Volume 57, Issue 11, 01 December 1972

Some Features of the Potential Surface
View Description Hide DescriptionNonempirical self‐consistent‐field calculations are reported for about 75 points on the potential surface for the isomerization. Due to interest in the possible non‐RRKM behavior of CH_{3}NC, the magnitude of the barrier to rotation of the methyl group is examined as a function of the reaction coordinate. The transition state or saddle point geometry is determined by minimizing the potential energy with respect to five geometrical parameters and maximizing with respect to a sixth. The geometries of CH_{3}NC and CH_{3}CN are also predicted and found to agree closely with experiment. Finally, it is established that, contrary to semiempirical results, the present theoretical approach does not predict the existence of a relative minimum in the reaction coordinate.

Equations Governing the Statistical Mechanical Distribution Functions of a Molecular Fluid Interacting with a Solid Boundary
View Description Hide DescriptionAn infinite set of integrodifferential equations, governing the equilibrium, statistical mechanical distribution functions of a molecular system in contact with a plane, solid wall, is derived. The derivation involves an examination of the effect on the distribution functions produced by an infinitesimal change in the applied external potential. The resulting equations are similar in form to the well‐known Bogoliubov‐Born‐Green‐Kirkwood‐Yvon equations, specialized to the fluid‐wall problem. However, unlike the BBGKY equations, the equations presented here are not restricted by the pair potential condition. The application of these equations to fluid adsorption and to other aspects of liquid state physics is discussed in detail.

Vibrational Deactivation of HF(v=1) in Pure HF and in HF‐Additive Mixtures
View Description Hide DescriptionThe laser‐excited vibrational fluorescence method has been used to obtain room temperature (294±2°K) vibrational relaxation rates for pure HF and in HF‐additive mixtures. Measurement of the quenching of HF(v=1) fluorescence in and HF‐additive collisions has yielded the following total deactivation rates: , and . The self‐relaxation rate for HF was found to be in dilute Ar mixtures and also with other additives. A slower rate has been measured in pure HF and is believed to indicate nonequilibrium of the rotational degrees of freedom during self‐relaxation of HF. Observation of 4.3 μ fluorescence from CO_{2}(00°1) and double exponential fluorescent decay from mixtures has led to the following rates for CO_{2}(00°1) and H_{2}(v=1) deactivation: , and The room temperature data are much faster than predicted from an extrapolation of the available high‐temperature shock tube results. The equal, near gas kinetic rates found for HF relaxation by H_{2}O and D_{2}O suggest that strong chemical bonding forces may be responsible for the HF‐water relaxation.

Atomic Force Constants in Some First Row Compounds
View Description Hide DescriptionBy analysis of a vibrational frequency sum rule a set of force constants characteristic of H, C, N, O, and F atoms was found. These quantities, called atomic force constants, have the remarkable property of being independent of the details of molecular geometry or bonding multiplicity. Hence, it is possible to compute the sums of the squares of the normal frequencies of compounds involving these elements without explicit prior knowledge of their structures.

Calculation of Atomic Force Constants from Electron Densities
View Description Hide DescriptionAn expression is derived which relates molecular electron densities to the atomic force constants obtained from an analysis of the frequency sum rule for polyatomic molecules. Using approximate electron densities computed by Pople and Segal by the CNDO method [J. A. Pople and G. A. Segal, J. Chem. Phys. 43, S136 (1965)], it was found that not only the magnitudes of the atomic force constants for H, C, N, O, and F atoms were accounted for, but also their observed independence of bond multiplicity.

Infrared Spectra of Several New Lanthanide Oxide‐Silicate Glasses
View Description Hide DescriptionThe preparation and the infrared spectra of 10 new lanthanide oxide‐silicate glasses are reported. The three strongest regions of absorptions in the base glass (SiO_{2}/Na_{2}O/CaO) are maintained, although some shifts in frequencies do occur with the addition of lanthanide oxides. The 1050 cm^{−1} absorption in the base glass, assigned as the silicon‐oxygen stretching mode within the SiO_{4} tetrahedron, shifts toward lower frequency by about 10–25 cm^{−1}; the silicon‐oxygen stretching between tetrahedra at 780 cm^{−1} and the silicon‐oxygen bending modes at 475 cm^{−1} do not show any significant shifts. Evidence is presented that crystallization may occur in these glasses on standing, and this may be connected with the half‐filled shell effect in the lanthanide series.

Proton and Fluorine Nuclear Magnetic Resonance Observations on Hypofluorous Acid, HOF
View Description Hide DescriptionThe proton and ^{19}F chemical shifts have been measured for liquid HOF at low temperature, and the proton shift has been measured for the gas at room temperature. The results indicate that the hydrogen and fluorine atoms in the molecule carry charges of approximately +0.5e and −0.5e, respectively.

Low‐Frequency Vibrations in Molecular Solids. XVIII. Torsional Modes and Barriers to Internal Rotation of Some Isopropyl Compounds
View Description Hide DescriptionFar‐infrared spectra of solid (CH_{3})_{2}CHCl, (CD_{3})_{2}CHCl, (CH_{3})_{2}CHBr, (CD_{3})_{2}CDBr, (CH_{3})_{2}CHI, (CD_{3})_{2}CHI, (CH_{3})_{2}CHCN, (CH_{3})_{2}CHOH, and (CD_{3})_{2}CDOD have been studied from 33 to 500 cm^{−1}. The A′ and A″ torsional modes have been observed and assigned at 248 and 283, 178 and 208, 256 and 272, 189 and 205, 246 and 253, 190 and 198, 230 and 242, 237 and 277, and 169 and 194 cm^{−1}, respectively, for the above molecules. From these assigned frequencies, the torsional barriers were calculated to be 4.48, 4.54, 4.51, 4.77, 4.11, 4.73, 3.63, 4.18, and 3.94 kcal/mole, respectively. These barrier values are compared to those obtained for some similar compounds and certain trends are noted. Some of the lattice frequencies have been assigned to librational and translational motions on the basis of the isotopic shifts with deuteration.

Thermochemistry of the Molecular Species LiO, LiO^{+}, and Li_{2}O^{+}
View Description Hide DescriptionMolecular species in the system were studied by electron‐impact mass spectrometry and the data were used to derive the dissociation energy of LiO and the ionization potentials of LiO and Li_{2}O. From studies of the gaseous equilibria Li+O_{2}=LiO+O and Li_{2}O+O=2LiO and from the composition of saturated vapor over Li_{2}O(c), the value is obtained. The ionization potentials were found to be I.P.(LiO) =8.45 eV and with an uncertainty of 0.20 eV, leading to and The data are compared with the results of some theoretical calculations, and the chemical bonding in these molecules is discussed briefly.

^{14}N Quadrupole Resonance Study of a Hydrogen Bond: Hexamethylenetetramine Triphenol
View Description Hide DescriptionThe nuclear quadrupole resonance spectrum of hydrogen bonded hexamethylenetetramine triphenol was observed at 77°K and at room temperature. The absorption lines were assigned to two inequivalent nitrogen sites. N(1), which is not hydrogen bonded, gave e ^{2} qQ/h=4665.7 kHz and at 77°K. N(2), which takes part in an hydrogen bond, has e ^{2} qQ/h=4208.1 kHz and also at 77°K. By comparing these data with the spectrum of pure hexamethylenetetramine (HMT) the effects of the hydrogen bond on the HMT nitrogen sites could be obtained. It is concluded that the nitrogen site N(2) loses a few hundredths of an electron from its lone pair orbital as a result of the hydrogen bond interaction.

Electron Spin Resonance Spectrum of the Chlorodisulfanyl (S_{2}Cl) Radical in Inert Matrices at 4.2°K
View Description Hide DescriptionA new species, the chlorodisulfanyl radical (ClSS), has been produced by photolysis of dichlorodisulfane (Cl_{2}S_{2}) in inert matrices at 4.2°K. The identification of ClSS rests on the complete simulation of its well resolved electron spin resonance spectrum. A versatile computer program was developed for this purpose. The method of computation is perfectly general and takes into account the noncoincidence of the principal axes frames of the various tensors in the spin Hamiltonian which, apart from the usual g and Atensors, includes a quadrupole coupling tensor and nuclear Zeeman term. The chlorodisulfanyl radical possesses anisotropicg and hyperfinetensors which have principal axes rotated relative to each other by 10° in the molecular plane. In addition to this, the fact that the chlorodisulfanyl radical has been found to have a quadrupole coupling tensor which is of comparable magnitude to the hyperfine interaction tensor leads to a rather complicated ESR spectrum for the randomly oriented species. Our work shows that the chlorodisulfanyl radical is a ``π radical.'' The anisotropy of the hyperfine coupling tensor can be explained by spin polarization of the bond rather than by contributions from spin density on neighboring sulfur atoms.

High Resolution Infrared Spectra of the Parallel Bands of Phosphorous Pentafluoride
View Description Hide DescriptionThe v _{3} and v _{4} parallel bands of PF_{5} were recorded at a resolution of ∼0.06 cm^{−1}. The J structure of the P and R lines was resolved, and we obtained a value of B _{0}=0.10470. The lowest lying fundamental frequency v _{7} is estimated to be 166±15 cm^{−1}.

Saturated Liquid Properties from the Mie(n, 6) Potential and the Barker‐Henderson Perturbation Theory
View Description Hide DescriptionThe perturbation theory of Barker and Henderson [J. Chem. Phys. 47, 4714 (1967)] has been used to test various Mie(n, 6) intermolecular pair potentials for their ability to predict liquid properties. The properties studied were the residual energies, entropies, and heat capacities in four saturated liquids: argon, nitrogen, methane, and perfluoromethane. The potential energy function parameters (ε/k, σ, n) used in most cases are those obtained by Klein [Natl. Bur. Std. (U.S.) AECD‐TR‐67–67] from second virial coefficient data. It is shown that it is possible to obtain a considerable improvement in predicted liquid properties if the parameter n is allowed to vary from the value 12 usually assigned to this parameter.

ESR Study of Radicals in γ‐Irradiated Polycrystalline AsF_{3} and AsCl_{3}
View Description Hide DescriptionThe free radicals produced in frozen, polycrystalline AsF_{3} and AsCl_{3} by γ irradiation have been characterized by ESR and shown to be and, most probably, Hyperfineinteractions with arsenic are observed in each case and in ligand hyperfine splittings by three fluorine atoms, two of one kind and one of another, are also seen. The ESR parameters are consistent with an approximately planar‐T configuration for with the odd electron largely in an orbital perpendicular to the plane.

Square‐Well Potential. III. Transport Properties of Liquids
View Description Hide DescriptionThe Davis‐Rice‐Sengers square‐well theory of transport for simple dense gases and liquids is tested with Yvon‐Born‐Green theoretical pair correlation functions for . Comparison with experiment shows that the theory correctly predicts the qualitative features of liquid argontransport properties and quantitatively is very good at high temperatures and densities in the liquid region. An adjustment of intermolecular potential parameters is shown to improve the predictions of the theory uniformly. Some comments are made concerning the success of this theory in light of recent studies of the Rice‐Allnatt theory.

Total Scattering Cross Sections in the Velocity Range 760–2600 m/sec
View Description Hide DescriptionMeasurements of the total scattering cross section Q for are reported over a range 760 m/sec≤ v _{ r }≤2600 m/sec in the relative speed. The data have been fit with a piecewise continuous potential that also gives a good fit to the diffusion coefficients, has the theoretical C _{6} coefficient, and joins smoothly with the short range a priori computed potential.

Unified Theory of Orientational Relaxation
View Description Hide DescriptionA mathematically simple model for orientational relaxation in liquids is presented. This theory, expressed in terms of Mori's formalism for generalized hydrodynamics, is developed with three orientational variables interrelated by three coupled linear transport equations. The three variables are where is a relevant Wigner rotational transformation function. In appropriate limits the theory reduces to that for rotational diffusion, gas‐like extended rotational diffusion (GLED) and solid‐like oscillatory rotations (SLOR) or cell model motions. This theory, which we call the pseudo‐GLED‐SLOR theory, therefore gives a unified picture, encompassing all limits, of molecular rotations in liquids. The assumptions, and consequently the results, differ slightly from those usually introduced in the GLED and SLOR theories; the various limiting forms of molecular reorientation are obtained in the present theory via restrictions on the quantities, whereas the usual quantities of interest are the molecular angular velocity, the intermolecular torques, and the rate of change of torques. It is for this reason that we have introduced the term ``pseudo'' in describing the theory. The only restriction that must be placed on the theory is that changes impulsively, but of course, different assumptions concerning the magnitudes of the other variables lead to different limiting physical situations. In appropriate limits, the present theory exhibits most of the interesting features of the rotational diffusion theory, Gordon's extended rotational diffusion theory, Steele's inertial effects and Ivanov's jump theory; furthermore, it predicts rotational or torsional side bands in the frequency spectrum of the molecular orientational autocorrelation function. In the far wings it predicts an frequency dependence. The theory treats and as dynamical quantities and only is treated as a Markoffian variable. A careful analysis is presented of the differences between the correlation timewhere is the autocorrelation function of and the spectral half‐width

On Improved WKB (Uniform Asymptotic) Quantum Conditions, Dunham Corrections, the Langer Modification, and RKR Potentials
View Description Hide DescriptionAn improvement to the WKB quantum condition for the rotation‐vibration levels of diatomic molecules, known empirically to give RKR potentials of increased accuracy and to account for the Dunham correction Y _{00}, is derived using uniform asymptotic methods. The role of the Langer transformation in this problem is also discussed.

Electron Excitation Cross Sections for , and
View Description Hide DescriptionElectron excitation cross sections using the Born approximation are given. Two types of Slater wavefunctions have been used, and the results are compared with other theoretical calculations and experimental data where available.

Effects of Liquid Structure on dc Transport Coefficients in Brownian‐Like Solutions
View Description Hide DescriptionWe determine the Ohmic and Hall conductivities for an infinitely dilute Brownian‐like electrolyte by solving the generalized Fokker‐Planck equation for the stationary value of the carrier particle distribution function. This is done by expanding at each field order in the natural parameter of smallness, γ = (solvent molecule mass/carrier mass)^{1/2}. The corrections to the lowest order results (Brownian motion) are determined, and the Hall coefficient is then found. The value of unity obtained, identical to the Brownian motion value, indicates that liquid structure effects are not significant in this type of system.