel, J. Opt. Soc. Am. 38, 222 (1948)] which was successful in determining frequencies for TBr and TCl was used to determine the water vapor frequencies. Many of these water vapor frequencies are presented as the best available calibration points in the 1300—2100 cm—1 region, accurate to ±0.3 cm—1.
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Doublet States of Benzyl Radical

Yuji Mori

J. Chem. Phys. 24, 1253 (1956); http://dx.doi.org/10.1063/1.1742751 (1 page) | Cited 2 times

Online Publication Date: 7 October 2004

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Abstract Unavailable

Hydration Energy of Ions

Chimao Komatsu and Jun‐ichi Shimokawa

J. Chem. Phys. 24, 1253 (1956); http://dx.doi.org/10.1063/1.1742752 (2 pages)

Online Publication Date: 7 October 2004

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Abstract Unavailable

Radiation Chemistry of n‐Hexane and Cyclohexane Liquids

H. A. Dewhurst

J. Chem. Phys. 24, 1254 (1956); http://dx.doi.org/10.1063/1.1742753 (2 pages) | Cited 10 times

Online Publication Date: 7 October 2004

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Abstract Unavailable
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