Volume 51, Issue 7, 01 October 1969

LCAO–MO–SCF Calculations Using Gaussian Basis Functions. III. Determination of Geometry by SCF Calculations, CF_{2}
View Description Hide DescriptionResults are presented of an LCAO–MO–SCF investigation of the geometry of the CF_{2} molecule. It is shown that a well‐chosen Gaussian set is sufficient to determine reliably the geometry of triatomic molecules. A Walsh‐type orbital diagram is given which shows a number of features which differ from the predictions of Walsh. The bonding in CF_{2} is discussed in terms of the Walsh diagram and the population analysis results of a calculation using a more extensive basis set.

Total Energy in Iterative Hückel Theories
View Description Hide DescriptionThe relationship between the operator for the MO's and the operator for the total energy is studied through an expansion technique. Various cases are discussed. The Wolfsberg–Helmholz approximation is found to be an improper choice if applied to the elements of directly. However, it may be incorporated into via introduction into .

Apparent Molar Volumes and Osmotic Coefficients in Dilute Electrolyte Solutions
View Description Hide DescriptionThe apparent molar volumes and the osmotic coefficients of different types of electrolytes in dilute aqueous solutions are calculated on the basis of the Mayer theory. The sums which appear in the equations are calculated for different values of the ionic strength and suitable functions of the sums are represented graphically. The results show that the Mayer theory accounts in a satisfactory way for the molar volumes and the osmotic coefficients in very dilute solutions, with the distance of closest approach used as the only adjustable parameter. The limits of this agreement of the theory with the experiments are discussed.

Systematic Trends in the Coupling Constants of Directly Bonded Nuclei
View Description Hide DescriptionThe indirect coupling constant has been observed for the magnetic nuclei in 50 different pairs of directly bonded X–N atoms. A synopsis is given of the reported values along with the corresponding reduced constant which depends only on the molecular electronic structure. There are three nuclei, N=^{1}H, ^{13}C, and ^{19}F for which is now known for 15 or more different nuclei X, enough that trends are visible in the dependence of K_{XN} upon the position of X in the periodic table. The sign of K^{XN}(positive for H_{2}) changes across the table somewhat between Groups V and VI, the sense of the change for N=^{19}F being the reverse of that for N=^{1}H and ^{13}C. Furthermore, there is a marked increase in the magnitude of with increasing nuclear charge of atom X in each Group, for negative as well as positive coupling constants. The significance of these observed trends is considered. The Ramsey theory for the electron coupling of the nuclear spins includes orbital, spin‐dipolar, and contact contributions. For directly bonded atoms, the orbital contribution is zero unless there is multiple bonding, the tendency for which decreases with increasing in a given Group. The spin‐dipolar contribution increases with increasing ; however, it is positive, and the values calculated are an order of magnitude smaller than those found experimentally for . A model is presented attributing the observed trends to the contact contribution, which depends upon the nature of the bonding orbitals employed by each atom in the bond. If both atoms employ ns orbitals in the bond, the direct contact interaction term, which is positive, dominates. The bonding of Group VII and, to a lesser degree, Group VI atoms employs primarily orbitals. In such atoms the contact interaction is indirect, involving polarization of the core electrons and a change in sign of the term. The contact term with inclusion of such core polarization effects provides a model consistent with the data available. The model is used to predict the signs, in some cases also the magnitudes, of several coupling constants not yet observed. For example, in NF_{3}, OF_{2}, and F_{2}, we expect to be negative, to be positive, and probably to be positive. A number of features are discussed including the coupling in highly ionic bonds such as the Rb, Cs, and H fluorides, and the relationship of the model to nuclear hyperfineinteractions in atoms and ions with unpaired spins and in organic free radicals.

Transient of One‐Carrier Injections in Polar Liquids
View Description Hide DescriptionThe transient space‐charge‐limited current technique developed in crystals is made to fit polar liquids: First, from a theoretical point of view the injection is no longer only limited by space charge, the electrode–liquid contact being non‐Ohmic; second, from an experimental point of view, the electric field distribution is at every moment determined by means of the electro‐optic Kerr effect, and known ions are injected by permselective membranes. Applying this technique makes it possible to estimate the mobility of different carriers injected into different polar liquids and brings out high mobility values of about 2 × 10^{−3} cm^{2} V^{−1}·sec^{−1}. Account is taken of the influence of bulk liquidmotion to explain the high values of ionic velocities obtained.

Density Effects on the Transport Coefficients of Gaseous Mixtures
View Description Hide DescriptionA modified Boltzmann equation for mixtures, which includes the effects of collisional transfer and three‐particle collisions, is presented. This equation is then solved by a perturbation expansion. General expressions for the fluxes are derived, and the transport coefficients are expressed in terms of the perturbation coefficients. Finally, the various integrals encountered in the development are evaluated numerically.

Dufour Effect in Liquid Mixtures
View Description Hide DescriptionThe Dufour effect in the liquid state has been investigated for 10 systems. Dufour coefficients have been estimated from the experimental data. The values of Dufour coefficients have been compared with those for thermal‐diffusion coefficients estimated from the known data on the soret coefficient using measured values of diffusion coefficients recorded in the paper.

New Approach for Evaluating Lattice‐Configurational Thermodynamic Properties
View Description Hide DescriptionAs a generalization of earlier work of the author [J. Chem. Phys. 40, 2248 (1964); 45, 1080 (1966)] a completely noncombinatorial method is derived which gives for any state the exact thermodynamic properties of a system of particles on a lattice infinite in one dimension. The method appears to be essentially equivalent to, but somewhat simpler in development and application than, the matrix method used for the same problems recently. Interaction of unit configurations is explicitly considered only at lattice boundaries, leading directly to a set of independent algebraic equations giving the complete solution for a specified state. Two simple examples are given to which alternative combinatorial procedures can be readily applied without approximations, yielding identical explicit results. The general method first given is modified for the imposition of artificial density constraints, and as an illustration it is shown how this variation improves markedly, over the range of disordered densities, the convergence to an infinite plane of the hard‐core square‐lattice fluid with nearest‐neighbor exclusion.

Effect of Temperature on the Reactions of Electrons during the Radiolysis of Liquid n‐Propanol
View Description Hide DescriptionPurified n‐propanol was irradiated at temperatures from − 120° to + 264° and increased from 4.1 to 5.9 over this range. Solutions of electron scavengers (acid and nitrous oxide) were irradiated at − 120°, + 25°, and 140°. The values of for absolutely pure n‐propanol were estimated to be 4.3 at − 120°, 4.9 at 25°, and 6.0 at 140°. The value of ≈ 4.3 estimated at − 120° was assumed to be independent of temperature. The free‐ion yield was , 1.2 at + 25°, and 0.8 at 140°. A reaction mechanism was proposed and the measured hydrogen and nitrogen yields were subjected to kinetic analysis; homogeneous kinetics were used for the reactions of the free ions and nonhomogeneous kinetics were used for the reactions in spurs. The activation energy of dielectric relaxation (6.1 kcal/mole) is greater than that of diffusion (∼ 4.5 kcal/mole); it was necessary to use a time‐averaged value of the dielectric constant for the smaller ion–electron separation distances at − 120°, but the static value was satisfactory elsewhere. The reaction has a rate constant of about 5 × 10^{5} sec^{−1} at 25° and has an activation energy of 4.5 kcal/mole and an entropy of activation of − 19 cal/deg·mole. Only a fraction of the electrons that undergo geminate neutralization lead to hydrogen formation; the value of the fraction is 0.29 at − 120°, 0.52 at + 25°, and 0.63 at 140°.

Application of the Refined Model of Nonhomogeneous Kinetics to the Reactions of Electrons during the Radiolysis of Ethanol and 2‐Propanol. Energies and Entropies of Activation of the Reactions of Solvated Electrons with Alcohols and with Water
View Description Hide DescriptionThe yields of nitrogen and hydrogen from the radiolysis of solutions of nitrous oxide in ethanol and in 2‐propanol at temperatures from about − 100° to + 140° have been calculated by the refined model of the nonhomogeneous kinetics of ionic reactions in irradiated alcohols. The calculated yields agree satisfactorily with those measured experimentally. The value was assumed for both liquids. In “absolutely pure” ethanol the values of and were estimated to be, respectively, 5.3 and 1.7 at − 112°, 5.3 and 1.5 at + 25°, 6.3 and 1.4 at 90°, and 6.9 and 1.2 at 145°. For the decomposition of the solvated electron [Eq. (8)] in ethanol at 25°, , and . In “absolutely pure” 2‐propanol the values of and were estimated to be, respectively, 4.1 and 1.2 at −85°, 4.9 and 1.3 at + 25°, and 5.4 and 1.0 at 140°. For the decomposition of the solvated electron in 2‐propanol at 25°, , and . In each of the liquids methanol, ethanol, 1‐propanol, 2‐propanol, and water, Reaction (8) has an activation energy approximately equal to that of dielectric relaxation, which is also approximately equal to that of diffusion. It is concluded that Reaction (8) is approximately thermoneutral and that the enthalpy of solvation of RO^{−} is more than 70 kcal/mole more negative (exothermic) than that of the electron in each of the five liquids. The activation energy might be used either to rearrange the solvent molecules about the reaction site or for the migration of the electron to a suitably oriented site. The large negative entropy of activation is related to the specific structure required by the transition state to increase the solvation energy of the negative species by more than 70 kcal/mole.

Chemical‐Shift Concertina
View Description Hide DescriptionThe phase‐alternated experiment in liquids, a multiple‐pulse NMR experiment capable of scaling chemical shifts, is examined theoretically and experimentally. The theory of the experiment is worked out using both the average‐Hamiltonian and classical magnetic‐dipole techniques, and the results from the two methods are compared. The effects of nonideal pulse cycles are discussed. Theoretical results are compared with experimental data, and a high‐resolution NMR spectrum with scaled chemical shifts is presented.

Low‐Energy Electron‐Impact Study of the 12–14‐eV Transitions in Nitrogen
View Description Hide DescriptionA high‐resolution low‐energy electron spectrometer has been constructed and used to study the nitrogen energy‐loss spectrum in the 12–14‐eV region. The relative intensities of the , 3, and 4 bands of the transition between 12.65–12.84 eV and the intense 12.92‐eV composite transition have been studied in detail at primary energies from 15–50 eV and scattering angles of 1°–40°. The relative intensities of the bands of up to were found to remain invariant with respect to changes in primary energy and scattering angle. However, the ratio of the 12.93‐eV peak to the transition decreased by a factor of 3, with increasing scattering angle from 1° to 40°, independent of primary energy. The strong angular dependence of the relative intensities for these transitions suggests that the differential‐scattering cross section for the Rydberg state at 12.93 eV is much more strongly peaked in the forward direction than that for the state. The effect of multiple scattering on these transitions was investigated. At low energies, the intensity of a peak at 13.2 eV increased relative to the bands with increasing scattering angle. There may be a singlet–triplet transition at this energy.

Low‐Energy Electron‐Impact Study of the First, Second, and Third Triplet States of Benzene
View Description Hide DescriptionThe six lowest excited states of benzene have been investigated in the gas‐phase free molecule at low pressure by electron‐impact spectroscopy. Incident electron energies of 13.6 and 20.0 eV and scattering angles from 9° to 80° were used. Three singlet–singlet transitions at 5.0, 6.2, and 6.9 eV were identified. These transitions agree with the results of optical absorption and higher‐energy electron‐impact experiments. In addition, three triplet states were observed at 3.9, 4.7, and 5.6 eV. The positions of the first two triplet states agreed with optical data on solid benzene and threshold electron‐impact experiments. The third triplet state at 5.6 eV was assigned on the basis of the relative intensity of the transition at various scattering angles. The ratio of the intensity of this transition to the allowed singlet–singlet transition at 6.9 eV was in a constant proportion to the corresponding ratio for the first triplet state (3.9 eV) at all scattering angles. The spacings of the first and second and second and third triplet states in benzene were determined to be 0.80 and 0.85 eV. The difference in the spacing is not significant with respect to experimental error.

Thermodynamics of Rare‐Earth–Carbon Systems. II. The Holmium–Carbon and Dysprosium–Carbon Systems
View Description Hide DescriptionThe vaporization of the systems holmium–carbon and dysprosium–carbon has been studied by means of the Knudsen‐effusion–mass‐spectrometric technique. In addition to the gaseous atoms, dicarbide and tetracarbide molecules were identified, and their bond and atomization energies were obtained. The values found are practically coincident for the two systems. A determination of the heats of formation for HoC_{2}(s) and DyC_{2}(s) has also been made.

Thermodynamics of Rare‐Earth–Carbon Systems. III. The Erbium–Carbon System
View Description Hide DescriptionA sample of erbium dicarbide has been prepared by direct reaction of the elements in a graphite lined molybdenum crucible. The vaporization of the dicarbide has been studied by means of the Knudsen‐effusion–mass‐spectrometric technique over the temperature range 1750–2500°K. The vapor species above ErC_{2}(s) were found to be Er(g) and, as minor constituent, ErC_{2}(g). From the vapor‐pressure equation the enthalpy of vaporization of ErC_{2}(s) to Er(g) was found to be . From this value the standard heat of formation of C‐rich ErC_{2}(s) was calculated to be − 18.5 ± 0.4 kcal/mole. The stability of ErC_{2}(g) molecule has also been determined.

Ab Initio Studies on
View Description Hide DescriptionA 38‐configuration wavefunction was calculated for at , the experimental equilibrium distance, to give an energy of − 14.92196 hartree and an electric moment of 1.578 a.u. This function gave 79% of the binding energy and 73% of the correlation energy. Comparative studies were made with the important zeroth‐order configurations, , and with previous work on the molecule. The polar nature of BeH^{+} appears to be best described in terms of a valence‐bond picture, where hybridization amply explains the charge transfer.

Reaction of Carbon Dioxide with Atomic Oxygen and the Dissociation of Carbon Dioxide in Shock Waves
View Description Hide DescriptionThe reaction of oxygen atoms with carbon dioxide has been investigated from 2800–3200°K using the decomposition of N_{2}O as a source of oxygen atoms: O+CO_{2}→CO+O_{2} (1). Over the temperature range, the value of was found to be , which is much larger than the recent literature value. The addition of molecular oxygen decreased the observed rate of CO_{2} removal in Reaction (1). The decomposition of CO_{2} in the second‐order pressure region in neon diluent was investigated over the temperature range 2900–4000°K, and it was shown that the contribution of Reaction (1) to the gross decomposition rate is significant, but does not account for the anomalously low activation energy of CO_{2} decomposition. The corrected first‐order rate constant for the reaction CO_{2}+Ne→CO+O+Ne (2) at a density of 1.35 × 10^{18}particle/cm^{3}, is . The rate constant for the reaction O_{3}+NO→N+O_{2} (3) is estimated as at 3000°K, and a suggested upper limit for the rate constant of the reaction NO+CO_{2}→NO_{2}+CO (6), is at the same temperature.

Electron Densities from Gas‐Phase Electron Diffraction Intensities. I. Preliminary Considerations
View Description Hide DescriptionThe intensity of electrons and x rays scattered by a freely rotating molecule is determined, in the kinematic approximation, solely by the nuclear–nuclear, electron–nuclear, and electron–electron radial distribution functions of the molecule. Although these functions are one‐dimensional, the latter two contain some information about the three‐dimensional distribution of electrons in the molecule because the electrons are distributed relative to several nuclear reference positions and the spatial distribution of the nuclei is known. The purpose of this series of papers is to investigate the extent to which this information can be deciphered. Although published accounts have purported to show that the electron density can be determined uniquely from the scattered intensity, we demonstrate that, in fact, the transfomation is not unique. Nevertheless, if certain, not unreasonable, restrictions are imposed upon the form of , it becomes possible to make fairly detailed inferences about the three‐dimensional character of the density. We propose a procedure which, although not guaranteeing a unique transformation, provides a means for deriving chemically significant knowledge about the molecular electron density from experimental gas‐phase intensities.

Electron Densities from Gas‐Phase Electron Diffraction Intensities. II. Molecular Hartree–Fock Cross Sections
View Description Hide DescriptionDifferential cross sections for electron scattering based on molecular Hartree–Fock electron densities are compared with cross sections based on the independent‐atom approximation for the molecules C_{2}, N_{2}, O_{2}, F_{2}, and CO. The results show that bonding effects on the electron density manifest themselves to the extent of several percent in the scattered intensity at small scattering angles. Furthermore, molecule‐to‐molecule variations in the shifts of electron density are clearly reflected in variations in the functional form of the scattered intensity. A comparison of the calculated intensities for N_{2} and O_{2} with preliminary experimental intensities suggests that electron scattering techniques now in development should be able to provide information about bonding and electron correlationeffects competitive in accuracy with that of current quantum‐mechanical calculations.

Crystal‐Field Spectra of Ions. V. Tetrahedral Co^{2+} in ZnAl_{2}O_{4} Spinel
View Description Hide DescriptionAbsorption and fluorescence spectra of Co^{2+} in the tetrahedral site of ZnAl_{2}O_{4} spinel (gahnite) at low temperatures have been observed and analyzed. The resulting energy‐level diagram includes four quartet states and nine doublets, and has been interpreted first in terms of a weak field formalism without spin–orbit coupling. In this analysis the “free‐ion” levels for were deduced and compared with those for a free ion outside the influence of the crystalline environment. The reduction in the electrostatic interaction parameters and in the crystal is due to the effect of covalency. A second approach has been used to analyze the fine structure of the energy levels in terms of a strong field spin–orbit formalism. The fine structure can be explained for all the bands on the basis of simple spin–orbit splitting, but the possibility of a Jahn–Teller distortion of the state cannot be entirely eliminated.