Volume 50, Issue 4, 15 February 1969

Photoionization of HCN: The Electron Affinity and Heat of Formation of CN
View Description Hide DescriptionA re‐examination of the photoionization of HCN has revealed two processes, , and , not previously reported. The difference in threshold values for the two processes leads directly to the electron affinity for CN, 3.82 ± 0.02 eV. The threshold for the second process leads to , but remains a major source of uncertainty.

Optical Spectra of Cr^{3+} Impurity Ions in Ferroelectric LiNbO_{3} and LiTaO_{3}
View Description Hide DescriptionThe optical absorption,luminescence, and excitation spectra of LiNbO_{3} and LiTaO_{3}doped with chromium impurities are examined as a function of temperature. Several interesting differences between these spectra and those of other chromium‐doped oxides are noted. The most important differences are the large halfwidth of the Cr^{3+}‐ion “R” lines (∼50 cm^{−1} at 4.2°K) and the absence of any “R”‐line luminescence down to 4.2°K. Instead, a broadband emission peaking at about 1 μ is observed. It is shown that these differences arise from the low value of the crystal‐field parameter at the Cr^{3+}‐ion site in LiNbO_{3} and LiTaO_{3}, so that the zero‐phonon state of the Cr^{3+} ion lies at a lower energy than the state. Point‐charge calculations of for several oxides, including LiNbO_{3} and LiTaO_{3}, and other considerations suggest that the most probable sites of the Cr^{3+}‐ion impurities are the Nb/Ta sites and not the Li sites.

Multiple‐Quantum Transitions in Nuclear Magnetic Resonance of Strongly Coupled Spin Systems
View Description Hide DescriptionThe nuclear magnetic resonance multiple‐quantum spectra of thiophene and o‐dichlorobenzene have been determined and analyzed. Yatsiv's theory, in spite of the fact that in the present cases simplifying assumptions are not fulfilled, correctly predicts frequencies, frequency shifts, and rf field amplitudes for maximum signal. A single less restrictive assumption is proposed which leads to the same conclusions as Yatsiv's. The intensities observed for MQ transitions are weaker than those predicted and the disagreement increases with the number of quanta involved.

NMR Doublet Splitting in Aqueous Montmorillonite Gels
View Description Hide DescriptionDoublet splitting in the NMRspectrum of montmorillonite clay–water systems arises from the preferred orientation of water molecules on clay gels. The small magnitude of the doublet splitting compared to that expected for motionless molecules indicates dynamic preferential orientation of the water in the clay–water systems. The fact that the doublet splitting is observed for the D_{2}O–clay gels at all temperatures but only for the H_{2}O–clay gels at low temperatures and relatively small water content suggests the importance of hydrogen exchange in the observation of the H_{2}O doublet. Hydrogen exchange “washes out” the proton doublet but not the deuteron doublet. The reason for this is the difference in the proton and deuteron nuclear spininteractions which give rise to the doublet.

Optical Absorption by Charge‐Transfer Excitons in Linear Molecular Crystals
View Description Hide DescriptionThe optical absorption of linear molecular crystals is investigated theoretically. A generalization of the theory of excitons in linear molecular crystals was carried out by Merrifield who constructed the excited states of the crystal by mixing monomolecular states (Frenkel excitons) and bimolecular ionized states in which an electron is removed from one molecule in the crystal and placed on a second (charge‐transfer states). If the monomolecular optical transition is allowed, we find that the optical absorption consists of a series of bound states and a continuum absorption, which gives rise to photoconductivity; the strength of all the absorption is predominantly borrowed from the Frenkel exciton. The experimental possibilities may be classified into three cases: (1) the Frenkel exciton, the charge‐transfer state with electron and hole at nearest neighbors, and the state with the electron and hole at large separation are well separated in energy. This case gives rise to a strong absorption line, small charge‐transfer sidebands, and very small absorption into the continuum. (2) Near resonance between Frenkel and nearest‐neighbor charge‐transfer states. The strong absorption is now shared by two absorption lines with weak sidebands and very small continuum absorption. (3) Resonance between the Frenkel state and the states with the electron and hole at large separation. This case corresponds to autoionization in a solid, the bound states have very weak absorption, and a strong sharp line will be observed within the continuum absorption. The width of the resonance line is directly proportional to the background absorption.

Intramolecular Triplet Energy Transfer in Poly(1‐vinylnaphthalene)
View Description Hide DescriptionPoly(1‐vinylnaphthalene) in a rigid glass at 77°K exhibits a delayed fluorescence due to triplet–triplet annihilation following intramolecular triplet energy transfer through the naphthalene chromophores. Delayed fluorescence does not appear in the spectrum of 1‐ethylnaphthalene at equivalent concentrations, about . Delayed emission from the polymer but not from 1‐ethylnaphthalene is quenched by piperylene. End groups are more important than chain length in the control of triplet migration in the homopolymer; experiments with 1‐vinylnaphthalene‐methyl methacrylate copolymers, however, indicate that some minimum chain length is required for efficient annihilation.

Self‐Consistent Field Theory for the Electronic Structure of Polymers
View Description Hide DescriptionA general SCF–SCAO theory for computations of the electronic structure in polymeric species is presented. The theory is essentially a tight‐binding model expressed in a manner close to the self‐consistent field–LCAO matrix formalism and restricted to closed‐shell cases. Particular care has been taken to ensure a theory which can be easily applied in practical applications. A computer program, polymol, has been programmed and a short description is included at the end of this paper. Throughout the paper reference is given to the (H_{2}) infinite chain, as an example.

Electronic Consequences of Vibrational Deficiency in Polyatomic Molecules
View Description Hide DescriptionVibrationally deficient molecules have been defined as those molecules whose symmetry species for the normal vibrational modes of a molecule fail to span all of the irreducible representations of the corresponding point group. A comprehensive group‐theoretical study of all of the finite point groups and of the infinite point groups and has been undertaken in order to determine the extent of vibrational deficiency for various molecular geometries. An important electronic consequence of vibrational deficiency is the identification of special examples of electronic transitions which are forbidden even when considering perturbation by a single antisymmetric normal vibrational mode. Thus, in the second part of this group‐theoretical study, electric‐dipole selection rules have been determined in order to ascertain possible examples of these forbidden transitions in vibrationally deficient molecules. First‐order forbidden vibronic transitions are found to be physically possible in certain polyatomic molecules in , , , , and point groups. An analysis of electronic transitions of vibrationally deficient molecules in the above point groups was made in order to establish and to predict examples of this specially forbidden transition which will be manifest as an anomalously weak absorption. A second electronic consequence of vibrational deficiency is predicted in small polyatomic molecules where missing antisymmetric vibrations may have a critical influence on the pathway of intramolecular radiationless processes. The probability of a radiationless transition in an isolated polyatomic molecule may be considered to depend upon a vibrational factor and an electronic factor. This present work indicates that in vibrationally deficient molecules, the electronic factor may have a significant influence on the nonradiative transitions. The fluorescence of SO_{2} from the second excited singlet state to the ground state is considered as a possible example of the influence of the electronic factor on radiationless processes in vibrationally deficient molecules.

Vibrational Energy Transfer in Gases: Atom–Triatomic‐Molecule and Diatomic–Diatomic‐Molecule Collisions
View Description Hide DescriptionThe interconversion of molecular vibrational energy and translational energy is investigated by a Monte Carlo method and numerical integration of the equations of motion. Colinear collisions of a linear triatomic molecule (having Morse bond potentials) with an atom via a Lennard‐Jones 6–12 potential were investigated, and histograms characterizing the probability of transfer of various amounts of energy were constructed. Colinear collisions of two diatomic molecules (Morse bond potentials) interacting via a 6–12 potential were studied, and information on vibration–vibration transfer was obtained. In both models, total energies were in the range 1–20 × 10^{−12} erg.

Collisional–Radiative Electron–Ion Recombination Rate in Rare‐Gas Plasmas
View Description Hide DescriptionThe minimum de‐excitation rate of a recombining electron in the atom is calculated by using Gryzinski's formulation for the electron–atom collision process and Bates and Damgaard's Coulomb approximation for the radiative transition probability. The calculated minimum rate is taken to be the electron–ion collisional–radiative recombination rate. The electron–ion recombination rates are measured in a decaying plasma produced by a transient discharge. The comparison between the theoretical calculations and experimental results for five rare‐gas (He, Ne, Ar, Kr, and Xe) plasmas is presented.

Temperature Coefficient of Hypersonic Sound and Relaxation Parameters for Some Liquids
View Description Hide DescriptionThe spontaneous Brillouineffect has been used to determine the variation of sound speed with temperature in the temperature range of − 30° to + 160°C above the relaxation frequencies in dibromomethane, dichloromethane, and carbon disulfide, below any relaxation frequency of acetone and nitrobenzene, and in the region of dispersion in chloroform, carbon tetrachloride, benzene, and acetic acid. In some cases the speeds have been corrected for dispersion. The temperature coefficient of sound and the parameters that characterize the relaxation have been evaluated and compared with other determinations. The sound speeds as a function of temperature have also been measured in water and five viscous liquids; 1‐octanol, ethylene glycol, aniline, glycerol, and pentachlorobiphenyl. A simplified form of the Isakovich–Chaban theory involving a single temperature‐dependent relaxation time has been used to predict the dispersion in glycerol and pentachlorobiphenyl and the amplitude absorption coefficient in glycerol from ultrasonic data. The predicted speeds are in quantitative agreement with the measured values. The observed amplitude absorption coefficient is shifted to higher temperature as the more complete theory of Isakovich and Chaban would predict.

Radial Distribution Functions and Equation of State of the Hard‐Disk Fluid
View Description Hide DescriptionWe evaluated by a Monte Carlo method the hard‐disk radial distribution function at densities: ( is equivalent to the close‐packed density of hard disks). The results were used to find out the relative merits of solutions of the four integral equations (the Born–Green–Yvon, the modified Born–Green–Yvon, the Percus–Yevick, and the convolution–hypernetted‐chain equations) describing approximately the behavior of the radial distribution function. We also evaluated the first several density coefficients of the pressure and the radial distribution functions corresponding to these approximate equations. The Padé approximants formed by the calculated coefficients for the approximate equations were found to satisfactorily describe pressures for these equations over the range of low to medium density of the hard‐disk fluids. A simple analytic expression, Eq. (13), for the pressure which describes fairly well the dense hard‐disk fluid was also derived by using the modified Born–Green–Yvon equation. This expression yields better or comparable results for virial coefficients and pressures at low and medium fluid densities compared with the results obtained from the Percus–Yevick equation in combination with the virial theorem.

Polarization of Electronic Transitions of Aromatic Hydrocarbons
View Description Hide DescriptionThe polarizations of the fluorescence,phosphorescence, and triplet–triplet absorption of a series of aromatic hydrocarbons were determined by the method of “photoselection.” The compounds studied; phenanthrene , chrysene , and picene exhibit relatively intense and well‐characterized luminescence as well as clearly defined singlet–singlet and triplet–triplet absorption spectra. All spectra including the singlet–singlet absorption spectra were measured in dilute solutions of organic glasses at 77°K. For all five compounds the polarization of the fluorescence was primarily in‐plane short axis, the phosphorescence principally out of plane, and the T–T absorption mainly in‐plane long axis. Variations in the polarization of vibronic bands within a given transition were noted, as were differences in detail between light and heavy compounds. The polarization results permit the assignment of the states involved in these transitions in addition to confirming the , nature of the upper triplet state.

Electrical Conductivity of Silver Bromide Membranes and the Diffuse Double Layer
View Description Hide DescriptionElectrical impedancemeasurements have been made on a system consisting of an AgBr membrane separating identical aqueous solutions of AgNO_{3}. Metallic silverelectrodes immersed in the solutions complete a cell for dc resistancemeasurements related to the transport of Ag^{+} ions through the membrane/solution system. Measurements have been made at solute concentrations between and and at temperatures ranging from 20°–180°C, with pressurization of the conductance cell. The results obtained are interpreted in terms of a theoretical description which treats the specific resistance of the membrane as a sum of two parts, one of which is simply related to the resistivity of AgBr in bulk. The other component arises from the formation of diffuse double layers at the membrane/solution interfaces. Analysis of the data in terms of this theory permits the evaluation of , the partition coefficient for Ag^{+} ions, which is equal to the ratio of the concentration of Ag^{+} ions in the aqueous solutions at the isoelectric point to the concentration of Ag^{+} interstitial ions in bulk AgBr. The concentration of Ag^{+} ions in aqueous solution at the isoelectric point is also determined. It is found that , and , where is the absolute temperature, and , the Boltzmann constant, is equal to 8.61×10^{−5} eV/°K. Our values for are higher than those reported by other authors working with freshly prepared sols and with systems similar to that employed in this study. These discrepancies are attributed to aging effects and to differing experimental conditions.

Lingering Time of the Proton in the Wells of the Double‐Minimum Potential of Hydrogen Bonds
View Description Hide DescriptionThe movement of a proton which moves in a one‐dimensional effective double‐minimum potential and can pass by means of the tunnel effect from one well into the other was investigated. The lingering times of the proton in the potential wells (a) and (b) were calculated for more than 150 potential models as functions of the height of the potential barrier separating the two wells, the energy difference , and separation of the minima. In the determination of the lingering times, it was assumed that the proton at time is to be found with certainty in one of the wells and can be represented by means of a statistical operator related to the eigenstates of a one‐well Hamiltonian , respectively. The times determined on this basis were compared with those which result with a quasiclassical method from the classical frequency of oscillation of a particle in a well and from the penetration coefficient of the potential barrier. The deviation between the values determined with both methods is largest if an eigenvalue of becomes approximately equal to an eigenvalue of . For the potential model a polynomial of fourth degree in the position coordinate was chosen. The eigenfunctions of as well as those of the effective Hamiltonian corresponding to were represented as linear combinations of eigenfunctions of the harmonic oscillator with angular frequency . was chosen so that the mean square deviations of the approximated eigenvalues of became as small as possible for the states of lowest energy.

Ring‐Puckering Vibration of 2,3‐Dihydrofuran
View Description Hide DescriptionThe far‐infrared spectrum of 2,3‐dihydrofuran vapor has been examined from 33 to 500 cm^{−1}. Twelve sharp branches have been observed between 70 and 350 cm^{−1}. These bands are assigned to transitions of the anharmonic ring‐puckering vibration which is described by the following relation in reduced coordinates: . Such a potential predicts a puckered molecule in the ground and first excited states, a barrier to planarity of 83 cm^{−1}, and a 0–1 transition of 20.5 cm^{−1}. There is considerable disagreement between the previously predicted far‐infrared spectrum and that observed.

Dependence of Friction at Wet Contacts upon Interfacial Potential
View Description Hide DescriptionAn analysis is made of the forces contributing to the coefficient of friction between two solids, at least one of which is an electronic conductor, through a film of liquidelectrolytes. It is shown that the friction coefficient should vary parabolically with potential. The derived expression, without calibrated constants, fits experimental measurements of the dependence of friction coefficients as a function of applied interfacial potential.

Electron Paramagnetic Resonance Studies of the Triplet State of Coumarin and Related Compounds
View Description Hide DescriptionElectron paramagnetic resonance and optical experiments have been performed on the lowest photoexcited triplet state of coumarin and structurally related molecules which were randomly oriented in a rigid matrix at 77°K. The fine structure of the paramagnetic resonance spectrum of coumarin measured at 9.2 GHz can be described by the spin Hamiltonian with the zero‐field‐splitting energies , and , assuming an isotropic value. These zero field splitting energies and a phosphorescence lifetime of 0.54 sec indicate that the lowest triplet state of coumarin is of a character.

Quantum Transition Probabilities for Atom–Triatomic‐Molecule Collisions
View Description Hide DescriptionThe method of Shuler and Zwanzig is extended to permit the calculation of collisional transition probabilities for triatomic molecules having harmonic intramolecular potentials and interacting impulsively with the bombarding atoms. Only colinear systems are considered. The results are qualitatively similar to those obtained for atom–diatomic systems. Excitation of the symmetric mode of oscillation is favored over the antisymmetric mode in the systems considered.

Fluorescence of Benzene Vapor at Low Pressures
View Description Hide DescriptionThe intensity and spectral distribution of fluorescence from the first excited singlet state of benzene in the pressure range 0.05–7 × 10^{−5} torr has been studied by monitoring a number of prominent bands. Fluorescence was excited by Hg 2537‐Å radiation. At pressures below 0.01 torr, the intensity of every band monitored is directly proportional to benzene pressure. This indicates that both the quantum yield and the spectrum of benzene fluorescence are invariant in this pressure domain, at least to within the 10% scatter of the data. The constant quantum yield is estimated to be near 0.4 so that significant non‐radiative relaxation occurs. These pressures extend by more than two orders of magnitude into the low‐pressure region where hard‐sphere collisions cannot effect relaxation of molecules. The implications of these data with respect to radiationless relaxation processes in isolated molecules are discussed. Collision‐induced relaxation (probably vibrational relaxation) of some of the benzene vibronic states excited by Hg 2537‐Å absorption can be observed at 0.05 torr, and this has been studied in pure benzene and in mixtures of benzene and CO. The efficiency of ground‐state benzene in depopulating these states is about one in two hard‐sphere collisions. CO is about half as effective. The rate of vibrational relaxation by CO is seen to differ among the several excited states populated by Hg 2537‐Å absorption.