Volume 37, Issue 11, 01 December 1962

Absorption Spectra of Hydrogen‐Halide—Rare Gas Mixtures
View Description Hide DescriptionThe null‐gap regions of the 1–0 bands of HCl and HBr have been investigated with a gratingspectrograph of very high resolution. The experiments were performed using an absorption tube of 90 cm length and a hydrogen‐halide pressure of 25 cm Hg. The hydrogen halide was pressurized with argon, krypton, or xenon of density 2 to 5 amagats. The sensitivity of the apparatus was such that absorption features 10^{—4} the intensity of the P(1) line of HCl could be observed with ease.
The absorption features observed are complex, relatively sharp, and totally different when argon, krypton, or xenon is used as the pressurizing gas. It is suggested that the hydrogen‐halide molecule forms a molecular complex with the rare‐gas atoms used as pressurizing agents. The discrete induced absorption features have an intensity considerably less than 10^{—3} of the intensity of the P(1) line of HCl per amagat density of pressurizing gas. In HBr the ``induced absorption features'' have approximately two to three times the relative intensity observed in HCl.

Interactions between Ordinary Vibrations and Hindered Internal Rotation. I. Rotational Energies
View Description Hide DescriptionThe effect of vibration‐hindered rotation interactions on the rotational energy levels of molecules containing a symmetric internal rotor has been re‐examined theoretically. The complete Hamiltonian has been derived and includes terms which are due to Coriolis coupling and to the explicit dependence of the kinetic energy on the angle of internal rotation.
Over‐all and internal rotation are separated from vibration, in zeroth order, by means of the Eckart and Sayvetz conditions. Difficulties in previous treatments are traced back to the application of these conditions. For each vibrational state, an approximate Hamiltonian for over‐all and internal rotation is obtained by a Van Vleck perturbation treatment in which torsional denominators are assumed to be negligible. A correction for these denominators is determined by taking the first term in a power series expansion.
A preliminary transformation, similar to that described by Hecht and Dennison, is used to remove zeroth‐order coupling between the angular momenta of over‐all and internal rotation. Simple product wavefunctions, then, form a suitable basis for evaluating first‐order energy corrections due to higher‐order coupling of internal and over‐all rotation.
Symmetric rotors, slightly asymmetric rotors, and asymmetric rotors with relatively high barriers to internal rotation are each treated separately. Empirical frequency expressions for rotational transitions of all three types of molecule are given. The symmetric rotor formula is identical in form to Kivelson's but the empirical constants must be interpreted differently. A symmetric rotor analysis was done on CH_{3}SiF_{3} and CD_{3}SiF_{3}. K→K, J—1→J transitions of slightly asymmetric rotors obey a particularly simple frequency relation. Two groups of asymmetric rotor transitions are tractable: (1) The 0_{0,0}→1_{0,1}, ½[1_{1,0}→2_{1,1}+1_{1,1}→2_{1,2}], and 2_{2,1}→3_{2,2} transitions, where the designation of levels is for a prolate rotor, and (2) transitions between the two members of an asymmetry doublet.

Electronic Spectrum of 2,2′‐Paracyclophane
View Description Hide DescriptionThe polarized absorption and fluorescence spectra of single crystals of 2,2′‐paracyclophane at 20°K were recorded in the region 3300–3100 Å. The spectra consist of narrow lines of which 87 could be measured in absorption and nine in emission. Single crystals having two different planes developed could be prepared sufficiently thin for measurements. The spectra obtained could be divided into two components, one characteristic of a transition moment parallel and the other perpendicular to the unique axis of the tetragonal crystal. These polarization directions are characteristic of molecular directions since in this case no Davydov splitting is to be expected in view of the high symmetry of the crystal. The absorption system is analyzed satisfactorily as representing the forbidden component of the benzene ^{1} A _{1g }→^{1} B _{2u }transition in the ``dimer'' molecule. A totally symmetric progression‐forming frequency of 240 cm^{—1} is assigned as the intermoiety vibration. The appearance of a weak 0–0 transition is interpreted as due to a small‐amplitude twist of the moieties relative to one another.

Effect of Partial Draining on the Intrinsic Viscosity of Flexible Macromolecules
View Description Hide DescriptionThis calculation applies the theory of Zimm to the problem of the partial draining of Gaussian coils. Zimm's free‐draining eigenfunctions are assumed to be sufficiently accurate as eigenfunctions in the nondraining limit, and the function required for the intrinsic viscosity is tabulated as a function of a draining parameter in a manner similar to that of Kirkwood and Riseman. The use of a scaling factor as proposed by Kurata and Yamakawa is shown to give low results with a maximum error of the order of 10%. The first relaxation time is tabulated and found to be a rather weak function of the draining parameter.

Varying Orbital Exponents in Molecular Orbital Theory
View Description Hide DescriptionBy means of the variational principle a set of conditions is derived for the orbital exponents which minimize the energy in the LCAO form of molecular orbital theory, using Slater atomic orbitals. These equations are to be solved simultaneously with Roothaan's conditions for the best LCAO coefficients. The method is illustrated for the molecular ion H_{2} ^{+} and the molecule He_{2}.

Optical Spectrum of K_{3}IrCl_{6}
View Description Hide DescriptionThe complete matrices of the spin‐orbit interaction for the d ^{4}, d ^{6} configurations are given in a strong cubic field scheme. Intermediate coupling calculations have been carried out for the energy levels of K_{3}IrCl_{6}, and lead to a satisfactory interpretation of the observed optical spectrum.

Nitric Oxide Bands near 1 μ in Shock‐Heated Air
View Description Hide DescriptionThe banded radiation from a strong radiating system has been observed in the near‐infrared spectrum of shock‐heated air. The dependence of the radiant intensity upon species concentration and temperature, as well as an estimate of the oscillator strength, indicate that the radiation results from transitions between excited electronic states of nitric oxide. This system is shown to be a significant contributor to the infrared emission spectrum of high‐temperature air.

Rate of Dissociation of N_{2}O_{4} by Ultrasonic Absorption Measurements
View Description Hide DescriptionSound‐absorption measurements as a function of the sound frequency in the range of 78 to 394 kc/sec have been made in gaseous mixtures of nitrogen tetroxide, nitrogen dioxide, and a third inert gas. Inert gases studied were nitrogen, argon, and carbon dioxide. The absorption coefficient per wavelength varies with frequency in the typical bell‐shape manner associated with a relaxation mechanism. The frequency of maximum absorption increases with increasing concentration of N_{2}O_{4}, is nearly independent of the total pressure, and varies only slightly with temperature in the range 25° to 40°C. The sound absorption is ascribed to the perturbation of the equilibrium reaction N_{2}O_{4}=2NO_{2}. The (equilibrium) rate of dissociation of N_{2}O_{4} is calculated using an extension of the theory developed by Freedman. It is concluded that the dissociation of N_{2}O_{4} proceeds according to a Lindemann unimolecular mechanism; specific rate constants for the limiting low‐concentration and high‐concentration regions at 25°C are 4.5×10^{6} liter mole^{—1} sec^{—1} and 1.7×10^{5} sec^{—1}, respectively. The relative efficiencies of the various molecules for energizing N_{2}O_{4} are: N_{2}O_{4}, 1.0; NO_{2}, 1.0; N_{2}, 0.50; Ar, 0.30; CO_{2}, 1.0. Measured absolute values of the absorption coefficients are in good agreement with calculated values. The effects of viscosity,heat conduction, and vibrational heat capacity relaxation on the observed magnitude of the absorption are considered negligible.

Low‐Energy Collision Cross Sections of H^{—} and OH^{—} Ions in Oxygen
View Description Hide DescriptionElastic and inelastic collision cross sections have been measured for collisions of H^{—} and OH^{—} ions in oxygen gas in the energy range 4–350 eV. An improved collision chamber was used for the measurements. The majority of the inelastic collisions in the case of OH^{—} are apparently due to electron detachment, but in the case of H^{—}, charge exchange or an ion—molecule reaction or both predominate, particularly at the low energies. In the range 4–26 eV the interaction potential derived from the elastic scattering of OH^{—} in O_{2} is V (eV) = —18.4/r ^{5.34}(r in Å). The large amount of inelastic scattering observed for H^{—} in O_{2} precluded an accurate determination of the interaction potential in this case. The electrons produced in electron‐detachment collisions of negative ions are shown to have energies considerably in excess of thermal energy.

NMR Relaxation Times in Solid White Phosphorus: Diffusion and Rotation
View Description Hide DescriptionNuclear magnetic resonancerelaxation times have been measured for solid white phosphorus by spin‐echo techniques. The diffusion coefficient calculated from T _{2} in the α phase can be represented aswhere D _{0}=0.077±0.014 cm^{2}/sec, and ΔH=12.1±0.1 kcal/mole. The correlation time for rotation calculated from T _{1} in the β phase can be represented bywhere t _{0}=6.04×10^{—14} sec, and ΔH=4.02±0.02 kcal/mole. The distance between phosphorus atoms in the P _{4} molecule is found to be 2.24±0.03 Å from the value of T _{1} at the T _{1} minimum in the β phase.

Reaction Kinetics of a Long Chain Molecule
View Description Hide DescriptionA long chain molecule is considered, of which each segment carries a reactive group. It is assumed that the reactivity of each group depends upon whether zero, one, or two of its nearest neighbors have reacted. The average fraction of reacted groups is determined as a function of time. This is done by first deriving appropriate equations to describe the kinetics and then solving these equations. The results are illustrated by a number of graphs which show the average fraction of reacted groups as a function of time for different ratios of the reactivities.

Lattice Combination Bands in Infrared Spectra of Molecular Solids
View Description Hide DescriptionIt is customary in the discussion of infrared spectra of molecular solids, and of ionic solids containing polyatomic ions, to divide the normal vibrations of the nuclei into two classes: (1) Lattice or external modes, low‐frequency vibrations which are approximately motions of whole molecules, and (2) molecular or internal modes, high‐frequency vibrations similar to the vibrations of free molecules. The observed spectra are then interpreted in terms of absorption by these fundamentals, and combination bands involving two or more fundamentals. In this paper we discuss combination bands between lattice modes and internal modes. It is shown that a certain amount of information about the intensity of such bands and their temperature dependence can be predicted without a solution to the complete dynamical problem of the lattice vibrations.

Proton NMR Spectra of Disubstituted Benzenes
View Description Hide DescriptionPrecise values of the coupling constants and chemical shifts at infinite dilution in cyclohexane have been determined for an extensive series of related disubstituted benzenes. A method of rigorous analysis of the A_{2}B_{2}proton spectra of the para‐disubstituted benzenes is presented.

Proton Magnetic Resonance Spectra of 2‐Pyridines. The Strong‐Coupled AA′KL System
View Description Hide DescriptionThe 60‐Mc/sec spectra of 2‐chloro, 2‐cyano, 2‐bromo, and 2‐acetyl pyridines are studied and analyzed as ABKL and AA′KL systems. The results are compared with the exact ABCDsolution given by a computer. It is shown that if one of the coupling constants is greater than the corresponding chemical shift, the AA′KL approximation can give a good account of the frequencies of the lines of the experimental spectrum, but not so good for the intensities. The molecular parameters calculated with both approximate methods differ only some hundredths of a cycle per second from the values given by the computer.
An iterative method based on the use of average group frequencies and average splittings and improved by the use of the principle of least squares is fully described.

Thermal Study of Crystal Field Splittings in Erbium Ethylsulfate
View Description Hide DescriptionThe heat capacities of erbium ethylsulfate and yttrium ethylsulfate have been measured in the range 12°—300°K. The magnetic contribution of the erbium ion has been evaluated with the help of an assumption concerning the difference in lattice contributions between the erbium and yttrium salts. This contribution agrees, to within experimental error, with the experimental energy level scheme for the ^{4}I_{15/2} state published by E. H. Erath [J. Chem. Phys. 34, 1985 (1961)].

Computation of Asymmetric Rotator Constants from Energy Moments. IV
View Description Hide DescriptionThe energy‐moment procedure is used to develop expressions which are helpful for the analysis of centrifugal distortion effects in asymmetric top spectra. In principle, all first‐order distortion constants can be evaluated if a sufficient number of transition frequencies are available from experiment.

Proton Chemical Shifts and Pi‐Electron Distributions in the Hydroxy‐Benzenes
View Description Hide DescriptionThe protonmagnetic resonance spectra of phenol, hydroquinone, catechol, resorcinol, and pyrogallol have been studied, and the chemical shifts of the aromatic protons relative to benzene determined. The chemical shifts for the isolated molecules were obtained by making measurements in two solvents and extrapolating to a medium of unit dielectric constant. The electric fields at the protons from the C–O and O–H bond dipoles were calculated, and their contributions to the protonchemical shifts were removed by employing the approximate relation derived by Buckingham. It was assumed that the remaining parts of the chemical shifts were due to changes in the pi‐electron distributions. Hückel molecular orbital calculations were performed, and it was shown that the corrected chemical shifts, δ_{ i }, can be expressed in the formwhere q_{i} is the excess number of pi electrons on the ith carbon atom, q_{i} ′ is the sum of those on the two adjacent carbon atoms, and q_{i} ″ is the sum of those on any oxygen atoms ortho to the ith proton. The constants a, a′, and a″ were evaluated by fitting the chemical‐shift data with a least‐squares procedure. The derived constants depended sensitively on the values chosen for the necessary Coulomb and resonance integrals. It was not possible to conclude whether sigma inductive effects should be included or not, so it is suggested that they be omitted for the time being. By requiring reasonable values for the constants, i.e., a≅7, a′≅1, and a″≅0 ppm/electron and searching for closest agreement between calculated and observed chemical shifts, it was possible to choose as the most appropriate molecular orbital parameters, α_{O}=α_{C}+0.75 β_{CC}, and β_{CO}=1.0 β_{CC}.

Infrared Spectrum of Methylsilylacetylene
View Description Hide DescriptionThe compound methylsilylacetylene has been prepared for the first time and its vibrational spectrum has been obtained and assigned. All but two of the fundamentals have been identified. The rotational Q branches of the perpendicular bands have been resolved for the three group modes of SiH_{3}, and a comparison of the Coriolis coupling constants with those of other silyl‐containing molecules indicates a low or vanishing barrier to internal rotation. The relative intensities of the Q branches further supports this observation.

Charge Exchange between Gaseous Ions and Atoms
View Description Hide DescriptionA calculation of symmetric resonant charge exchange cross sections has been made for a selection of atoms in the velocity range where the impact parameter method is applicable. Cross sections for other atoms can be estimated by interpolating in terms of their ionization potentials. The results are in fair agreement with experiment. A similar calculation has been attempted for asymmetric nonresonant charge exchange processes. The approximations used are more restrictive in this calculation, the calculations being only semiquantitative in nature. The cross section of an asymmetric charge exchange process is determined in terms of the ΔE of the reaction and the ``average'' ionization potential of the two atoms. The results are qualitatively in agreement with experiment. A very brief discussion of approaches for extrapolating data to lower velocities, where the rectilinear orbit impact parameter method is not applicable, is given.

Pair Distribution in the Rigid‐Sphere System by the Method of Particle Scaling
View Description Hide DescriptionBy use of the scale of interaction distance as a coupling constant, integral equations for the molecular distribution functions are derived and discussed with particular reference to the calculation of the pair distribution for rigid‐sphere systems. It is shown that considerable improvement over the usual superposition approach results upon retention of the superficial form of the superposition approximation, but with a suitably defined effective local density. Specifically, the equation becomes exact over half the range of the coupling parameter. The fourth virial coefficient in the equation of state is correct in this theory, in comparison with an ordinary superposition value 61% low. Generalization of the effective density analysis to the case of arbitrary potentials is briefly discussed.