Volume 39, Issue 3, 01 August 1963
Index of content:
39(1963); http://dx.doi.org/10.1063/1.1734283View Description Hide Description
Absolute absorption intensities of the infrared‐active fundamentals in dilute crystalline solutions of benzene in deuterated benzene and vice versa have been measured. The intensities are, within experimental error, equal to those measured for the pure crystals.
The spectroscopic resolution was sufficient to show clearly the effects of isotopic dilution on the crystal multiplets.
39(1963); http://dx.doi.org/10.1063/1.1734284View Description Hide Description
In dye photoconductors which have a very high density of traps, such as rhodamine‐B and crystal violet, it is possible to build up a density of spins ∼1016/cm3 in strong illumination. The kinetics of rise and decay of these spins can be directly related to those of photoconductivity, and the spins are believed to be associated with trapped conduction electrons. Since the magnitude of the ESR signal is a measure of the number of electrons, the assumptions regarding mobility which have been made to account for the conductive behavior can be tested. In general, the conclusion that the mean or drift mobility has an exponential temperature dependence corresponding to a monoenergetic trap depth has been confirmed. The mean mobility of electrons is estimated to be ∼1× exp (— Et /kT) cm2/V·sec. The previously observed irregularities in the photoconductive behavior of rhodamine‐B arise from the existence of a considerable population of unpaired electrons which do not contribute directly to conduction, but interchange with those which do. Some salts of crystal violet which have appreciable semiconductivities were found to have spin densities ∼1017/cm3 in the dark.
Calculation of Exact Eigenfunctions of Spin and Orbital Angular Momentum Using the Projection Operator Method39(1963); http://dx.doi.org/10.1063/1.1734286View Description Hide Description
Using the projection operator technique a code has been written for the IBM‐7090 to generate electronic wavefunctions which are eigenfunctions of both spin and orbital angular momentum. All the functions which arise in the L—S coupling of any allowed system of electrons in a single s, p, d, or f shell can be computed as well as some functions for a few electrons in the g shell. Also, functions arising in the coupling of electrons in different shells are obtained, and these eigenfunctions are of particular interest in configuration interaction studies of atomic structure. A few representative eigenfunctions are listed. In addition an auxiliary code was written to give the terms arising in L—S coupling.
39(1963); http://dx.doi.org/10.1063/1.1734288View Description Hide Description
It is suggested that measurements of the maximum pressure difference across a capillary due to thermal transpiration can be used for the determination of the molecular relaxation time of the gas (usually rotational relaxation). This pressure difference is related to the translational thermal conductivity of the gas, which in turn is affected by the relaxation times. Available experimental data on thermal transpiration are analyzed in this way, and the results compared with other determinations of relaxation times. The results, although scanty, indicate that the method has promise. The greatest asset of the method is its extreme experimental simplicity; the greatest liability is that two approximate theories intervene between the experimental measurements and the calculated relaxation times.
39(1963); http://dx.doi.org/10.1063/1.1734289View Description Hide Description
Partition functions for nonrigid rotators are obtained for the linear, spherical‐top, and symmetric‐top cases. From these are derived expressions giving the corrections to the thermodynamic functions due to centrifugal distortion as functions of the rotational distortion constants D. Numerical examples are given for HCN, methane, and ammonia.
39(1963); http://dx.doi.org/10.1063/1.1734290View Description Hide Description
Hartree—Fock self‐consistent field calculations of the Roothaan (LCAO—MO) type have been carried out on an electronic computer for LiH using an extended set of basis functions. Configuration interaction calculations result in a total molecular energy of 99.3% and a dissociation energy of 89.3% of the experimental values. It is found that large contributions occur from pπ orbitals in configuration interaction. Using a general method developed in the present work, the electric‐field gradient is calculated in LiH. With Klemperer, Gold, and Wharton's measurement of the LiH quadrupole coupling constant, the quadrupole moment of the Li7 nucleus is found to be —4.4×10—26 cm2. This sign is unambiguously determined to be negative, in agreement with theoretical predictions from nuclear models. The dipole moment of LiH is calculated to be —5.89 D, and the quadrupole coupling constant of deuterium in LiD is calculated to be 35.3 kc/sec.
39(1963); http://dx.doi.org/10.1063/1.1734291View Description Hide Description
A simple method has been developed to generate the matrix elements of the operator exp (—βξ2) in the representation of the harmonic oscillator. These matrix elements are useful in double‐minimum problems where the potential energy function may conveniently be represented by a perturbed harmonic oscillator with a Gaussian barrier. Some representative calculations involving such potential wells will also be presented.
Nuclear Magnetic Relaxation and Diffusion in Liquid CH4, CF4, and Mixtures of CH4 and CF4 with Argon39(1963); http://dx.doi.org/10.1063/1.1734292View Description Hide Description
The longitudinal nuclear magnetic relaxation times and diffusion coefficients of CH4, CF4, and mixtures of CH4 and CF4 with argon have been measured at temperatures between the freezing points and the boiling points of the liquids by use of spin‐echo techniques. Misch metal was used as a getter to remove oxygen from the samples. The relative numbers of spins per unit volume have also been measured. The measured values of the relaxation timeT 1 are compared with values calculated on the assumption that the relaxation is due to spin—rotational interactions and to intra and intermolecular dipole—dipole interactions. The calculated and measured values of (1/T 1) differ by a factor of as much as 4 for pure liquid CH4 and as much as 12 for the argon—CH4 mixture. The calculated and measured values of (1/T 1) for pure liquid CF4 and for the argon—CF4 mixture agree quite well if reasonable values of the spin—rotational interaction constants are assumed. The calculated contribution of the spin—rotational interactions to (1/T 1) is negligible for liquid CH4, and is comparable to the contributions of the dipole—dipole interactions for liquid CF4.
39(1963); http://dx.doi.org/10.1063/1.1734293View Description Hide Description
Empirical internuclear potential functions have been used to predict higher‐order spectroscopic parameters for ground and excited states of a representative sample of diatomic molecules. The parameters, viz., second‐order anharmonicities, ω e ye, rotational—vibrational coupling constants, γ e , and the first‐order vibrational corrections to the second‐order rotational constants, β e , have been computed through the Dunham relations for the Hulburt—Hirschfelder, Varshni III, and Lippincott empirical internuclear potential functions. A table of Dunham‐corrected equilibrium vibrational frequencies and equilibrium internuclear distances is given. The predicted values for the higher‐order spectroscopic parameters are compared with experimental values as found in the literature. Deviations of predicted from experimental values are discussed from different approaches. The empirical functions discussed should be useful in obtaining estimates of ω e ye, γ e , and β e when such values are not available because of limited experimental data.
39(1963); http://dx.doi.org/10.1063/1.1734294View Description Hide Description
Processes at the dark hole discharge surface of photoconducting anthracene in contact with aqueous inert electrolyte have been examined. O2 was shown to be consumed and anthraquinone formed due to electrolysis. Directional etching of the (001) discharge surface was shown to occur and related to (010) slip planes which were probably developed during growth from the melt. Significance of defects to current carrier trapping was indicated and possible mechanism of carrier discharge was discussed.
39(1963); http://dx.doi.org/10.1063/1.1734295View Description Hide Description
Photolysis of cis‐stilbene in the vapor phase at 170° leads to the formation of trans‐stilbene, phenanthrene, and hydrogen. The formation of phenanthrene is not eliminated by the addition of oxygen (35 mm) or nitric oxide (6 mm), nor is the rate affected by large excesses of ether or cyclohexane. It is believed that phenanthrene and hydrogen are formed from cis‐stilbene by an intramolecular process which probably proceeds in a single step—the elimination of hydrogen occurring at the same time as the closure of the third ring. The reaction is also observed to occur in the pyrolysis of cis‐stilbene at 550°. Qualitative results on the photolysis and pyrolysis of 1,4‐diphenyl‐1,3‐butadiene in the vapor phase are reported. Quantum yields for the formation of phenanthrene in the photolysis of cis‐stilbene in cyclohexane solution have been obtained. An earlier report that phenanthrene is a product in solution only in the presence of oxygen has been confirmed. The dissimilarities between the mechanisms of the formation of phenanthrene in the vapor phase and in solution are discussed.
39(1963); http://dx.doi.org/10.1063/1.1734296View Description Hide Description
The kinetics of chemisorption are analyzed by aid of a very simple model. Due account is taken of the role played by geometrical factors (resulting from the finite size of the molecules) whereas both possible modifications of the activation energy with surface coverage and dissociation on the surface are neglected. The physical aspects of the model are discussed. Some exact numerical results as obtained by the Monte Carlo method are given. The mathematical formulation of the problem is made, yielding an approximate kinetic equation where steric effects are taken account of. The possibility is discussed for this model to be generalized in a more complete theory as well as its interest for further studies in the field of elementary heterogeneous catalyticreactions.
39(1963); http://dx.doi.org/10.1063/1.1734297View Description Hide Description
The polymer concentration dependence of the Donnan equilibrium parameter was studied using an interionic interaction theory based on a spherical model for the macro‐ions. It was found that the calculated value of the equilibrium parameter generally decreased quite sharply at first with increasing polymer concentration, increased after reaching a minimum, and then decreased again. The macromolecular dimension was assumed to be independent of the polymer concentration. Also, the theoretical value of the parameter varied more sharply with polymer concentration as the concentration of simple electrolyte decreased. The parameter decreased with increasing macro‐ion radius and became negative when large values of the radius were assumed.
39(1963); http://dx.doi.org/10.1063/1.1734298View Description Hide Description
Rotational spectra of pentafluorosulfur bromide observed with a video microwave spectrometer in the region 51–54 kMc/sec were fitted to the following molecular constants and structural parameters: S32F5Br79–B 0 = 1172.153±0.002 Mc/sec, DJ = 0.0672±0.0400 kc/sec, DJK = 0, eQq(Br79) = 800±5 Mc/sec; S32F5Br81–B 0 = 1159.875±0.002 Mc/sec, DJ = 0.1612±0.0400 kc/sec, DJK = 0, eQq(Br81) = 705±5 Mc/sec; θF–S–F(axial) = 88° (assumed), d S–Br = 2.1902±0.0065 Å, d S–F = 1.5970±0.0025 Å. The long S–Br bond distance is attributed to the steric interaction between the bromine atom and the F4 group. The value of the quadrupole coupling constant for the bromine nucleus suggests that the S–Br bond is predominantly covalent with some ionic character from resonance forms involving a positive charge on the bromine atom.
39(1963); http://dx.doi.org/10.1063/1.1734299View Description Hide Description
Nonempirical calculations of the electronic structure of the ammonia molecule are carried out using a ``bond‐orbital'' and a ``modified electron‐pair'' function. The calculated binding energies are 0.348 a.u. (76% of the experimental value) and 0.381 a.u. (83%), respectively. The best theoretical value previously known was 0.378 a.u., the result of a self‐consistent LCAO calculation including limited configuration interaction.
It is concluded that the ``modified electron‐pair'' function is an adequate simple approximation, and the ``frozen core'' approximation employed in the calculation is satisfactory.
The dipole moment is also calculated, and reasonable agreement with the experimental value is obtained.
39(1963); http://dx.doi.org/10.1063/1.1734300View Description Hide Description
Viscosities and second virial coefficients of five molecular gases considered cannot be reproduced by a single pair potential function for central forces. Contributions of quadrupole interactions to the second virial coefficient, but not the viscosity, account adequately for the differences over wide ranges of temperature for the following values of molecular quadrupole moments (in units of 10—26 esu): H2, 0.52; N2, 1.90; CO, 2.81; CO2, 4.59; C2H4, 3.92. These are compared with other estimates, and the legitimacy of the assumptions is discussed.
39(1963); http://dx.doi.org/10.1063/1.1734301View Description Hide Description
Molecular orbital calculations using the Hückel LCAO theory and the approximate configuration interaction treatment suggested by McLachlan have been performed on a large series of nitrosubstituted aromatic anion radicals. By properly adjusting the Coulomb and resonance integrals for the nitro group, a good quantitative correlation is obtained between the calculated spin densities and the experimental protonhyperfine splittings for most of the compounds studied. Procedures are developed to account for the variations in hyperfine splittings with different solvents, and an equation is formulated which gives excellent predictions of the splitting from N14 nuclei in the nitro groups. In addition, the calculations provide a basis for the qualitative discussion of the effects of sterically hindered nitro groups on the hyperfine splittings, and of the apparently anomalous spin densities and linewidth variations in some of the meta‐dinitrobenzene anions. Polarographic half‐wave potentials are also correlated with the calculated pi‐electron energies. Experimental data are given for the ESRspectra of several substituted nitrobenzene anions not previously reported.
39(1963); http://dx.doi.org/10.1063/1.1734302View Description Hide Description
Excitation of the π electrons in thin films of polystyrene and some similar polymers has been observed in the characteristicenergy lossspectra of 20‐keV electronsscattered at zero angle. The observed energy loss of approximately 7 eV corresponds to the strong uv absorption near 1800 Å in benzene and its derivatives. An energy loss of 6.97±0.10 eV was measured in films of atactic and isotactic polystyrene, styrene ethylene copolymer, and poly 2,3,4,5,6‐pentadeuterostyrene, and an energy loss of 7.25±0.15 eV was measured in poly 2,3,4,5,6‐pentafluorostyrene. These energy losses appeared as sharp peaks superimposed on a very broad and more intense loss peak with a maximum at 21.3±0.3 eV in all the electronenergy lossspectra obtained. The results for the energy loss attributed to the π electrons are correlated with relevant uv absorption data. A discernible decrease in the measured ∼7‐eV loss occurred during electron bombardment of the specimens, and is attributed to film contamination and breakdown. The angular distribution of the intensity of each loss in isotactic polystyrene about zero scattering angle was also measured.