Volume 52, Issue 11, 01 June 1970

New Adsorption Isotherm for Heterogeneous Surfaces
View Description Hide DescriptionA general method is proposed to obtain adsorption isotherms for heterogeneous surfaces from the arbitrary energy distribution functions if the Langmuir isotherm represents the individual homotattic sites. The method is limited to the temperature dependent distribution functions only. It is observed that the number of distribution functions, yielding physically meaningful isotherms, is extremely restricted on mathematical grounds. The method yields only one adsorption isotherm that is new and simple; the corresponding distribution function, however, seems to be more characteristic of homogeneous surfaces having a strictly limited energy distribution rather than that of heterogeneous surfaces with a wide variation of distributive energies.

Flash Photolytic Production, Reactive Lifetime, and Collisional Quenching of
View Description Hide DescriptionCollisional quenching of at room temperature by O_{2} and a variety of foreign gases has been investigated with a pulsed lifetime measurement technique. has been produced in a pulsed mode through flash photolysis of O_{2} in the vacuum uv and has been detected through the emission of the (0, 0) band at 7620 Å of the forbidden transition. The (0, 0) band intensity has been measured as a function of time after the photolysis flash and as a function of the O_{2} and foreign gas pressures. Quenching rate constants are derived from the reactive lifetimes. The photolytic production of from O_{2} and the quenching by O_{2} has been studied at O_{2}pressures from 0.02–100 torr. The observations at low O_{2}pressures from 0.02 to about 1 torr are consistent with the previously established fast production mechanism, in the Schumann–Runge continuum region. No emission of the (1, 1) and (2, 2) atmospheric bands has been observed indicating that under the conditions employed, is either initially formed only to a relatively small degree in this mechanism or that is relaxed or quenched by O_{2} within less than 10^{3} collisions. From the (0, 0) band fluorescence decay rates measured at O_{2}pressures from 0.02 to about 0.5 torr a quenching rate constant of 4.5 × 10^{−16} cm^{3} molecule^{−1}·sec^{−1} is derived. At higher pressures, the decay rate deviates from a linear dependence on the O_{2}pressure indicating that the reactive lifetime is influenced by some secondary process at these pressures. The decay rate measured for example at 20 torr, O_{2} would correspond to a quenching coefficient of 4.8×10^{−17} cm^{3} molecule^{−1}·sec^{−1}. Quenching of by He, Ne, Ar, Kr, Xe, H_{2}, N_{2}, CO, CO_{2}, SF_{6}, NH_{3}, H_{2}O, CH_{4}, C_{2}H_{6}, C_{2}H_{4}, NO, NO_{2}, and N_{2}O has been investigated by measuring reactive lifetimes at constant O_{2}pressures as a function of the added foreign gas pressures. Quenching rate constants are reported and compared with previous results.

Asymptotic Relations between the Thomas–Fermi–Dirac and Thomas–Fermi Atom Models. II. Extension of the Case of Low Atomic Number
View Description Hide DescriptionThe asymptotic relation between the pressure with exchange in the Thomas–Fermi–Dirac atom model and the corresponding pressure without exchange in the Thomas–Fermi model for the case of low atomic number considered in the first paper of this series is generalized by including a correction corresponding to the first‐order Coulomb contribution to the energy of the atom, in addition to the kinetic energy of the electrons alone. Comparison is made with numerical results obtained by direct solution of the Thomas–Fermi–Dirac equation.

Relaxation Behavior of the Freely Jointed Chain
View Description Hide DescriptionA method is presented for treating the relaxation behavior of the freely jointed chain model of a random coil polymer. Exact results are exhibited for the relaxation of quantities linear in chain coordinates. For the treatment of quantities quadratic in chain coordinates, a numerical approach is employed and exemplified by obtaining the autocorrelation in the square of end‐to‐end length for chains of up to 16 beads. In both cases, the rapid approach of the behavior of the freely jointed chain of beads to that of the Rouse model of statistical segments is demonstrated.

Collision Induced Dissociation of Molecular Ions
View Description Hide DescriptionVelocity vector distributions of the fragment ion products of the dissociative collisions of O_{2} ^{+}, N_{2} ^{+}, NO^{+}, and N_{2}O^{+} with He have been determined, using projectile‐target relative kinetic energies which are one to three times the bond energy of the molecular ion. The most probable dissociation event produces a fragment ion whose velocity is very nearly the same as that of the original projectile ion. Fragment ions also appear at smaller velocities and larger scattering angles, and the importance of these features increase with increasing initial relative energy. Three models for the dissociation are discussed, and it is concluded that a version of the stripping model is most nearly consistent with the data.

Molecular Motions in Several Solids Studied by Nuclear Magnetic Relaxation in the Rotating Frame
View Description Hide DescriptionRotating frame nuclear magnetic relaxation times have been measured as a function of temperature from 117 to 290°K for perfluorocyclohexane, cyclohexane, 2,2‐dichloropropane, neopentane, and tetramethylammonium iodide. The data are interpreted in terms of molecular rotation and diffusion in the solid state.

Application of an Approximate Percus–Yevick Equation for Liquid Water
View Description Hide DescriptionAn approximate Percus–Yevick equation for liquid water is suggested. The approximation involves the splitting of the potential of average force for two particles into a sum of a direct, angle‐dependent pair potential and an angle‐independent indirect potential. The angle‐dependent pair potential is chosen in such a way that the characteristic tetrahedral geometry for the relative orientation of two water molecules is favored. Employing this potential function in the integral equation produces a pair correlation function which carries the main features of the experimental pair correlation function for liquid water.

Far‐Infrared and Raman Spectra of Phosphonium Chloride and Phosphonium Chloride‐d _{4}
View Description Hide DescriptionThe far‐infrared spectra of thin films of PH_{4}Cl and PD_{3}Cl have been recorded at −170°C. Raman spectra of polycrystalline samples of both compounds were also recorded at −170°C. One libration and three translations were observed as well as eight internal modes. Several combinations and overtones were assigned and the zone‐edge wavenumber of a second libration has been inferred. The barrier restricting re‐orientation of the PH_{4} and PD_{4} ions has been calculated from the observed librational wavenumbers to be 8.5 kcal/mole and forces contributing to the barrier are discussed. The lattice dimensions of PH_{4}Cl were determined to be and from the x‐ray diffraction pattern of a polycrystalline sample.

Electron Paramagnetic Resonance of (Agpy_{2})^{2+} in Nitric Solution at 77°K
View Description Hide DescriptionThe paramagnetic resonance spectrum of (Agpy_{2})^{2+} in frozen nitric solution has been observed at 77°K. It exhibits silverhyperfine as well as superhyperfine structure, this latter due to interaction with two equivalent nitrogen nuclei. Due to a strong axial anisotropy the principal values of the hyperfine and superhyperfine interaction tensors may be determined. Wavefunctions are calculated for the unpaired electron as well as its density in the metal ion and the ligands. The experimental values are consistent with the picture of a hole in the Ag shell in an oblate tetragonal octahedron, which is partially transferred to an nitrogen hybrid. Coefficients for the wavefunctions are given and the ring C–N–C angle found in reasonable agreement with independently estimated values.

Comments on the Analysis of Atomic Correlation Energies
View Description Hide DescriptionAnalysis of correlation energies is advocated in terms of average values of electronic kinetic energy, electron–nuclear attraction energy, and electron–electron repulsion energy, rather than pair energies. Exploratory calculations on the two‐electron and three‐electron isoelectronic sequences are reported.

Ethereal Electrons
View Description Hide DescriptionSolutions of K, Rb, and Cs in dimethoxyethane consist primarily of metal cations and anions. The latter are ionized by light at wavelengths between 700 and 1000 nm to yield solvated electrons. Electron recombination occurs by a second‐order mechanism involving an M·species, and rate constants have been estimated from ESR data. Photoelectrons emitted from Rb^{−} are highly polarized, and an explanation combining spin–orbit and exchange interactions with an adiabatic dissociation is proposed.

Induction Forces. An Exact Treatment of Charge Overlap Effects through Third Order
View Description Hide DescriptionThe interaction of a ground‐state atom or ion, consisting of a nucleus and a single electron, with a charge is considered in detail as a model for discussing induction forces through third order in the interaction potential. Expressions for all the angular components of the first‐order wavefunction and for all the individual nonexpanded second‐order induction energies are given in closed form. Exact numerical values for the total third‐order induction energy and its individual nonexpanded components, through terms varying as at long range, are given in tabular form for the H–H^{+} interaction. The results are discussed with emphasis on the effects of charge overlap on induction forces through third order and on the complicated structure of the third‐order energy in terms of its individual nonexpanded induction energies. In the Appendix the Green function approach to the problem is discussed with the relevant Green functions being obtained as solutions of differential equations rather than by direct summation of their spectral expansions.

Adsorption of Inert Gases on Tungsten: Measurements on Single Crystal Planes
View Description Hide DescriptionThe adsorption of Ar, Kr, and Xe on the (110), (120), (100), (211), and (111) planes of a tungstenfield emitter was studied under conditions of immobile adsorption and also under conditions of surface equilibrium. The relative dipole moments and heats of binding could be determined, and it was found that both these quantities were largest on the (110) plane. A discussion in terms of charge transfer bonding is presented to rationalize these results. It was found that chemisorption of oxygen prevented the relatively strong first layer adsorption observed on the clean surface, and also the dipole moment associated with it.

Simple and Accurate Approximation for the Centrifugal Factor in RRKM Theory
View Description Hide DescriptionAn approximate form for the low pressure centrifugal effect is derived for RRKM unimolecular rate theory calculations. Comparisons are made with earlier approximations and with a more exact result. The effects on the observed activation energy and extension to the region of falloff are described.

Effect of Ion Pairing on the Value of the Naphthalene Anion Radical
View Description Hide DescriptionMeasurements have been made of the values of the naphthalene radical anion associated with several alkali‐metal cations at a series of temperatures and in different solvents. It has been suggested previously that the temperature dependences of the factors of spectra exhibiting alkali‐metal splittings can be explained either in terms of equilibrium changes between two paired species (Hirota model) or in terms of changes in the populations of the vibrational energy levels of a paired species of fixed electronic structure (Atherton–Weissman model). Evidence is presented to show that the Hirota model adequately accounts for the g‐factor variations of the sodium naphthalenide ion pair in tetrahydrofuran, but not for the cesium naphthalenide ion pair in 1,2‐dimethoxyethane. It is argued that the latter ion pair is probably a tight ion pair which does not incorporate solvent molecules, and that the variations of the spectral parameters of such complexes are best described by the Atherton–Weissman model.

Theory of the Hyperfine Splittings of Pi‐Electron Free Radicals. III. Methyl Radical in a Pyramidal Configuration: Temperature Dependence of the Hyperfine Splittings
View Description Hide DescriptionNonempirical calculations for methyl radical (CH_{3}·) in a pyramidal configuration were performed using two minimum basis sets of Slater‐type orbitals, one in which orbital exponents were chosen according to Slater's rules (unoptimized) and the other in which they were optimized by minimization of the SCF energy. The spin‐restricted SCF plus configuration‐interaction method, including all spin‐adapted configurations with single and double excitations of space orbitals, was employed. The temperature dependence of the contact hyperfine splittings was computed assuming that the variation with temperature arises from the out‐of‐plane bending motion. Agreement with experiment at various temperatures is good. The optimized‐basis values of the temperature coefficient of the proton splitting, , are about 20%–50% too large and the unoptimized‐basis results are about 10%–25% too small. Temperature coefficients of the carbon‐13 splitting calculated using the optimized and unoptimized basis sets also bracket the experimental values, from which they deviate by less than 10%, which is within the experimental uncertainty. The variation of the spin densities at the magnetic nuclei with the out‐of‐plane angle is analyzed in detail. Other results of the calculation are discussed, namely, the equilibrium molecular geometry, an approximate frequency for the bending motion, and the incomplete orbital following.

Crystal Structure of Luminescent ZnSiP_{2}
View Description Hide DescriptionZnSiP_{2}crystallizes with the chalcopyrite structure: there is no detectable difference in x‐ray scattering between luminescent and nonluminescent crystals. The level of impurity, either in the form of chemical dopant, physical defect, or a departure of less than about 1% from complete order at the Zn and Si sites hence determines if the crystal luminesces or not on excitation by an electron beam. The lattice constants of this tetragonal crystal at 298°K are and . The space group is , and there are four formulas in the unit cell. A total of 2023 reflections were measured with the luminescent crystal, and 1600 with the nonluminescent crystal, using pexrad. The final agreement factor, based on a combination of 197 symmetry‐independent reflections from the first crystal and 176 from the second, is 0.049. Each Zn is tetrahedrally surrounded by 4 P atoms at 2.375 ± 0.001 Å distance, and each Si by 4 P atoms at 2.254 ± 0.001 Å. All phosphorus tetrahedra have four P–P edges of length 3.832 ± 0.002 Å. The two remaining independent P–P edges are of 3.968 ± 0.001 Å distance in the ZnP_{4} tetrahedra, and are of 3.684 ± 0.001 Å in the SiP_{4} tetrahedra.

Dipole Moment of the First Excited State of Fluorobenzene
View Description Hide DescriptionA Stark effect is observed in the rotational fine structure of the 0–0 band of the lowest‐lying singlet state of fluorobenzene. Splittings are found in both and branches. This enables us to determine the excited‐state dipole moment to be . This result is discussed in relation to previous measurements on substituted benzenes, and it is shown that the previously observed correlation between structure and dipole moment for excited states also extends to fluorobenzene.

Identifying the Lowest Excited Singlet State of Biphenyl and Its Analogs
View Description Hide DescriptionFrom experimental evidence it is inferred that the broad structureless absorption band of biphenyl at about 2500 Å is composed of bands from three transitions, a weak transition similar to the transition of benzene and two stronger transitions similar to the and transitions of benzene. Bands from these transitions are separated in rigid biphenyl analogs such as 9,10‐dihydrophenanthrene and fluorene. Certain fluorescence characteristics of biphenyl (such as decay time and quantum yield ) are distinctive of the weak and “hidden” transition and a dramatic change in these characteristics is observed when a crossover of the two lowest excited states is achieved in the analogs of biphenyl. Specific substituents, when positioned in the para position (such as a phenyl or vinyl group in p‐terphenyl or 4‐vinylbiphenyl, respectively), are particularly efficacious in producing a crossover of levels. In these cases, the lowest excited state is an allowed transition similar to one component of the degenerate transition in benzene. Since the intense absorption bands are maximally shifted by substituents on the para position, the transition moment must be long‐axis polarized as predicted theoretically. Bridging is particularly effective in producing a bathochromic shift because the phenyl rings can be constrained to lie in a relatively coplanar and linear configuration. The magnitude of the shift imparted to the various states depends on the bridging element. From the value of the ratio , the assignment of the lowest excited singlet state can be determined: In fluorene, dibenzofuran, and 9,10‐dihydrophenanthrene, it is ; in carbazole and phenanthrene, ; and in 2‐phenylfluorene and 2‐phenyl‐9,2′‐methylenefluorene, .

Elementary Model of the Broadening of Localized Transitions in a Simple Liquid
View Description Hide DescriptionThe line shapes corresponding to localized electronic or vibrational transitions in a simple liquid are studied using a model. The model is defined by a Hamiltonian taken to be linear in the instantaneous force acting on a molecule. One consequence of this assumption is the appearance of the force autocorrelation function in the line‐shape formulas. It is shown that in the weak coupling limit, in the lowest order of approximation, the transition line shape is Lorentzian. In the next approximation the line shape has a frequency dependence given by the convolution of the lowest‐order Lorentzian with the frequency‐dependent force autocorrelation function. Some implications of the model are discussed, and a rationalization given to interpret variations in the line shapes of Raman transitions corresponding to totally symmetric and nontotally symmetric vibrations.