Volume 20, Issue 5, 01 May 1952

On the Lifetime of the Lower Triplet States of Benzene
View Description Hide DescriptionTransition probabilities and selection rules are calculated for the lower triplet‐singlet transitions of benzene. The relativistic spin‐orbit coupling term combines the triplet state with an intermediate singlet state, and then dipole transition to the ground state occurs. The selection rules are deduced group‐theoretically, and the transition probabilities are calculated using the LCAO one‐electron approximation. The effect of vibration is discussed. The theoretical results obtained agree with Shull's and McClure's experimental results.

An Expansion Theorem of the Density Matrix
View Description Hide DescriptionA general theorem is proved on the density matrix of quantum statistics. Let the density matrix bewhere the operators H_{l} 's are not always commutable. ρ{M} can be expanded in series of the formwhere {m _{1}}_{ M }, ··· {m_{n} }_{ M } are subsets of operators chosen from the set {M} and operators belonging to different subsets are commutable. The summation is over all the possible choices of the sets {m _{1}}, ··· {m_{n} }. is defined bywhere suffix s means the symmetrization by changing the order of the products. And ρ^{*}{m} is defined bywhich is proved to be O(β^{ m+1}). Some possible applications are briefly discussed.

Theoretical Considerations Concerning Hammett's Equation. II. Calculation of σ‐Values for Toluene and Naphthalene
View Description Hide DescriptionThe electron distributions in toluene and naphthalene are calculated by the LCAO MO method. The Coulomb integrals of the methyl carbon atom in toluene and the central atoms in naphthalene are assigned small increments which are justified by qualitative reasoning. These increments are treated as empirical parameters and adjusted to give the best correlation between electron densities and Hammett's σ‐values. The parameters so derived are shown to obey the expected qualitative relations and lead to a good correlation of electron densities and σ‐values.

Specific Heat of Synthetic High Polymers. I. A Study of Polyethylene Including a Statistical Theory of Crystallite Length
View Description Hide DescriptionData are given for the specific heat of granular, sheet, annealed, and drawn samples of polyethylene from −20° to 200°C. From the data, changes in enthalpy and entropy between these temperatures have been calculated and an estimate made of the free energy of the cold drawing process. The percentage of crystallinity calculated from the enthalpy value is given as a function of temperature and compared with similar estimates from x‐ray and density measurements. The applicability of Flory's important theory of crystallization in high polymers to the polyethylene data is studied. A new statistical treatment of crystallite length distribution similar to, but more mathematically exact than Flory's, is also presented. Curves based partly on theory and partly on experiment are given for the weight distribution of crystallites as a function of chain length for annealed and drawn polythene.

Note on the Flow of Vapor Between Liquid Surfaces
View Description Hide DescriptionThe mass flow of vapor from a liquid surface at temperature T _{0} to another surface of the same liquid at temperature T _{1}(T _{1}<T _{0}) may be very readily determined in the case of one‐dimensional flow from the conservation relations for mass and momentum. These relations involve both the coefficient of evaporation and the coefficient of condensation. It is therefore possible to determine the condensation coefficient which has heretofore not been accessible to measurement. A new method for determining the evaporation coefficient is also made available. The temperature of the vapor between the liquid surfaces may also be found when viscous effects in the vapor flow are neglected.

Orientation Effects in Solutions of Alcohols
View Description Hide DescriptionAn attempt is made to relate the free energy, heat, and entropy effects involved in the solution of alcohols in nonpolar solvents with the molecular interactions in the solutions. A simple model for the alcohol molecules is proposed, and the thermodynamic functions for a one‐dimensional array, and in a simple case for a three‐dimensional array, are determined by the methods of statistical mechanics. The results for the three‐dimensional array are used to examine the assumption of ``repeatable step'' association with a definite equilibrium constant, and cast some doubt on the justification for this assumption. It is concluded that a more complete treatment of the three‐dimensional array should provide a satisfactory basis for the complete description of the experimental facts.

Directed Valence in P_{4} and As_{4}
View Description Hide DescriptionIt has been reported that three best spd hybrid bond orbitals may be constructed at mutual angles of 73°9′ and 133°37′, but these bond orbitals have not been adapted to actual molecules. We can obtain trigonal pyramid bond orbitals which have mutual angles of 73°9′ and strength 3. When an angle between the directions of three equivalent bond orbitals is introduced as a parameter to these bond functions, variation of strength of these bond orbitals with the angle may be illustrated. These hybrid bond orbitals may be adapted to P_{4} and As_{4}. It is reported that P_{4} and As_{4} molecules have bond angle 60°, the four atoms lying at the tetrahedron corners and the bonds along the tetrahedron edges. Hultgren has applied pd hybrid bond orbitals to such a configuration. Assuming that the s orbital is used in hybridization, we can obtain stronger bond orbitals than that by pd hybridization. Such spd trigonal pyramid bond orbitals have strength 2.970 (only slightly less than that of the best spd hybrid bond orbital) at bond angle 60°. It seems to be more probable that spd hybrid orbitals are used in the bond formation in P_{4} and As_{4} molecules; the unshared pair occupies the fourth hybrid orbital (containing all of the residual s parts) which has 76.5 percent s character at bond angle 60°.

Microwave Spectra of CHBr_{3} in the Region from 11 to 12.5 Centimeters
View Description Hide DescriptionThe spectrum of rotational transition J=0→1 of bromoform has been estimated to lie in a 10‐cm region. In this region, however, the spectroscopy has not yet been studied because of small absorption. Some of the present authors (S. K., K. T., and S. H.) had examined its detectability by the preliminary experiment with a cavity spectrometer. In the present paper more precise measurement using an absorption cell of 9 meters in length and its analysis by means of the theory proposed by some of the authors (M. M. and T. I.) are described. Thirty‐two lines due to the hyperfine structure of the rotational transition were measured in the region from 2400 to 2660 mc/sec. The width of line was smaller than 2 mc/sec at 3 mmHg. The theory agreed well with the experiment. The value of the moment of inertia obtained here agrees with the result of electron diffraction, and this moment seems not to change appreciably by a low frequency deformation vibration. The quadrupole coupling constant of Br nucleus is nearly equal to that of CH_{3}Br molecule.

Purification of Hydrocarbons for Use as Solvents in Far Ultraviolet Spectroscopy
View Description Hide DescriptionThe ultraviolet transmission of four hydrocarbons, n‐heptane, isopentane, 3‐methylpentane, and methylcyclohexane, are shown at various stages of purification. The particular advantages of each as a solvent in far ultraviolet spectroscopy is discussed with emphasis on the remarkable transmission of isopentane when purified.

The ``α''‐Band of Formaldehyde and the Relation Between the Ultraviolet Absorption and Fluorescence Systems
View Description Hide DescriptionA fine‐structure analysis is presented of part of the ``α''‐band of formaldehyde which lies at λ3700. It is shown that the ``α''‐band and the ``A'' band of formaldehyde which lies at λ3530 have neither the upper nor the lower state in common. It is also shown that the lower state of the ``α''‐band is one in which one quantum of the antisymmetric vibration ν_{6}″ is excited. The vibrational structure of the fluorescence system is discussed in the light of these results.

Polarizability Model of Effective Charges
View Description Hide DescriptionThe effective charge dμ/dr (μ=dipole moment, r=interatomic distance) is computed for linear diatomic and triatomic molecules from an expression for μ which includes the effect of induced atomic dipoles. Agreement with observation is possible only if the atomic polarizabilities α are considered to be variable with r. α′=dα/dr is obtained in good numerical agreement with values previously derived from Raman effect data. Thus, a reasonably consistent classical picture can be established that covers dipole moments, infrared intensities, and Raman line depolarization factors.

Normal Frequencies of a Simple Cubic Lattice. III
View Description Hide DescriptionFor a simple cubic crystal, with forces resisting displacement along and perpendicular to the connecting line between closest neighbors, the secular equation for the internal motions is rigorously broken down to ultimate factors of the formin which ν_{ x }, etc., are the normal frequencies of the one‐dimensional crystal.
The corresponding frequency distribution shows no indication of the ``infinities'' found by Montroll for a model with central forces between first and second neighbors.

The Exchange of Water between Co(NH_{3})_{5}H_{2}O^{+++} and Solvent
View Description Hide DescriptionThe rate of exchange of water between Co(NH_{3})_{5}H_{2}O^{+++} and solvent has been measured by a method involving isotopic assay of the bound water. The half‐time for the exchange is independent of salt concentration and of acidity over a range of these variables and is 24.5 hr at 27°. The half‐time is increased by SO_{4} ^{=}, indicating that complex ion formation competes with the exchange process and thus supporting an S_{N}1 mechanism as a reaction path. The equilibrium quotient was measured as 1.019±0.001.

On the Determination of Rotational Line Half‐Widths of Diatomic Molecules
View Description Hide DescriptionA simple closed‐form expression is obtained for the fractional intensity of radiation absorbed by vibration‐rotation bands with collision‐broadened spectral lines. The resulting expressions greatly reduced the labor involved in obtaining apparent rotational half‐widths from experimental measurements.

Absolute Quantum Efficiencies of Luminescence of Organic Molecules in Solid Solution
View Description Hide DescriptionAbsolute quantum yield measurements of fluorescence and phosphorescence have been made for a number of organic molecules dissolved in a transparent solid solution (E.P.A.) at 77°K. The quantum efficiencies range from nearly zero for bromobenzene to 0.6 for benzophenone. The measurements are believed to be accurate to about 10 percent. The nonradiative processes, which account for the quanta not re‐emitted, are discussed. If the radiationless processes all originate in the triplet state, the triplet state lifetimes measured in solid solution can be corrected to give the natural lifetime of the triplet (phosphorescent) state. Since one cannot tell a priori that this assumption is justified, other experiments are necessary. If the singlet‐triplet absorption strength is known, one can tell whether this correction should be applied or not, and infer the origin of the radiationless transition. Finally, a comparison of quantum yields in solid solution with quantum yields in other phases suggests that the mechanism of radiationless transitions, in the absence of concentration quenching and specific solvent and quencher action, is intramolecular potential surface crossing, followed by the transfer of excess vibrational energy to the solvent.

The Spectra and Electronic Structure of the Tetrahedral Ions MnO_{4} ^{−}, CrO_{4} ^{−−}, and ClO_{4} ^{−}
View Description Hide DescriptionWe have made use of a semiempirical treatment to calculate the energies of the molecular orbitals for the ground state and the first few excited states of permanganate, chromate, and perchlorate ions. The calculation of the excitation energies is in agreement with the qualitative features of the observed spectra, i.e., absorption in the far ultraviolet for ClO_{4} ^{−}, two strong maxima in the visible or near ultraviolet for MnO_{4} ^{−} and CrO_{4} ^{=} with the chromate spectrum displaced toward higher energies. An approximate calculation of the relative f‐values for the first transitions in CrO_{4} ^{=} and MnO_{4} ^{−} is also in agreement with experiment.
The data on the absorption spectra of permanganate ion in different crystalline fields is interpreted in terms of the symmetries of the excited states predicted by our calculations.

An Investigation of the Pyrolyses of Cumene, t‐Butyl‐benzene and p‐Cymene, and the Relevant Bond Dissociation Energies
View Description Hide DescriptionThe pyrolysis of cumene, p‐cymene, and t‐butyl‐benzene has been investigated. From the experimental data the relevant bonddissociation energies and the heats of formation of the respective radicals have been computed.

Infrared and Raman Spectra of Fluorinated Ethanes. IV. The Series CH_{3}–CH_{3}, CH_{3}–CH_{2}F, CH_{3}–CHF_{2}, and CH_{3}–CF_{3}
View Description Hide DescriptionThe infrared spectra of ethyl fluoride and 1,1‐difluoroethane vapors have been obtained in the egion from 2 to 38μ, and the spectra of the liquids from 2 to 22μ, with the aid of LiF, NaCl, KBr, and KRS‐5 prisms. The Raman spectra of both compounds were studied in the liquid phase with a three‐prism glass spectrograph of linear dispersion 15A/mm at 4358A. Depolarization ratios were determined for the stronger bands. The Raman spectrum of 1,1‐difluoroethane was also obtained for the gaseous phase.
A complete assignment of fundamental frequencies is proposed for each molecule and used in a detailed interpretation of the spectra and for the calculation of thermodynamic functions over the temperature range 298–600°K and at the boiling point.

Rotation‐Vibration Spectra of Diatomic and Simple Polyatomic Molecules with Long Absorbing Paths VIII. The Spectra of Trideuteromethylacetylene and Diacetylene from 1.2μ to 0.7μ
View Description Hide DescriptionThe absorption spectra of CD_{3}C_{2}H and diacetylene have been investigated under high resolution (21‐ft grating) in the photographic infrared with absorbing paths of up to 27‐meter atmospheres obtained by multiple reflections. For CD_{3}C_{2}H and 3ν_{1} and 4ν_{1} bands were resolved and analyzed yieldingand, therefore, for the moment of inertia about an axis perpendicular to the symmetry axisThis result, taken in conjunction with the work of Herzberg, Patat, and Verleger on CH_{3}C_{2}H, confirms that the C–C bond length is abnormally short in this molecule. The value obtained wasFor diacetylene the rotational structure of four parallel bands was analyzed yieldingleading toThe structure of the bands shows diacetylene to be a symmetrical linear molecule. By assuming values for the C–H and C≡C bond lengths the length of the C–C single bond was calculated to be

Dimensions of Polybutadiene‐Type Molecules
View Description Hide DescriptionThe calculation of root‐mean‐square end‐to‐end distances (R_{p} ) is carried out for polybutadiene‐type molecules. A table and graphs are given for this dimension as a function of the fraction of 1,2 and 1,4 addition and the percentage cis‐ and trans‐configuration about the double bonds remaining in the chain. Also the root‐mean‐square radius of gyration (R_{g} ) for molecules with all 1,4 addition has been calculated. It is found that R_{p} ^{2}=6R_{g} ^{2} as is true for polymer molecules all of whose bonds can rotate completely freely and for those molecules where freely rotating bonds maintain fixed valence angles. Free rotation about the single bonds, a linear chain, no volume exclusion effect, and a polymer molecule with many monomer units are assumed.