Volume 21, Issue 3, 01 March 1953

Infrared and Raman Spectra of Fluorinated Ethanes. V. The Series CF_{3}CF_{3}, CF_{3}CF_{2}Cl, CF_{3}CFCl_{2}, and CF_{3}CCl_{3}
View Description Hide DescriptionThe infrared spectra of CF_{3}CF_{2}Cl, CF_{3}CFCl_{2}, and CF_{3}CCl_{3} vapors have been obtained in the region from 2 to 38μ, and the spectra of liquid CF_{3}CF_{2}Cl and CF_{3}CFCl_{2} in the region from 2 to 22μ, with the aid of LiF, NaCl, KBr, and KRS−5 prisms. The Raman spectra of all three compounds in the liquid state, and of gaseous CF_{3}CF_{2}Cl, were studied with a three‐prism glass spectrograph of linear dispersion 15A/mm at 4358A. Depolarization ratios were determined for most of the Raman bands.
All fundamental vibration frequencies except the lowest (torsional) have been assigned for each molecule, and the observed spectra have been interpreted in detail.

On the Interaction of Closed Shells
View Description Hide DescriptionIn calculating repulsive forces between closed shells, two essentially different methods have been used. It is shown in this paper that they should not be expected to give equal numerical results, and attention is called to some finer methodological points in the theory of exchange forces. Tables I—III give numerical results for the interaction of neutral He atoms.

The Emission Spectrum of OH from 1.4 to 1.7 μ
View Description Hide DescriptionThe first overtone region of OH has been measured in emission from an oxyacetylene flame in the region of 1.6μ. The rotational structure in the P branch of the 2→0 band, from K=4 through K=19, of the 3→1 band, from K=4 through K=15, and of the 4→2 band, from K=4 through K=10, has been identified. For each K value there are four lines. These are resolved for values of K>7. From the intensities of the lines, a vibration‐rotation temperature has been determined. For the mixture of gases burned in this work with small flames, it was found that the ``temperature'' was 2600±100°K.

On the Existence of a Hidden Transition in Biphenyl
View Description Hide DescriptionThe 2500A transition of biphenyl is interpreted as a superposition of a strong and a weak transition corresponding to the 2100A and 2600A transitions of benzene. Evidence for the location of the weak transition near 2700A is given. The spectra of the m‐ and p‐polyphenyls are interpreted similarly to the biphenyl spectrum. Bending has about the same effect on the intensity and the position of the first strong transition of polyphenyls with m‐ and p‐structure as it has on the corresponding transition of cata‐condensed hydrocarbons.

The Infrared Spectra of Tetranitromethane
View Description Hide DescriptionCooling curve investigations show that the transition between the two crystalline forms of tetranitromethane occurs at −99.8°C and its character suggests an order‐disorder transformation. The infrared spectra of tetranitromethane were obtained at 25°C (vapor), 18°C (liquid), −40°C (solid I), −88°C (solid I), −104°C (solid II) and −126°C (solid II). The spectra of the vapor are best interpreted by a molecule with symmetry whereas reported Raman spectra indicate symmetry in the liquid. Satisfactory agreement between these and the x‐ray diffraction data require molecules of both symmetries. A complete lack of selection rules was observed in the spectra throughout the solid range.

Theoretical Considerations Concerning Hammett's Equation. IV. Calculation of ρ‐Values
View Description Hide DescriptionThe assumption is made that the effect of a meta or para substituent X on the reactivity of a reacting center Y in a compound [Complex chemical formula] depends only on the electron density change induced by the substituent in the atom at which Y is attached to R. Using this assumption relative values of Hammett's reaction constant (ρ) are calculated for a given reaction in several series of compounds having the above formula. The calculations require the computation of the electron density changes induced by substituents in the atom at which Y is attached to R. The computations are carried out by the semiempirical LCAO MO method for several cases where R and the benzene ring form part of a single conjugated system. The resulting relative ρ‐values are compared with experimental data. Reasonable agreement is found.

The Entropy and Low Temperature Heat Capacity of Neptunium Dioxide
View Description Hide DescriptionThe heat capacity of a two‐gram sample of neptunium dioxide was determined from 10 to 315°K in an adiabatic calorimeter. At 298.16°K the molal entropy and enthalpy calculated from the heat capacity data are 19.19±0.1 cal deg^{−1} and 2770±15 cal, respectively. A pronounced hump was found in the heat capacity curve of neptunium dioxide at 25.3°K similar to that found by Jones, Gordon, and Long in uranium dioxide at 28.7°K. This anomaly in the heat capacity is suggestive of a cooperative phenomenon and is attributed to the incidence of antiferromagnetism below the temperature of the maximum in the heat capacity. A calorimeter for gram scale samples and a modification of the cryostat design of Ruehrwein and Huffman so as to employ only liquid helium and liquid nitrogen as refrigerants are described.

High Temperature Susceptibility of Permanent Dipole Lattices
View Description Hide DescriptionVan Vleck's exact classical treatment of dipolar materials is modified and extended. (For convenience, his expansion of the susceptibility χ in powers of T ^{−1} is replaced by an expansion of the effective molecular polarizability α_{ s }.) The present procedure exhibits the dependence of the coefficients of T ^{−p } on lattice sums over certain typical interactions within ``clusters'' of dipoles. This feature, together with an extension to the fourth‐order term, sheds light on the analytic character as well as numerical accuracy of the spherical approximation. The exact treatment also provides a standard of comparison for all other approximation methods. The fourth‐order coefficient is evaluated for a simple cubic arrangement of the dipoles, and for the Onsager liquid model.
The spherical result, at least in the high temperature range, includes the most important types of interactions within clusters; it reproduces the exact series through the third‐order term, and differs from the exact simple‐cubic fourth‐order term by only 5 percent. In addition, when evaluated for the Onsager liquid model, the spherical solution is apparently an improvement over Onsager's solution.

A Detailed Formulation of Kinetic Processes. II. The Role of Collision Processes
View Description Hide DescriptionA detailed treatment is given of the activational processes occuring in both unimolecular and bimolecular processes. Such a treatment leads very naturally to the postulate of two critically energized species, one related to the products and one to reactants. In the case of unimolecular isomerizations it is shown that the properties of either one or both of these species may dominate the rate of the nonequilibrium reaction rate expression, and the form of the rate expression is given in terms of the Slater theory of unimolecular reactions.
In the case of unimolecular decompositions, only the complex corresponding to reactants is important, whereas in the inverse case of association reactions only that for the products is of importance. Both of these types of reactions have the same form of pressure dependence in the steady‐state concentration region. The above considerations apply even when the reactions are not reversible. That is, the critically energized complex related to products is still of importance in determining the reaction rate. In the case of bimolecular and higher order processes, a detailed investigation shows that the activational processes are always maintained at their equilibrium values, and there is no region in which the rate constants will show a significant dependence on concentration of inert gas.

A Theory of Cooperative Phenomena. III. Detailed Discussions of the Cluster Variation Method
View Description Hide DescriptionA series of approximations for the statistical mechanics of order‐disorder, proposed by Bethe, Takagi, Yang‐Li‐Hill, Kikuchi, and others, are investigated in detail in two ways. (1) A new interpretation of the method for constructing the combinatory factor is presented in order to give a better understanding of the nature of approximations. (2) The partition functions with approximate combinatory factors are expanded to compare with the rigorous expansion and the discrepancies between them are investigated in detail. One of the conclusions is that in order to obtain a higher approximation, it is necessary to use the basic figure ``closed'' with respect to the cluster of the preceding approximation. In appendices, an improved treatment of the body‐centered cubic lattice (Ising model) is given, and Bethe's fundamental assumptions are derived from our scheme.

Rotation‐Vibration Spectra of Diatomic and Simple Polyatomic Molecules with Long Absorbing Paths. IX. The Spectra of the HCN and DCN Molecules from 2.5μ to 0.5μ
View Description Hide DescriptionThe photographic infrared spectrum of HCN has been investigated using a 6‐meter concave gratingspectrograph and absorption paths up to 600 meters. The near infrared spectra of HCN and DCN have been investigated using a gratinginfrared spectrometer with a lead sulfide cell as a detector. The interference fringes from a Fabry‐Perot etalon have been used as wavelength standards for the recording spectrometer. Twenty‐four bands of HCN and six bands of DCN have been measured. From these measurements earlier work has been corrected, and the zero‐order frequencies and anharmonic constants have been determined for both HCN and DCN. Perturbations have been found in the vibrational levels of HCN. Corresponding perturbations occur in the B_{v} values, and it has been shown that even apparently unperturbed B_{v} values are not linear functions of the vibrational quantum numbers. The B_{e} values for HCN and DCN were found to be 1.4849 cm^{−1} and 1.2118 cm^{−1}. From these B_{e} values the C–H and C–N internuclear distances in the equilibrium position have been found to be 1.0657A and 1.1530A, respectively. From the zero‐order frequencies the force constants have been determined.

On the Radiofrequency Spectrum of the Components of a Sodium Chloride Beam. The Dimerization of the Alkali Halides
View Description Hide DescriptionThe transitions Δm_{I} =±1, Δm_{J} =0 for both Na and Cl were studied at high magnetic field in a beam produced by the evaporation of sodium chloride. The observed spectra could not be fully described in terms of the known internal interactions of a diatomic molecule or the interaction of a diatomic molecule with an applied field. It is suggested that the unexplained features of the spectra result from the presence in the beam of molecules of the type (NaCl)_{2}. Similar effects have been observed in sodium fluoride and sodium iodide.

A Semi‐Empirical Theory of the Electronic Spectra and Electronic Structure of Complex Unsaturated Molecules. I.
View Description Hide DescriptionA semi‐empirical theory is outlined which is designed for the correlation and prediction of the wavelengths and intensities of the first main visible or ultraviolet absorption bands and other properties of complex unsaturated molecules, and preliminary application of the theory is made to ethylene and benzene.
The theory is formulated in the language of the purely theoretical method of antisymmetrized products of molecular orbitals (in LCAO approximation), including configuration interaction, but departs from this theory in several essential respects. First, atomic orbital integrals involving the core Hamiltonian are expressed in terms of quantities which may be regarded as semi‐empirical. Second, an approximation of zero differential overlap is employed, and an optional uniformly charged sphere representation of atomic π‐orbitals is introduced, which greatly simplify the evaluation of electronic repulsion integrals and make applications to complex molecules containing heteroatoms relatively simple. Finally, although the theory starts from the π‐electron approximation, in which the unsaturation electrons are treated apart from the rest, provision is included for the adjustment of the σ‐electrons to the π‐electron distribution in a way which does not complicate the mathematics.
Electronic energy levels in the theory are expressed in terms of ionization potentials of atoms, resonance integrals of bonds, Coulomb repulsion integrals between two π‐electrons on the same atom and between two π‐electrons on different atoms, and penetration integrals between π‐electrons and neutral atoms. Preliminary applications to ethylene and benzene in which only the carbon‐carbon resonance integral is treated as an empirical quantity show that the theory can reproduce the results of the purely theoretical method with very little labor. The reasonableness of considering all of the above quantities as semi‐empirical is pointed out, however, and it is through a detailed examination and exploitation of this in the second paper of this series that correction for the inadequacies of the π‐electron approximation is made and improved agreement with experiment is attained.

Interatomic Electric Quadrupole‐Quadrupole Coupling in Salts of Cerium
View Description Hide DescriptionWe have calculated the magnetic properties of a cerium salt in terms of the one‐atom (crystalline field) model at temperatures greater than 1°K. Because the cerium ion is not in an S state, its electronic charge distribution has a quadrupole moment; we have determined the influence of interatomic electric quadrupole‐quadrupole interactions on the magnetic moment and optical rotation at very low temperatures. In cerium ethylsulfate this coupling is antiferromagnetic with a characteristic temperature of τ=0.01〈r ^{2}〉^{4} degrees, where 〈r ^{2}〉^{½} is the rms radius of the 4f orbit in A. This interaction may be at least partly responsible for a low temperature anomaly found by Becquerel, de Haas, and van den Handel, as well as for the sharp increase in specific heat noticed during adiabatic demagnetization. In other salts τ may be of opposite sign (ferromagnetic case) and possibly much larger (∼1°K).

The Hydrodynamic Stability of Flame Fronts
View Description Hide DescriptionThe hydrodynamic stability of a plane flame of finite thickness is treated by investigating the temporal behavior of first‐order infinitesimal disturbances. This work is a generalization of earlier studies and takes into account the effect of distortion on burning velocity. The general equations of motion for the disturbance in a viscous gas under the influence of gravity are derived and solved. Horizontal and upward propagating plane flames are always unstable and those propagating downward are unstable under most conditions, so their measured transformation velocity under such conditions does not equal the stationary burning velocity. The calculated maximum cell size for downward propagation (λ_{max}=32U_{u}U_{b} ×10^{−4} cm) and the cell size for a flame propagated by thermal conduction (λ_{thermal}=22k/C_{p} ρ_{ u } U_{u} ) are in good agreement with existing experimental observations. The variation of cell size with pressure yields the pressure dependence of the burning velocity. The sudden appearance of cells in slow hydrocarbon flames (U_{u} ≈10 cm/sec) observed at stoichiometric in going from lean to rich mixtures, indicating a corresponding decrease in flame thickness, is advanced as provisional evidence of a shift in the dominant propagation mechanism in these flames—from diffusion by atomic radicals for lean flames to thermal conduction for rich ones.

Note on the Absorption Spectrum of Iodine in Oxygenated Solvents and the Dissociation of Iodine Water
View Description Hide DescriptionData are presented on factors in the appearance of the tri‐iodide absorptionspectrum in solutions of iodine in water and in the alcohols. Some implications of the dissociation of iodine in water for the theory of the iodine‐solvent interaction are pointed out.

Electric Resistivity of Interstitial Compounds of Graphite
View Description Hide DescriptionAssuming that the formation of interstitial compounds is accompanied by creation of excess holes in the otherwise full band of graphite, it is shown that a linear energy‐momentum relation at the Brillouin zone corners is incapable of explaining the decrease of the electric resistance with oxidation. It appears that for a more general model the decrease in relative resistance should be independent of temperature for large oxidations if suitable corrections for the initial conditions are made. Data for polycrystallinegraphite corrected for the existence of an energy gap and of excess holes in the untreated material give curves which converge for higher oxidation with the curve for natural graphite. Discussion of the low temperature properties of graphite leads to the conclusion that large graphite crystals possess slightly overlapping zones.

On the Molecular‐Orbital Theory of Conjugated Organic Compounds with Application to the Perturbed Benzene Ring
View Description Hide DescriptionThe electronic structure of a molecular system is investigated by using the idea of molecular orbitals. The behavior of the separate molecular orbitals and the orbital energies under the influence of the substitution of one or more heteroatoms, considered as perturbations, is examined. A series of quantities, separate charge orders, bond orders, and mutabilities are introduced, giving information about some characteristic physical and chemical properties of the compound. The perturbation scheme is carried out explicitly to the second order in the energies and to the first order in the orbitals, and special attention is paid to the treatment of degenerate levels. The overlapping problem is fully discussed. The basic results are independent of any empirical parameters, and they may be used either in the naïve semi‐empirical theory or in a more elaborate theoretical approach based on an antisymmetrized molecular wave function.
As an example, numerical applications are carried out in detail on benzene. Separate charge orders, bond orders, and mutabilities are tabulated, and orbital energies for a perturbed benzene ring with one or two heteroatoms are explicitly given.

The Absorption Spectrum of Cyclopropane in the Vacuum Ultraviolet. Note on the Absorption Spectrum of Methyl Cyclopropane
View Description Hide DescriptionThe spectrum of cyclopropane has been investigated from 600A to 2200A with high dispersion. Three very broad electronic transitions with apparent maxima at 1594, 1449, and 1202A were found. A strong continuous absorption begins at 1123A, and no resolved transitions could be observed at shorter wavelengths. A very weak band system consisting of twelve bands was found between 1889 and 1816A. It is concluded that the electronic transitions arise from excitation of an electron from a bonding molecular orbital localized principally in the carbon ring. The weak transition is interpreted as a forbidden transition. A tentative analysis of the bands in this transition is given. A note on the absorptionspectrum of methyl cyclopropane is included.

Some Heavy Water Rotational Absorption Lines
View Description Hide DescriptionThree new heavy water rotational absorption lines have been observed in the microwave region. One of these lines and another line previously observed by McAfee have been identified as HDO lines by a study of the variation of their intensities with isotopic molecular concentration. By interpreting their Stark structure, the two HDO lines are assigned as follows: HDO:8_{−1}→8_{0} at 24 884.85 Mc/sec and HDO:6_{−2}→7_{−6} at 26 880.47 Mc/sec. In addition, results on the Zeeman spectra of the two identified HDO lines are presented.