Volume 27, Issue 2, 01 August 1957

Equations for a Lattice Gas. II. Multio‐Cmponent Systems
View Description Hide DescriptionAn expression is developed for P/k T for a multi‐component lattice gas with an arbitrary lattice as a multiple power series in a set of kth nearest‐neighbor interaction parameters, λ_{ a b } ^{ k }, where a and b index the components, with the coefficients functions of the activity set z. By straightforward differentiation, corresponding expressions are obtained for other thermodynamic variables, and also for the probability of finding a pair of particles of specified components on a pair of specified sites. A transformation is outlined which permits the substitution of the number density set ρ for the activity set as independent variables.

Structure of the Methylamine Molecule. I. Microwave Spectrum of CD_{3}ND_{2}
View Description Hide DescriptionThe spectrum of CD_{3}ND_{2} has been investigated in the 24 000–36 000 Mc region and about thirty lines have been assigned. The rotational spectrum exhibits a fine structure as a result of internal rotation and inversion. An approximate treatment of these internal motions is formulated and shown to give an excellent fit of the observed spectrum. A treatment of Stark effects and nuclear quadrupoleinteractions is developed and applied to the CD_{3}ND_{2}spectrum. The relation to the CH_{3}NH_{2}spectrum is discussed.
Molecular constants of CD_{3}ND_{2} determined from the spectralanalysis are: torsional barrier height H=684.7±2 cm^{‐1}; dipole moment components μ_{ a }=0.265 D, μ_{ c }=1.299 D, total μ=1.326±0.015 D; N^{14}quadrupole coupling constants χ_{ aa }=2.35 Mc, χ_{ bb }=2.12 Mc, χ_{ cc }=—4.47 Mc. Structural parameters calculated from data on CD_{3}ND_{2} and CH_{3}NH_{2} are: r _{CH}=1.093 A (assumed), ∠HCH=109°28′ (assumed), r _{CN}=1.474 A, r _{NH}=1.011 A, ∠HNH=105°52′, ∠CNH=112°3′; the nitrogen atom is located 0.091 A from the CH_{3} symmetry axis.

Structure of the Methylamine Molecule. II. Theory of Internal Motions and Application to CD_{3}ND_{2}
View Description Hide DescriptionA general theory is developed for the two low‐frequency internal motions which influence the microwave spectrum of methylamine. The interactions of the over‐all and internal rotations with the inversion motion are treated quantum‐mechanically for the case where the potential barriers to inversion and internal rotation are high. The theory justifies the method of analysis of the CD_{3}ND_{2} spectrum which was given in paper I of this series. An expression is obtained for the empirical inversion parameters F_{Kτ} defined in I, and is shown to give an excellent fit of the experimental results for CD_{3}ND_{2}. The inversion splitting constant obtained from this calculation is 2246.0±5 Mc. The significance of this constant and of the other molecular parameters which enter the theory is discussed.

Nonresonant Absorption of Symmetric Top Molecules. Shape of the Nonresonant Spectra
View Description Hide DescriptionThe nonresonant or relaxation absorptionspectrum was mapped out for the symmetric top molecules CH_{3}F, CH_{3}Cl, CH_{3}Br, CH_{3}I, CH_{3}CN, CHF_{3}, CClF_{3}, and (CH_{3})_{3}N. A cavity method was used to determine the absorption at several frequencies in the range 1200 to 24 000 Mc at pressures up to 2 atmos unless limited by the vapor pressure.Absorption due to the rotational lines was found to be important unless the frequency and pressure were kept sufficiently low. The results for CClF_{3} and (CH_{3})_{3}N closely fit the Debye equation and lead to an accurate evaluation of the dipole moment, namely, 0.50_{0}×10^{‐18} esu and 0.60_{1}×10^{‐18} esu, respectively. The nonresonant spectra of the remaining molecules, which have larger dipole moments, deviate from the Debye shape in a manner that is characteristic of a distribution of line widths.

SCF LCAO MO Study of Li_{2}
View Description Hide DescriptionAn LCAO molecular orbital calculation using the full six‐electron Hamiltonian has been performed on Li_{2} at a nuclear separation equal to the experimental internuclear distance. The molecular wave function consisted of one antisymmetrized product made up of molecular orbitals formed as the best linear combinations of Slater 1s, 2s, and 2pσ atomic orbitals. The orbital exponents for these atomic orbitals were respectively 2.69, 0.64, and 0.53 as determined by a variational calculation on the lithium atom. In computing the molecular dissociation energy, the energy of two separated lithium atoms was taken to be that obtained by this variational calculation. The computed dissociation energy was found to be 0.33 ev compared with the experimental value of 1.05 (where a slight correction for zero‐point energy has been made). The ratio of the computed molecular ground‐state energy to the experimental is 0.9902 while the difference of these quantities is 4.00 ev. Certain other molecular constants are calculated and compared with available experimental data.

Study of the A ^{1}Π→X ^{1}Σ^{+} Bands of B^{11}F with a Vacuum Echelle Spectrograph
View Description Hide DescriptionThe A ^{1}Π→X ^{1}Σ^{+} bands of B^{11}F which had been found by Chrétien and Miescher were now studied with the aid of a higher dispersion spectrograph and more accurate molecular constants were obtained, i.e., . Λ‐type doubling was observed in the A ^{1}Π state, and a brief discussion of the doubling is given in this report.

Absolute Temperatures below 1°K : Chromic Methylammonium Alum as a Thermometric Substance
View Description Hide DescriptionThe method of gamma‐ray calorimetry has been employed to determine the entropy‐temperature relation for a single‐crystal of chromic methylammonium alum in the range 0.015°—1°K. A critical discussion of possible sources of error is given; the accuracy in T is estimated to be approximately 5% throughout the region investigated. There is close agreement between the Hebb‐Purcell theoretical S—T relation and the present data down to 0.07°K. The fact that the susceptibility‐entropy relation varies considerably for different specimens at temperatures below 0.06°K suggests that S—T measurements are of limited value in that region, especially from a thermometric point of view.

Burning of a Liquid Droplet. III. Conductive Heat Transfer within the Condensed Phase during Combustion
View Description Hide DescriptionThe problem of internal heating by conduction during the combustion of a spherical fuel droplet is examined.
The analysis indicates that the temperature pattern within such a system is governed by the dimensionless ratio of burning rate coefficient to thermal diffusivity of the liquid. During combustion the temperature in the center of the droplet may closely approach the surface temperature for liquid fuels commonly employed in propulsion. Such an increase in temperature may lead to thermal degradation and carbon formation observed during the combustion of certain organic compounds.

Heat Capacity of Holmium from 15 to 300°K
View Description Hide DescriptionThe heat capacity of holmium has been measured over the range 15 to 300°K. Two maxima have been observed which occur at 19.4 and 131.6°K. The one at the lower temperature exhibits a dependence on the thermal history of the sample and this dependence was investigated. The thermodynamic functions have been tabulated and a correlation made of the contributions to the entropy at room temperature. The value of S ^{0} _{298.16} is 17.97 cal (°K)^{—1} (g atom)^{—1} to which the magnetic contribution is R ln (2J+1).

Vibrational Spectrum of 3,3,3‐Trichloropropene‐1
View Description Hide DescriptionThe Raman spectrum and qualitative depolarizations of the Raman bands of the liquid phase of 3,3,3‐trichloropropene‐1 and the infrared spectra of the liquid and gas phases have been obtained. A very low Raman frequency, Δν=99 cm^{—1}, attributable to the torsional vibration of the CCl_{3} group about the C–C bond was observed and a number of the Raman bands were found to be highly depolarized. The observed frequencies consequently have been assigned on the basis of a planar structure (symmetry group C_{ 8 }).

Vibrational Spectra of sym‐Trioxane
View Description Hide DescriptionThe Raman spectra of liquidsym‐trioxane contained in a sealed, electrically heated Raman tube, and of a crystalline aggregate and a single crystal of the compound, have been photographed with a 3‐prism glass spectrograph of reciprocal linear dispersion 15 A/mm at 4358 A. The infrared spectrum of trioxane vapor has been reinvestigated with the aid of a 1‐m absorption cell and a Perkin‐Elmer double pass spectrometer equipped with CsBr, NaCl, and LiF prisms. The 17 active fundamentals have been assigned as follows: Species a _{1}: 2853, 2792, 1496, 975, 943, 752, and 524 cm^{‐1}; species e: 3031, 2753, 1477, 1408, 1305, 1175, 1072, ca. 1050, ca. 460, and 307 cm^{‐1}. The spectra have been interpreted in detail, and their dependence upon the state of aggregation has been discussed.

Raman and Infrared Intensities in the Vibrational Spectra of Hydrocarbons. I. Skeletal Vibrations of Straight Zigzag Chains
View Description Hide DescriptionThe vibrational frequencies and normal coordinates of finite, straight, zigzag chains are calculated from an Urey‐Bradley potential, the boundary effects being taken into account by a perturbation method. The dominant perturbation terms fall off with 1/N ^{2} (N = number of C atoms) and are found to be negligible for N>5. The intensities of infrared and Raman bands are calculated without using the simplifications implied in ``bond moment'' and ``bondpolarizability'' theories. All the vibrations are found inactive as fundamentals in infrared absorption. The Raman active vibrations produce branches of lines with relative intensities approximately 1, 1/9, 1/25..., 1/N ^{2} and with line spacing rapidly decreasing with increasing N. The strong Raman line observed near 890 cm^{‐1} cannot be assigned to a vibration of the carbon skeleton. One low‐frequency vibration (v∼1150/N cm^{‐1}) perpendicular to the molecular plane should be Raman active. Its low intensity (it has not been observed so far) indicates cylindrical symmetry of the polarizability about the molecular axis.

Heats of Combustion of Some Peroxides and the Heats of Formation of Acetate, Propionate, and Butyrate Radicals
View Description Hide DescriptionHeats of combustion of acetyl, propionyl, and butyryl peroxide were measured using a bomb calorimeter. The heats of formation obtained are: ΔHf = — 127.9 for acetyl peroxide, — 148.2 for propionyl peroxide, and — 161.0 for butyryl peroxide (in kcal/mole for the liquid state at 25°C). The heats of formation of the acetate, propionate, and butyrate radicals have been computed and the relative stability of the acetate compared to the benzoate radical is discussed.
The RC(O)O–H bond dissociation energies in the respective acids and the sums of electron affinities plus solvation energies of the respective ions are computed.
These calculations seem to indicate that acidic properties of carboxylic acids are due to the high electron affinities+solvation energies of R·COO radicals, and not to the low R·CO·O–H bond dissociation energies, since the latter are comparatively high.

Hydrogen Bonding in Radical Reactions. Some Remarks on CF_{3} Radicals
View Description Hide DescriptionStudies of the decomposition of acetyl or propionyl peroxide on the one hand and benzoyl peroxide on the other seem to demonstrate that Ph·COO radicals form hydrogen bonds with carboxylic acids, while the nonpolar alkyl radicals do not form such bonds.
The formation of hydrogen bonds facilitates the hydrogen transfer between the carboxylic acid and the polar radicals.

Electronic Structure of Ammonia
View Description Hide DescriptionA self‐consistent field calculation of the normal state of the ammonia molecule is made in the molecular orbital approximation. The molecular orbitals are expressed as linear combinations of all valence and inner shell orbitals of the atoms, and all interactions of the ten electrons are included. The total molecular energy, —56.096 au, is 99.2% of the experimental value. The dissociation energy, 0.3308 au, is about 72% of the experimental value. The calculated dipole moment (1.486 Debye) is almost equal to the experimental value (1.46D). The two lowest ionization potentials are calculated as 9.94 and 16.20 ev, and are probably within one ev of the experimental values. An equivalent orbital representation is obtained from the molecular orbitals and directional features of distribution of electron density are discussed. The integrals over atomic orbitals were all evaluated by standard mathematical methods, which is discussed in an appendix.

Electronic Spectra and Structure of the Carbonyl Group
View Description Hide DescriptionA theoretical treatment of the electronic structures of compounds containing the carbonyl group has been developed. The method employs the self‐consistent field (SCF) procedure to determine the best molecular orbitals, for the lowest configuration, which can be formed as linear combinations of the atomic orbitals (LCAO—MO). Semiempirical methods are used throughout to determine the numerical values of all core parameters and electronic repulsion integrals. By a judicious choice of parameters and integrals it is possible to describe semiquantitatively the π‐electron ionization potentials,n→π and π→π electronic transition energies, and π‐electronic contribution to the dipole moment of formaldehyde, glyoxal, and p‐benzoquinone. The effect of configurational interaction (CI) upon the calculated transition energies is considered for the n→π and for the π→π transitions.

Effect of Adsorbent Perturbation on B.E.T. Theory
View Description Hide DescriptionThe statistical mechanical derivation of the B.E.T. equation has been extended to include perturbations of the adsorbent by the adsorbate. The thermodynamic functions have been recalculated to include this effect. The thermodynamic functions for the adsorbent as well as the adsorbate have been calculated.

Ultraviolet Spectra and Electronic Structure of Metallic Complexes. I. Chloroammine Cobalt (III) Complexes
View Description Hide DescriptionIn order to study the nature of the so‐called ``first, second, third, and specific bands'' of the metallic complexes, the semiempirical M.O. method has been applied to a series of [Co(NH_{3})_{6—n }Cl_{ n }]^{(3—n) +} (n=0, 1, 2 (cis, trans)) type complexes taking π electrons of the ligands into consideration. The agreement between the calculated and observed energies of transition is satisfactory partly due to the appropriate values of the parameters used. Moreover, the following conclusions have been obtained by the present calculation: (1) The magnitude of the splitting of the first band depends upon the overlap integral, S(3dπ, npπ) and also the ionization potential of the ligand (π). (2) The splitting of the first band in the cis‐complex is small compared to that of the trans‐complex, since, in the former, the three orbitals, from which electrons are excited to produce the low‐energy absorptions, lie at nearly the same energy. (3) Two strong bands in the ultraviolet region are due to the transitions approximately from the ligand level to the metal level, and therefore, correspond to the so‐called ``third bands.'' They will show ``blue‐shift'' in polar media. (4) The general rule that the trans‐complex shows the third bands at longer wavelength than that of the cis‐complex can be accounted for more satisfactorily if the Cl–Cl interaction in the cis‐complex is considered. (5) The spectra of other halogenoammine complexes are reasonably interpreted in a similar manner.

Vibrational Intensities. VIII. CH_{3} and CD_{3} Chloride, Bromide, and Iodide
View Description Hide DescriptionAbsolute intensity measurements have been made on the fundamental vibrations of methyl chloride, bromide, and iodide, and their fully deuterated derivatives, by integrating the optical density over the absorption bands. The bands were fully pressure broadened by using up to 80 atmos of foreign gas. Band separations were made graphically. The results are analyzed in terms of the dipole moment derivatives with respect to symmetry coordinates in the molecule, (∂p/∂S_{i} ). The data on the different isotopic species are shown to yield consistent results, and this requirement of consistency has also been used as an aid in the analysis. In the E‐class vibrations the signs of the dipole moment derivatives have been determined unambiguously by assuming the permanent dipole to be directed CH_{3} ^{+}–X^{—}.

Normal Coordinates in the Methyl Halides
View Description Hide DescriptionThe potential‐energy functions found by Chang for the methyl halides have been put into valence‐type form and revised to eliminate inconsistencies and to accord with the true (nontetrahedral) geometry and the normal frequencies (corrected for Fermi resonance and anharmonicity). The resulting valence‐type force constants and normal coordinates are given for light (CH_{3}) and heavy (CD_{3}) chlorides, bromides, and iodides.