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1 Dec 1958

Volume 29, Issue 6, pp. 1199-1430

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Energy Levels, Atom Populations, Bond Populations in the LCAO MO Model and in the FE MO Model. A Quantitative Analysis

Norman S. Ham and Klaus Ruedenberg

J. Chem. Phys. 29, 1199 (1958); http://dx.doi.org/10.1063/1.1744700 (16 pages) | Cited 20 times

Online Publication Date: 13 August 2004

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Quantitative 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

Norman S. Ham and Klaus Ruedenberg

J. Chem. Phys. 29, 1215 (1958); http://dx.doi.org/10.1063/1.1744701 (15 pages) | Cited 43 times

Online Publication Date: 13 August 2004

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A 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

Norman S. Ham

J. Chem. Phys. 29, 1229 (1958); http://dx.doi.org/10.1063/1.1744702 (3 pages) | Cited 28 times

Online Publication Date: 13 August 2004

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The 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

Klaus Ruedenberg

J. Chem. Phys. 29, 1232 (1958); http://dx.doi.org/10.1063/1.1744703 (2 pages) | Cited 16 times

Online Publication Date: 13 August 2004

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A 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

Hirosuke Yumoto

J. Chem. Phys. 29, 1234 (1958); http://dx.doi.org/10.1063/1.1744704 (6 pages) | Cited 3 times

Online Publication Date: 13 August 2004

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If 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 thermodynamical properties caused by the existence of rotational isomers. The heat of reaction and the quantity of the remaining lactam ring at the equilibrium for α−,β−,γ−,δ−, 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

Martin Karplus, Aron Kuppermann, and Leonard M. Isaacson

J. Chem. Phys. 29, 1240 (1958); http://dx.doi.org/10.1063/1.1744705 (7 pages) | Cited 5 times

Online Publication Date: 13 August 2004

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For 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

B. F. Gray

J. Chem. Phys. 29, 1246 (1958); http://dx.doi.org/10.1063/1.1744706 (2 pages) | Cited 3 times

Online Publication Date: 13 August 2004

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A 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

Walter J. Lehmann, Jerome F. Ditter, and I. Shapiro

J. Chem. Phys. 29, 1248 (1958); http://dx.doi.org/10.1063/1.1744707 (9 pages) | Cited 20 times

Online Publication Date: 13 August 2004

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Infrared spectra, in the 2 to 15 μ range, of equilibrium mixtures of various proportions of B2H6 and B2D6 are reported. These mixtures contain twenty‐one different species (represented by seven molecular formulas ranging from B2H6 to B2D6), which exist in equilibrium with one another and cannot be separated by chemical or physical means. However, the spectra of the individual formula groups B2D5H and B2H5D 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 B2H6 and B2D6 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

Charles Muckenfuss and C. F. Curtiss

J. Chem. Phys. 29, 1257 (1958); http://dx.doi.org/10.1063/1.1744708 (16 pages) | Cited 35 times

Online Publication Date: 13 August 2004

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The 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

Charles Muckenfuss and C. F. Curtiss

J. Chem. Phys. 29, 1273 (1958); http://dx.doi.org/10.1063/1.1744709 (5 pages) | Cited 61 times

Online Publication Date: 13 August 2004

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An 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

Richard J. Bearman

J. Chem. Phys. 29, 1278 (1958); http://dx.doi.org/10.1063/1.1744710 (9 pages) | Cited 33 times

Online Publication Date: 13 August 2004

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A 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 solution theory 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

M. Krauss and J. F. Wehner

J. Chem. Phys. 29, 1287 (1958); http://dx.doi.org/10.1063/1.1744711 (11 pages) | Cited 18 times

Online Publication Date: 13 August 2004

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The 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 2Π, 4Σ—, and 2Δ states of CH, the 3Σ— state of NH, and the 2Π 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

A. Piekara and S. Kielich

J. Chem. Phys. 29, 1297 (1958); http://dx.doi.org/10.1063/1.1744712 (9 pages) | Cited 10 times

Online Publication Date: 13 August 2004

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Formulas are developed for the molar constants of five nonlinear effects of molecular orientation in liquids; namely, the dielectric saturation 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 RP, RCM, RK, and RS 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 dielectric saturation 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 saturation effect 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 saturation effect 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, CaSO42H2O

Masao Atoji and R. E. Rundle

J. Chem. Phys. 29, 1306 (1958); http://dx.doi.org/10.1063/1.1744713 (6 pages) | Cited 59 times

Online Publication Date: 13 August 2004

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Using 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

A. J. C. Nicholson

J. Chem. Phys. 29, 1312 (1958); http://dx.doi.org/10.1063/1.1744714 (7 pages) | Cited 15 times

Online Publication Date: 13 August 2004

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A 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

Martin Saunders and James B. Hyne

J. Chem. Phys. 29, 1319 (1958); http://dx.doi.org/10.1063/1.1744715 (5 pages) | Cited 65 times

Online Publication Date: 13 August 2004

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The 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 K3=5.60 l2/M2 and 4.78 l2/M2, respectively and a monomer‐tetramer curve with K4=28.4 l3/M3 for methanol. The data of Becker et al.1 on the ethanol‐carbon tetrachloride system have been fitted to theoretical curves for monomer‐trimer K3=5.19 l2/M2 and monomer‐tetramer K4=44.9 l3/M3.

Thermal Motion in Ice and Heavy Ice

Alfred Zajac

J. Chem. Phys. 29, 1324 (1958); http://dx.doi.org/10.1063/1.1744716 (4 pages) | Cited 8 times

Online Publication Date: 13 August 2004

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Changes 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

C. W. F. T. Pistorius

J. Chem. Phys. 29, 1328 (1958); http://dx.doi.org/10.1063/1.1744717 (5 pages) | Cited 36 times

Online Publication Date: 13 August 2004

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The force constants of 10 molecules and 5 ions of the type XY6 belonging to the Oh symmetry are calculated from the observed frequencies by Wilson's F—G matrix method, using Raman and infrared data. Although only one force constant is neglected, imaginary results were found in the cases of MoF6 and WF6. Possible causes for this are discussed.

Reaction of Oxygen Atoms with Nitric Oxide

Paul Harteck, Robert R. Reeves, and Gene Mannella

J. Chem. Phys. 29, 1333 (1958); http://dx.doi.org/10.1063/1.1744718 (3 pages) | Cited 19 times

Online Publication Date: 13 August 2004

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The 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→NO2+M). At room temperature the reaction coefficient was found to be k2=7.6×10‐32 cm6 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

A. F. Stevenson and Hari L. Bhatnagar

J. Chem. Phys. 29, 1336 (1958); http://dx.doi.org/10.1063/1.1744719 (4 pages) | Cited 6 times

Online Publication Date: 13 August 2004

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The 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.

Calculation of the Energies of Triatomic Hydrogen Using a Modified Roothaan Procedure

Willard E. Meador

J. Chem. Phys. 29, 1339 (1958); http://dx.doi.org/10.1063/1.1744720 (7 pages) | Cited 6 times

Online Publication Date: 13 August 2004

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Potential energies for some linear, symmetrical configurations of H3 have been calculated using a modified Roothaan procedure with configuration interaction, and including a variable shifting parameter. Calculations for two excited states are also given along with detailed discussions of the various energy functions. The results are found to be very close to those obtained by Hirschfelder, Eyring, and Rosen.

Static Space Charge and Capacitance for a Single Blocking Electrode

J. Ross Macdonald

J. Chem. Phys. 29, 1346 (1958); http://dx.doi.org/10.1063/1.1744721 (13 pages) | Cited 40 times

Online Publication Date: 13 August 2004

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Static space‐charge distributions in materials having one charge blocking and one ohmic electrode are considered with special emphasis on the situation where charge carriers of only one sign are mobile but which may recombine bimolecularly with fixed charges of opposite sign. The dependence of potential, charge, and electric field on distance from the blocking electrode cannot be obtained exactly in closed form but various simple approximate relations are obtained and are compared with accurate digital computer solutions of the exact relation between potential and distance. Comparison is most significant when the distance scale is normalized by the effective Debye length, a quantity which is shown to depend on recombination ratio when charges of only one sign are mobile. The dependence of total space‐charge and differential and static space‐charge capacitance on applied potential and recombination is obtained in closed form, and it is shown that recombination can lead to peaks in the curves of static and differential capacitance versus applied potential. Observation of these peaks should afford a simple method of determining recombination ratio and other pertinent parameters of the material. Finally, the addition of a charge‐free layer in series with the space‐charge region is considered, and the effect of such addition on differential capacitance investigated. The combination of a charge‐free layer and space‐charge region represents a combination of Mott's and Schottky's theories of rectification insofar as capacitance effects are concerned and is therefore pertinent to measurements on barrier‐layer rectifiers as well as to material with a completely blocking electrode.

Composition of Nitrogen Oxide Equilibria

Eleonora van Beek‐Visser

J. Chem. Phys. 29, 1358 (1958); http://dx.doi.org/10.1063/1.1744722 (3 pages)

Online Publication Date: 13 August 2004

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The nitrogen oxide equilibrium is recalculated on the basis of the new spectroscopic value for the dissociation energy of nitrogen. Complete tables of the composition are given in the temperature range 2–5000°K. The maximum amount of fixed nitrogen (at 1 atmos pressure and a nitrogen oxygen ratio as in natural air) is ∼5 mole percent and occurs at a temperature of ∼3500°K. The influence of the N/O ratio is indicated.

Isotropic Nuclear Resonance Shifts

Harden M. McConnell and Richard E. Robertson

J. Chem. Phys. 29, 1361 (1958); http://dx.doi.org/10.1063/1.1744723 (5 pages) | Cited 318 times

Online Publication Date: 13 August 2004

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It is shown that isotropic (or average) nuclear resonance shifts for a nucleus in a paramagnetic molecule in solution, and in a polycrystalline solid, can be used to distinguish between Fermi contact and ``pseudocontact'' contributions to isotropic nuclear‐hyperfine interactions. The pseudocontact interaction is that isotropic hyperfine coupling which arises from the combined effects of (electron‐spin)‐(nuclear‐spin) coupling, (electron‐orbit)‐(nuclear‐spin) coupling, and electron spin‐orbit interaction. When the magnetic hyperfine interaction between the electronic moment and nuclear spin is approximated by a point dipolar interaction, and the isotropic hyperfine interaction is exclusively pseudocontact, then the isotropic nuclear shift in a polycrystalline solid exceeds the solution shift by the factor 3(g∥+g⊥)/(g∥+2g⊥) where g∥ and g⊥ are the spectroscopic splitting factors parallel and perpendicular to the molecular symmetry axis. Isotropic shifts due to the Fermi contact interaction are the same for both solid state and solution cases.

Expression in Terms of Molecular Distribution Functions for the Entropy Density in an Infinite System

R. E. Nettleton and M. S. Green

J. Chem. Phys. 29, 1365 (1958); http://dx.doi.org/10.1063/1.1744724 (6 pages) | Cited 97 times

Online Publication Date: 13 August 2004

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An expression for the entropy in a finite subvolume of an infinite fluid, originally proposed by Strato‐novich on the basis of information theory, is rewritten in terms of functions related to the potentials of average force. The result exhibits a correction to the corresponding expression obtained by H. S. Green for a finite system, in the form of a series in powers of the concentration, of which the first terms have been investigated by Richardson. By neglect of correlations of three or more molecules and powers of the density higher than the third, the result is specialized to the case of a gas of low density, for which the configurational entropy per molecule is calculated with use of the radial distribution obtained by Kirkwood for hard‐sphere and hard‐core Lennard‐Jones potentials.
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