Volume 61, Issue 9, 01 November 1974

Magnetothermodynamics of Ce_{2}Zn_{3}(NO_{3})_{12} · 24H_{2}O. I. Heat capacity, entropy, magnetic moment from 0.5 to 4.2 °K with fields to 90 kG along the a crystal axis
View Description Hide DescriptionThe magnetic moment and heat capacity of a 4.059 cm diam. spherical single crystal of ceriumzinc nitrate hydrate (CZN) has been measured with stabilized fields of 0, 1000, 2500, 5000, 10 000, 15 000, 25 000, 40 000, 65 000, and 90 000 G along the a crystal axis, from 0.5 to 4.2°K. The zero of electronic entropy was reached at fields of 90, 65, and 40 kG and the lower temperatures. The isoerstedic entropy changes derived from heat capacity series were interconnected by 28 series of temperatures vs fields on isentropes. Analysis of the heat capacity data established that the first excited doublet is (61.0±0.3+7.8×10^{−10} H ^{2}) cal/mole (h/2π) above the zero field ground state.H is in gauss. The splitting factor of the ground state doublet was evaluated calorimetrically as g _{H}=1.817_{5}−7.88×10^{−12} H ^{2} G ^{−2}. Near 0.5°K, and over the range 40–90 kG, the total magnetic moment reaches temperature‐independent limits at each field. Subtracting the low temperature limiting value of the temperature‐dependent moment, 5075–6.60×10^{−8} H ^{2}G · cm^{3}/mole Ce^{3+}, from the total, enabled the evaluation of the differential temperature‐independent susceptibility as 2.632×10^{−2}−7.8×10^{−14} H ^{2} cm^{3}/mole Ce^{3+}. Thus, M _{limit T→0} = (5075+2.632×10^{−2} H−6.60×10^{−8} H ^{2}−2.6×10^{−14} H ^{3}) G · cm^{3}/mole Ce^{3+}, where H is in gauss. Smoothed correlated values of the heat capacity,entropy, enthalpy, internal energy, magnetic moment and its isoerstedic temperature coefficient, differential isothermal magnetic susceptibility, and the isothermal work of magnetization have been tabulated over the range 0–90 kG and 0.5–4.2°K. The problem of obtaining crystals of CZN which approximate stoichiometric proportions has been discussed. The principal purpose of the data is to lay a foundation for subsequent measurements needed to establish a temperature scale for CZN to the millidegree region.

Multiple scattering method based on overlapping atomic spheres with application to the TCNQ molecule
View Description Hide DescriptionThe theoretical foundation of the self‐consistent statistical exchange (X α) multiple scattering method based on overlapping atomic spheres is presented. After discussing the principal assumptions and approximations, the theory is illustrated by a study of the electronic structure of the TCNQ molecule. Satisfactory results are obtained for the energy level structure and electronic charge distribution if the atomic sphere radii are chosen in accordance with the following guidelines: (a) the calculated first ionization energy should agree with experiment; and (b) the calculated virial coefficient should be equal to −2. The present work suggests that the overlapping sphere model can be used to obtain realistic electronic structures for large planar organic molecules as well as for arrays of such molecules.

Crystal structure of NH_{4}ClO_{4} at 298, 78, and 10 °K by neutron diffraction
View Description Hide DescriptionThe crystal structure of ammonium perchlorate has been studied at 298, 78, and 10°K by means of neutron diffraction. The NH_{4}ClO_{4} crystal has an orthorhombic unit cell, space group Pnma, with four formula units per cell at all three temperatures. The unit cell dimensions at 298°K are a=9.20, b=5.82, c=7.45 Å, as determined previously; at 78°K, a=9.02, b=5.85, c=7.39 Å; and a=8.94, b=5.89, c=7.30 for 10°K. Initial positions of H atoms were determined from a difference Fourier map of the room temperature data. However, a least‐square refinement of these data did not converge. The thermal motions and orientations of the ammonium groups at low temperature (10 and 78°K) were determined by means of a constrained refinement which treated the ammonium group as a rigid body; these results are compared with the results obtained by the conventional least‐squares method. Both refinements show that the librational motions about one of the three principal axes have particularly large rms amplitudes: 21° for the 10°K structure and 30° for the 78°K structure. Each ammonium group is surrounded by 10 oxygen atoms with short N ⋯ O distances ranging from 2.9 to 3.25 Å. The group and group each have essentially ideal tetrahedral structure. They are linked together by N–H ⋯ O type hydrogen bonds, one for each hydrogen, to form a three‐dimensional network. Examination of the rms amplitudes for libration and the hydrogen bonding of the ions indicates that two of the four hydrogens are bound identically, one hydrogen is bound more rigidly, and the fourth more weakly. These results suggest that the rotational motions of the ammoniums are quite complex even at 10°K.

Theoretical study of curve crossing: ab initio calculations on the four lowest ^{1}Σ^{+} states of LiF
View Description Hide DescriptionThe potential curves of the four lowest ^{1}Σ^{+} states of LiF have been studied by ab initioconfiguration interaction methods, using a contracted Gaussian basis set of better than double‐ζ quality, augmented with diffuse basis functions on the fluorine atom. The choice of orbitals and selection of configurations were carried out with the objective of obtaining a balanced treatment of the four states and of the different regions of the potential curves. ``Generalized valence‐bond'' orbitals, obtained from ground‐state MCSCF calculations, together with ``improved virtual orbitals,'' were found suitable for the construction of the configuration functions. The latter were energy selected from all single and double excitations relative to a set of 12 ``reference configurations,'' chosen to include all contributions found important for any of the four states at any internuclear distance. The expected avoided crossing between the lowest covalent and ionic structures is found at an internuclear distance of about 11 bohr, compared to the experimentally deduced value of 14 bohr, due to the considerable difficulty in obtaining a balanced description of the electron correlation of the separated species, particularly the F^{−} ion. A set of diabatic potential curves was generated from the two lowest adiabatic curves by a novel procedure based on the Rittner model of the ionic state. A set of adjusted adiabatic potentials was obtained from the diabatic curves after shifting the ionic diabatic curve downward by 0.42 eV to correct for the error in the computed electron affinity of the fluorine atom, resulting in a shift of the avoided crossing to the correct internuclear distance of 14 bohr. The dipole moments of the four states were computed as a function of internuclear distance and were interpreted in terms of the electronic structure.

Lattice model for a binary mixture of hard rods of different lengths. Application to solute induced nematic→isotropic transitions
View Description Hide DescriptionA statistical mechanical treatment for two‐component mixtures of hard rods placed on a simple cubic lattice is presented. Each mixture is composed of two types of rods of different length‐to‐breadth ratios; and the pressure‐to‐temperature ratios are chosen so that the system is anisotropic when only longer rods are present but isotropic when composed of only shorter rods. Such solutions can be induced to undergo a first‐order anisotropic‐isotropicphase transition, with a small two phase region, by increasing the concentration of the shorter rods. The dependence of this transition on the parameters of the model is described and deviations from ideal solution behavior are discussed. Recent experimental data are cited and compared with the results of the lattice calculation.

Ultraviolet‐ and x‐ray‐induced radicals in frozen polar solutions of L‐tryptophan
View Description Hide DescriptionAcid, neutral, and alkaline matrices containing the aromatic amino acid L‐tryptophan have been uv and x irradiated at 77 K, and the irradiation products examined by ESR and optical absorptionspectroscopy. Three types of tryptophan radicals have been detected: (1) T_{1ox}, supposedly the tryptophan cation, which has a characteristic optical absorption band around 600 nm and a singlet ESRspectrum at g=2.004 of width around 25 G, (2) T_{2ox}, probably the radical formed by H abstraction at N_{1}, which absorbs light around 550 nm and has a narrow singlet ESRspectrum (g=2.004, H=13–14 G), and (3) T_{red}, assumed to be the radical formed by H addition at C_{7}, showing an ESRspectrum which is a triplet of triplets with hfs constants a _{1}=39 G and a _{2}=12 G. T_{1ox} is formed by photoionization of tryptophan or by the reaction of tryptophan molecules with x‐ray induced oxidized solvent radicals such as in matrices containing LiCl or HCl, O^{−} in alkaline solutions, and sulphuric acid radicals in matrices containing H_{2}SO_{4}. T_{2ox} is formed by radical conversion of T_{1ox} in acid matrices, and is probably the main oxidized tryptophan radical present in alcohol matrices. T_{red} is formed by the reaction of electrons as well as H atoms with tryptophan molecules.

Perturbation corrections to Koopmans' theorem. III. Extension to molecules containing Si, P, S, and Cl and comparison with other methods
View Description Hide DescriptionThe method of ordinary third‐order Rayleigh Schrödinger perturbation theory together with the geometric approximation is used to evaluate the vertical ionization potentials of HCl, H_{2}S, H_{3}P, H_{4}Si, H_{3}SiF, and H_{3}CCl. The ``1 1/2‐zeta'' STO basis set employed permits excellent agreement between theory and experiment to be attained. Computations on H_{2}O, N_{2}, and F_{2} using GTO basis sets show that the present method is equivalent to the many‐body techniques employed by other workers.

Vibrational spectrum and force field of uranium hexafluoride
View Description Hide DescriptionA total of 44 bands in the infrared and Raman spectra of ^{238}UF_{6} vapor has been measured using long‐path absorption cells and multiple‐reflection Raman cells. The types of contours exhibited by these bands, and analogous contours in the spectrum of SF_{6}, are discussed. Overtone and combination bands with resolved Q branches are used to estimate the anharmonicity corrections for the stretching fundamentals. The infrared contours of ν_{3} (at 228 K) and ν_{4} (at 256 K) have yielded estimates for the Coriolis constants ζ_{3} and ζ_{4} that satisfy the sum rule. The ^{235}UF_{6}–^{238}UF_{6} frequency shifts in these fundamentals have also been measured. All of these data, plus vibrational amplitudes from the electron diffraction study of Seip, have been combined to determine the general quadratic harmonic force field of UF_{6}. Only three valence force constants are appreciably different from zero: f_{r} =3.85±0.05, f _{α}≈f _{α}−f_{a′a} = 0.12±0.01, and f_{rr} (cis interaction)=0.30±0.02, all in mdyn/Å. The large differences between this force field and that previously determined for WF_{6} are attributed to the effects of f‐orbital contributions in UF_{6}.

Electronic and geometric structure of the free XeF_{6} molecule
View Description Hide DescriptionThe absorptionspectrum of gas phase XeF_{6} (from Ljubljana Fluor Chemistry Institute) was investigated in the region from 50 to 170 eV using the synchrotron radiation of DESY. We did not succeed in finding further evidence for the electronic isomers hypothesis of Goodman. Our spectrum can be explained if we assume that at room temperature XeF_{6} consists of only one molecular species of slightly distorted O_{h} geometry (Bartell and Gavin model). Nearly all other experimental results are consistent with this.

Vibrational relaxation in the A ^{1} A′(^{1} B _{1}) electronic state of 4‐methyl‐1,2,4‐triazoline‐3,5‐dione
View Description Hide DescriptionThe fluorescence decay rate from selected vibronic levels of the A ^{1} A′(^{1} B _{1}) excited electronic state of 4‐methyl‐1,2,4‐triazoline‐3,5‐dione has been examined as a function of added inert gas pressure. A simple, physically reasonable model is presented from which vibrational relaxation rates may be explicitly determined. The relaxation rate constants have been found to be 6.3×10^{5} Torr^{−1} sec^{−1} for collisions with helium, 7×10^{5} Torr^{−1} sec^{−1} for argon, 2.5×10^{6} Torr^{−1} sec^{−1} for CCl_{4}, 15×10^{5} Torr^{−1} sec^{−1} for O_{2}, and 75×10^{5} Torr^{−1} sec^{−1} for cyclohexane.

Forbidden transitions in the emission spectrum of atomic aluminum
View Description Hide DescriptionThe emission spectra of species evaporated by a laser pulse from an alumina surface in air have been studied. In addition to the well‐known spectrum of Al, several groups of weak and forbidden lines are identified. The spatial distribution of line intensity and the Stark shifts have been measured. The results are discussed in connection with the plasma shielding effect in laser‐solid coupling and the reduction of aluminum by a high‐temperature method. A weak doublet of lines is tentatively attributed to a transition involving the 3s 3p ^{2 2} D state.

Electrostatic model for the rotational potential in ammonium halides
View Description Hide DescriptionAn electrostatic model for the rotational potential of an ammonium tetrahedron in a cubic field is proposed. The rotational potential can be written as a rapidly converging series of kubic rotator functions. The NX_{4} ion, where X is hydrogen or deuterium, performs small angular motions about the minimum of the potential in both the ordered and disordered states, giving rise to librational energy levels. The anharmonic portion of the energy levels, both from the kinetic and potential energies, accounts for good agreement with infrared absorption data in NH_{4}Cl, ND_{4}Cl, NH_{4}Br, and ND_{4}Br. We use a one parameter fit to these data and then compute the potential barriers for rotations about threefold and fourfold axes of the tetrahedron. The difference between the transition temperatures for ND_{4}Cl and NH_{4}Cl is also explained.

On a model for the temporal oscillations in the Belousov‐Zhabotinsky reaction
View Description Hide DescriptionThe detailed chemical mechanism for the temporal oscillations in the Belousov‐Zhabotinsky reaction, which was suggested by Field, Körös, and Noyes [J. Am. Chem. Soc. 94, 8649 (1972)], has been reconsidered by Field and Noyes [J. Chem. Phys. 60, 1877(1974)], who suggest a simplified five step scheme to explain the chemical behavior that is observed. Their reaction equations are discussed here, and a method for finding bounds for closed stable trajectories in the phase space of the dimensionless concentrations of the HBrO_{2}, Br^{−}, and Ce(IV) is given. Simple bounds are obtained and compared with the numerical solution found by Field and Noyes. The existence of such bounds proves that the equations suggested by Field and Noyes are globally stable for large enough disturbances from the steady state and provide necessary conditions for the existence of bounded temporal oscillations.

Perturbation effects on lifetimes in
View Description Hide DescriptionVariation of lifetimes induced by a perturbation have been measured by the phase‐shift technique. The transition studied is in , where perturbations occur in several bands between and A ^{2}Π_{ u }. The perturbed lifetimes measured on selected rotational lines of the 1→2 band are found to increase from 60 to 90 ns in agreement with the values calculated from the nonperturbed lifetimes and the relative energies of the interacting levels.

Light scattering of spheroids. III. Depolarization of the scattered light
View Description Hide DescriptionThe effect of the magnetic dipole and electric quadrupole upon the depolarization of light scattered by spheroids that are not very small compared to the wavelength is investigated. It is found that the three degrees of depolarization, ρ_{ u }, ρ_{σ}, and ρ_{π}, differ appreciably in their response to changes in the parameter values α (related to spheroid size), p (axial ratio), and m (relative refractive index). These differences should allow one to determine both molecular weight and physical dimensions of nonspherical macromolecular scatterers and the volume and dimensions of compact, nonspherical, colloidal particles conclusively from depolarization measurements within a wide dimensional range not accessible to the classical Rayleigh‐Gans theory of depolarization.

Polymer viscosity in concentrated solutions
View Description Hide DescriptionOur previous theory of polymerviscosity (which completely incorporates hydrodynamic interactions) is generalized to the case of polymer solutions at finite concentration. The specific viscosity of the polymer solution is expressed in a multiple scattering type cluster expansion which is formally in powers of the polymer concentration. We explicitly treat the case of concentrated solutions or the case of undiluted polymers in the absence of entanglements. It is shown that the presence of the other polymers leads to a screening of the intrachain hydrodynamics interactions when the natural size of a free polymer chain becomes on the order of the average volume available per chain in solution. We show how the screening is responsible for the transition from a polymer intrinsic viscosity which varies as M ^{1/2} (M is the polymer molecular weight) in the infinitely dilute limit to a Rouse‐like specific viscosity which varies as M in the concentrated limit. It should be noted that the screening cannot be described if the popular preaveraging approximation is employed for the hydrodynamic interactions.

Gas‐discharge polymerization
View Description Hide DescriptionA synthesis of the study that we undertook on the polymerization of monomer vapors in an alternating luminescent discharge is presented. After a brief description of the deposit apparatus, the experimental study of the deposit parameters has been given. The study relates to the influence of the discharge frequency (50 Hz to 6 MHz), of the discharge duration and its current density, of the substrate temperature, and of the monomerpressure (7×10^{−2} to 3 torr). Thereby it is demonstrated that the polymerization takes place in the interelectrode space rather than on the electrodes above a frequency of about 10^{5} Hz, that the deposit thickness is a linear function of time (15 s to 10 mn), and that for a given substrate temperature and pressure it is necessary not to exceed a certain current threshold above which there is not any increase of the growth rate but rather a degradation of the forming layer. Finally it is shown that too high a pressure lowers the film growth rate as a result of the cooling of discharge electrons following an increase of the shocks in the discharge. These experimental results permit an explanation of the film formation on the substrate by the association of two phenomena: the monomer‐molecule adsorption on the substrate which yields the matter to be polymerized and the electrical discharge which furnishes the necessary active particles to initiate and thereafter maintain the polymerization mechanism. In the second part of this article, an experimental and theoretical verification of this hypothesis has been undertaken. At first, the case of an dc electrical discharge is considered which permits the demonstration that the active particles are the positive ions of the discharges. Next, the multilayer adsorption phenomenon following the BET (Brunauer, Emmet, and Teller) theory is presented, and it is shown that this is in good agreement with the experimental results of the first part. Finally a radical polymerization scheme is proposed enabling the determination of an analytical expression for the polymer formation speed which agrees well with the experimental findings.

Fluctuations in chemical reactions around the steady states
View Description Hide DescriptionBirth‐and‐death type master equations for linear chemical reactions in closed and open systems are solved to discuss the properties of fluctuations. For nonlinear chemical reactions the generating functions of the probability of number fluctuation are usually second order differential equations, and a method for obtaining the moments of fluctuations is presented with applications to simple examples. The deterministic kinetic equation is valid for large systems and the second moments are the same as those of Poisson distributions in open systems treated here, while for the higher moments this is not always the case.

Spin coupling of two identical complex ions. I. Theory
View Description Hide DescriptionBy means of a Heitler‐London procedure, theoretical expressions for the ESR parameters of a pair of identical complex ions with spin S =(1/2) are derived. The conditions for spin coupling and for a disalignment of the g and fine‐structure tensors are discussed. The calculation of the contributions of the dipolar and exchange interactions, respectively, shows that the last one, which causes the singlet‐triplet energy separation, gives anisotropic contributions to the zero‐field splitting, owing to the effect of the spin‐orbit coupling. Moreover, such contributions are in competition with those of the dipolar interaction. The crucial importance, for the exchange interaction, of a mixed ground state is shown. Its dependence on the form of the ligand orbitals is also pointed out.

Zeeman nuclear quadrupole resonance line shapes in powders (I = 3/2)
View Description Hide DescriptionTheoretical absorption line shapes are presented for Zeeman perturbed nuclear quadrupole resonance transitions (I = 3/2) in polycrystalline materials for the case in which the rf field is parallel to the Zeeman field. For a nuclear spin of 3/2, the pure quadrupole transition frequency ν_{ Q }(1+η^{2}/3)^{1/2} is insufficient to independently determine either ν_{ Q }, the strength of the quadrupole interaction, or η, the asymmetry in the electric field gradient tensor. Application of a magnetic field removes the degeneracy of the energy levels producing, in general, four orientation dependent transition frequencies from which the quadrupole parameters can be determined. Computer simulated powder lineshapes are presented which are exact in η and are to first order in applied magnetic field strength. Frequencies of the features of the line shape are plotted as a function of η. The features of the line shape are due to crystallites aligned such that the applied field is parallel to one of the principal axes of the electric field gradient tensor. The combined nuclear electric quadrupole and nuclear Zeeman Hamiltonian has been solved exactly for these special orientations. Exact frequency expressions are calculated for these orientations of field with respect to sample. These correspond to the frequencies of the features of the line shape.