Volume 66, Issue 2, 15 January 1977
Index of content:

A systematic study of an isomorphous series of organic solid state conductors based on tetrathiafulvalene
View Description Hide DescriptionThe solid state physical properties of an isomorphous series of TTF salts (TTF_{11} (SCN)_{6}, TTF_{11} (SeCN)_{6}, and TTF_{7}I_{5}) were examined. While there was no noticeable trend in the conductivity (as a function of temperature and anion), the effective Fermi energy (?_{ F }) and the magnetic susceptibilitytransition temperature exhibited a definite trend as a function of anion. There is a correlation between the above properties and subtle variations in solid state structure of each of the above salts.

Two‐photon spectroscopy in the gas phase: Assignments of molecular transitions in benzene
View Description Hide DescriptionRo‐vibronic resolved two‐photon excitation spectra of benzene, C_{6}H_{6}, and C_{6}D_{6} have been measured in the region of the S _{1} ←S _{0} transition which is parity and symmetry forbidden in two‐photon absorption but can be induced by suitable ungerade vibrations. Rotational envelopes for the vibronic transitions are calculated for circular and linear polarized light excitation and are in good agreement with experiment. The polarization behavior is shown to change strongly across even a single band contour of a totally symmetric vibronic two‐photon transition. The polarizationanalysis even for a randomly rotating gas phase molecule provides a severe constraint on the possible assignments and hence is an important tool for the assignment of new transitions. About 85% of the observed two‐photon excitation spectrum of benzene can thus be assigned. The appearance of combination bands shows that anharmonic mixing plays an important role in the excited state.

Shear transformation to produce a new phase of polymeric sulfur nitride (SN)_{ x }
View Description Hide DescriptionThe solid‐state synthesis of a new phase of (SN)_{ x } is reported. X‐ray diffraction results show that mechanical shear induces a transformation of the known, monoclinic phase (space group P2_{1}/c) to a phase of orthorhombic symmetry(probable space group P2_{1}2_{1}2_{1}). The unit cell parameters of the shear‐induced phase of (SN)_{ x } are a=6.251, b=4.429, and c=4.807 Å. Since the approximate chain repeat dimension (b) and the chain symmetry (2_{1}) are the same before and after the transformation, the chain geometries for the two phases of (SN)_{ x } are predicted to be quite similar, if not identical. However, important differences are expected for interchain interactions that have been previously shown to be essential in understanding various properties of the monoclinic phase of (SN)_{ x }. Both phases of (SN)_{ x } are shown to be stable with respect to thermally‐induced interconversion for temperatures up to 175°C. Molecular packing calculations are used to predict structural aspects of the shear‐induced phase and the relationship between parent and daughter phases. The latter results are consistent with the monoclinic‐to‐orthorhombic transformation being martensitic in character.

Effects of ion speed distributions in flow‐drift tube studies of ion–neutral reactions
View Description Hide DescriptionThe effects of non‐Maxwellian ion speed distributions on ion–neutral reaction rate constantsmeasured in drift tubes are examined experimentally and are compared to the predictions of recent theories. The rate constants of strongly kinetic‐energy‐dependent ion–molecule reactions of O^{+} with O_{2}, N_{2}, and NO are measured separately in helium and argon buffer gases, in which the O^{+} speed distributions are expected to be very different. The differences between the helium‐buffered and argon‐buffered rate constants are often substantial. When different, the argon‐buffered values are generally larger than the helium‐buffered values at the same mean energy, indicating that the O^{+}‐in‐argon distribution has a larger high‐energy ’’tail’’ than the O^{+}‐in‐helium distribution. The differences between the two sets of data are compared to predictions from (a) the Monte Carlo trajectory calculations of Lin and Bardsley, and (b) the moment solution of the Boltzmann equation of Viehland and Mason, both described in accompanying papers. The excellent agreement demonstrates that the non‐Maxwellian ion speed distributions now pose no problems in the interpretation and application of the k i n e t i c‐e n e r g y aspects of the rate constants of atomic–ion reactions studied in rare‐gas‐buffered drift tubes.

Statistical–mechanical theory of gaseous ion–molecule reactions in an electrostatic field
View Description Hide DescriptionA theory is developed for gas‐phase swarm measurements of ion–molecule reactions in electrostatic fields of arbitrary strength. The theory allows measurements of reaction rate coefficients made at low temperatures and strong electric fields to be converted directly to equivalent thermal rate coefficients at elevated temperatures inaccessible by direct methods. It is not necessary to calculate the ion velocitydistribution function explicitly, or to unfold the reaction cross section from the rate data. In first approximation the measured rate coefficient is equal to the thermal rate coefficient at an effective temperature calculated directly from the measured ion drift velocity. Higher approximations are obtained from more detailed analysis of the dependence of the rate coefficient and drift velocity on electric field strength. Comparison is made with experimental data reported in an accompanying paper by Albritton e t a l. In another accompanying paper, Lin and Bardsley compare the present theory with their detailed Monte Carlo calculations.

Monte Carlo simulation of ion motion in drift tubes
View Description Hide DescriptionThe motion of a swarm of ions in a uniform electric field is studied by simulating the motion of a single ion through many collisions with neutral atoms in order to obtain the drift velocity, average energy, and velocity distribution for the ions. For K^{+}ions in He at low field strengths, the results agree well with the solutions of the Boltzmann equation by Kumar and Robson; and for K^{+} in Ar at all field strengths, the computed mobilities demonstrate that the Viehland–Mason moment method can give useful results, especially if carried through to third order. The velocity distributions computed for O^{+}ions in He and Ar are used in the accompanying paper by Albritton e t a l. to analyze drift tube measurements of O^{+} reaction rates. Significant deviations from the Maxwell–Boltzmann form have been found and are seen to have important effects in that application. Velocity distributions have also been obtained for Li^{+} in He. The sensitivity of ionic mobilities to changes in the ion–atom interaction potential is examined with particular reference to K^{+}ions in Ar.

Photoionization studies of the Kr_{2} and Ar_{2} van der Waals molecules
View Description Hide DescriptionThe photoionization efficiency curves of the Kr_{2} and Ar_{2} van der Waals dimers were obtained with the molecular beam technique in the wavelength ranges 850–965 Å (12.848–14.586 eV) and 750–855 Å (14.501–16.531 eV), respectively. The ionization potential of Kr_{2} was found to be 12.87±0.015 eV (963.7±1.2 Å), which agrees with the value obtained by Samson and Cairns. The ionization potential of Ar_{2} was found to be 14.54±0.02 eV (852.7±1.2 Å). Using the known ground statedissociation energies of Kr_{2} and Ar_{2}, the dissociation energy of Kr^{+} _{2}, D _{0}(Kr^{+} _{2}), is deduced to be 1.15±0.02 eV and that for Ar^{+} _{2}, D _{0}(Ar^{+} _{2}), is 1.23±0.02 eV. The photoion yield curves of Kr_{2} and Ar_{2} are compared with that of Xe_{2}. Prominent autoionization structure was observed to correspond to Rydberg molecular states which are derived from the combination of a normal and an excited atom in the 4p ^{5} n s (or 4p ^{5} n d) configuration for Kr and 3p ^{5} n s (or 3p ^{5} n d) configuration for Ar.

Low‐temperature magnetic characteristics of tetrahedral CoCl_{4} ^{2−}. III. Magnetic exchange in paramagnetic Cs_{2}CoCl_{4}
View Description Hide DescriptionThe results of low‐temperature studies of the magnetic characteristics of Cs_{2}CoCl_{4} are reported. Single‐crystal principal‐axes magnetic susceptibility measurements between 1.5 and 20 K have been fit to an exchange‐modified spin‐3/2 single‐ion model. Heat capacitymeasurements between 1 and 30 K on Cs_{2}CoCl_{4} and between 4 and 25 K on Cs_{2}ZnCl_{4} have been used with a corresponding states procedure to obtain the magnetic heat capacity of Cs_{2}CoCl_{4}. All the results generally indicate a large zero‐field splitting of 14 to 16 K with the possibility of a rhombic distortion of the CoCl_{4} ^{2−} ion. Both the susceptibility and heat capacitymeasurements indicate the presence of significant magnetic exchange. At the lower temperatures the heat capacity results appear to be describable by an X Y linear chain model, in agreement with structural considerations in conjunction with the theoretically expected behavior of tetrahedral cobalt(II).

Mixing character and its application to irreversible processes in macroscopic systems
View Description Hide DescriptionThe ’’Principle of Increasing Mixing Character,’’ first described by Ruch and the present author, is presented in a somewhat modified formulation. The theory is then developed in such a way as to make it applicable to irreversible processes in nonideal systems. In systems described by a large number of parameters for which the ’’exponential assumption’’ (essentially the same as the well‐known local‐equilibrium assumption) can be made, the entire content is contained in a single, intuitively appealing expression. The result is applied to a simple example: diffusion in the Landau model of a nonideal solution.

SCF calculations for hydrogen in a spherical box
View Description Hide DescriptionSCF calculations for a hydrogen atom in a spherical box have been performed. The basis functions are products of STO’s and cutoff functions. The variations of the energy and the hyperfine splitting as functions of r _{0}, the sphere radius, have been studied.

Force–velocity cross correlations and the Langevin equation
View Description Hide DescriptionCross correlations of the velocity with the total force, the mean force, and the fluctuating force are evaluated for the Langevin equation and for a generalized version which has been suggested for a Brownian particle in an incompressible fluid of nonzero density. In the latter case all of the cross correlations follow a power law decay with the first ∼t ^{−5/2} and the second two ∼t ^{−3/2} for large t so that the t ^{−3/2} decays cancel. It is shown that the failure to consider the effects of these cross correlations leads to inconsistencies, in particular, the failure to satisfy the stationarity condition. The cross correlation of the fluctuating force with the velocitymeasured at the same time gives the rate at which energy is put into the system by this force and is shown to be equal to the rate at which energy is lost due to the dissipative effect of the mean force. The inertial response of the fluid to the motion of the Brownian particle is also evaluated. Comparisons are made between the original general treatment by Kubo and more recent developments in which a specific frequency dependent hydrodynamic drag is used. A relationship between the velocity autocorrelation function, the fluctuating force autocorrelation function, and the velocity–fluctuating force cross correlation is proven.

The use of Lanczos tridiagonalization in bounding eigenvalues
View Description Hide DescriptionLanczos tridiagonalization is applied to several problems: the one dimensional quartic oscillator, the two dimensional quartic oscillator, and a finite difference version of the latter. In each case high accuracy upper and lower bounds are established in excellent agreement with previous calculations.

Mass spectrometric observations of some polyatomic gaseous rare earth oxides and their atomization energies
View Description Hide DescriptionFrom Knudsen effusion mass spectrometric examination of reactions of the type M(g)+MO(g) =M_{2}O(g), 2MO(g) =M_{2}O_{2}(g), and 2MO(g) =MO_{2}(g)+M(g), the atomization energies ΔH°_{0} (kcal/mole) of the following new species have been estimated: Eu_{2}O(g), 174±12; Gd_{2}O(g), 236±10; Tb_{2}O(g), 243±12; Ho_{2}O(g), 216±14; Lu_{2}O(g), 266±14; Eu_{2}O_{2}(g), 324±17; Gd_{2}O_{2}(g), 427±17; Tb_{2}O_{2}(g), 432±21; Ho_{2}O_{2}(g), 407±26; GdO_{2}(g), 314±17; and HoO_{2}(g), 307±25. Atomization energies ΔH°_{0} (kcal/mole) revised from literature are presented for the following: Sc_{2}O(g), 236±16; Y_{2}O(g), 249±13; La_{2}O(g), 265±13; Y_{2}O_{2}(g), 438±28; La_{2}O_{2}(g), 459±28; Ce_{2}O_{2}(g), 472±15; CeO_{2}(g), 344±5; and NdO_{2}(g), 318±20. The variation of the atomization energies of the M_{2}O(g), M_{2}O_{2}(g), and MO_{2}(g) species along the lanthanide series follows a similar pattern observed for the atomization energies of the MO(g) species and the heat of sublimation of the corresponding metals. Predictions of the atomization energies of the yet unobserved rare earth oxide species of the types above have been made. The standard heats of formation at 0°K of the gaseous rare earth oxides are also presented.

Group theoretical classification of the tunneling–rotational energy levels of water dimer
View Description Hide DescriptionA permutation‐inversion group theoretical classification scheme for the tunneling–rotational levels of the water dimer molecule is given. Electric dipole selection rules and nuclear spin statistics are discussed. Application of these results to the microwave spectrum of water dimer, observed by molecular beam techniques, is also presented.

The structure of water dimer from molecular beam electric resonance spectroscopy
View Description Hide DescriptionMolecular beams of hydrogen bonded water dimer, generated in a supersonic nozzle, have been studied using electric resonance spectroscopy. Radiofrequency and microwave transitions have been observed in (H_{2} ^{16}O)_{2}, (D_{2} ^{16}O)_{2}, and (H_{2} ^{18}O)_{2}. Transitions arising from both pure rotation and rotation–tunneling occur. The pure rotational transitions have been fit to a rigid rotor model to obtain structural information. Information on the relative orientation of the two monomer units is also contained in the electric dipole moment component along the A inertial axis μ_{ a }, which is obtained from Stark effect measurements. The resultant structure is that of a ’’t r a n s‐linear’’ complex with an oxygen–oxygen distance R _{OO} of 2.98(1) Å, the proton accepting water axis is 58(6) ° with respect to R _{OO}, and the proton donating water axis at −51(6) ° with respect to R _{OO}. This structure is consistent with a linear hydrogen bond and the proton acceptor tetrahedrally oriented to the hydrogen bond. The limits of uncertainty are wholly model dependent and are believed to cover variations from the zero‐point vibrational structure observed to the equilibrium structure. μ_{ a } shows strong dependence on J and K and is about 2.6 D. Centrifugal distortion constants have been interpreted in terms of the monomer–monomer stretching frequency and give ω=150 cm^{−1}.

Angular entropy: The information content of molecular scattering angular distributions
View Description Hide DescriptionThe concept of the angular entropy arises from consideration of the information content of a scattering pattern, i.e., an angular distribution of collision products. It is shown that information theory (I.T.) provides the framework for evaluation and interpretation of the entropy (and entropy deficiency) of an angular distribution of reactive, inelastic, or elasticscattering. The differential cross section σ (ϑ) is converted to a normalized probability density function (pdf), P (u) [u= (1/2)(1−cosϑ)], from which the angular surprisal is obtained as −lnP (u). The average over u of the surprisal yields the angular entropy deficiency. (A histogrammic approximation to the continuous pdf can provide a simple estimate of ΔS). Examples are presented of reactive and inelastic molecular scattering patterns and of various prototype angular distributions giving insight into the angular entropy. The I.T. method is also applied to elasticscattering of atoms and molecules. It inherently demands the elimination of the well‐known ’’classical divergencies’’ (the forward infinity and rainbow spike). These problems disappear when quantal (or semiclassical) differential cross sections are used. Nevertheless, the forward cone makes the dominant contribution to the angular entropy deficiency for elasticscattering at moderate energies. The rainbow structure introduces some entropy deficiency, but the quantal interferences in σ (ϑ) contain little information (in the strict I.T. sense). However, nuclear symmetry effects are found to be significant.

Divanadium
View Description Hide DescriptionThe metal concentration and matrix conditions which favor the dimerization of vanadium atoms to divanadium molecules are quantitatively assessed using optical spectroscopy. A simple kinetic theory is presented which enables small metal clusters to be identified in the presence of atomic species. This approach makes use of the fact that a metal atom being deposited is capable of diffusing either on the matrix surface or within a narrow region (the reaction zone) near the matrix surface before its kinetic energy is dissipated sufficiently to immobilize it. The surfacediffusion pathway is found to predominate over the statistical generation of dimers. The kinetic result, which suggests that V_{2} is formed on the matrix surface rather than in the gas phase, is also borne out by the intriguing observation that for a given metal deposition rate the dimer‐to‐monomer ratio decreases as one increases the atomic weight of the noble gas used to isolate them, with Ar giving the most V_{2} and Xe the least. Careful concentration experiments in Ar, Kr, and Xe matrices permit the uv–visible transitions of V_{2} to be identified and the extinction coefficient ratio ε_{ V }/ε_{ V } _{2} to be determined. A qualitative molecular orbital description of V_{2} is presented in the light of iterative extended Hückel calculations. These computations suggest that high spin divanadium has a strong metal–metal bond which is mainly 4s in character with only small contributions from the degenerate d _{ x z,y z } π‐bonding set. Visible absorptions observed in the 600–450 nm region are tentatively assigned to electronic transitions localized mainly between the V–V σ‐bond and the d‐orbital manifold.

Coupled states cross sections for rotational excitation of H_{2}CO by He impact at interstellar temperatures
View Description Hide DescriptionCross sections for rotational excitation of ortho formaldehyde due to collision with helium are computed following the coupled states (CS) formalism and compared with recent coupled channel (CC) results obtained employing the same a b i n i t i oconfiguration interactionintermolecular potential. The CS equations are integrated at 9 scattering energies between 25 and 95°K using a basis set of 16 ortho H_{2}CO states (1⩽j⩽5). The CS procedure with the orbital angular momentum quantum number l set equal to the total angular momentumJ yields the correct order of magnitude for scattering cross sections. Qualitative differences are found, however, in the energy dependence of some inelastic transitions.

Tests of alkali ion‐inert gas interaction potentials by gaseous ion mobility experiments
View Description Hide DescriptionGaseous ion mobilities are mainly dependent on ion–neutral collision energies in the range 0.03–1 eV and, using a recently developed kinetic theory method, can be directly related to ion–neutral interaction potentials. In this paper, experimental mobilities are used to test recent theoretical calculations based on the electron–gas model of the interaction potentials for the twelve combinations of Li^{+}, Na^{+}, K^{+}, and Rb^{+} with He, Ne, and Ar. The model potentials are quite good, but some systematic discrepancies with experimental mobilities exist. These discrepancies are analyzed in terms of the relation between the mobility and the ion–atom potential.

On accurate quantum mechanical approximations for molecular relaxation phenomena. Averaged j _{ z }‐conserving coupled states approximation
View Description Hide DescriptionA rigorous formal theory of relaxation phenomena within the framework of the averaged j _{ z }‐conserving coupled states (j _{ z }CCS) (A j _{ z }) approximation is developed. Using the expressions obtained in this paper, the A j _{ z } approximation is shown to yield pressure broadening cross sections which are in exact agreement with full close coupling results for a He+HCl model system. Previous j _{ z }CCS approximations to pressure broadening cross sections, which were in complete disagreement with close coupling for all systems studied, are shown to be the result of incorrect labeling of j _{ z }CCS T‐matrices by total angular momentumJ rather than by the effective orbital angular momentum ?. The correctly labeled results are not only found to be highly accurate but also considerably simpler than the expressions resulting from incorrectly labeled j _{ z }CCS T‐matrices. Expressions are also derived for NMR spin–lattice relaxation cross sections within the A j _{ z } approximation. Because the decoupled dynamical equations may be solved much more easily than the full exact CC ones, it is now feasible for the A j _{ z } pressure broadening and spin–lattice relaxation cross sections to be computed in an iterative procedure. This will enable one to use such experimental data as a tool for determining molecular interactions.