Volume 28, Issue 4, 01 April 1958

Electronic Structures of the Methyl Radical: Effect of 3s Atomic Orbital of Carbon
View Description Hide DescriptionBy taking the 3s orbital of carbon into account, the self‐consistent‐field (SCF) LCAO—MO method has been applied to the ground state of the methyl radical. The 3s AO used has been determined for the valence state V _{4}(1s ^{2}2s2pπ_{+}2pπ_{—}3s) by a variational procedure, so that the orbital exponent of the 3s simple Slater AO obtained is 0.6374 instead of Slater's value 0.4833. For the other states with 3s AO, it is similarly concluded that good approximate 3s orbitals cannot be obtained by using Slater's rule, and more satisfactory shielding constants for the extra‐valence‐shell electron are given. Interactions between all electrons have been taken into consideration but the orthogonality relationship between 1s orbitals of carbon and hydrogen has been assumed. For the MOs occupied in the ground state, the forms are hardly changed by the inclusion of the 3s AO, and the contribution of the 3s AO is very small. For the lowest vacant orbital, however, this contribution is exceedingly great and qualitatively the conventional approximation by the 3s AO is rather more satisfactory than the use of the antibonding LCAO—MO constructed by the valence‐shell orbitals. In the lower electronic states calculated, such properties are prominent and the agreements with the observations are relatively good, especially by the inclusion of the 3s AO. The influence of the other extra‐valence‐shell orbitals is discussed.

Role of Atomic Valence States in Molecular Energy Calculations
View Description Hide DescriptionAb initio calculations of molecular binding energies are examined critically in a basis of antisymmetrized products of approximate atomic state functions (the approximate composite functions of Moffitt). It is shown that much more accurate results may be expected if the binding energy is calculated relative to a suitably defined generalized valence state V of the dissociation products. The energy of this state V relative to the ground state of the dissociation products is estimated from atomic spectral data. This procedure leads directly to the intra‐atomic correlation correction previously proposed by the author as a necessary modification of Moffitt's method of atoms in molecules.
Detailed calculations are carried out for the ground states of the molecules LiH and BH, and for the ground and excited states of the benzene molecule (in the usual π‐electron approximation). In each case the intra‐atomic correlation correction leads to a substantial improvement in the accuracy of the results.

Unlike Molecular Interactions and Properties of Gas Mixtures
View Description Hide DescriptionRecently we have developed a set of semiempirical combination rules which may be utilized to calculate the intermolecular potentials for unlike pairs of molecules from the known potentials for like pairs on the modified Buckingham exp—six model. It is, therefore, necessary to see how far these combination rules can reproduce the transport properties of binary gaseous mixtures over large ranges of temperature and concentration. With this end in view various transport properties such as themal diffusion,interdiffusion,thermal conductivity, and viscosity have been calculated for a large number of binary mixtures and the computed values compared with the experimental data. It is found that the agreement between the theory and experiment is quite satisfactory. It is concluded that this set of combination rules can be used with success to predict the transport properties of gaseous mixtures within the limits of experimental error.

Transitions in Adsorbed Monolayers. I. Experimental
View Description Hide DescriptionThis first of three papers describes the preparation of sodium bromide samples on which adsorbed krypton and methane exhibit transitions in the region below one monolayer. The isotherms for these gases are reported for temperatures ranging from 64 to 85°K. The nitrogen isotherms at various temperatures show no such transition, and are discussed from the point of view of the BET theory. A device for maintaining a constant level of liquid nitrogen under reduced pressure is also described.

Transitions in Adsorbed Monolayers. II. Theoretical
View Description Hide DescriptionIn anticipation of the experimental comparisons to be given in Part III, the grand partition function is employed to derive the isotherm and the two‐dimensional equation of state corresponding to a model of localized monolayeradsorption similar to that of Rushbrooke, in which the lateral vibrational partition function is permitted to depend on the occupation number of neighboring sites. This treatment includes the Fowler ``crude'' isotherm as a special case. As a competing theory, a parallel development is given for the van der Waals model of mobile adsorption. Equations are presented for the critical parameters, and for the determination of the coexistence curves for these models. Finally, graphical comparisons are made which demonstrate the experimental distinguishability of the three theories on plots which rectilinearize one at a time.

Transitions in Adsorbed Monolayers. III. Results and Comparisons
View Description Hide DescriptionThe experimental and theoretical results of the two preceding papers [B. B. Fisher and W. G. McMillan, J. Chem. Phys. 28, 549 and 555 (1958), hereafter referred to as Parts I and II] are combined to yield ``experimental'' values of the adsorption parameters for nitrogen, krypton, and methane on sodium bromide. These are compared with the results of extensive theoretical calculations of the adsorption energy χ, the lateral interaction energy w and the frequencies of various vibrational modes. Of the several parameters, the agreement between theory and experiment is best for χ; of the several gases, the agreement is best for krypton. An appendix gives fitted functions for inverse sixth power lattice sums, and for the electric field strength above the 100 surface of an fcc ionic lattice.

Microwave Spectra of Molecules Exhibiting Internal Rotation. III. Trimethylamine
View Description Hide DescriptionThe first two rotational transitions of trimethylamine have been studied. The spectrum of the ground vibrational state follows a symmetric‐rotor pattern with the following constants:

Delayed Fluorescence of Complex Molecules in the Vapor Phase
View Description Hide DescriptionIt has been found that the vapors of several fluorescent aromatic hydrocarbons have two components in their fluorescence. These have the same emission spectrum but greatly differing decay times. The lifetime of the fast component is probably that which would be predicted from the strength of the absorptionspectrum. This investigation was concerned with the slow component whose decay was exponential with a lifetime of the order of milliseconds. Detailed observation of the behavior of this lifetime as several experimental conditions were changed has shown that a bimolecular process is responsible for the delayed emission. A mechanism is proposed and discussed in detail.

Photoconductivity of Anthracene. IV. Bulk Photoconduction in Single Crystals
View Description Hide DescriptionBulk photoconduction of anthracenesingle crystals has been measured using monochromatic light. The intensity and voltage dependences are found to depend on the field direction and the wavelength of the exciting light. The spectral response of photoconduction depends on the field direction. A model is proposed to account for these observations and for the space charge effects that are found to occur. This model rests mainly on the assumptions of a higher mobility for the positive charge carriers and the nonreplenishment of charge carriers at the evaporated silverelectrodes. Recombination of carriers is deduced, and a quantitative relationship between spectral response and extinction coefficient is found.

Photoconductivity of Anthracene. V. Effect of Imperfections on the Bulk Photocurrent
View Description Hide DescriptionBulk photocurrents of anthracene have been measured on crystals of high purity, scintillation crystals, and crystals irradiated with thermal neutrons. It is found that the source and treatment of the crystals strongly affects the spectral response and the voltage and intensity dependence of the bulk photocurrent. This can be related to the density of the imperfections in the crystals. Direct evidence for the existence of traps was furnished by the electrical analog of the thermoluminescent glow curves and by the increase of the photocurrents with red radiation.

Bulk Viscosity and Shear Viscosity in Fluids According to the Theory of Irreversible Processes
View Description Hide DescriptionM. Green has connected the shear and bulk viscosities with the fluctuations of the virial. It is shown here that the virial theorem is correct at every moment, including the fluctuations, if the integral of the pressure over the volume is taken. For monoatomic fluids the bulk viscosity is calculated after introducing an unknown correlation length; for fluids with internal degrees of freedom or with two‐state structure, the usual equations follow very easily. For the shear viscosity one finds a formula similar to that of Eyring by making some assumptions about correlations.

Proton Magnetic Resonance Chemical Shift of Free (Gaseous) and Associated (Liquid) Hydride Molecules
View Description Hide DescriptionIn order to study the factors giving rise to protonresonancechemical shifts of free molecules, as well as the association shifts due to hydrogen bonding,protonresonance measurements were carried out for a variety of simple hydride molecules in both the liquid and gaseous states. It is found that the proton shifts in the gaseous state can be interpreted in terms of the combined effect of the electronegativity and magnetic anisotropy of the atom to which the proton is bonded. The proton signals measured in the liquid state near the melting point, which correspond to maximum association, show large shifts to lower magnetic field relative to the corresponding gas signals. It is suggested that the association, or hydrogen bond shifts, in a system Y ——— H — X can be interpreted largely in terms of the reduction of the diamagnetic circulation in the H — X bond by the electrostatic field of the Y donor. Further possible contributions in certain anomalous cases are also considered.

Resonance in Sterically Hindered Aromatic Molecules
View Description Hide DescriptionMany aromatic molecules, typical of which are the triphenylmethyl radical and cis‐stilbene, cannot have the planar structure which would maximize the resonance energy, because of steric hindrance. A semiempirical method of treating such molecules has been developed. It is assumed that the primary effect of the steric strain is to rotate the phenyl groups out of the plane of the molecule. The resulting reduction in resonance energy is estimated using the valence‐bond method. The steric interaction energies are calculated using a method of Eyring, based on the ``perfect pairing approximation'' of valence bond theory. A plot of the sum of these two energiesvs twist angle gives the equilibrium configuration, and the effective resonance energy of the molecule.
The triphenylmethyl radical has a predicted twist angle of 32°, and is stabilized partly by its resonance energy and partly by steric strain in hexaphenylethane. The theoretical twist angle for the free radical di‐p‐anisyl nitric oxide is 25°, as compared with an experimental result of 33°. A close balance between steric strain and resonance in biphenyl leads to virtually free rotation about the central bond. Finally, it is shown that steric hindrance accounts for the energy difference between the cis‐ and trans‐isomers of stilbene and azobenzene.

Energy Exchange between Cold Gas Molecules and a Hot Graphite Surface
View Description Hide DescriptionMethane or ethane do not decompose on clean graphitesurfaces up to 2300°C as long as the mean free path of the gas molecules exceeds the dimensions of the reaction cell. An investigation of the energy exchange between a hot graphitesurface and cold molecules impinging on it revealed an accommodation mechanism of temporary adsorption followed by evaporation at critical temperatures essentially independent of the filament temperature as long as the latter is higher than the former. The evaporation temperature for methane is far below its decomposition temperature.

Higher Approximations for the Transport Properties of Binary Gas Mixtures. III. Isotopic Thermal Diffusion
View Description Hide DescriptionTables of the reduced isotopic thermal diffusion factor as a function of a reduced temperature are given for the exp‐six potential with potential parameter α=12, 13, 14, 15, and for the Lennard‐Jones (n—6) potential with potential parameter n=12, ∞. These tables are based on recently derived higher approximations and are intended to supersede previous tabulations, which are of lower accuracy.

Isotope Effect and Structure of the B_{2}O_{3} and B_{4}O_{6} Molecules
View Description Hide DescriptionA systematic application of the Teller‐Redlich product rule to the isotope effect has been carried out for several of the most likely structures of the B_{2}O_{3} molecule, and tetrahedral B_{4}O_{6}. It is pointed out that an isotope effect of the magnitude reported by Dows and Porter in the infrared emission (2013 and 2114 cm^{—1} for B_{2} ^{11}O_{3} and B_{2} ^{10}O_{3}, respectively) is incompatible with the bipyramidal (D _{3h }) model they consider, as well as with the linear (D _{∞h }) structure. Less symmetrical structures of B_{2}O_{3} (C _{2}, C _{2v }, and C _{3v } symmetries) are not excluded; neither is the tetrahedral B_{4}O_{6} structure. These conclusions are reached by using in conjunction with the product rule the theorem that the frequency of each and every vibrational mode of a molecule is a monotonic function of each atomic mass. This makes it possible to set bounds on the isotope effect of individual modes of each symmetry type, and this procedure should be generally useful. A proof of the theorem stated is given in the Appendix.

Theory of Potentials of Average Force and Radial Distribution Functions in Ionic Solutions
View Description Hide DescriptionThe procedure employed by Mayer for the calculation of osmotic pressure and activity coefficients of ions in solution from the Fuchs expansion of the grand potential in multicomponent systems is applied to the recently obtained expansion of the potential of average force in these systems. The resulting multiply infinite series are summed to give a series analogous to the original expansion, involving the Debye‐Hückel potential of average force in a remarkably simple way. A similar expansion for the radial distribution function is presented. Explicit expressions for both quantities, exact through terms of first order in the ionic concentration, are given. An expansion for the osmotic pressure, analogous to the virial expansion, is presented. The presence of the Debye‐Hückel potential of average force in all these expansions is discussed, and the possibility of obtaining the potential of average force exact through terms of second order in the ionic charging parameters is indicated. Possible applications to ionic conductivity,diffusion, and viscosity are discussed. Additional applications to the theory of defects in ionic crystals, impurity conduction in semiconductors, etc., are suggested. The significance of the individual terms in the new expansions is discussed. Proof of an n‐fold convolution theorem for Fourier transforms is presented.

Statistical Thermodynamics of Quantum Fluids
View Description Hide DescriptionAn approximate technique for determining the thermodynamic properties of quantum fluids by the method of molecular distribution functions is developed. It consists of a separation of the problem into two parts, the determination of the classical pair distribution function at an effective temperature τ, and the quantum‐mechanical calculation of τ. It is further shown that all thermodynamic quantities of interest can be easily computed if τ is known.

Propagation of Electronic Excitation in Insulating Crystals
View Description Hide DescriptionA general method for the description of nonstationary excited states of an insulating crystal is outlined. For the general case, the time‐dependent wave function is given implicitly by means of a simple generating function. In the nearest‐neighbor approximation, the solution can be given explicitly in terms of Bessel functions. The effect of an idealized crystal surface on exciton propagation is examined. The exciton behaves as though repelled by the surface.

Ligand Field Theory of Ni(II) Complexes. I. Electronic Energies and Singlet Ground‐State Conditions of Ni(II) Complexes of Different Symmetries
View Description Hide DescriptionA parametric method of calculating the electronic energies of an ion of configuration 3d ^{8} (3d ^{2}positrons) when placed in a ligand field of point charges or dipoles is described. The method is applicable with a change of sign of the energy matrix elements to ions with a 3d ^{2} electronic configuration. By use of the experimentally determined free ion term energies for the Ni(II) ion the calculations are made specific. The final energy eigenvalues obtained here are for the Ni(II) ion in four and six coordinated complexes of tetragonal, octahedral, cis‐, and trans‐planar symmetries. All free ion states of the same multiplicity and symmetry arising from the ground‐state configuration were allowed to interact. An effective interelectron distance, dipole moment, and point charge were used as parameters. Some of the numerical results for specific values of the parameters are given as examples. The remainder of the energy calculations are tabulated in the dissertation. Minimum field strength conditions necessary for a four coordinated complex to become diamagnetic are determined using the calculated energies. The relative ease of conversion to a singlet ground state in the different symmetries is noted and the effect of an axial field on the change in multiplicity is obtained from the results of the calculations for the six‐coordinated complexes. The results will also be used subsequently to assign the low intensity electronic spectra obtained for a series of Ni(II) chelates of appropriate symmetries and to explain the effect of solvent on the spectra and magnetic moments of these chelates.