Volume 46, Issue 2, 15 January 1967

Effect of Hydrogen Bonding on the Electrical Conductivity of Organic Solids
View Description Hide DescriptionThe bulk electrical conductivities of a series of monocarboxylic and polycarboxylic aromatic acids and some derivatives of these acids have been measured in order to study the effect of hydrogen bonding on conductivity. Electrical measurements were made on carefully purified, polycrystalline samples, compressed to remove voids, using a guarded direct‐current method. The measurements were characterized by time‐dependent currents which decreased to equilibrium values in times ranging from seconds to hours. The temperature dependence of the conductivity followed the usual exponential law for all the compounds. The activation energy for conduction, E_{a} , was independent of the polarization effects and sample purity and served as a reliable parameter for comparison among the compounds. A definite relationship existed between E_{a} and the position and number of carboxyl groups on an aromatic system. This relationship was interpreted in terms of the hydrogen bonding and electron withdrawing properties of the carboxyl groups on the assumption that the aromatic pi electrons were involved in the generation of charge carriers. Those substituents which tended to reduce the electron density of the aromatic system produced a rather substantial increase in the activation energy. Extended intermolecular overlap resulting from the hydrogen bonding of polycarboxylic acids produced a decrease in E_{a} .

Mechanisms of Energy Transfer Involving Trivalent Eu and Nd
View Description Hide DescriptionThe mechanism of energy transfer between Eu and Nd and the migration of excitation between Eu ions in the Na_{0.5}(Y, Eu, Nd)_{0.5}Wo_{4} tungstates and (Y, Eu, Nd)_{2}O_{3} sesquioxides are examined. Transfer from Eu to Nd appears to be predominately by dipole—dipole interactions. At high Eu concentrations energy may migrate between exchange coupled Eu ions, however, the migration requires thermal activation.

Quantum Dynamics of Anharmonic Oscillators. III. The Morse Oscillator
View Description Hide DescriptionQuantum calculations of the dynamics of a Morse oscillator with a Gaussian initial wave packet have been performed. As previously observed in other simple oscillators the classical and quantum expectation values for the coordinate exhibit significantly different behaviors, especially after the first few cycles. Some theories of chemical kinetics require the classical‐mechanical calculation of lifetimes which may be quite long compared to vibrational periods. These theories deserve re‐examination in view of the dynamical behavior observed in the present work.

Correlation between Exchanging Electrons
View Description Hide DescriptionAttempts to introduce overlap and exchange into a purely general study of interatomic or intermolecular long‐range forces lead to complicated, physically opaque expressions for the interaction energy. A study is made of a most simple system, two hydrogen atoms at large distances, taking overlap and exchange rigorously into account. This system is especially interesting due to the failure of the Heitler—London wavefunction to describe adequately the lowest‐triplet (^{3}Σ_{ u } ^{+})—lowest‐singlet (^{1}Σ_{ g } ^{+}) separation at very large distances. A formal study separates the interaction energy into a ``generalized dispersion'' and ``generalized exchange—correlation'' energy. A many‐configuration calculation performed at an internuclear distance of 8 a.u. shows that, whereas certain configurations yield the well‐known dispersion energy, other configurations, particularly those of the excited charge‐transfer type, correct for the erroneous triplet—singlet separation. This distinction reflects the introduction of two distinct types of correlation effects which are investigated in terms of the two‐electron distribution function.

Radiationless Transitions in Polyatomic Molecules. I. Calculation of Franck—Condon Factors
View Description Hide DescriptionRadiationless transitions between two electronic states are studied for a system consisting of a polyatomic molecule in a medium where vibrational relaxation is rapid. The transition rate is then governed by a vibronic matrix element and a vibrational overlap factor. Only the latter, known as the Franck—Condon factor and denoted by F, is investigated in detail. For harmonic oscillatorsF derives from shifts in equilibrium distance (displacements) and shifts in frequency (distortions). It is shown that for radiationless transitions involving large energy gaps (E), F is dominated by distortions, whereas for optical transitions it is dominated by displacements of the oscillators. These distortions lead to an approximately exponential decrease of F with increasing E. An isotope rule for F is derived which is valid for both displaced and distorted oscillators provided E is not too small. Since all formulas are of the form F (E), where E is the principal variable, comparison with experiment is only possible for a class of related molecules. Within this class E should vary a great deal but all other parameters should either be constant or vary in a simple, systematic manner. The dependence of some of these parameters on the number of oscillators involved in the transition is examined. Finally the theory is extended to molecular crystals and the corresponding liquids. It is concluded that in these systems the rate constant of an intramolecular radiationless transition must be equal to or smaller than that in dilute solutions, except when excited dimers are present in the initial state.

On the Pressure Broadening of Molecular Multiplet Spectra
View Description Hide DescriptionGas‐phase line shapes and band contours are calculated for microwave spectra involving fine structure levels due to electron spin and/or orbital angular momentum, or vibrational angular momentum. We use the impact approximation, and a semiclassical treatment of the molecular rotation. The line shapes are expressed in terms of a set of cross sections which depend on the transfer of angular momentum by collisions. Different results are found, depending on whether the spin and rotation are coupled together strongly [Case (a)] or weakly [Case (b)]. Good agreement is obtained with microwave measurements on NO [Case (a)] and O_{2} [Case (b)]. The results may be applied to study the angle‐dependent shape of intermolecular forces.

Paramagnetism of Carbazyl and Hydrazyl Free Radicals
View Description Hide DescriptionStatic magnetic‐susceptibility measurements in the temperature range 1.4°—300°K are reported on powder samples of the stable aromatic free radicals N‐picryl−9‐aminocarbazyl (PAC), 2,2‐diphenyl−1‐picrylhydrazyl in the 106°C mp [DPPH(I)] and 137°C mp [DPPH(II)] crystal modifications, 2‐phenyl−2‐p‐nitrophenyl−1‐picrylhydrazyl (DHNO_{2}·) and 2,2‐bis(p‐nitrophenyl)−1‐picrylhydrazyl [D(NO_{2})_{2}·]. Radical concentrations in the range from 0.81 to 0.99 and Weiss constants in the range −36° to −5.2°K are determined. The measurements are interpreted assuming that the magnetic behavior is due to alternating antiferromagnetic exchange‐coupled linear chains. Exchange integrals are inferred from fitting theoretical curves to the susceptibility maxima. Evidence is presented for the presence of random dilution by diamagnetic sites in PAC.

Orientation‐Averaged Amplitude of the One‐Quantum Term in the Neutron Scattering Law for Molecular Gases
View Description Hide DescriptionThe amplitude of the one‐quantum term in the scattering law for coherent scattering of neutrons by molecular gases is calculated using a generating‐function approach. The phase factor exp (iκ·b) is averaged jointly with the amplitude factor (κ·γ_{ν}) (κ·γ_{ν′}), as opposed to the more common technique of approximating the joint average by the product of the average of each factor. Results of example calculations show that the correction is of the same magnitude as the result of the conventional calculation.

O−17 Nuclear Magnetic Resonance of Manganese (III) Tris(Acetylacetonate)
View Description Hide DescriptionThe ^{17}O NMR signal of manganese (III) tris(acetylacetonate) was studied in the temperature range 26°—83°. From the temperature dependence of the shift of this signal, a hyperfine interaction constant of 1.88 G is found. This result is used to estimate the covalent character of the σ metal—oxygen bond. An upper limit of 0.077 is found for the mixing coefficient of the oxygen 2s orbitals in the bonding molecular orbitals of the complex. The electron spin transverse relaxation time is estimated from the linewidths of the ^{1}H and ^{17}O resonances to be in the range 10^{−11} to 10^{−12} sec.

Extended‐Average‐Energy Method for Perturbation Problems
View Description Hide DescriptionAn extended‐average‐energy (eae) method for approximating the first‐order perturbationwavefunction ψ_{1} is presented. This method gives the best ψ_{1} of the form f(q)ψ_{0}, where f is a function of a single variableq occuring in the perturbation. In the case of a one‐dimensional problem our ψ_{1} is exact. A procedure is suggested for extending this treatment even further to obtain the exact ψ_{1} for multidimensional problems. Application is made to the polarizability of atomic hydrogen and electron correlation in the helium isoelectronic sequence.

Surface Dye Sensitization. I. Selenium
View Description Hide DescriptionSurface dye sensitization of amorphous Se has been studied. Maximum quantum efficiencies measured were in the range from 10^{−2} to 10^{−1}. The dye coatings were deposited onto the surfaces from their respective methanol or benzene solutions. Five dyes were used for the sensitization: crystal violet, pinacyanole, methylene blue, phenosafranine, and nitrosobenzene. The enhanced photocurrents due to the dye coatings occured at wavelengths longer than those corresponding to the intrinsic bandgap energies of Se. The maximum enhanced response was in the range from 5500 to 7000 Å, depending on the dye. The enhanced photocurrents corresponded to injection of carriers from the surface into the bulk photoconductor,electrons for some dyes (crystal violet and pinacyanole) and holes for others (methylene blue, phenosafranine, and nitrosobenzene).

Surface Dye Sensitization. II. Sulfur
View Description Hide DescriptionSurface dye sensitization of polycrystalline orthorhombic sulfur has been observed. The dyes used for the sensitization were rhodamine B and pinacyanole. Maximum enhanced photoresponse occurred in the wavelengths from 4500 to 6000 Å. Quantum efficiencies up to slightly over 10^{−2} have been measured. The observed photocurrents corresponded to electron injection from the sulfur—dye interface into the sulfur.

Atom—Molecule Kinetics at High Temperature Using ESR Detection. Technique and Results for O +H_{2}, O +CH_{4}, and O +C_{2}H_{6}
View Description Hide DescriptionA technique is described for the measurement of atom—molecule rate constants over the temperature range 300°—1000°K. It combines a heated fast‐flow reactor with ESR atom detection, the ESR cavity being located at a fixed position outside the heated reactor. The system should be useful with a wide variety of reactions, and yields rate constants having ±10% precision independent of temperature. This is also the absolute accuracy when the reaction stoichiometry is known or can be determined by auxiliary mass‐spectrometric analysis. Results on some O‐atom reactions are (in cubic centimeters per mole·second units): In the O+CH_{4} case, the stoichiometry determined both in this work and by others indicates that the mechanism subsequent to the initial step may be although [8] and [9] are not definitely established, and other mechanisms are discussed. Little can be said about the O+C_{2}H_{6} mechanism at present. It is shown that the pre‐exponential factors and activation energies for these three hydrogen abstraction reactions are in reasonable relation to each other.

Studies of Ion—Neutral Reactions by a Photoionization Mass‐Spectrometer Technique. I
View Description Hide DescriptionThe use of a photoionizationmass spectrometer for ion—molecule reaction studies is described. Ion‐source pressures up to 200 μ are employed, measured directly with a McLeod gauge. A method is described for determining ion residence times in the ion source at constant repeller field, using a pulsed‐light source. Drift velocities, diffusion coefficients, and ion temperatures are given for N_{2} ^{+} ions in air as derived from an analysis of ion pulse shapes. Reaction studies are reported for nitrogen ions in air and nitrogen, and for hydrogen ions in hydrogen. The associated rate constants are derived.

Studies of Ion—Neutral Reactions by a Photoionization Mass‐Spectrometer Technique. II. Charge‐Transfer Reactions of Argon Ions at Near‐Thermal Energies
View Description Hide DescriptionA photoionizationmass spectrometer has been employed to study charge transfer involving ^{2} P _{3/2} argon ions at ion‐source pressures 15 to 60 μ and with a source acceleration potential of 0.5 eV. The average energy of the reacting ions are calculated and are found to be less than 0.17 eV. The following rate constants were obtained: A^{+}+NO→A+NO^{+}, k=3.9×10^{−10} cc/molecule·sec; A^{+}+O_{2}→A+O_{2} ^{+}, k=1.1×10^{−10} cc/molecule·sec; A^{+}+CO_{2}→A+CO_{2} ^{+}, k=7.0×10^{−10} cc/molecule·sec; A^{+}+CO→A+CO^{+}, k=1.25×10^{−10} cc/molecule·sec; A^{+}+N_{2}→A+N_{2} ^{+}, k=0.66×10^{−10} cc/molecule·sec. The theoretical implications are discussed.

Theoretical Investigations of Translation—Rotation Energy Transfer: (H_{2}, He) and (D_{2}, He) Systems
View Description Hide DescriptionThe classical analysis of translation—rotation energy transfer in (H_{2}, He) and (D_{2}, He) systems is reported. The accurate, a prioripotential surface obtained by Krauss and Mies has been employed in a generalized, three‐body Monte Carlo calculation to obtain, as a function of temperature, relaxation times and collision numbers for the 0→2 and the 2→0 rotational transitions in both H_{2} and D_{2}. A negative dependence upon temperature is obtained in each case. The relaxation times for the 0→2 transition in H_{2} range from 7.725×10^{−8} sec at 100°K to 3.491×10^{−8} sec at 700°K. For the 2→0 deexcitation the corresponding values are 9.00×10^{−8} and 4.30×10^{−8} sec. When a van der Waals attraction term, whose magnitude is estimated from PVT data, is added to the Krauss—Mies surface, the values for the 0→2 transition decrease to 3.1×10^{−8} sec at 100°K and 2.0×10^{−8} sec at 700°K. Corresponding decreases occur for the 2→0 transition. Calculated relaxation times for D_{2} are 50%—100% smaller than those obtained for H_{2}. These results are in satisfactory agreement with available experimental data and appear to be more accurate than previous theoretical results.
The energy‐transfer mechanism has been investigated and found to be smooth and continuous with transfer occurring in about 10^{−13} sec. The most favorable approach angle for transfer is found to be about 60°.
Two other empirical potential surfaces have been employed to estimate the effect of potential well depth and the assumption of pairwise additivity of molecular potentials. It is found that as the well depth increases, the relaxation time decreases in a manner previously predicted by Parker. The assumption of pairwise additivity is found to yield results for the relaxation times which are low by about a factor of 2. The magnitude of this error, coupled with calculations employing off‐center, pairwise potentials, indicates that the repulsive centers in H_{2} are located about 0.16 Å from the nuclei.

Theory of the Far‐Ultraviolet Spectrum of Polypeptides in the β Conformation
View Description Hide DescriptionThe electronic excited states in polypeptides of the β conformation corresponding to the lowest energy π—π^{*}transition are derived from molecular‐exciton theory. Transition energies are calculated in the monopole—monopole approximation, and the results are compared with polarized film spectra obtained in the present study, as well as with experimental data of other investigators. It appears that either parallel sheets or mixtures of parallel and antiparallel sheets are present in poly‐L‐lysine solutions and films.

Thermally Stimulated Trap‐Emptying Measurements in Phthalocyanine
View Description Hide DescriptionTraps with a density of 10^{14}/cm^{3} and an activation energy of 0.36 eV were found in both metal‐free and lead phthalocyanine single crystals using thermally stimulated trap‐emptying measurements. These traps were responsible for fast trapping observed in transient current measurements.

On the Equation of State of the Rigid‐Disk Fluid
View Description Hide DescriptionThe modified Yvon—Born—Green (YBG) equation of Rice and Lekner is solved for a system of rigid disks. The equation of state calculated from the solutions of the modified YBG equation is in nearly perfect agreement with the molecular‐dynamics data of Alder and Wainwright up to p/ρkT=4.78, which is the Kirkwood limit for the stability of the fluid phase.

Energy Levels of Np^{3+} in LaBr_{3}
View Description Hide DescriptionThe polarized absorption and emission spectra of single crystals of LaBr_{3}doped with nominally 0.15% and 0.75% ^{237}Np have been recorded between 5000 and 25 000 cm^{−1} at temperatures of liquid helium and nitrogen. Fluorescence excitation spectra and both parallel and perpendicular Zeemanspectra were also recorded. Based on the number, polarization, and magnetic behavior of Stark components appearing in distinct groups, as well as on preliminary 5f‐hydrogenic calculations, 14 absorption groups were identified as levels of the ground electronic configuration 5f ^{4} of Np^{3+}. The assumption of a pure 5f ^{4} electronic configuration does not lead to a satisfactory interpretation of the spectrum; however, the inclusion of electrostatic configuration interaction permits a satisfactory fitting of the observed levels with an rms deviation in energy of 86.4 cm^{−1} using the parameters: E ^{1}=3394.3±29.1, E ^{2}=14.19±0.22, E ^{3}=317.5±1.9, ζ_{5f }=1969.2±10.8, α=35.0±2.2, and β=−802.4±11.3 cm^{−1}. Using 25 crystalline‐field‐split Stark components of the ^{5} I _{4,5,6,7} levels of the ground multiplet, a first‐order crystal‐field perturbation calculation was performed. An rms deviation in energy of 8.0 cm^{−1} is obtained using the parameters: B _{2} ^{0}=−22.8±8, B _{4} ^{0}=−86.7±2.4, B _{6} ^{0}=−70.8±0.9, B _{6} ^{6}=+857.1±12.0 cm^{−1}. The negative value obtained for B _{2} ^{0} represents a crystal‐field shielding in excess of 100% and is discussed in some detail. Parallel and perpendicular Zeeman interactions are also discussed in some detail.