Volume 58, Issue 2, 15 January 1973

Low temperature chiral nematic liquid crystals derived from β‐methylbutylaniline
View Description Hide DescriptionThe synthesis and some basic physical properties of three new liquid crystals are reported. Each of these compounds has been synthesized in both pure chiral and racemic versions. It is demonstrated that a mixture of the chiral and racemic versions of a compound produces a chiralnematic liquid crystal which behaves as a one component system in which the torsion of the helical structure varies linearly with composition, while other thermodynamic properties are independent of composition.

ESR studies of the triplet state of [n.n] paracyclophanes
View Description Hide DescriptionESR experiments were performed on the triplet state of randomly oriented paracyclophanes in a variety of rigid glasses at temperatures ranging from 103 to 15°K. Spectra were recorded for [2.2]; [3.3]; (4,7,12,15)‐tetramethyl [2.2]‐paracyclophane and stagger‐ring paracyclophane. For all the samples except stagger ring, a four‐ringed paracyclophane, only the H _{min} feature was observed from which D*, the root‐mean‐square zero‐field splitting, was calculated. For stagger ring the triplet spectrum has two features in the region in addition to the H _{min} feature. From these, the zero‐field splittings, D and E, were calculated. The triplet spectra for the paracyclophanes show that there is strong transannular interaction with electron delocalization over all benzene rings. There is evidence for strongly coupled intramolecular exciton effects. The effect of increasing the inter‐ring separation from [2.2] paracyclophane to [3.3] paracyclophane is to decrease the transannular interaction. The effect of methyl substitution is to increase transannular effects relative to the parent compound. Transannular interactions in stagger ring are greater than in [2.2] paracyclophane despite the increased electron delocalization possible through the introduction of more than two rings. The large value of E for stagger ring represents a significant deviation from axial symmetry for the zero‐field‐splitting tensor and indicates that the methylene bridges, the methyl substituents, or the ring distortion, may make important contributions to the electronic distribution of the triplet state.

Molecular theory of the translational Stokes‐Einstein relation
View Description Hide DescriptionA molecular‐statistical derivation is presented for the Stokes‐Einstein expression for the translational diffusion constant for a Brownian (large) particle. The friction constant is expressed in terms of a correlation function of the forces on the particle, and this correlation function is related to the correlation function of pressure fluctuations in a volume equal to that of the particle. Whereas the forces are those on the particle surface, the pressure fluctuations are a property of the liquid solvent. The amplitude of the pressure fluctuations can be obtained from fluctuation theory and the time dependence can be obtained from hydrodynamics, which in turn can be derived from molecular‐statistical considerations. Although the exact numerical factors cannot be obtained, the linear dependence of the friction constant on the radius of the Brownian particle is derived. Finally, a discussion of the diffusion constant for small diffusing particles is presented.

Laser scattering measurements of droplet growth in binary mixtures. I. H_{2}O and air
View Description Hide DescriptionDroplet growth rates in a Wilson cloud chamber were measured in an air‐H_{2}O medium. Growth rates were accurately determined in the size range 0.45–10 μm by detection of oscillations in the intensity of polarized light scattered at 30° from a laser source. Pressure and initial temperature were measured in the chamber for use in the computation of three droplet growth theories for comparison to experiment. Experiments were conducted in supersaturations ranging from 1.49 to 3.45.

Rotational energy transfer in pure HCN and in HCN‐rare gas mixtures by microwave double resonance and pressure broadening
View Description Hide DescriptionMicrowave double resonance studies have been made of collision‐induced rotational transitions occurring in pure HCN and in HCN in the presence of He, Ar, or Xe. Double resonance intensities and phase shifts have been determined as a function of pressure for HCN l doublets up to from the pumped transition. The effects of Ar and Xe are similar and quite distinct from those of He. In the latter case the , transition is strongly preferred while in the former case no preferences are observed. Collision broadening linewidth parameters have been determined for the J=6, 7, 8, and 10 HCN l doublets for the pure gas and for the three rare gas collision partners. Experimental evidence is presented that indicates that quantum coherenceeffects are being observed in both Stark and double resonance absorption spectroscopy. An analysis is presented that utilizes the experimental total cross sections (linewidths) in a linear kinetic model of the energy transfer processes to determine partial cross sections (rates of collision induced transitions) that reproduce the double resonance data. General consideration of the atom‐dipole collision dynamics allows a preferred set of rates to be selected for each collision partner from several sets that are found to reproduce the data.

Microwave double resonance studies of rotational relaxation in polar gases
View Description Hide DescriptionFour‐level, modulated microwave double resonance has been used to study rotational energy transfer in some dilute polar gases. A survey has been made of double resonance signals observable in four asymmetric rotors: trimethylene oxide, β‐propiolactone, cyclobutanone, and cis‐difluoroethylene. Double resonance intensities have been measured in vibrational ground and excited states. Also, angular momentum reorientation caused by intermolecular collisions has been studied by microwave double resonance. Four‐level experiments have been performed on individual components of ethylene oxide and 3,3,3‐trifluoropropyne and on components of ICN. These experiments provide evidence that the energy transfer and momentum reorientation occurring during collisions are determined by the long range dipole‐dipole interaction. Qualitatively, a first‐order perturbation theory description of the collision process accounts for the selection rules of the observed collision‐induced transitions.

Concerning Cartesian tensors that are invariant under point group transformations. The zero components
View Description Hide DescriptionA method for obtaining some general results concerning the components of Cartesian tensors that are invariant under symmetry transformations is presented. The type and number of components which must be zero in order for a tensor (of any rank) to be invariant under any of the 32 crystallographic point groups are given.

Semiclassical theory of rearrangement and exchange collisions
View Description Hide DescriptionA semiclassical theory of rearrangement and exchange collision processes is developed as an extension of the semiclassical theory of inelastic collisions reported in the earlier papers in this series. The uniform WKB solutions are again used to obtain the WKB solutions of a set of intergrodifferential equations that describe the relative motions of the collision fragments in various channels. The solutions obtained are free of the turning point difficulty characteristic of the usual WKB solutions and thus most suitable for various calculations. The S matrix is constructed from the WKB solutions and given in terms of quadratures involving Airy functions. Approximation of the S matrix thus constructed is also discussed along with a discussion on a possibility of exploiting curve crossings.

Electron transmission spectroscopy: Resonances in triatomic molecules and hydrocarbons
View Description Hide DescriptionCompound states of triatomic molecules and simple hydrocarbons are studied using electron transmission spectroscopy.Structures in the derivative of the current transmitted through a gas‐filled collision chamber are interpreted as resonances in the electron‐molecule cross sections. At low electron energies (0–6 eV) we observe, in N_{2}O, H_{2}S, and C_{2}H_{4}, broad and featureless structures which we identify as shape resonances. In the same energy range, the molecules CO_{2}, NO_{2}, C_{6}H_{6}, and SO_{2} exhibit narrow structures which form vibrational progressions. In CO_{2}, NO_{2}, and C_{6}H_{6}, these vibrational progressions are identified as shape resonances; in SO_{2}, the interpretation is not clear cut. No low‐energy resonances are observed in H_{2}O and in CH_{4}. At higher energies (9–17 eV) we observe sharp structures for H_{2}O, H_{2}S, N_{2}O, CO_{2}, and C_{2}H_{4} (but not for C_{6}H_{6} and CH_{4}). These structures form bands, each band consisting of a vibrational progression. The states which are responsible for the bands consist of two Rydberg electrons moving in the field of a particular positive‐ion core. These bands are similar to those found previously in diatomic molecules.

Kinetic study of electronically excited phosphorus atoms, P(3 ^{2} D_{J} , 3 ^{2} P_{J} ), by atomic absorption spectroscopy
View Description Hide DescriptionElectronically excited phosphorus atoms, P(3^{2} D_{J} ) and P(3^{2} P_{J} ), generated by pulsed photolytic initiation, have been monitored photoelectrically in absorption by attenuation of atomic resonance radiation. Rate constants for the collisional deactivation of these two atomic states are reported for the gases H_{2}, O_{2}, and PCl_{3} and the resulting rate data discussed in terms of the effects of spin and orbital symmetry in the collision intermediate.

Equations‐of‐motion method including renormalization and double‐excitation mixing
View Description Hide DescriptionThe equations‐of‐motion method is discussed as an approach to calculating excitation energies and transition moments directly. The proposed solution [T. Shibuya and V. McKoy, Phys. Rev. A 2, 2208 (1970)] of these equations is extended in two ways. First we include the proper renormalization of the equations with respect to the ground state particle‐hole densities. We then show how to include the effects of two‐particle‐hole components in excited states which are primarily single‐particle‐hole states. This is seen to be equivalent to a single‐particle‐hole theory with a normalized interaction. Applications to various diatomic and polyatomic molecules indicate that the theory can predict excitation energies and transition moments accurately and economically.

Magnetic resonance and relaxation in NH_{4}ClO_{4}
View Description Hide DescriptionThe proton spin‐lattice relaxation, second moment, and magnetization of NH_{4}ClO_{4} have been investigated between 1.5 and 100°K, using pulse NMR techniques. The system has a T_{1} minimum at 29°K and, below 20°K, evidences nonexponential recovery with a relatively weak temperature dependence. The second moment gradually increases from 1.3 G^{2} to at 2°K. Spin conversion is observed below 4°K. The data are interpreted with reference to the possible hindered rotor levels of the ion.

Spectra of the xenon fluorides XeF_{2} and XeF_{4} in the far uv region
View Description Hide DescriptionThe absorption of gaseous and solid XeF_{2} and XeF_{4} has been measured in the region of 50–160 eV. It was possible to reproduce the absorption line shapes observed between 61 and 73 eV by semiempirical calculations based on the one center‐one electron model. According to these results, the observed lines could be assigned to transitions from 4d and 4p Xe subshells into ``5p'', 6s, 6p, and 7p levels. The spin orbit splitting of the molecular 4d level has been found to be almost equal to the free atom case. For the first time, a ligand field splitting of core levels is observed. In addition to this, spin orbit and ligand field splittings are measured to occur in the upper levels. The transition in XeF_{4} suggests a dynamic Jahn‐Teller effect. The gross structure of the spectra in both phases is practically identical for both XeF_{2} and XeF_{4}. The absorption lines of the Rydberg transitions are strongly broadened in the spectra of the solidified gases.

Absolute rate constants for the reaction O(^{3} P)+NO_{2→}NO+O_{2} over the temperature range 230–339°K
View Description Hide DescriptionUsing the technique of flash photolysis‐resonance fluorescence, absolute rate constants have been measured for the reaction. Over the temperature range 230–339°K, the rate constant was found to have the value , independent of temperature. At stratospherictemperatures, this rate constant is about a factor of two faster than indicated from previous measurements.

Potential energy curve of the state of H_{2}
View Description Hide DescriptionThe serious disagreement between ab initio and Rydberg‐Klein‐Rees potential energy curves for the state of H_{2} is discussed and explanations suggested. A ``best available'' hybrid potential energy curve for the state is then proposed.

Resolution of motions in the three solid phases of methylammonium chloride (CH_{3}NH_{3}Cl) by NMR
View Description Hide DescriptionThe α, β, and γ phases of solid methylammonium chloride (CH_{3}NH_{3}Cl) and its partially deuterated analogs (CD_{3}NH_{3}Cl and CH_{3}ND_{3}Cl) were investigated using temperature dependent static and rotating frame proton spin‐lattice relaxation times,T _{1} and , respectively. Broadline protonmagnetic resonance studies were performed in the supercooled γ phases of two of the substances. Discontinuities in the spin‐lattice relaxation plots were observed at the reported and phase transitions for CH_{3}NH_{3}Cl. It was found in our experiments that partial deuteration of this salt causes the transition temperature to shift to higher temperatures. The motions in the three modifications of these substances were analyzed using the spin‐lattice relaxation data and the second moments for the supercooled γ phase. A resolution of the CH_{3} and rotations about the axes was accomplished in the γ and β phases. The onset of CH_{3} reorientations in the γ and β phases occurs at lower temperatures than those for , while the frequencies of these motions are quite close to each other in the β forms and further apart in the γ modifications. In the α phases CH_{3} and seem to rotate relatively fast about the axes and more or less as a unit. The various motional parameters were derived from calculated fits to our relaxation time data. The NMR results pertaining to the three phases of these compounds are discussed and related to other studies.

Internal state distribution of alkali dimers in supersonic nozzle beams
View Description Hide DescriptionBy spectroscopicallyanalyzing the white light and laser‐induced fluorescence excited in a nozzle beam of Na_{2} molecules, we have measured the population distribution of the (v,J) levels of the ground state. The Na_{2} molecules are produced in nozzle beams with various stagnation pressures (50–240 torr) of alkali metal and with nozzles of different throat diameters (0.12–0.50 mm). We find at a stagnation pressure of 50 torr and a nozzle diameter of 0.5 mm a Boltzmann distribution characterized by a vibrational temperature of and a rotational temperature of . Beams under different stagnation conditions have essentially the same internal state distribution. Studies of K_{2} dimers produced in a nozzle beam with various stagnation pressures (20–300 torr) and a 0.25 mm nozzle throat diameter also show cooling in both vibrational and rotational modes. A search is made for atomic fluorescence arising from the photodissociation of dimers in high vibrational levels of the ground state. No evidence is found for the presence of vibrationally‐excited dimers in the nozzle beam.

Theoretical development of a virial relationship for spatially defined fragments of molecular systems
View Description Hide DescriptionThe original statement of the proposal that a molecular charge distribution can be spatially partitioned by a particular surface into fragments whose average kinetic and potential energies obey the virial relationship, involves an arbitrary choice of origin for the definition of the nuclear virial. A development of the fragment virial relationship is presented here which closely parallels Slater's derivation of the molecular virial theorem. This development provides an independent condition for the determination of the origin and demonstrates that it is determined by a property of the system. The surface which partitions the charge distribution ρ(x) of the total system into fragments (A) and (B) is defined by the gradient vector , passing through the point at which ρ(x) attains its minimum value between a pair of adjacent nuclei. The consequences of the restraints which the fragment virial relationship places on a molecular system are discussed with reference to the question of the transferability of the spatially defined fragments between different systems and with respect to the possibility of imposing the restraints directly in the calculation of the properties of a system.

On a nearly proton‐ordered structure for ice IX
View Description Hide DescriptionSingle‐crystal neutron diffraction shows that ice IX, the low‐temperature modification of ice III, has an almost completely proton‐ordered structure in which the ordered component contains two types of water molecules, type 1 in a site of no point symmetry, and type 2 on a twofold axis, each forming four hydrogen bonds in a three‐dimensional framework. The configuration of the water molecules is slightly but significantly altered from that of water vapor. Independent O–D distances, which do not differ significantly from one another, average (corrected for thermal motion), and are increased by 0.012 Å over the vapor value. The shift in O–D stretching frequency ν_{1} from vapor to ice IX corresponds to a slope , which agrees with the slope predicted from spectroscopic anharmonicity constants. D–O–D bond angles are not decreased from the vapor value (104.5°) despite the smaller angles into which the water molecules donate protons (98.2°, 100.8°); the same effect occurs also in ice II and oxalic acid dihydrate. The ordered molecules are oriented into the available angles that differ the least from 104.5°, but the orientation is not completely symmetrical in relation to these angles so that the H‐bond bend angles are substantially larger than the minimum possible. Observed amplitudes of thermal vibration, interpreted in terms of rigid‐body motion of the molecules, indicate that restoring forces for H‐bond distortion are approximately isotropic, ignoring the low‐symmetry molecular environments. The amplitudes correspond to appropriate average vibrational frequencies. About 4% of the deuterons in the structure are not in the ordered sites, but occupy the alternative sites that also provide hydrogen bonding. The retention of this partial disorder may be an effect of quenching through the transition range from ice III to ice IX, or it may be an inherent feature of the ice IX structure as achievable experimentally.

Mass spectrometric studies of tetrafluorohydrazine and the difluoroamino radical
View Description Hide DescriptionA mass spectrometer with a collision‐free modulated molecular beam sampling system was used to obtain the mass spectrum of N_{2}F_{4} and to study ionization and dissociation processes in NF_{2} and N_{2}F_{4}. The mass spectrum of N_{2}F_{4} differs significantly from previous studies, particularly in regard to the ion intensity ratio, indicating that considerable decomposition had occurred in earlier work. Surprisingly, dissociation of N_{2}F_{4} into NF_{2} radicals at 300°K at very low pressures, for which the degree of dissociation should be almost 100% at equilibrium, was found to be a slow process, an N_{2}F_{4} molecule readily surviving the order of 10^{5} wall collisions without decomposing. To obtain substantial conversion of N_{2}F_{4} into NF_{2}, it was necessary to send the sample through a heated line. Appearance potentials were determined for selected ions from N_{2}F_{4} and NF_{2} and the relevant processes identified. The bond dissociation energy was directly obtained from the appearance potentials of the ion from NF_{2} and N_{2}F_{4}. Other thermochemical energies measured in this study include: , and .