Volume 48, Issue 5, 01 March 1968

Numerical Solution of the S‐Limit Schrödinger Equation
View Description Hide DescriptionNumerical solutions to the S‐limit Schrödinger equation have been obtained for He and Li^{+}. Using these the energy and the expectation values and were calculated and compared to the radial configuration interaction values. The results demonstrate that the direct numerical solution of many partial differential equations in chemical physics can be accomplished in a practical and straightforward manner.

Neutron‐Diffraction Refinement of the Crystal Structure of Barium Chlorate Monohydrate Ba(ClO_{3})_{2}·H_{2}O
View Description Hide DescriptionA single‐crystal neutron‐diffraction study has been made to determine the shape and coordination of the water molecule in Ba(ClO_{3})_{2}·H_{2}O. The intensities of 557 neutron reflections—partial three‐dimensional data with —have been measured, and the structure has been refined to an factor of 0.080. Although the earlier x‐ray structure is basically correct, there are significant differences in the two sets of structural parameters. The structure contains hydrogen bonds of length , in which the distance is 0.958 ± 0.011 Å (corrected for thermal motion) and the angle is 163.6 ± 0.9°. The orientations of the interproton vectors found in the present study agree with those determined by the protonmagnetic resonance method to within 2.5°.

Barrier Studies in the Halopropenes. III. Microwave Spectra, Molecular Structure, Quadrupole Coupling Constants, Orientation of the Field Gradient Tensor, and Barrier to Internal Rotation in cis‐1‐Chloro‐2‐fluoropropene
View Description Hide DescriptionThe microwave spectra of cis‐CH_{3}FC:CH^{35}Cl and cis‐CH_{3}FC:CH^{37}Cl have been observed in the ground torsional state. The ground‐state rotational constants for cis‐CH_{3}FC:CH^{35}Cl are , and . The ground‐state rotational constants for cis‐CH_{3}FC:CH^{37}Cl are , and . The ^{35}Cl quadrupole coupling constants along the appropriate inertial axes in the ground state of cis‐CH_{3}FC:CH^{35}Cl are , and , and for the corresponding ^{37}Cl isotope, and . Second‐order quadrupole coupling effects have been used to obtain a direct measurement of the nonzero off‐diagonal element of the tensor for the ^{35}Cl species. The off‐diagonal element is . Analysis of the ground torsional state spectra for the ^{35}Cl species yields a barrier to internal rotation of the methyl group of .

Dependence of the Rate of Electrodic Redox Reactions on the Substrate
View Description Hide DescriptionThe steady‐state velocities of an electrodic redox reaction have been determined on noble metals and some of their alloys. They are expressed in terms of the exchange current densities. Correspondingly, measurements of 's as a function of temperature are recorded. The heats of activation at the reversible potential are independent of the properties of the substrate. However, log (reaction rate at the reversible potential) is linear with the work function of the substrate. Reactions in Cl^{−} containing solutions have velocities greater than those in SO_{4} _{– –} solutions, and the ratio depends upon the substrate in the order Pd > Au > Pt. The lack of dependence of the heat of activation upon the substrate is consistent with an electron transfer and not an atom‐transfer model for the electrodic redox reactions. It is consistent with a weak interaction model. The dependence of the exchange current densities upon the substrate can be shown quantitatively to depend on the change of electrokinetic potential with the change of substrate‐solution PD (potential difference) which occurs by carrying out the same reaction at a series of interfaces at which the metal‐solution PD's are different, while the reversible potentials are the same. The anion effects cannot be due to blocking or bridging. They may be due to change in the potential arising from a differing contact adsorption of the anions.

Metastable Phases in the Pb–Sb and Pb–Bi Systems
View Description Hide DescriptionUtilizing the splat cooling technique of rapid quenching from the melt, the Pb–Sb and Pb–Bi alloy systems were investigated at –190°C. In large parts of both systems, metastable single‐phase alloys were obtained instead of equilibrium two‐phase alloys. New phases found include a bcc (W‐A2‐type) Pb–Sb phase, a primitive cubic coordinated Pb–Sb phase (possibly of the NaCl–B1 type), and a complex Pb–Bi phase. The terminal solubilities, especially those of Pb in Sb and Bi, were strongly enhanced with an appreciable decrease of the rhombohedral angle ; atomic volumes are given.

Dielectric Study of Intermolecular Association in Isomeric Octyl Alcohols
View Description Hide DescriptionThe equilibrium dielectric constants of eight liquid isomeric octanols have been measured over a wide range of temperature, and the data are analyzed in terms of the Kirkwood correlation factor. A simple molecular model based on hydrogen‐bond associative equilibria involving both ring dimers and linear chain n‐mers is developed. Equilibrium constants for ring and chain formation are deduced, and it is concluded that entropic factors, which can be correlated with the geometry of the molecules, are the principal basis for differences between isomers. At relatively high temperatures those species whose − OH group is most sterically blocked prefer to form rings, while those whose − OH group is relatively accessible tend to form open chains. In all cases, chains become the preferred species at low temperatures. for hydrogen‐bond formation in chains is estimated as about − 6.7 kcal/mole; for rings, about − 4.5 kcal/mole. varies from − 16 to − 30 eu/mole for chains and from − 13 to − 20 eu/mole for rings.

Dielectric Relaxation in Isomeric Octyl Alcohols
View Description Hide DescriptionThe dielectric constant and loss of eight isomeric octanols has been measured over a wide range of temperature and frequency. Two distinctly different types of dispersion loci are found: For those alcohols whose –OH group is so sterically hindered that association into linear chains is unfavorable, a very small, very broad dispersion, characterized by relatively short relaxation times, is found. For less hindered species, the low‐frequency, relatively slow, dispersion is Debye‐like, and two high‐frequency dispersion regions have been resolved in two compounds. The molar activation energies for all three dispersion regions are closely similar and . The activation energy for the principal (Debye‐like) dispersion is strongly dependent on the steric hindrance of the –OH group. Activation energies vary from about 8 to 20 kcal so that rupture of a hydrogen bond is an unlikely rate‐determining step.

Growth and Decay of Delayed Luminescence
View Description Hide DescriptionWe have investigated the rise lifetimes and decay lifetimes of the long‐lived luminescences of the following systems: a naphthalene‐d_{s}, a phenanthrene, and a triphenylene solution in a rigid‐glass matrix; a phenanthrene‐d_{10}, a phenanthrene, a naphthalene‐d_{s}, and a chrysene solution in a biphenyl crystal; and chrysene in solution in a phenanthrene crystal. It has been found that the luminescence rise time is invariably shorter than the luminescence decay time. This phenomenon is satisfactorily explicable on the basis of the following attitudes: In rigid glasses, triplet‐triplet absorption events contribute to depopulation of the triplet state and decrease the rise time; in mixed crystals, on the other hand, triplet‐triplet annihilation events are dominantly responsible for abbreviating the rise time. The effects of excitation intensity and excitation wavelength on the delayed luminescence rise times of rigid‐glass solutions, and the effects of excitation intensity, concentration of guest species, and temperature on the delayed luminescence rise times of mixed‐crystal systems are discussed. The activation energies for the annihilation process were obtained from a first‐order analysis of the luminescence decay and rise times. The agreement between calculated activation energies and spectroscopic energy gaps is satisfactory and validates the postulated kinetic processes.

Semiempirical Molecular‐Orbital Calculations. VI. Dimers of Benzene
View Description Hide DescriptionSemiempirical charge self‐consistent MO calculations have been carried out for a large number of benzene dimers of different geometric conformations (e.g., , etc.). It has been found that the most stable excimer conformation is not the most symmetric (i.e., ), but rather one in which the rings are rotated relatively about the axis and/or tilted, one with respect to the other. The lifetime of excimer fluorescence can be satisfactorily explained in two ways: (1) The transition is made vibronically allowed in much the same way as the transition of benzene; or (2) the excimer possesses or symmetry, in which case a very small relative tilting of the benzene planes can induce transition moments of proper magnitude without invoking vibronic effects at all. A number of suggestions are made concerning solvent effects, and the presence of underlying continua in discrete absorption spectra, etc. In particular, a concept of contact excimer absorption is broached and rationalized. The results of computation are in excellent agreement with the general run of available experimental data.

High‐Temperature Vaporization and Thermodynamics of the Titanium Oxides. III. Vaporization Characteristics of the Liquid Phase
View Description Hide DescriptionVaporization experiments with liquid samples of TiO, Ti_{3}O_{5}, Ti_{4}O_{7}, Ti_{5}O_{9}, and TiO_{2} were performed, and the residues were analyzed by x‐ray diffraction procedures. The results show that the congruently vaporizing composition lies between the composition Ti_{3}O_{5} and the composition Ti_{4}O_{7} instead of at the composition Ti_{3}O_{5} as is the case for crystalline samples. The importance of this conclusion in vapor‐pressure studies leading to thermodynamic values and for stuctural relationships between solid and liquid Ti_{3}O_{5} is discussed.

ESR Spectrum of the Radical Species Trapped in X‐Irradiated Single Crystals of Dimethyl (9‐fluorenyl) Sulfonium Bromide
View Description Hide DescriptionThe electron spin resonance spectrum of single crystals of dimethyl (9‐fluorenyl) sulfonium bromide, irradiated with x‐rays at room temperature, reveals the presence of three free‐radical species. Two of these have been identified with reasonable certainty as (CH_{3})_{2}SBr (A) and 9‐fluorenyl (B). The third radical (C) is probably one in which the unpaired electron is mainly localized on a sulfur atom i.e., RS. The components of the hyperfine coupling and tensors for these radicals have been determined and the results discussed in terms of the electronic structure of these radicals. For radical A the ^{79}Br and ^{81}Br nuclear quadrupole coupling constants were also determined.

Dissociative Electron Attachment to Hydrogen Halides and their Deuterated Analogs
View Description Hide DescriptionThe swarm‐beam technique has been employed to study the electron‐attachment processes in HX and DX (X = halogen) molecules. Attachment cross sections as a function of electron energy, corrected for the finite width of the electron beam, are reported for the direct dissociative attachment, i.e., HX(or DX) + e→H (or D) + X^{−}. There is a strong increase in in going from HCl to HBr to HI, i.e., with decreasing energy of the dissociative‐attachment peak. The ratio of for isotopic species is found to be very nearly equal to the square root of the inverse ratio of the reduced masses of the products. In addition to the direct dissociative electron attachment to HX and DX molecules, a separate attachment process occurs at thermal electron energies.

Dissociative Electron Attachment to Molecules
View Description Hide DescriptionDissociative‐electron‐attachment cross sections (some unpublished) for 30 molecules are summarized, evaluated, and discussed within the framework of the resonancescattering theory. The dissociative‐attachment peak cross section, , is found to be a strong function of the peak (resonance)energy,, with a break in this dependence at the energy where electronic excitation of the neutral molecule begins to occur. Based on the experimental data, three groups of molecules have been distinguished: (i) those where is less than the energy,, of known electronic excited states of the neutral molecule, and the negative‐ion state is purely repulsive in the Franck‐Condon region, (ii) those where , and (iii) those with exceptionally small for which a vertical onset for dissociative attachment occurs. For the molecules in group (i) varies almost as , while for group (ii) is a much stronger decreasing function of the resonanceenergy. For group (i) the effect of autoionization on is small, and isotopic effects on are contained within the square root of the inverse ratio of the reduced masses of the products. For group (ii) and especially group (iii) the effect of autoionization on is large and so are the isotopic effects on .

Statistical‐Mechanical Theory of Polymers. I. An Integral Equation for the Excluded‐Volume Effect
View Description Hide DescriptionStatistical mechanics of a single polymer in a continuous medium is considered. Partition function, the reduced distribution functions, and related statistical concepts are defined. Thermodynamic functions of the system are calculated in terms of the distribution functions. Finally, a Kirkwood‐Born‐Green integrodifferential equation is derived for the excluded‐volume effect, and its approximate solution for the case of a ringpolymer is given. The results show that the zeroth‐order approximate solution of the integral equation is equivalent to the self‐consistent approximation of Edwards and of Reiss. The mean‐square radius of gyration in this approximation varies as power of the molecular weight.

Effect of Side‐Group Interactions on the Mean Dimensions of Vinyl Polymers
View Description Hide DescriptionMean‐square end‐to‐end distances for stereoregular vinyl polymers with interacting side groups are calculated. It is found that the steric interaction of the side groups always results in a shrinkage of the molecule as a whole, the effect being more pronounced for the syndiotactic conformation. As the side‐group diameter increases, both isotactic and syndiotactic polymers tend to a limiting configuration which is probably helical. It is proposed that the difference in the degree of shrinkage between isotactic and syndiotactic polymers may be used as a criterion for measuring tacticity of partially tactic polymers.

Extension of the CN Red and Violet Band Systems
View Description Hide DescriptionThe wavelengths and intensity distributions for the red and violet bands which were observed in a mixture of active nitrogen and CH_{4} are given. Bands which originate in the and states with excitation energies in the range 4.5‐6 eV are well developed. The wavelength range studied was 3000‐6700 Å. About 20 of the violet bands and 30 of the red bands have not been reported previously.

Atomic Integrals Containing r_{23} ^{λ} r_{31} ^{μ} r_{12} ^{v}
View Description Hide Descriptionstates of atoms may be calculated to high precision by means of expansions containing correlation factors of the form . Resulting integrals may be expressed as sums of auxiliary functions which are evaluated by algebraic methods. Explicit expressions, suitable for computer programing, are given for such integrals for three‐electron atoms; these include integrals containing correlation factors with linked indices, , with any set of (integral) values . Expressions are based on an expansion of in terms of Legendre polynomials in ; coefficients of this expansion are represented by a conveniently evaluated formula and some numerical values are given. The expressions given here have been found quite convenient in preliminary calculations of lithium ground state.

Absolute Oscillator Strengths of the Strongest Bands within the Dipole‐Allowed Absorption Spectrum of Nitrogen
View Description Hide DescriptionThe absolute absorption values of four bands of N_{2} in the 958‐972‐Å region, , and , have been determined using a 3‐m spectrometer as absorption cell with N_{2} gas pressures in the 10^{−6}−10^{−4}‐torr range, using the helium continuum with differential pumping, and double‐beam, windowless photoelectric recording with pulse‐counting electronics. More than 10 times narrower spectral bandwidth (0.04 Å) was realized than previously reported in photoelectric absorption work at these wave‐lengths, thus enabling work down to more than 100 times smaller numbers of absorbing molecules. The consequent reduction of the effects of line saturation made possible the evaluation of absolute values which are compared with other absolute and relative determinations from lifetime and electron impact measurements.

Best Choice for the Coupling Operators in the Open‐Shell and Multiconfiguration SCF Methods
View Description Hide DescriptionThe meaning of the nonunique solution for the equations derived by Das for the extended Hartree‐Fock problem is explored and a new set of equations is suggested. This set has a unique solution and leads to an easier calculation than the additional condition used by Das. It can be applied also to the so‐called CMC‐SCF method.

Studies of IBr, ICl, and I_{2}Cl_{6} Crystal Properties by Means of the Mössbauer Effect in ^{129}I. I. Chemical Bonds
View Description Hide DescriptionUsing ^{129}I as Mössbauer nucleus, the properties of ICl, IBr, and I_{2}Cl_{6}, as well as I_{2}Cl_{4}Br_{2}, were investigated. From the well‐resolved spectra of the quadrupole splitting, the , the parameter, and the isomer shift with respect to the standard ^{66}Zn^{129}Te source are derived. These data are used to deduce the electron population of I. On the basis of the sensitivity of the isomer shift to the character of the bond, it is shown that no hybridization occurs. The linear dependence of the isomer shift on the holes is found to extend to values higher than 1. A relationship is derived to include as well as when iodine is in a high valence state.