Volume 29, Issue 6, 01 December 1958

Energy Levels, Atom Populations, Bond Populations in the LCAO MO Model and in the FE MO Model. A Quantitative Analysis
View Description Hide DescriptionQuantitative results for fourteen representative organic molecules are derived and analyzed on the basis of the LCAO MO model and on the basis of the FE MO model. Calculated are, besides the energy levels, the atom populations and the bond populations, quantities defined in a recent paper as an accurate measure of the distribution of electrons.
The results of the LCAO MO model and of the FE MO model are then compared, and for the more important quantities considerable agreement is found. The origin of the agreements and disagreements is shown to be different from the one generally supposed.
Because of their general usefulness, complete tables are given for the eigenvalues and eige nvectors of the fundamental topological matrices associated with the molecules investigated.

Mobile Bond Orders in Conjugated Systems
View Description Hide DescriptionA comparative study is made of the following bond orders: MO bond orders of Coulson, MO bond orders of Mulliken, MO bond populations of Platt‐Ruedenberg‐Scherr, VB bond orders of Pauling. The comparison is carried through on the basis of theoretical derivations and on the basis of numerical calculations for a large number of molecules. The main results are: an accurate functional connection between the Coulson and Mulliken bond orders; the characterization of a new type of bond order based on bond populations, and related linearly to bond lengths; a MO expression for VB bond orders.

Mobile Bond Orders in the Resonance and Molecular Orbital Theories
View Description Hide DescriptionThe bond orders of the resonance theory are shown to be identical with certain molecular orbital quantities which are similar to the usual MO bond orders. This equivalence, related to similar results of Dewar and Longuet‐Higgins, suggests that the two theories, also in their simplified forms, are not so widely different as it is sometimes supposed.

Theorem on the Mobile Bond Orders of Alternant Conjugated Systems
View Description Hide DescriptionA generalization of Hall's theorem for Coulson bond orders in alternant molecules is derived. The new relation expresses general bond order‐like quantities in terms of the topological molecular matrix. Specialization to the Mulliken bond orders furnishes an exact relation between the Coulson and the Mulliken bond order matrices in the ground state of alternants.

Interpretation of Chain‐Ring Equilibria in the Polymerization of Substituted ε‐Caprolactam
View Description Hide DescriptionIf one of the hydrogens in ε‐caprolactam is substituted by a methyl or an ethyl group, the quantity of the lactam monomer remaining in its polymerization reaction is greater than that for the unsubstituted one. When the alkyl groups higher than ethyl are introduced, the lactam ring can hardly be polymerized. These shifts in chain‐ring equilibria are explained by the change in the thermodynamicalproperties caused by the existence of rotational isomers. The heat of reaction and the quantity of the remaining lactam ring at the equilibrium for , and ε‐monomethyl and γ‐ethyl derivatives were estimated from this point of view. The calculated and the observed values are in good agreement.

Quantum‐Mechanical Calculation of One‐Electron Properties. I. General Formulation
View Description Hide DescriptionFor a one‐electron operator, general formulas for weighted transition functions, weighted density functions, and their integrals are introduced. A detailed treatment is given of the expressions that are obtained from these formulas when they are applied to a system whose wave functions are expanded in a series of determinants of one‐electron spin orbitals. Explicit consideration is given to the nonorthogonality problem and a method for the exact inclusion of overlap terms is formulated. The simplifications resulting from the use of the single determinant approximation and orthonormal functions are discussed. A brief evaluation of the suitability of the formulation for digital computer calculation is given.

On the Approximate Calculation of Eigenfunctions
View Description Hide DescriptionA method is given for determining the variable parameters in a trial wave function which is independent of the minimum energy criterion. The energy is given as the root of a secular equation, but the value obtained may be above or below the true value. It is shown that the results of the method approach those of the standard one as the trial function becomes a better approximation to the true one, by applying it to the series of two‐electron ions.

Infrared Spectra of Partially Deuterated Diboranes
View Description Hide DescriptionInfrared spectra, in the 2 to 15 μ range, of equilibrium mixtures of various proportions of B_{2}H_{6} and B_{2}D_{6} are reported. These mixtures contain twenty‐one different species (represented by seven molecular formulas ranging from B_{2}H_{6} to B_{2}D_{6}), which exist in equilibrium with one another and cannot be separated by chemical or physical means. However, the spectra of the individual formula groups B_{2}D_{5}H and B_{2}H_{5}D were obtained by spectroscopically compensating for other species present in the equilibrium mixtures. An assignment of the observed and unobserved fundamental frequencies of the four molecules represented by the two formulas is made with the help of previously published data on B_{2}H_{6} and B_{2}D_{6} and by application of the noncrossing rule and the product and sum rules. Comparisons with published spectra of partially deuterated ethylenes and dimethylaminodiborane support these assignments.

Kinetic Theory of Nonspherical Molecules. III
View Description Hide DescriptionThe kinetic theory of nonspherical molecules has been extended to multicomponent mixtures. The treatment is based on a set of generalized Boltzmann equations analogous to that used in the treatment of a pure gas, which are solved by a perturbation method similar to that of Chapman and Enskog. The transport coefficients are obtained in terms of a set of multidimensional integrals which depend on the dynamics of collisions of nonspherical molecules. These integrals are related to the ``bracket'' integrals of Chapman and Cowling and are generalizations of similar integrals which appear in the treatment of a pure gas of non‐spherical molecules. These integrals are reduced to four‐dimensional integrals, the integrands of which depend only on the geometry of the molecules, and the integrations are carried out over the surfaces of the two molecules. As an example, the final integrations are carried out for the spherocylindrical model. The coefficients of diffusion,thermal diffusion, shear and bulk viscosity, and thermal conductivity for a binary system are obtained in terms of two parameters characteristic of the shape and mass distribution of each molecule. The coefficient of self‐diffusion is used to compare the thermal conductivity of a pure gas with that given by a modified form of the Eucken approximation.

Thermal Conductivity of Multicomponent Gas Mixtures
View Description Hide DescriptionAn equation is derived for the complete second approximation to the thermal conductivity of multicomponent gas mixtures. The result is found to be identical with an ``approximate'' formula for the thermal conductivity derived on the assumption that the thermal diffusion coefficients are negligibly small.

Statistical Mechanical Theory of the Thermal Conductivity of Binary Liquid Solutions
View Description Hide DescriptionA statistical mechanical theory of the thermal conductivity of solutions results from a generalization to the space of molecular pairs of the linear expressions appropriate to the thermodynamics of irreversible processes for the mean forces in singlet configuration space. When simplifying assumptions of the equilibrium regular solutiontheory are introduced into the general expression, the thermal conductivity of the mixture is obtained in terms of the thermal conductivities of the pure components, the self‐diffusion coefficients, mole fractions, and molar volumes. Numerical calculations are in semiquantitative agreement with experiment.

Correlation Correction Study of CH, NH, and OH
View Description Hide DescriptionThe semiempirical intra‐atomic correlation correction (ICC) of Hurley and a configuration‐interaction (CI) calculation are applied to previous single configuration calculations of the ground states of CH, NH, and OH. Results are reported for the ^{2}Π, ^{4}Σ^{—}, and ^{2}Δ states of CH, the ^{3}Σ^{—} state of NH, and the ^{2}Π state of OH. The binding energies and dipole moments obtained for the hydrides are compared with experimental values and with the results of a similar calculation by Hurley of the ground states of these molecules. Results of a calculation of the Fermi contact term of the magnetic hyperfine interaction are also given.

Theory of Orientational Effects and Related Phenomena in Dielectric Liquids
View Description Hide DescriptionFormulas are developed for the molar constants of five nonlinear effects of molecular orientation in liquids; namely, the dielectricsaturation in electric, magnetic, or optical fields and the electric as well as the magnetic birefringence. No assumption is made concerning the nature of the intermolecular forces, and no special model of molecular interaction is introduced. If the molecules may be considered to possess axial symmetry, four correlation factors R_{P}, R_{CM}, R_{K}, and R_{S} can be derived. These factors appear in the formulas of the molar constants of the Cotton‐Mouton and Kerr effects, and of the effect of dielectricsaturation in an electric, magnetic, or optical field. The correlation factors have been calculated as functions of θ^{(pq)}, the angle between the axes of symmetry of the pth and qth molecules, in the absence of a biasing field. The theory makes it possible to predict the value of the magnetodielectric saturationeffect in diamagnetic liquids, as well as the photodielectric saturation, relating these phenomena to magnetic or electric birefringence. Moreover, the meaning of this theory consists in the fact that it gives a quantitative explanation of the inverse saturationeffect appearing in some polar liquids and increasing their dielectric constant. Satisfactory results have been obtained by applying this theory to such phenomena as light scattering in liquids or the lowering of the freezing point, in which the orientationally dependent intermolecular forces play an important part.

Neutron Diffraction Study of Gypsum, CaSO_{4}2H_{2}O
View Description Hide DescriptionUsing neutron diffraction data, the crystal structure of gypsum has been refined by Fourier and least squares methods. The hydrogen bond distance was found to be 2.82 A rather than 2.71 A, reported previously. The hydrogen positions are consistent with those obtained from nuclear magnetic resonance. The O–H distance is 0.99±0.03 A, and it appears that the O, H, O atoms are collinear. Infrared and Raman results are discussed in terms of the refined structure.

Measurement of Ionization Potentials by Electron Impact
View Description Hide DescriptionA comparison has been made between the different methods of extracting ionization potentials from ionization efficiency curves measured by electron impact. Conventional methods are usually accurate to ±0.1 ev but the assumptions on which they are based are such that no further increase in accuracy can be expected. These methods sometimes give wildly inaccurate results; the main cause of this is the presence of fine structure in the ionization efficiency curve. Morrison's method of determining ionization potentials, because it detects fine structure, enables measurements accurate to ±0.02 ev to be made. Other methods which detect fine structure are equally accurate but require more complex apparatus.

Study of Hydrogen Bonding in Systems of Hydroxylic Compounds in Carbon Tetrachloride through the Use of NMR
View Description Hide DescriptionThe hydroxyl NMR frequencies for t‐butanol, phenol, and methanol have been measured as functions of concentration in carbon tetrachloride solution. The curves obtained were found to fit well to theoretical curves calculated for monomer‐trimer equilibrium for t‐butanol and phenol with K _{3}=5.60 l^{2}/M^{2} and 4.78 l^{2}/M^{2}, respectively and a monomer‐tetramer curve with K _{4}=28.4 l^{3}/M^{3} for methanol. The data of Becker et al. ^{1} on the ethanol‐carbon tetrachloride system have been fitted to theoretical curves for monomer‐trimer K _{3}=5.19 l^{2}/M^{2} and monomer‐tetramer K _{4}=44.9 l^{3}/M^{3}.

Thermal Motion in Ice and Heavy Ice
View Description Hide DescriptionChanges with temperature of x‐ray intensities of the 00l reflections in ice and heavy ice are investigated. From these the amplitudes of thermal motion of oxygen and hydrogen atoms are determined separately. This can be accomplished since only hydrogen atoms contribute to the 004 reflection. The thermal amplitudes of the oxygen atoms, which represent molecular amplitudes, can be expressed in terms of a constant Debye characteristic temperature; 224°K for ordinary ice and 237°K for heavy ice. The amplitudes of thermal vibration of the hydrogen and deuterium atoms as derived from absolute intensities of 004 at various temperatures, cannot be expressed in terms of a characteristic temperature. They consist of superimposed stretching, bending and librational motions. In addition to these a rotational motion of low zero point energy seems to be present.

Potential Field and Force Constants of Octahedral Molecules
View Description Hide DescriptionThe force constants of 10 molecules and 5 ions of the type XY_{6} belonging to the O_{ h } symmetry are calculated from the observed frequencies by Wilson's F—Gmatrix method, using Raman and infrared data. Although only one force constant is neglected, imaginary results were found in the cases of MoF_{6} and WF_{6}. Possible causes for this are discussed.

Reaction of Oxygen Atoms with Nitric Oxide
View Description Hide DescriptionThe rate of reaction of oxygen atoms with nitric oxide has been studied at several pressures (0.62, 0.85, 1.11 mm Hg) by measuring the relative intensities of the oxygen afterglow. The consumption of O atoms was observed as a three‐body recombination (NO+O+M→NO_{2}+M). At room temperature the reaction coefficient was found to be k _{2}=7.6×10^{‐32} cm^{6} molecules^{‐2} sec^{‐1}, with an average deviation of 6.5%. The third body was mainly argon.

Effect of Anisotropy on Light Scattering by Streaming Freely Flexible Linear Macromolecules
View Description Hide DescriptionThe theory of Peterlin, Heller, and Nakagaki is generalized to allow for each segment of the macromolecule possessing two different polarizabilities, one longitudinal and the other transverse. The polarization of the scattered light is then different from that given by the theory of PHN, which predicts the polarization to be that of ordinary Rayleigh scattering. Expressions for the four different differential cross sections which can be defined are derived.