Volume 61, Issue 10, 15 November 1974

Low temperature magnetic susceptibilities and phase transitions in two linear Ni^{2+} salts: TMNC and TMNB
View Description Hide DescriptionWe studied the magnetic susceptibilities parallel and perpendicular to the chain axis in TMNC in the temperatures ranges 20–13 K and 4.2–0.4 K. These experiments lead to T_{N} =(1.195±0.005) K, J/k_{B} =(1.09±0.10) K, D/k_{B} =(2.10±0.46) K. Because of the ferromagnetic character of the intrachain exchange parameter, the dipolar interchain interaction is much more important in TMNC than in isostructural TMMC, as shown by our calculations. In TMNB, a transition to a 3‐dantiferromagnetic ordered state was found at T_{N} =(2.680±0.010) K.

Diffusion measurements in dense gases. The systems He–Ar and He–Ne
View Description Hide DescriptionDiffusion experiments have been carried out in He–Ar and He–Ne mixtures at pressures from 40 to 150 atm and temperatures 80–300°K. Both systems, up to 150 amagat units of density, are in substantial agreement with the predictions of the Chapman‐Enskog theory and the Enskog‐Thorne extension to high density. In the He–Ar mixture, however, deviations are observed around 150°K in the neighborhood of the characteristic potential hole depth of pure Ar.

Spin‐orbit contribution to the zero‐field splitting in CH_{2}
View Description Hide DescriptionThe spin‐orbit contribution to the zero‐field splitting in methylene is calculated at bond angles of 135° and 180° using the correct microscopic Hamiltonian. The two lowest states of ^{1} A _{1} symmetry as well as the lowest states of ^{1,3} A _{2} and ^{1,3} B _{2} symmetry are considered in the second‐order perturbation treatment. Configuration‐interaction wavefunctions obtained using a double‐zeta‐plus polarization quality basis of contracted Gaussian‐lobe functions are used to describe each state. Spin‐orbit contributions to the splitting parameter, D, of 0.023 and 0.0245 cm^{−1} are obtained at 135° and 180°, respectively. Configuration interaction is found to reduce the spin‐orbit contribution at 135° by about 50%. Combining these results with the results for the spin‐spin dipole contribution to D gives D=0.807 cm^{−1} and E=0.049 cm^{−1} at 135° which is slightly higher than the current experimental value of D=0.76±0.02 cm^{−1}. The increase in the value of the parameter D from 0.807 cm^{−1} at 135° to 0.934 cm^{−1} at 180° is observed to come almost entirely from increased spin‐spin contributions at the larger angle.

Photoabsorption of solid carbon dioxide from 7 to 12 eV
View Description Hide DescriptionThe photoabsorption spectra of solid and gas phase carbon dioxide were measured in the region from 7 to 12 eV. Transition energies were found to be shifted in the solid, and one forbidden transition was anomalously enhanced relative to its gas phase counterpart.

Model of pre‐existing traps for electrons in polar condensed media. II. Effect of dipole‐dipole correlation
View Description Hide DescriptionA model of pre‐existing traps for electrons in polar condensed media is further developed. We calculate the distribution of the depth of pre‐existing traps taking into account the interaction between the dipoles. In this manner we consider the effect of temperature on the depth distribution. Inclusion of the dipole‐dipole interaction changes the results significantly.

Radiative and radiationless transition phenomena in 1,4‐, 1,3‐, and 1,2‐diazanaphthalene vapors
View Description Hide DescriptionA pulsed, frequency doubled dye laser has been used to study time and wavelength resolved emission from low pressure quinoxaline, quinazoline, and cinnoline vapors. The S _{1}, ^{1}(n−π*) states of quinoxaline and quinazoline undergo statistical limit intersystem crossing, while the S _{2} (π−π*) states undergo S _{2}−S _{1} and singlet‐triplet intermediate strong coupling. Excitation into S _{2} yields a two‐component ``fluorescence'' having an S _{1}‐type emission spectrum, and a longer component lifetime 10^{2}–10^{3} longer than predicted by the S _{0}−S _{2} f number. This anomalous emission is discussed principally in terms of a sequential decay theory of Tric and co‐workers. Intermediate strong coupling appears to evolve into statistical limit coupling as a function of excitation energy. The ^{3} B _{2} quinoxaline collision free phophorescence lifetime is within a factor of 2 of its value in condensed phases at low temperature. Thus the existance of rotational degrees of freedom in the gas does not significantly enhance the T _{1}→S _{0} intersystem crossing rate, in disagreement with a recent theory. Cinnoline exhibits no detectable long‐lived phosphorescence or intermediate strong coupling emission.

Localized molecular orbitals for polyatomic molecules. I. A comparison of the Edmiston‐Ruedenberg and Boys localization methods
View Description Hide DescriptionThe Edmiston‐Ruedenberg (ER) and Boys localization methods are compared for a number of boron hydrides and carboranes. The Boys localization equations are solved explicitly for the two‐orbital case and an iterative procedure for the multidimensional case is presented. The Boys analogs of Taylor's [J. Chem. Phys. 48, 2385 (1968)] ER equations are derived and the second‐order term is converted into a symmetrized quadratic form which is analogous to the ER equations of Switkes et al. [J. Am. Chem. Soc. 92, 3847 (1970)]. A limited second‐derivative test is employed in order to determine the nature of the convergence, and a transformation based on it is defined which successfully resolves structural ambiguities to which the standard two‐orbital transformation procedure is subject. The Boys and ER localization methods are in at least qualitative agreement for all molecules except 1,2‐C_{2}B_{4}H_{6}, where the Boys localization yields a structure with fractional bonds and no open three‐center B–C–B bonding. Previous ER localizations of 1,2‐C_{2}B_{4}H_{6} resulted in two open B–C–B three‐center bonds and no fractional bonding.

Low temperature magnetic susceptibility of uranium and rare earth tungsten oxide bronzes
View Description Hide DescriptionMagnetic susceptibilities of uraniumtungsten bronzes, U_{ x }WO_{3}, and their thorium‐diluted counterparts, U_{ x }Th_{0.10−x }WO_{3}, have been measured by the Faraday method over the range 1.6–300°K. The sharp, dilution‐independent antiferromagnetic behavior previously reported was not confirmed. Weiss constants observed showed a weak decline with dilution. Susceptibilities of light rare earth bronzes (RE=Pr, Nd) deviated at low temperatures from Curie‐Weiss behavior, probably because of changes in population of intra‐atomic levels. For the heavy rare earth bronzes (RE=Gd, Tb, Dy, Ho, Er), very small Weiss constants were observed. Near independence of the Weiss constants of conduction electron density and rare earth magnetic content suggests that the apparent Curie‐Weiss behavior is mainly a manifestation of crystal field interactions, not an indication of magnetic exchange effects.

Electronic and vibrational spectra of ions in potassium halide matrices
View Description Hide DescriptionOptical and infrared spectra of dichromate ions in KCl, KBr, and KI matrices are reported. Optical spectra of consist of three absorption bands that are attributed to the electronic transitions or and on the basis of molecular orbitals. Fine structure caused by coupled vibration‐electronic transitions is observed in the band. This fine structure further splits at low temperature (77°K) because of the symmetry lowering of the dichromate ion from T_{d} to C _{3v }. Infrared spectra show a number of lines. A model that assumes that the dichromate ion enters the lattice by replacing two halide ions with no charge compensating vacancy satisfactorily explains all the experimental results.

The calculation of equilibrium mole fractions of polar‐polar, nonpolar‐polar, and ion dimers
View Description Hide DescriptionMethods are developed for the calculation of equilibrium concentrations of polar‐polar, nonpolar‐polar, and ion dimers. These methods are based on the work of Stogryn and Hirschfelder, who derived the relative contribution of bound and metastably bound double molecules to the reduced second virial coefficient (B* _{ b } and B* _{ m }). A unique approach for reducing the non‐spherically‐symmetric Stockmayer potential for polar molecules to the Lennard‐Jones 6–12 form φ*=4[r ^{*−12}−(1+Ā)r ^{*−6}] is presented, where Ā is an average dipole orientation parameter and a monotonic decreasing function of temperature. Estimates of polar‐polar equilibrium dimer concentrations are obtained from analytical expressions for B* _{ b } and B* _{ m } derived from this potential. Nonpolar‐polar dimer concentrations are calculated with a similar approach using Ā_{np} (a temperature independent constant) and consideration of the second virial coefficient of gas mixtures. Ion dimers are treated via a pseudo‐second virial coefficient approach. Tables for Ā, B* _{ b }(T*), and B* _{ m }(T*) are given as a function of reduced temperature and dipole moment for polar molecules. Sample numerical calculations are also presented for all the types of dimers discussed, and compared with other results where possible.

Pressure dependence of electronic relaxation: A stochastic model
View Description Hide DescriptionWe have constructed an exactly solvable stochastic model describing the pressure dependence of electronic relaxation processes in polyatomic molecules. From it closed‐form algebraic expressions for time resolved emission intensities and quantum yields are extracted. Fundamental to this model are (1) a variation of the radiative and nonradiative decay rates of the electronic state with vibrational excitation within that state and (2) a ``step‐ladder'' collisional dynamics scheme similar in nature to those investigated by Montroll and Shuler and applied to diatomic molecules. We describe how this model can be used to obtain estimates of the average variation of the radiative and nonradiative decay rates with excess vibrational energy as well as the average vibrational energy transferred per vibrationally inelastic collision and the rate for this energy transfer process. Furthermore, the model suggests physical situations in which ``nonexponential'' electronic relaxation can be expected to be observed.

Microwave spectrum and internal rotation potential of propanal
View Description Hide DescriptionThe gas‐phase microwave spectrum of the gauche rotational isomer of propanal (propionaldehyde, CH_{3}CH_{2}CHO) has been studied in detail. Vibration‐rotation interaction between torsional energy levels which are split by quantum tunneling results in the splitting of several ground‐state absorption lines. Treatment of this interaction by methods described in an earlier paper successfully accounts for the anomalous spectrum. Observation of several predicted transitions (including transitions nominally forbidden) confirms the theoretical treatment and allows an accurate determination of the energy level splitting (471.80±0.07 MHz) of the two lowest levels of gauche propanal. This new information is used in the determination of an internal rotation potential, which is compared with recent theoretical calculations for propanal.

End‐chain flexibility and the nematic‐isotropic transition in liquid crystals: A lattice model of hard particles with rigid, rodlike, central cores and semiflexible pendant segments
View Description Hide DescriptionA simple cubic lattice model is utilized to develop the statistics of a system of hard particles with a rigid, rodlike, central core to each end of which is attached a semiflexible chain (tail). The core occupies L collinear sites on the lattice, whereas each of the tails occupies λ adjoining sites. An energy u (of order k T) is required for a tail segment to make a bend, i.e., to change direction. The partition function for the system is obtained by utilizing DiMarzio's counting method for the configurational partition function and an exact matrix method to determine the partition function for a tail. With L =5 (1≤λ≤6) and L =10 (1≤λ≤9), first order anisotropic (larger fraction of cores pointing in the preferred direction than in either of the two perpendicular directions) to isotropic phase transitions are found. The results of the model are compared with those for completely rigid rods, revealing that our transitions occur at higher densities and with smaller relative density changes. Our model is found to exhibit the same qualitative behavior, with increasing λ, in the transition temperature and transition entropy as has been observed for the nematic‐isotropic transition in various homologous series.

Semiclassical S‐matrix theory of vibrationally inelastic collisions between two diatomic molecules
View Description Hide DescriptionWe derive a semiclassical S matrix for vibrationally inelastic collisions between two diatomic molecules, assuming a collinear geometry. Our theory incorporates a quantum mechanical superposition principle with classical dynamics and, as such, is an extension of the atom‐diatomic molecule theory of Miller. The several approximations to the S matrix differ in the complexity with which the interference between various classical trajectories is treated. We report numerical calculations for H_{2}–D_{2} and D_{2}–D_{2} collisions based on two different interaction potentials. The cruder approximations yield transition probabilities which agree with exact quantum mechanical results to within a factor of 2. More sophisticated approximations to the S matrix yield excellent quantitative agreement with the quantum calculations. We also examine in detail the classical dynamics of the collision process and show that the molecules pass through a number of intermediate states during the encounter.

Simplified impedance/frequency‐response results for intrinsically conducting solids and liquids
View Description Hide DescriptionThe small‐signal ac response is considered of a system containing a single species of positive charge and a single species of negative charge. The charge carriers may be of many different types (ions, electrons,vacancies, etc.) and are assumed to have arbitrary mobilities and valences. Quite general boundary conditions are considered which encompass the range from complete blocking to zero blocking (infinite reaction rate at the electrodes) for positive and negative charges separately. The present paper deals primarily with approximations to an earlier exact solution of the problem which, in general, lead to an equivalent circuit made up of three parallel R C combinations in series. The elements of one of these parallel circuits, associated only with bulk effects, are frequency independent, and those of another, which are associated with nonzero blocking, may often be well approximated as independent. The third R C section arises from diffusion effects, involves frequency dependent elements, and exhibits approximate Warburg frequency response over a considerable frequency range. In general, Cole‐Cole or Nyquist impedance plane plots show three connected arcs, two of which are frequently good semicircles. These arcs are directly associated with the three R C sections. Under many conditions, only two of the three arcs may appear and melding of arcs into each other can also occur. Very simple, as well as less simple, approximations are developed for the impedances of the individual R C sections as well as the over‐all impedance of the system. The accuracy of these approximations is evaluated, and it is shown how they may be used in unambiguous cases to analyze frequency response data to yield estimates of mobilities, valences, electrode reaction rate parameters, and bulk charge concentrations. Surprisingly, it is found that for a certain mobility ratio range, the center arc, associated with electrode reactions, well approximates a depressed semicircle of the Cole‐Cole relaxation time distribution type, yet no distribution of relaxation times is present. Further, in the completely blocking case, where the center approximate semicircle is not depressed but has an infinite radius, the lower frequency portion does not necessarily begin with a vertical segment as frequency decreases but may be curved away from vertical over a considerable frequency range. General impedance results for the present unsupported conduction situation are found to be quite different in some ways from those following from supported electrolyte treatments. Such treatments should thus not be used to analyze unsupported situations. Finally, it is found that the parallel capacitance of the system, which may be far greater than ordinary double layer values, can exhibit appreciable regions of ω^{−m } frequency response with 0≤m ≤2, and with m =0.5, 1, 1.5, and 2 values especially prominent.

Wavelength dependence of the quantum yield of fluorescence and photoionization of indoles
View Description Hide DescriptionThe fluorescence quantum yields φ_{ f } (λ_{ x }) of L‐tryptophan and indole were measured relative to that of Rhodamine B as functions of the excitation wavelength λ_{ x } between 200 and 300 nm. Two different experimental geometries produced identical results, indicating that experimental artifacts were negligible. In aqueous solution at 296 K, φ_{ f } (λ_{ x }) increased by 45% for both solutes in going from 230 to 260 nm. Outside this wavelength region, φ_{ f } (λ_{ x }) was constant to within 2%. Similar results, although with a somewhat smaller shift in φ_{ f } (λ_{ x }), were obtained for tryptophan in an equivolume mixture of ethylene glycol and water EG/H_{2}O at both 296 and at 113 K, the latter temperature being below the glass transition temperature of this medium. The emission spectra and the phosphorescence to fluorescence ratios were independent of λ_{ x }, indicating that the shift in φ_{ f } (λ_{ x }) was not due to intersystem crossing from higher excited states. The shift in φ_{ f } (λ_{ x }) was accompanied by a considerable increase in the quantum yield of photoionization of tryptophan in aqueous solution below 260 nm. Hence, it is concluded that photoionization from higher states competes favorably with internal conversion to the fluorescent singlet state. For indole in methanol at 296 K and in EG/H_{2}O at 113 K, φ_{ f } (λ_{ x }) was independent of λ_{ x } to within 2%.

Luminescence of calcium tungstate crystals
View Description Hide DescriptionFluorescence, excitation, and pulsed fluorescence measurements have been made on a single crystal of CaWO_{4} over a wide temperature range. The temperature dependences of the integrated fluorescence intensities and lifetimes were obtained for different excitation wavelengths. A sharp increase in the fluorescence lifetimes is observed below about 75°K and zero‐phonon lines can be observed. These results are used to formulate a model for the tungstate luminescent center based on the ion in a crystal field of S _{4} symmetry. Energy migration and impurity trapping effects are also discussed.

Molecular model for ice clusters in a supersaturated vapor
View Description Hide DescriptionA molecular model previously applied to prenucleation water clusters is used to examine iceI_{h} embryos. The canonical partition function is evaluated for clusters having from 6 to 64 water molecules. The intermolecular vibrational free energies are extrapolated to clusters containing up to 120 molecules and free energies of formation, nucleation rates, and critical supersaturation ratios are calculated and compared with experiment. For the clusters studied, the iceI_{h} structure appears to be much less stable at all temperatures than the more spherical clathratelike cluster.

New optical method for studying anisotropic diffusion in liquid crystals
View Description Hide DescriptionA new approach to studying diffusion in liquid crystals is described in which the optically observable textural changes in a nematic phase caused by a cholesteric diffusant gives direct visualization of the concentration gradient. Utilizing either homeotropic of homogeneous alignments under different boundary conditions, and with and without an applied magnetic field, the parallel and perpendicular components of the diffusivity have been determined for a cholesteryl ester diffusing into N‐(p ‐methoxybenzylidene)‐p ‐n ‐butylaniline as a function of temperature. The diffusion coefficients in the isotropic phase can also be determined by annealing at a high temperature and quenching to room temperature, whereupon the cholesteric texture is again developed. Values of the diffusion coefficients and the activation energies of the diffusion process are discussed and compared to other available data.

Atomic force constants and the heat capacities of materials at elevated temperatures
View Description Hide DescriptionAtomic force constants for C, Si, and Ge in diamond,graphite, and crystalline silicon and germanium are determined by the analysis of the heat capacities of these materials. These force constants are then compared with those found in simple molecular analogs of these crystals. The dependence of the atomic force constants upon crystal and molecular structure is analyzed in terms of an ``atoms in molecules'' model. Using this model and approximate electron densities, determined by either Slater‐type atomic orbitals or the Thomas‐Fermi theory, the magnitudes of the atomic force constants were estimated and compared with their experimental values.