Index of content:
Volume 68, Issue 1, 01 January 1978

Self‐consistent treatment of the internal energy, chemical potential, and critical constants of liquid alkali metals and selected alloys
View Description Hide DescriptionA systematic investigation is made of the consequences of the pseudopotential theory of metals on the thermodynamic properties of metallic liquids, including mixtures. We obtain expressions for the internal energy, the Gibbs free energy, and excess chemical potentials of general metallic mixtures with any number of constituents. We recommend on this basis optimum pseudopotentials for all liquidalkali metals. We obtain good agreement for the excess chemical potental of lithium in selected alloys. Finally, on the basis of metallic theory, we obtain a new scaling law for the critical constants of liquid metals which seems to be well satisfied by the metals of the groups I and IIIa, except perhaps for lithium and thallium.

Mixed quantum model for gas–solid energy transfer
View Description Hide DescriptionA new quantum close‐coupling method for gas–solid scattering, the mixed quantum model (MQM), is proposed. A numerical application to gas–solid energy transfer for a six atom linear chain model solid is made. The MQM is based on a division of the solid into a primary zone containing those atoms directly struck by the gas atom and a heat bath which comprises the rest of the solid. The primary zone, a few particle system, is treated exactly within a coupled states framework. The heat bath, a many body system, is treated within a one‐phonon truncation of a heat bath coupled states phonon expansion. The MQM reliably describes gas–solid energy transfer at both low and high gas energiesE _{ g }. In contrast, a single oscillatormodel for the solid breaks down at low E _{ g } while the standard one‐phonon theory breaks down at high E _{ g }.

A theoretical prediction of vibrational enhancement for dissociative charge transfer in the HeH_{2} ^{+} system
View Description Hide DescriptionA model has been developed to treat dissociativecharge exchange occurring on excited‐state surfaces in the weak adiabatic limit. This process is analogous to collisionally induced predissociation with the added feature that electronic as well as translational energy is used to effect the dissociation. The consequences of weak adiabaticity and the location of the avoided crossing seam are to require the consideration of tunnelling through a barrier in the dissociation curve. An appealing feature of the model is the reduction of a three‐dimensional trajectory problem to one dimension by neglect of coupling of translation to vibration and rotation. Configuration interaction ground‐ and excited‐state calculations have been performed in the vicinity of the curve crossing seam for He^{+}+H_{2}→He+H^{+}+H. Use of the parameters derived from these a b i n i t i o results in the dynamics model yields cross section and rate coefficient values in qualitative agreement with experimental measurements. Vibrational excitation from the v=0 to v=1 states in H_{2} leads to an increase in cross section of approximately two orders of magnitude due to enhancement of the tunnelling.

Raman and infrared frequency shifts proceeding from ionization of perhalo‐p‐benzoquinones to radical anions
View Description Hide DescriptionThe vibrational assignment of the fundamental modes of 2,3,5,6‐tetrachloro‐ and 2,3,5,6‐tetrabromo‐p‐benzoquinone (chloranil and bromanil, respectively) radical anions is reported and compared with that of the neutral molecules. For this purpose the single crystal Raman and infrared spectra of bromanil are also given and interpreted. The absence of the vibronic effects present in the infrared spectra of some free radical salts is demonstrated, and the vibrational spectra of the potassium salts of both radical ions are shown to be interpretable in terms of substantially unperturbed molecular structures even in the case of crystalline samples. The vibrational assignments and their normal coordinate analysis allow one to obtain most of the relevant information on the frequency shifts proceeding from the addition of an extra electron to the perhalo‐p‐benzoquinone structure.

Theory of rare gas–group VI ^{1} S–^{1} D collision‐induced transitions
View Description Hide DescriptionThe collision‐induced ^{1} S–^{1} D emission of a Group VI metastable ^{1} S atom in the presence of a rare gas background is investigated theoretically. Approximate model potentials are constructed for the Group VI ^{1} S–rare gas interaction based on the mixed rare gas ground state potentials. The model is supplemented by a b i n i t i o calculations for ArO and by the RKR potential for XeO. Long range perturbation theory is used for the induced dipole transition moment, supplemented at short range by the available a b i n i t i o calculations on Ar, Kr, and Xe oxides. The model gives a satisfactory account of the measured emission coefficients for the rare gas oxides and sulfides and predicts emission coefficients for the rare gas selenides.

Change of molecular configuration in crystalline decanoic acid as studied by infrared spectra and normal coordinate analysis
View Description Hide DescriptionInfrared spectra of a well‐oriented crystalline film of decanoic acid were obtained in the range from room temperature to liquid‐helium temperature. Many absorption bands due to the carboxyl group and a band progression due to the CH_{2} wagging modes appear as doublets. In each doublet, one component decreases in intensity with lowering temperature and disappears near liquid‐helium temperature (type I), while another component increases in intensity with lowering temperature (type II). It is confirmed by normal coordinate analysis that the type I and II bands are ascribed to fundamental vibrations of the c i s and t r a n s isomers, respectively. The latter isomer would be produced from the former by double proton transfer in the decanoic acid dimer. From the temperature dependence of band intensities, the enthalpy and entropy differences between the two isomers are evaluated to be about 240 cal⋅mol^{−1} and 3.8 cal⋅mol^{−1}⋅deg^{−1}, respectively.

Hydrodynamic screening and viscous drag at finite concentration
View Description Hide DescriptionThe concentration dependence of steady linearized viscous flow in a suspension of spheres of number density ρ_{0} is studied using a new formulation of the ideas of hydrodynamic screening [cf. K. F. Freed and S. F. Edwards, J. Chem. Phys. 61, 3626 (1974)]. A concentration dependent effective pure fluid Navier–Stokes equation is derived via a mean field treatment similar in spirit to Debye–Hückel theory. The effective Navier–Stokes equation is shown to contain concentration dependence through an inverse screening length κ and a renormalized viscosity η[ρ_{0}]. The quantities κ and η[ρ_{0}] are expressed in terms of the zero frequency and small wavevector limit of the particle current autocorrelation function. The Green’s function of the effective Navier–Stokes equation (screened Oseen tensor) is determined for the case of incompressible flow. The velocity field v(r) for steady, incompressible flow past a sphere of radius R is then calculated for both slip and stick boundary conditions. From v(r), the concentration dependent drag coefficient ζ[ρ_{0}] for a sphere of radius R is determined in terms of κ and η[ρ_{0}]. The result gives a generalization of Stokes’ law to finite concentration suspensions. Finally, two simple approximation treatments of the particle current autocorrelation function are proposed and the forms they yield for η[ρ_{0}] and κ are discussed.

Orientational distributions in partially ordered solids as determined from NMR and ESR line shapes
View Description Hide DescriptionThe orientational distribution in partially ordered solids, drawn polymers, etc. is related with NMR and ESRline shapes governed by anisotropic shift, dipolar, or quadrupolar couplings. In principle, the theory yields the complete orientational distribution by numerical deconvolution or spectral fitting procedures. Furthermore, the line shape can be decomposed into subspectra that correspond to the moments of the orientational distribution. The theory is applied to ^{2} D‐NMR line shapes in partially ordered solid benzene, and to ESR nitroxide spin label spectra.

Raman evidence for thermally disordered energy states in various phases of ionic nitrates
View Description Hide DescriptionDetailed Raman studies of the symmetric stretching mode of a large number of nitrate salts have confirmed the presence of an anomalous second component not predicted by factor group analyses based on known crystal structures. Depolarization studies with oriented single crystals, decoupling studies with ^{18}O‐enriched samples, and temperature variation studies support previous suggestions that the new components are due to the presence of alternate sites which result from a dynamic disorder within the lattice. The alternate sites are present even for structures normally considered to be completely ordered and do not destroy the long‐range interactions (correlation field coupling) of the ordered part of the lattice. Phase transitions may be precipitated by the increase in these impurity type disordered states until the long‐range coupling of the ordered lattice can no longer be maintained.

Elementary finite order perturbation theory for vertical ionization energies
View Description Hide DescriptionThe analysis of ionization energies in Rayleigh–Schrödinger perturbation theory and in propagator theory, previously known separately through third order in electron interaction, are compared in detail using elementary algebraic methods and their equivalence is explicitly shown. Relaxation terms are identified as the ΔE _{SCF} contributions and appropriate rules are described for their construction from the electron propagator diagrams of arbitrary order. Correlation terms are obtained separately. The transition operator method is analyzed and found to differ from ΔE _{SCF} in third order, contrary to earlier claims.

Molecular collisions and depolarization of emission from I_{2} in the gas phase excited by circularly polarized light
View Description Hide DescriptionMolecular iodine in the gas phase is excited selectively to a single rotational–vibrational level of electronic state ^{3}Π_{O + } _{ u }(B) by a circularly polarized single mode tunable dye laser. By tuning the excitation frequency we have studied the dependence of polarization of the emission and the intensity asymmetries for the rotationally inelastic transitions J′→J′+δJ′ and J′→J′−δJ′ on the quantum numbers of J′ and v′. A theoretical study on the collision between two diatomic molecules was done without neglecting spatial orientation effects. The theory accounts for the high polarization in both the resonance emission and the emissions from rotational and rotational–vibrational energy transferred states, especially for high J′ states.

Far‐infrared and Raman spectra, powder x‐ray diffraction, and symmetry of crystalline ethylene oxide
View Description Hide DescriptionThe x‐ray diffraction pattern of powdered oxirane at 90°K, the far‐infrared spectrum of polycrystalline oxirane at 4.3°K, and polarized Raman spectra of oriented crystals of oxirane between 125 and 22°K, are reported. The spectra of the solid are reassigned and crystalline oxirane is found to belong to the monoclinic system, crystal class C _{2h }, with four molecules on general positions in the primitive unit cell.

Physical studies of nematic azoxybenzenes. I. Magnetic susceptibilities and the order parameter
View Description Hide DescriptionThe anisotropy of the magnetic susceptibility and the density of the series of nematic p,p′‐di‐n‐alkyl and p,p′‐di‐n‐alkoxy azoxybenzenes are reported as a function of temperature. Assuming that the molecules are effectively axially symmetric the anisotropy of the susceptibility is a direct measure of the nematic order parameter S. The results for S agree reasonably well with the predictions from Maier and Saupe’s theory of the nematic phase. With increasing chain length both the order parameter and the relative volume change at the nematic–isotropic transition alternate parallel to the nematic–isotropic transition temperature and the transition entropy.

Physical studies of nematic azoxybenzenes. II. Refractive indices and the internal field
View Description Hide DescriptionThe ordinary refractive index and the birefringence are reported for two homologous series of nematic liquid crystals, the p,p′‐di‐n‐alkyl and p,p′‐di‐n‐alkoxy azoxybenzenes. It is found that the high‐frequency dielectricanisotropy is proportional to the anisotropy of the magnetic susceptibility. For axially symmetric molecules this proportionality allows a simplification of the intricate problem of the internal field, which can be taken as independent of the anisotropy of the surroundings of a molecule. Representing a molecule by a homogeneously polarizable spheroid, an equation is derived which relates the anisotropic high‐frequency dielectricpermittivity to the anisotropic molecular polarizability, and which gives consistent results for both the solid state and the nematic phase.

Calculation of dipole correlation factors in liquid crystals with use of a semiempirical expression for the internal field
View Description Hide DescriptionThe internal field expression on a semiempirical basis in the preceding article, is applied in the generalization of the Kirkwood–Fröhlich theory for liquid crystals presented earlier by one of the authors. As an example correlation factors are calculated for two compounds in the nematic phase, and one in the smecticA phase.

The scalar‐product expression of boundary free energy for long‐range interacting systems
View Description Hide DescriptionThe scalar‐product formula of the excess free energy σ of a boundary between two phases (based on the lattice model) is proved for the case of interaction potential of the range longer than the nearest neighbor. The formula is exp(−Aσ/k T) =Σ[p ^{(I)}(ν_{1},ν_{2},...,ν_{ k }) p ^{(II)}(ν_{1},ν_{2},...,ν_{ k })]^{1/2} exp[α^{(I)}(ν_{1},ν_{2},...,ν_{ k })− α^{(II)}(ν_{1},ν_{2},...,ν_{ k })], where A is the sectional area parallel to the boundary, ν_{ i } is a configuration of an ith plane parallel to the boundary, p ^{(I)}(ν_{1},...,ν_{ k }) is the probability that k consecutive planes in the bulk I phase take configurations ν_{1},...,ν_{ k }, and the summation goes over all configurations ν_{1},...,ν_{ k }. The variable α^{(I)}(ν_{1},ν_{2},...,ν_{ k }) is a Lagrange multiplier to guarantee continuity of p ^{(I)}: Σ_{μ} p ^{(I)}(μ,ν_{1},ν_{2},...,ν_{ k }) = Σ_{μ} p ^{(I)}(ν_{1},ν_{2},...,ν_{ k },μ). The expression is checked by two examples. The σ for the two‐dimensional Ising model is calculated using a 3×2 cluster (i.e., a double square cluster made of six lattice points) with the ’’3’’‐side perpendicular to the boundary, and is compared with the previous σ calculated with a 2×3 cluster (with the ’’3’’‐side parallel to the boundary). The calculated σ’s agree well when the α terms are included. As a second example, surface tension σ of a liquid of a two‐dimensional lattice gas–liquid model (in which the first, second, and third neighbor pairs are excluded, and the fourth and fifth neighbor pairs attract) is calculated. It is then compared with σ calculated by a sum method (which calculates the equilibrium state of a sandwich system made of the gas and the liquid phases with the boundary between them). The agreement between the two calculations supports the correctness of the proposed σ expression.

Dependence of orthopositronium annihilation rates on density fluctuations in methane gas
View Description Hide DescriptionRecent experiments have shown that the annihilation rate of positrons which form orthopositronium in methane gas varies linearly with gas density at low densities, but significantly deviates from linearity at high densities. We present evidence that this annihilation behavior in methane results from density fluctuations that are characteristic of an imperfect gas.

Quantum mechanical theory of collisional ionization in the presence of intense laser radiation
View Description Hide DescriptionWe present a quantum‐mechanical formalism for treating ionizing collisions occurring in the presence of an intense laser field. The theory rigorously takes into account both the intense laser radiation and the internal electronic continuum states associated with the emitted electrons. We accomplish this essentially by combining discretization techniques, used in a recent study of fieldfree collisional ionization, with expansions in terms of so‐called electronic‐field representations for the quasi‐molecule‐plus‐photon system. This leads to a coupled‐channel description of the heavy‐particle dynamics which involves effective electronic‐field potential surfaces and continua. We also discuss qualitatively characteristic features of ionizing collisions accompanied by intense lasers, drawing comparisons with their fieldfree counterparts. Our remarks are designed to encourage experimental investigation of collisional ionization in the presence of intense lasers, and to stimulate further theoretical work. Because the electronic continuum meets requirements of exact energy resonance for absorption of a photon over large ranges of the internuclear separations, collisional ionization in an intense field should occur much more readily than other field‐influenced inelastic collisions, in which photon absorption is resonant only near potential surface pseudocrossings. We therefore suggest laser‐influenced ionizing collisions as very good candidates for experimental verification of the effects of intense laser radiation on inelastic collisional processes. We describe the anticipated behavior of the energy distribution of electrons emitted due to radiative coupling. Our comments are based on some physically reasonable assumptions about the electronic transition dipole matrix elements between discrete and continuum electronic states. Actual calculations of such matrix elements involve special electronic structure considerations, and these are outlined in some detail in an Appendix.

Lattice dynamical investigation of the rotator phase of n‐paraffins
View Description Hide DescriptionA lattice dynamical investigation was made in order to interpret the thermodynamical behaviors of the first‐order solid‐state phase transition of n‐paraffins from the orthorhombic or monoclinic to the rotator phase. The internal energy, the entropy, and the Helmholtz free energy of the rotator phase were evaluated in variation with chain length, lattice dimension, and temperature, using a model of cooperative rigid rotation accompanied with a small translational fluctuation along the chain axis. The contribution of the molecular vibrations to the thermodynamic functions was estimated by a lattice dynamical calculation in the quasiharmonic approximation from the density of states obtained by the normal coordinate treatment. An orthohexagonal lattice with the dimension of a=3^{1/2} b=8.31 Å was found to exhibit the minimum value of free energy at 300 K, as compared with the measured lattice dimensions of n‐C_{19}H_{40} (a=8.30 Å, b=4.79 Å) at 295.2 K. The calculated linear coefficient of thermal expansion α_{ a } (=α_{ b }) along the direction perpendicular to the c‐axis (the chain axis) is 1.4–1.7×10^{−4} K^{−1} which is quite similar to the mean value of α_{ a } and α_{ b } of the orthorhombic polyethylene (o‐PE) lattice at room temperature. The transition temperatures, the heat, and the entropy of transition were evaluated in variation with chain length. The theoretical transition points are 20–30°C higher than the observed ones. The calculated heat and entropy of transition are in good agreement with the experimental values.

Quantum dynamics in the effective system states basis. I. Mathematical structure and time‐dependent perturbation theory
View Description Hide DescriptionA molecule in the presence of a radiation field is described by a non‐Hermitian reduced effective Hamiltonian and its eigenvectors, the effective system states. These states form a natural basis for the evaluation of spectroscopic properties; its use requires a generalized formulation of quantum dynamics. The mathematical structure of the vector space defined by those states is investigated; that vector space is found to be a Banach space which reduces to Hilbert space if the energies of the effective system states become real. Time reversal symmetry is found to be an important feature of the overall problem. The generalized time development operator and the Schrödinger equation which defines it are deduced, and the effect of that operator on the effective system states is discussed. The proper generalization of time‐dependent perturbation theory in the interaction picture is then derived and its use in applications is discussed in general terms.