Volume 42, Issue 6, 15 March 1965

Nuclear Magnetic Dipole—Dipole Relaxation in Molecules with Internal Motion
View Description Hide DescriptionThe nuclear magnetic dipole—dipole relaxation for nuclei of spin ½ has been calculated for a model in which the length, as well as the orientation, of the internuclear separation vector varies as a result of internal molecular motion. In liquid molecules the internal motion increases the relaxation times, the effect of internal motion is to split the average of the inverse sixth power of internuclear separation into more terms, and most of these terms have shorter correlation times than for a system of rigid molecules with the same distribution of internuclear separation values.

Quantum Effect in the Diffusion of Gases in Liquids at 25°C
View Description Hide DescriptionThe study of the diffusion of gas solutes in CCl_{4} by Ross and Hildebrand is extended and refined to give the following figures for 10^{5} D in square centimeters per second at 25°C: in CCl_{4}: He, ∼20; Ne, ∼6.3 (subject to determination of solubility) ; O_{2}, 3.8; SF_{6}, 1.7. In (C_{4}F_{9})_{3}N; He, ∼13; H_{2}, 6.5; D_{2}, 5.55; Ne, ∼5.3; N_{2}, 2.35; Ar, 2.75. The method is shown to yield not merely relative but absolute values of diffusivity.
The product 10^{21} Dσ^{2}, where σ is the molecular diameter, rises in CCl_{4} from 45 for the heavier gases to 132 for He; in (C_{4}F_{9})_{3}N from 32 to 86 for He. There is a linear relation between these values and the square of the quantum parameters of de Boer. The quantum effect is much stronger in CCl_{4} than in (C_{4}F_{9})_{3}N in accord with their internal pressures, 3350 and 2170 atm, respectively.

Scattering from Fluids of Nonspherical Molecules. I. X Rays and Neutrons
View Description Hide DescriptionThe general theory of the statistical mechanics of nonspherical molecules is applied to the problem of the scattering of x rays and slow neutrons from a fluid composed of nonspherical molecules. Expressions for the differential scattering cross sections are derived for the cases of both elastic and inelastic scattering. General properties of the time‐dependent correlation functions are discussed, and a short‐time approximation is given and applied to the calculation of the inelastic neutron scattering cross section.

Scattering from Fluids of Nonspherical Molecules. II. Light
View Description Hide DescriptionThe statistical mechanical theory of nonspherical molecules is applied to the problem of the scattering of light from fluids composed of optically nonspherical molecules. Expressions for the scattered light intensity in the elastic and inelastic scattering cases are expressed in terms of angular moments of the generalized pair distribution function of the fluid. The special case of axial symmetry is considered, and comparison with previous theoretical and experimental work is briefly made.

Appraisal of the FOPIM Fast‐Converging Perturbation Method
View Description Hide DescriptionThe practicality of the first‐order perturbation‐iteration method (FOPIM) is appraised. After the first iteration, the expectation value of the energy is given by a nonanalytic function of the perturbation parameter λ. The asymptotic expansion of this function gives the energy accurately up to O(λ^{8}). The convergence of the asymptotic expansions is discussed. Two examples are considered: a perturbed ground‐state hydrogen atom, and a perturbed ground‐state linear harmonic oscillator.

Quantum Cell Model for Solids at Low Temperatures
View Description Hide DescriptionThe cell model has been widely applied to classical liquids and has recently been applied to quantum liquids. In the cell model it is assumed that each molecule moves independently in a cell formed by the neighboring molecules. This assumption is more reasonable for the solid state than for the liquid state. In the present investigation the cell model is applied to solids at low temperatures. Results are reported for Ar, H_{2}, D_{2}, and ^{4}He. Agreement with experiment is good.

Condensation of Supersaturated Vapor
View Description Hide DescriptionA formula for the current of drops for the case of the condensation on ions was derived using Frenkel's method. An approximate formula for the time of condensation, i.e., the time elapsed from the beginning of supersaturation up to its complete disappearance, was developed. This time was read from the oscilloscope record of temperature versus time for the expansion in the Wilson chamber. Experiments confirmed the theoretical formula. A rather complicated equation expressing the dependence of the mass of condensed vapor on time was established. It requires a numerical solution.

Ferroelectric Field of BaTiO_{3} as Measured by Electron Diffraction
View Description Hide DescriptionThe electrostatic field in a BaTiO_{3} crystal given by orientation of the ferroelectric domains is measured by observing the dielectric relaxation in terms of electron diffraction. This field amounts to about 200 kV/cm along the [210] axis.

Diffusion of Thallous Chloride in Single Crystals of KCl by a Novel Spectrophotometric Method
View Description Hide DescriptionA novel attachment to the Beckman DU spectrophotometer is described, by means of which the diffusion profile of some heavy‐metal ions in alkali halides may be recorded.
The diffusion of Tl^{+} ions in KCl in the temperature range 270°‐400°C was measured. It is concluded that the activation energy for the diffusion of Tl^{+} varies with temperature, parallel to that of the self‐diffusion of K^{+} ions, calculated from conductivity measurements. The diffusion constants of the Tl^{+}, at any temperature, are several orders higher, as the associated vacancies of the divalent impurities present are also involved in the diffusion process.

Experimental Oscillator Strengths of CO and CO^{+}
View Description Hide DescriptionThe radiative lifetimes of the B ^{2}Σ state of CO^{+} and the b ^{3}Σ state of CO have been measured to be (1.01±0.05) 10^{−7} and (8.6±0.9) 10^{−8} sec, respectively. The oscillator strengths of the first negative system of CO^{+} and third positive system of CO, calculated from these lifetimes, are (7.9±0.7) 10^{−3} and (8.9±1.5) 10^{−3}, respectively.

Irradiation Damage in Type I Diamond
View Description Hide DescriptionIn addition to the GRI and uv bands induced in all diamond by 0.78‐MeV electron irradiation, another optical absorption feature, which we have named the ND1 band, is found in all Type I diamonds. A single EPR line appears to be associated with the ND1 band.
It is suggested that the ND1 center arises from the combination of a defect product—probably an interstitial—and nitrogen in platelet form. Certain observations can only be explained by assuming that the ND1 centers are not distributed randomly through the crystal, but occur in clusters.
The ND1 center acts as an acceptor, the center (probably a vacancy) responsible for the GRI and uv band as a donor. In the ionized state, GRI is optically inactive; ND1 is optically active. Electron transfer by thermal excitation results in the bleaching of GRI and enhancement of ND1. Illumination with light in the ND1 band causes electron transfer in the reverse direction, restoring band strengths to their former condition. A model is proposed which defines the energies within the forbidden gap of the ground and excited states of GRI and ND1.

Deep Impurity States in Molecular Crystals: The Optical Excitation of a Substitutional Argon Atom in Crystalline Neon
View Description Hide DescriptionThe calculation of the first electronic transition of an argon‐atom impurity in a neon lattice is carried out in the Heitler—London scheme. The energy of this transition is taken to be the energy of the argon atomic transition, plus the correction to the SCF 4s orbital energy due to the presence of the crystal. The modification to the SCF 4s orbital is accomplished by the addition of charge‐transfer functions on neighboring neon atoms. It is shown that the choice of the SCF atomic function is a very bad starting point for these systems.
A general method for choosing basis functions for bound systems is presented. It is shown that for many cases a suitably chosen ``model Hamiltonian'' may be appropriate to a more complex system, and the case of a dielectrically screened hydrogenic ``model Hamiltonian'' is worked out for Ar–Ne.

Significant‐Structure Theory of Binary Mixtures. II
View Description Hide DescriptionThe significant‐structure theory has been successfully applied to the three binary systems involving carbon tetrachloride, benzene, and cyclohexane. In the first paper, the system carbon tetrachloride—cyclohexane was discussed. In this paper the other two systems, carbon tetrachloride—benzene and cyclohexane—benzene, are considered. The excess properties have been calculated on mixing at constant pressure as well as on mixing at constant volume. By taking account of the fact that the parameters in our theory are concentration dependent, a partition function for mixtures can be formulated in a similar way to those for single liquids.

Significant‐Structure Theory and Cell Theory for Two‐Dimensional Liquids of Hard Disks
View Description Hide DescriptionThe significant‐structure theory of liquids is applied to describe a two‐dimensional liquid of hard disks. The results are in quite good agreement with the molecular‐dynamics calculations. However, the virial expansion of the equation of state is in only fair agreement with the machine calculations. Cell theory is also applied to the two‐dimensional liquid; it is found that although the agreement with the molecular‐dynamics data is poor in the liquid range, the cell theory shows good agreement in the solid region.

Internal‐Rotation in Hydrogen Peroxide: The Far‐Infrared Spectrum and the Determination of the Hindering Potential
View Description Hide DescriptionThe torsional oscillation between the two OH groups of the hydrogen peroxide molecule is investigated through a study of the far‐infrared absorptionspectrum of the molecule. A 1‐m‐focal‐length vacuum gratingmonochromator was used to scan the region from 15 to 700 cm^{−1} with an average resolution of 0.3 cm^{−1}. The observed spectrum contains seven perpendicular‐type bands of which only the Q branches are resolved. The centers of the seven bands are at 11.43, 116.51, 198.57, 242.76, 370.70, 521.68, and 557.84 cm^{−1}. These bands result from transitions between different states of the internal rotation and their identification makes it possible to construct the internal‐rotation energy level scheme through the first five excited states. Relative to the torsional ground state, these levels occur at 11.43, 254.2, 370.7, 569.3, and 775.9 cm^{−1}.
A theory of internal rotation in the hydrogen peroxide molecule is developed for use in the analysis of the far‐infrared spectra. In this theory, the Hamiltonian is constructed assuming all structural distances and angles fixed except the dihedral angle x defining the relative position of the two OH bars. By the use of a contact transformation the Hamiltonian is put in the form H (asymmetric top)+H(internal rotation) where the interaction between the internal and over‐all rotations arises through the x dependence of the inertial parameters of H(asymmetric top). It is assumed that the relative position of the two OH bars is governed by a potential‐energy function of the form . The internal‐rotation wave equation is solved numerically by an electronic‐computer and the potential function parameters V _{1}=993 cm^{−1}, V _{2}=636 cm^{−1}, and V _{3}=44 cm^{−1} are chosen to fit the internal‐rotation energy‐level scheme. The trans and cis potential barrier heights are 386 and 2460 cm^{−1}, respectively, and the potential‐function minima are located 111.5° from the cis configuration. Diagonalization of the matrix of the complete Hamiltonian to second order by the use of perturbation theory is sufficient to account for the observed Q‐branch shapes in the far infrared region.
Two microwave frequencies observed by Massey and Bianco at 22 054.5 and 27 639.6 Mc/sec are identified from their Stark effects as the first excited‐state transitions J, K, n, τ=8, 6, 1, 1→7, 5, 1, 3 and J, K, n, τ=8, 5, 1, 3→9, 6, 1, 1, respectively, where the internal‐rotation quantum number n=1 denotes the first excited torsional state and where τ denotes trans symmetric (τ=1 and 2) or antisymmetric (τ=3 and 4) states. The form of the dipole moment operator is assumed to be μ_{0} cos(x/2) and μ_{0} is found to be 3.15 D in agreement with the value obtained from the torsional ground‐state transitions.
Two J=0 microwave series observed by Massey, Beard, and Jen in a mixed sample of the deuterated species D_{2}O_{2} and HOOD give confirmation of the potential function determined from the H_{2}O_{2}analysis. The K=4→5 series is identified as the D_{2}O_{2} first excited torsional state transition n=1→1, τ=4→2. The K=0→1 series is identified as the HOOD torsional ground‐state transition n=0→0, τ=4→2. Only very small changes in the trans barrier height are necessary to fit the constant terms of these series exactly. These changes, which are expected to arise from vibration‐internal rotation interactions, show a reasonable progression from H_{2}O_{2} to D_{2}O_{2}: V (trans, HOOH) = 386 cm^{−1}, V (trans, HOOD) = 381 cm^{−1} and V (trans, DOOD) = 378 cm^{−1}.

Concentration Depolarization of the Phosphorescence Emission
View Description Hide DescriptionThe degree of polarization (P) of the phosphorescence for several organic molecules is studied as a function of concentration (C) in the 10^{−4}−10^{−1} M range in rigid medium. For all of the molecules examined, P remains unchanged until C reaches 10^{−2} M; then P starts declining. The decline of P is shown to arise neither from the decrease in solvent rigidity nor from crystallization of the molecules studied. Two possibilities that might explain the decline of P are discussed: (a) the formation of a charge‐transfer complex that perturbs the direction of the emitting oscillator and (b) T—Tenergy transfer. The degree of polarization of some of the compounds studied does not change during the phosphorescence decay, a result that might favor the first possibility. The sensitivity of the value of the slope of the P–C curve to the phosphorescence lifetime provides evidence in support of the T—T energy‐transfer mechanism. At concentrations below 10^{−2} M, nonradiative S–S transfer seems to be either absent or relatively inefficient in depolarizing the phosphorescence emission in the systems studied. External heavy‐atom effects on the degree of polarization of the phosphorescence of aromatic hydrocarbons are found to be much greater when caused by haloaromatics than by ethyl iodide. This observation might be due to either a larger association constant or stronger spin—orbit perturbation for the former compounds than for the latter.

Benzene d‐6‐Sensitized Photoisomerization of Butene‐2 at Low Pressures by Long‐Path Infrared Spectroscopy
View Description Hide DescriptionThe benzene d‐6‐sensitized trans‐cis photoisomerization of butene‐2 has been studied by means of long‐path infrared spectroscopy. Relative quantum yields at pressures less than 1 mm were determined. Mechanisms for energy transfer in benzene d‐6 consistent with the data are presented.

Vibrational Energy Transfer in Gases. Atom—Diatomic Molecule Collisions
View Description Hide DescriptionThe interconversion of molecular vibrational energy and translational energy is studied; the equations of motion describing collinear collisions of a Morse diatomic molecule with a Lennard‐Jones 6–12 atom are integrated numerically. The effects of initial relative translational energy and initial vibrational energy are determined, and vibrational relaxation times are calculated by a Monte Carlo method at three different temperatures and with two different translational energy distributions.

Deduction of the Zero Differential Overlap Approximation from an Orthogonal Atomic Orbital Basis
View Description Hide DescriptionThe validity of the zero differential overlap approximation is investigated by means of a systematic expansion in terms of a parameter of the order of magnitude of a typical overlap integral between neighboring atoms. The terms of the Fock operator in a basis of orthogonal atomic orbitals can be arranged after different orders of the parameter. It is demonstrated that, by inclusion of second‐order terms, the conditions imposed by the zero differential overlap approximation are automatically fulfilled. Moreover, all the basic integrals are shown to be transferable in the first order and all but W in the second order. The connection with the ω technique in the Hückel method is also given. A numerical application has been made to ethylene and benzene.

Electronic Absorption Spectra of Square‐Planar d ^{8} Complexes in Different Crystal Environments
View Description Hide DescriptionPolarized crystal spectra of K_{2}PdCl_{4} and K_{2}PtCl_{4} have been measured at room temperature and interpreted by means of a vibronic intensity‐borrowing mechanism. Single‐crystal spectra of Magnus's green salt, Pt(NH_{3})_{4}PtCl_{4}, and its methylamine analog have also been measured, together with the powderspectra of a wide range of related salts. The visible absorptions are assigned to d—d transitions within axially perturbed anions, while a new infrared band in Magnus's green salt is identified with an intermolecular electron‐transfer transition.