Volume 54, Issue 10, 15 May 1971
Index of content:

^{17}O NMR Studies of Uranium Oxides
View Description Hide DescriptionThe ^{17}O NMR of ^{17}O‐enriched UO_{2}, BiUO_{4}, and KUO_{3} has been observed. A paramagneticNMR shift was observed for UO_{2} at 192.5, 299.5, and 405.2°K. The average isotropic coupling constant, , calculated from these shifts is 2.84 × 10^{−5} cm^{−1}. In this calculation of the magnitude of on the uranium atom in UO_{2} is determined assuming a ground state for the U^{4+}. Paramagnetic shifts were also observed for BiUO_{4} and KUO_{3} at 299.5°K. The value of for BiUO_{4} was determined to be 3.79 × 10^{−4} cm^{−1}. This value was calculated after assuming a ground state for U^{5+}. The same assumption in the case of KUO_{3} yielded a value of 1.08 × 10^{−3} cm^{−1} for . The validity of the assumption of pure Russell–Saunders ground states for these compounds is discussed. For KUO_{3} the previously published spin–orbit coupling constant and crystal field terms are used to calculate a more reliable value of on the central uranium atom. These calculations lead to a value of 7.01 × 10^{−4} cm^{−1} for . The important conclusions of this study are that the fractional character in these compounds is small and that there is a negative spin density on the ^{17}O nuclei. Apparently the major contribution to the hyperfine interaction arises from the involvement of excited metal orbitals and/or from exchange polarization of core electrons. The NMR spectra of KUO_{3} and BiUO_{4} show the effect of anisotropic hyperfine interactions. The anisotropic interactions in BiUO_{4} are shown to be predominantly in character. An analysis of the KUO_{3} spectrum indicates that anisotropic interactions are predominantly in character and that . The linewidth of the isotropic UO_{2} resonance is interpreted in terms of the Moriya spin‐exchange mechanism and the value of is found to be 1.2 × 10^{+13} sec^{−1}.

Inelastic Electron Scattering from Formaldehyde
View Description Hide DescriptionThe electron scatteringspectrum of H_{2}CO has been determined in the energy loss range between 0 and 16.0 eV. Three Rydberg series in the region 7–11 eV can be identified with the , and series reported in the literature by ultraviolet absorption studies. Oscillator strengths are determined for some of the Rydberg states and comparison is made with recent ultraviolet absorption work employing photoelectric methods of detection. A serious disagreement exists between the values obtained by the two methods for the Rydberg. Another Rydberg series, probably converging to the third ionization potential of H_{2}CO, is observed in the electron scatteringspectrum in the region 12.4–14.0‐eV energy loss. Erratic behavior of the quantum defects of the first Rydberg series as well as failure to detect the transition in H_{2}CO is discussed in the light of recent theories involving valence states which can seriously perturb members of a Rydberg series.

Vibrations of Glasslike Disordered Systems. I. Diatomic Chains in Two Dimensions
View Description Hide DescriptionA computer program has been written to generate disordered, two‐dimensional chains of randomly oriented B–A–B V‐shaped units with a Gaussian distribution of bond angles between successive units. The radial distribution function of the system shows it to be essentially vitreous in that it exhibits only short‐range order. The equations of motion are derived using a simplified valence force potential function, and the distribution of squared normal mode frequencies is obtained using the negative eigenvalue theorem. The frequency spectra are discussed in terms of the ordered chain in two dimensions and the glasslike disordered chain in one dimension. The existence of a band gap is confirmed, but the size and position are complicated by the disorder of the system, as is the over‐all shape of the spectrum. A feature in the spectra, near the LO zone‐edge frequency of the ordered chain, is found to be the result of wavelength‐dependent coupling between “transverse” and “longitudinal” vibrations. The more general results of the present calculations appear applicable to three‐dimensional models.

Radiationless Processes in Fluorobenzene
View Description Hide DescriptionThe triplet yield of fluorobenzene is studied by the biacetyl emission method. The effect of biacetyl pressure indicates a short triplet lifetime of 130 nsec for fluorobenzene in the gaseous phase. The absence of phosphorescence even in a solid matrix at low temperature is explained by a radiationless process from the triplet state of fluorobenzene. A weak sensitized emission from the first excited singlet state of biacetyl suggests that singlet–singlet energy transfer must be involved. Addition of cis‐2‐butene quenches the sensitized emission from the triplet state of biacetyl. The triplet yield of fluorobenzene results in a reasonable value of 1.03 for the sum of triplet and singlet yields on excitation at the 0–0 band.

Zeeman Effect in the Electronic Spectrum of Solid CS_{2}
View Description Hide DescriptionThe lowest‐energy singlet‐triplet transition of CS_{2} has been studied in the CS_{2} crystal at 4.2°K. The spectrum consists mainly of progressions in the bending mode . The following values for the upper state frequencies have been obtained and the unobserved electronic origin has been calculated to be at 24 739 cm^{−1}. Zeeman studies of the 3676‐Å band system have been used to assign a very weak component of a vibronic band of this system as a crystal field induced transition to the pair of spin sublevels of the triplet state . The zero field splitting (ZFS) parameter of 36 ± 1 cm^{−1} thus obtained for the vibronic state is comparable with the one calculated by Hougen [J. Chem. Phys. 41, 363, (1964)] from Zeeman line broadening experiments in the gas phase done by Douglas and Milton [J. Chem. Phys. 41, 357 (1964)] on comparable vibronic bands. The large value of the ZFS parameter can be explained if it is assumed that the and states are quite nearby.

Internal Conversion in Benzene, Benzene‐d _{6}, and Sulfur Dioxide
View Description Hide DescriptionLifetime studies of benzene and benzene‐d _{6} at pressures below 1 μHg, using an electron beam phase shift method, yield a lifetime of 73.5 ± 8.0 nsec for the measured levels of the state of benzene and lifetimes varying from 89 ± 9 to 113 ± 11 nsec for essentially the same levels in benzene‐d _{6}. From the measured absorption oscillator strength, the nonradiative processes depopulating the state must proceed at a rate of 1.2 ± 0.14 × 10^{7} sec^{−1}. These results are compared with previous theory and experimental data. Radiative lifetime measurements for SO_{2} have been extended from those given previously and have been reanalyzed with a model assuming spectral overlap of two different SO_{2} upper states. This analysis is shown to be consistent with certain previous discussions of the emission spectrum and, in particular, with those of Douglas^{3} concerning the anomalous lengthening of the ^{1} B̃ _{1}‐state radiative lifetime.

Additional WKB Inversion Relations for Bound‐State and Scattering Problems
View Description Hide DescriptionNew inversion relations for the diatom system (elasticscattering of two atoms by a single potential, or a bound diatomic molecule) are presented. They are exact within the WKB approximation for the relevant quantities and are closely related to the well‐known RKR expressions. Explicit formulas are given for bound‐state and scattering input.

Identification of the Lower Transitions in the Spectra of Uranyl Complexes
View Description Hide DescriptionThe typical low‐energy spectra of the uranyl complexes—both in solution and in the solid state—are interpreted by using group theory and qualitative molecular orbital theory. A comparative study of the effects of ligation on the spectrum shows that the observed facts can be rationalized by means of only one possible identification scheme. The band system situated at 20 000–22 000 cm^{−1} is due to a transition, while the band system at 22 500–27 000 cm^{−1} is due to a transition.

Self‐Consistent Molecular Orbital Methods. XI. Molecular Orbital Theory of NMR Chemical Shifts
View Description Hide DescriptionAb initio molecular orbital calculations of first row atom (C, N, O and F) NMRchemical shifts are presented for a variety of polyatomic molecules. Both minimal and extended basis sets are used and it is shown that at the minimal level, basis sets at the Hartree–Fock atomic level give a better description of magnetic shielding than do Slater‐type (exponential) orbitals. The extended basis set also gives a good description of magnetic shielding, features associated with anisotropic molecular environment being some‐what more adequately treated at this level. Calculated chemical shifts of nuclei which have similar positions relative to the origin of the vector potential describing the magnetic field are in good agreement with experiment. Agreement for the chemical shifts of nuclei which have markedly different positions relative to this origin is not as good.

Fluorine‐19 Nuclear Magnetic Resonance of the Liquid and Solid Phases of Fluorine
View Description Hide DescriptionFluorine‐19 NMR has been studied from 105 to 4.2°K in elemental fluorine. In the liquid phase the spin–rotational interaction determines the spin–lattice relaxation time except within about 17°K of the melting point, where the effect of a small amount of dissolved molecular oxygen becomes evident. Self‐diffusion coefficients have been measured in the liquid from 105°K to the melting point (53.5°K) and are well represented by the expression . Spin–rotational correlation times have been calculated from the experimental relaxation times. Nuclear dipolar correlation times have been estimated from the quasilattice‐random flight model. The product is a factor of 20 longer than predicted by the continuum theory of rotational diffusion. A root mean square angular jump of 2.6 rad is estimated from comparison of the experimental data with the large angular jump model of molecular rotation. , rotating frame , and spin–spin relaxation times were measured in the phase from 53.5 to 45.5°K. The phase is a plastic crystal with relatively rapid translational diffusion and very rapid, but anisotropic, rotational diffusion. is essentially unchanged from the liquid to the phase. The self‐diffusion coefficients are accounted for entirely by an increase in the work required to create a vacancy in going from the liquid to the phase. In the phase, below 45.5°K, a small amplitude mode of molecular motion persists. A 15° “tilt” motion of the molecules is assigned to the minimum observed in in the phase. A shallow minimum in is assigned to spin diffusion to molecular oxygen impurities and occurs due to the proximity of the oxygen electronic spin–lattice relaxation rate to the fluorine larmor frequency.

New High‐Density Equation of State for Gases
View Description Hide DescriptionA new equation of state is proposed for the high‐density region of gases. This equation is applied to the recent measurements of a number of gases and fits well within experimental error. The equation is characterized by five constants: three which are substance and temperature dependent, and two which are both substance and temperature independent. Values of all constants are given for the gases considered. Two liquid isotherms are also examined and also are fit by the equation, as are the calculated isotherms for soft spheres and Lennard‐Jones spheres.

Measurement of the Polarizabilities and Field Evaporation Rates of Individual Tungsten Atoms
View Description Hide DescriptionThe relative field evaporation rates of tungsten kink site atoms at (110) plane edges and the absolute field evaporation rates of individual tungsten adatoms on tungsten (110) planes have been measured covering nine orders of magnitude. From the experimental data, the effective polarizabilities of the tungsten kink site atoms and the adatoms are found to be 4.6 ± 0.6 and 6.8 ± 1.0 Å^{3}, respectively. A theoretical consideration is given to explain why the effective polarizability of metal surface atoms depends on the atom‐to‐surface mirror plane distance, and therefore the atomic sites. The calculation also reveals a first power field dependent energy level shift, which is dependent upon the atom‐to‐surface plane distance. It is further shown that the classical image potential no longer holds at a distance smaller than 1 Å from the metal surface.

Raman Scattering from Molecular Crystals. I. Powdered Naphthalene
View Description Hide DescriptionThe Raman spectrum of powdered naphthalene has been measured at room temperature using 6328‐Å He–Ne laser excitation and a double monochromator with photoelectric detection and digital recording. Eighty‐six lines are observed, among them all the fundamentals assigned by Hanson and Gee [J. Chem. Phys. 51, 5052 (1969)] from Raman, phosphorescence, and fluorescence spectra. Using narrow slits (0.5–1 cm^{−1}) several asymmetric and multiple lines are discovered and resolved into separate components. Five weak, very broad lines are discovered and interpreted as second‐order lines or combinations of intramolecular and lattice vibrations. The width is determined for some of the lines. Intensities are given for all lines.

Exciton Theory of the Electronic States of Dye–Polymer Complexes. II. Stationary States of Helical Complexes
View Description Hide DescriptionThe stationary states are found for a system composed of one or two dye molecules attached to an infinite single stranded helical polymer. It is assumed that each dye and monomer has a stack of separable excited vibronic levels belonging to a fixed electronic state.

Time‐of‐Flight Spectroscopy of CO_{2} Photodissociation in the Vacuum Ultraviolet. Electron Emission from Cesium Surface by Metastable Singlet Oxygen Atoms
View Description Hide DescriptionTime‐of‐flight spectroscopy has been employed in conjunction with metastable photofragment detection by electron emission from metal surfaces to study the photodissociation of CO_{2} in the vacuum ultraviolet at wavelengths longer than 1050 Å. Irradiation was performed by unfiltered light. However, some wave‐length selection was provided by the CO_{2} absorption itself and by choice of window material, LiF and CaF_{2}. The metastable detector was coated with cesium. The photodissociation,, has been observed where O* can be and/or only. The result implies that the deactivation of metastable singlet oxygen atoms at a cesium surface produces electron emission. The analysis of the flight time distribution of O* shows that in the wavelength range from about 1160–1050 Å more than 50% of the dissociation leads to internally excited with considerable amounts of vibration‐rotation energy.

Collision‐Induced Vibrational Excitation and Dissociation of Hydrogen with Alkali Atoms and Ions from 2 to 50 eV
View Description Hide DescriptionInelastic energy losses for Na^{0}, Na^{+}, K^{0}, and K^{+}backscattered from H_{2} and D_{2} have been measured. At center‐of‐mass energies below15 ∼ eV for Na and ∼ 20 eV for K, the collisions yield vibrational excitations which are compared with the one‐dimensional exact classical calculations of Secrest. The vibrational excitation in the Na^{+}–H_{2} and Na^{0}–H_{2} system is in excellent agreement with three‐dimensional classical calculations of Cheng and Wolfsberg. Above these energies the molecules are dissociated but the energy loss distribution of the alkali projectile remains sharp and in the case of Na–H approaches the maximum loss possible at 50 eV.

Single‐Center Calculations on the Electronically Excited States of Equilateral H_{3} ^{+} Ion
View Description Hide DescriptionA theoretical investigation of the excited electronic states of the equilateral triangular H_{3} ^{+} ion is reported. Ab initio calculations were performed for the lowest energy states of symmetries , and , using the single‐center expansion configuration‐interaction method. For each state we have obtained the potential‐energy curve in symmetry. The calculated state energies are expected to be in error by at most 0.01 hartree (6 kcal/mole). Two of the excited states and were found to be purely repulsive with respect to the totally symmetric nuclear coordinate, while three excited states and showed minima with respect to the totally symmetric nuclear coordinate. However, arguments based on group‐theoretical correlation between our calculated state energies and the energies of possible dissociation products suggest that none of the excited states considered achieves an absolute energy minimum in symmetry. For the allowed electric dipole transitions and we have calculated the vertical (Franck–Condon) transition energies, oscillator strengths, and polarizations. The nature of the excited‐state energy curves, at the ground‐state equilibrium geometry, indicates that in every case only continuum absorption from the ground state would be observed experimentally.

Normal Mode Calculation of Grüneisen Thermal Expansion in n‐Alkanes
View Description Hide DescriptionThe normal mode problem is solved for a semirigid chain of beads in a quasiharmonic potential in order to separate the inter‐ and intrachain parts of the specific heat. The effects of lattice vibrations are included in an approximate way. The usual Grüneisen relation, , valid only for acoustical modes, is generalized for optical modes to give , where and are the entropy and frequency cutoff of mode . The predicted thermodynamic properties of the system are unusually sensitive to chain length because of interchain thermal energy effects. The parameters are given values from independent solid n‐alkane data, and the calculated results are shown to predict quite well experimental and behavior of the n‐alkanes.

On a Derivation of a Boltzmann Equation for Homogeneous Systems
View Description Hide DescriptionThe derivation of a Boltzmann equation for homogeneous systems by Prigogine et al. has been generalized and simplified by an introduction of a binary collision expansion instead of the perturbation expansion of the resolvent operator for the Liouville operator. Such binary collision expansion makes the derivation much simpler than the perturbation expansion. The result, however, agrees with that of Prigogine et al. and the reason for the agreement is briefly discussed.

Effects of the Langer Transformation on the Calculation of Internuclear Potential Curves
View Description Hide DescriptionThe Langer transformation is applied to the radial equation for internuclear motion. The quantization integral is obtained and applied to the calculation of the effective potential curve by the Rydberg–Klein–Rees method. First‐ and second‐order RKR expressions for the turning points are derived. It is shown that the Langer transformation affects the RKR method in all orders.