Volume 64, Issue 1, 01 January 1976
Index of content:

Differential cross sections for elastic electron scattering. II. Charge cloud polarization in N_{2}
View Description Hide DescriptionRelative elastic differential cross sections for electron scattering from N_{2} molecules have been measured with a crossed beam technique in order to investigate the influence of charge cloud polarization. The angular range studied was 3 to 135 deg and the electron energies were betwee 90 and 1000 eV. Comparison with theoretical calculations based on the independent atom model using partial wave atomic scattering factors shows strong deviations at small scattering angles. This discrepancy is discussed from the point of view of charge cloud polarization. It is found that calculations including an additional polarization potential improve the theoretical description of the experimental small angle data.

A group theoretical approach to geminal product matrix elements
View Description Hide DescriptionExpressions enabling systematic compilation of Hamiltonian and overlap matrix elements for an antisymmetrized multiterm geminal product trial function are derived, using double coset (DC) decompositions and subgroup adapted irreducible representations of the symmetric group, S _{ N }. The trial function may describe an even electron atomic or molecular system in any total spin eigenstate, and the geminals may be nonorthogonal, have arbitrary permutational symmetry, and be explicit functions of interelectronic distance. A DC decomposition is used to factor out permutations not exchanging particle labels between geminals (elements of the interior pair group, S ^{ n } _{2}, n≡N/2). This reduces the sum over N! permutations to a sum over DC generators. If the irreducible representation λ (S) of S _{ N } is adapted to S ^{ n } _{2} each geminal is projected into its singlet or triplet component. The DC generators are chosen such that each has the form Q P, where Q permutes odd particle labels only and P is a permutation of geminals (element of the exterior pair group, S _{?}). With the aid of matrices called DC symbols an algorithm for these generators is derived, and used to find explicit sets for N=2, 4, 6, and 8. The N‐electron Hamiltonian and overlap integrals arising with a particular DC generator Q P are factored into products of smaller integrals, called cluster integrals, according to the cycle structure of Q. The cluster integrals are of only three main types—overlap, one‐cluster energy, and two‐cluster energy (analogs of orbital overlap, 1‐electron, and 2‐electron integrals) —and are further classified by order (number of geminals), geminal permutational symmetry, and in some cases pattern of connection. Matrix element compilation is systematic in that all N‐electron integrals are products of a relatively small number of different types of cluster integral, and that N‐electron integrals with similar factored forms are collected together in the summation. From counting the different cluster integrals required, it is concluded that a geminal product calculation not using orbital expansion is feasible only for systems with eight or less electrons. In some cases semiempirical calculations with correlated geminals might be considered, for the more complex cluster integrals (those of high order) are quite small for a system approximating a collection of localized electron pairs. The matrix element expressions are specialized for three cases—all geminals being singlets, strongly orthogonal geminals, and identical geminals. Comparison is made with a recently developed diagrammatical method.

Violations of Kleinman symmetry in nonlinear optics: The forbidden coefficient of α‐quartz
View Description Hide DescriptionThe magnitude, sign, and dispersion of the Kleinman forbidden nonlinear optical coefficient d _{14} for α‐quartz has been measured via second harmonic generation. The results, relative to d _{11} (α‐SiO_{2}), are +0.009 and +0.026 for λ_{0}=1.064 μ and 0.532 μ, respectively. The dispersion of the ratio d _{14}/d _{11} qualitatively agrees with a recent theoretical prediction that d _{14}/d _{11}∝ω^{2}. A microscopic model in terms of bonds and electron lone pairs of symmetry C _{∞} shows the Si→O bond polarizability β_{14} to be ten times smaller than the corresponding polarizability found for I→O and Te→O bonds.

Electron energy loss measurements on pyrene (C_{16}H_{10}) vapor
View Description Hide DescriptionElectron energy loss spectra from 0 to 25 eV were measured with 50 keV electrons on pyrene vapor. The results indicate the existence of five strong excitations between 3.9 and 7.0 eV, identified as π–π* excitations. Four of them exhibit vibrational sublevels with 0.17 eV energy separation. Less pronounced maxima of the energy loss function are observed between 8 and 11 eV, which cannot be interpreted conclusively. Broader structures between 11 and 18 eV are attributed to excitations involving σ states. The present results are related to absorption measurements on pyrene in solution and to investigations of pyrene single crystals. Values for the solution and crystal shift of the different π–π* excitations are obtained (∼−0.2 eV).

Helium diffraction from tungsten (112)
View Description Hide DescriptionThe diffractive scattering of helium from W(112) in the [11̄0] azimuth is presented for incidence angles from 20° to 70°, surface temperatures from 1000 to 1600 K, and beam temperatures from 300 to 650 K. The first order beams are the only nonspecular features observed and their angular positions and relative intensities are reproduced well by semiclassical scattering calculations. Debye–Waller analysis of thermal attenuation gives a surface Debye temperature lower than the bulk, but larger than that derived from electron scattering.

Scattering of argon and neon from W(112)
View Description Hide DescriptionThe angular scattering distributions of thermal Ne and Ar beams incident in the [11̄0] azimuth of the W(112) surface are presented as a function of angle of incidence, surface temperature, and beam temperature. For Ne, the distributions are rainbow patterns similar to those observed for Ne on LiF for small angles of incidence. They coalesce into a broad lobe at an incidence angle of 70°. Argon scattering is unilobular and similar in all details with Ar scattering from the smoother W(110) surface. Ne appears to be in the inelastic regime while Ar is trapping dominated.

A semiclassical model for atomic scattering from solid surfaces—He and Ne scattering from W(112)
View Description Hide DescriptionA semiclassical formalism is presented which predicts specular atomic scattering from close‐packed surfaces and either ’’rainbow’’ or diffractive scattering from strongly periodic surfaces. The intensities are a series of δ functions at the Laue conditions modulated by the product of the classical intensities and a structure factor accounting for interference among multiple trajectories within a unit cell. Narrow energy distributions in the incident beam and/or long wavelengths result in well‐resolved diffracted beams, while broad distributions and/or small wavelengths result in coalesced beams which display only the ’’rainbowlike’’ intensity envelope. A simple elasticmodel using a 6–9 potential has been used to predict He and Ne scattering from W(112). For helium the peak positions and relative peak heights agree with the measuredscattering essentially within experimental reproducibility, but the peak widths calculated with this elasticmodel are too narrow and the intensity maxima too large. Neon calculations reproduce qualitatively the rainbow patterns observed in the experiments but neither the intensities nor the positions of the rainbow features are correct, indicating the existence of large inelastic effects.

Absolute rate constant determinations for the deactivation of O(^{1} D) by time resolved decay of O(^{1} D) →O(^{3} P) emission
View Description Hide DescriptionAbsolute rate constants for the deactivation of O(^{1} D) atoms by some atmospheric gases have been determined by observing the time resolved emission of O(^{1} D) at 630 nm. O(^{1} D) atoms were produced by the dissociation of ozone via repetitive laser pulses at 266 nm. Absolute rate constants for the relaxation of O(^{1} D) (×10^{−10} cm^{3} molecule^{−1}⋅s^{−1}) by N_{2}(0.30±0.01), O_{2}(0.41±0.05), CO_{2}(1.2±0.09), O_{3}(2.4±0.1), H_{2}(1.3±0.05), D_{2}(1.3±0.05), CH_{4}(1.3±0.3), HCl(1.4±0.3), NH_{3} (3.4±0.3), H_{2}O(2.1±1.0), N_{2}O(1.4±0.1), and Ne (<0.0013) are reported at 298 K. The results obtained are compared with previous relative and absolute measurements reported in the literature.

Time dependent variational approach to semiclassical dynamics
View Description Hide DescriptionExplicitly time dependent methods for semiclassical dynamics are explored using variational principles. The Dirac–Frenkel–McLachlan variational principle for the time dependent Schrödinger equation and a variational correction procedure for wavefunctions and transition amplitudes are reviewed. These variational methods are shown to be promising tools for the solution of semiclassical problems where the correspondence principle, classical intuition, or experience suggest reasonable trial forms for the time dependent wavefunction. Specific trial functions are discussed for several applications, including the curve crossing problem. The useful semiclassical content of the time dependent Hartree approximation is discussed. Procedures for the variational propagation of density matrices are also derived.

The 3d→4s bands of transition metal ions in LiF and NaF
View Description Hide DescriptionThe absorption spectra in the range 5–10 eV for divalent transition metal ions in the host crystals LiF and NaF are presented. Several features of the spectra show that most of the bands observed are well described as 3d→4s transitions. Thus, the effect of reducing the lattice constant of the host crystal is to increase the transition energy; the intensities of the transitions are low and are dependent on temperature or on the presence of a local charge compensator. The variation of transition energy with atomic number follows that of the free ions. Detailed assignments of the bands are discussed.

The mutual diffusion study in the systems containing benzene or benzene‐d _{6} at 25 °
View Description Hide DescriptionThe mutual diffusion coefficients of benzene and benzene‐d _{6} were measured at low solute concentrations in each of the following solvents:n‐hexane, cyclohexane, dodecane, and hexadecane. The observed mutual diffusion coefficients for the systems containing benzene‐d _{6} were consistently lower than those observed for the corresponding systems containing benzene. The results of this investigation show that a measurable isotope effect exists in liquid diffusion and that the magnitude of the effect depends on the physiochemical properties of the solvents. The magnitude appears to be more closely related to the viscosity of the solvents than to the molecular weights of the solvents.

Chemiluminescence from thallium–fluorine reactions
View Description Hide DescriptionChemiluminescence from reactions of thallium with fluorine has been observed in a dilute flame experiment. Atomic emission from the highest observed Tl (6 ^{2} D _{5/2,3/2}) states (103.5 kcal above ground state) is shown to arise from energy transfer processes. The role of the metastable Tl (6 ^{2} P _{3/2}) state in energy transfer processes is discussed. Weak molecular emission from TlF (A ^{3}Π–X ^{1}Σ, B ^{3}Π–X ^{1}Σ) has been observed.

Elastic and nonelastic cross sections for Ar* (^{3} P)+HBr(X ^{1}Σ)
View Description Hide DescriptionThe energy dependence of the differential scattering of metastable Ar* (^{3} P) by ground state HBr(X ^{1}Σ) has been studied at four relative kinetic energies from 60–160 meV over an angular range of 4–120 deg c.m. The position and curvature of rainbow maxima, which are observed at each energy, are used to obtain LJ(12,6) potential parameters. The position of the minimum r _{ m }=4.44±0.8 Å is the same as that for K+HBr, and the well depth, ε=25.2±1.1 meV, is about 4% larger than ε (K+HBr). The scattered intensity shows a distinct falloff at large angles compared to that expected for elastically‐scattered Ar*. This depletion, caused by quenching of Ar*, is analyzed in terms of an optical model to determine the threshold and energy dependence of the quenching cross section. The nonelastic cross section increases from a threshold of 25 meV to a nearly constant value of 41 Å^{2} at 160 meV. The optical analysis predicts a maximum of 42.5 Å^{2} at 215 meV.

Reactions and quenching of vibrationally excited hydroxyl radicals
View Description Hide DescriptionRate constants for the deactivation of vibrationally excited hydroxyl radicals by the inert gases Ar, O_{2}, N_{2}, H_{2}, and D_{2} have been determined. Additionally the rate constants for the reaction HO(v)+O_{3}→ products have been measured and found to decrease from 11×10^{−12} to 3.7×10^{−12} cm^{3} molecule^{−1}⋅ sec^{−1} from v=9 to v=4. Hydroxyl radicals were generated in a large tank at low pressures from the reaction of hydrogen atoms and ozone. The radicals were formed in excited vibrational states (v?9), and the excited radicals, v=4 to 9, were observed by visible light emission from high overtone transitions. Vibrational populations and the rate constants for loss processes were deduced from observations over a wide range of wavelength and pressure fitted to a comprehensive model of the system.

Difficulties with the Maier–Saupe theory of liquid crystals
View Description Hide DescriptionThe Maier–Saupe anisotropicdispersion energy is estimated and found to be an order of magnitude smaller than the value usually assumed in the liquid crystal theory. The idea behind the estimate is to compare the anisotropic part of the dispersion energy to the average dispersion energy. This is done with the help of the relation R∼ (Δα/3α)^{2}, where R is the ratio of the perturbation theory sums involved in the anisotropic and average dispersion energies and Δα, α are the polarizabilityanisotropy and average polarizability, respectively. It is suggested that the t o t a l attractive force contributes to the stability of nematic liquid crystals through both a small change in the radial correlations and any density change at the mesomorphic transition (at constant volume the latter is zero). In the resulting picture of liquid crystals the repulsive forces play the primary role.

Theory of Fourier transform ion cyclotron resonance mass spectroscopy. I. Fundamental equations and low‐pressure line shape
View Description Hide DescriptionThe fundamental relationships for linewidth and resolution for all forms of ion cyclotron resonance spectroscopy are derived. Mass resolution and frequency resolution are shown to be numerically identical in all forms of ion cyclotron resonance spectroscopy. TheoreticalFourier transform ion cyclotron resonance (FT–ICR) spectralline shape has been calculated for the low‐pressure limit in which there are essentially no ion–molecule collisions during the observation period. Absorption, dispersion, and magnitude (absolute‐value) line shapes are illustrated and discussed. FT–ICR linewidth and resolution are calculated as a function of ionic mass and charge, applied magnetic field strength, and data acquisition time, for various linewidth criteria, and the results are tabulated. FT–ICR linewidth and resolution are then expressed in terms of ionic mass, computerdata storage size, and minimum specified ionic mass in the FT–ICR mass range, for various linewidth criteria, and the results are tabulated. Next, FT–ICR upper mass limit is calculated as a function either of ionic charge, applied magnetic field strength, and data acquisition time, or computerdata storage size and minimum specified ionic mass in the FT–ICR mass range, and the results are tabulated for several linewidth criteria. For the same observation time and linewidth criterion, FT–ICR zero‐pressure resolution is 47% better than with conventional ’’drift’’ cell or ’’trapped‐ion’’ cell ICR detection. Finally, the theoretical basis for the FT–ICR spectral segment extraction technique is described, for use in enhancing FT–ICR resolution by several orders of magnitude.

Localized orbitals and short‐range molecular interactions. IV. Nonadditivity in quartet and quintet states of hydrogen atoms
View Description Hide DescriptionThe separation of the short‐range interaction energy into Coulombic and penetration components introduced in Paper I of this series is extended to open‐shell systems of maximum spin multiplicity. A b i n i t i o calculations with a minimal set of 1s Slater orbitals are reported for the quartet state of H_{3} (isosceles triangles) and for the quintet states of tetrahedral and square H_{4}. Nonadditivity of short‐range interactions is seen to arise from the penetration of nonorthogonal localized open‐shell orbitals into the core provided by nuclei and unperturbed electrons of all other groups, a result already found for closed shells. The validity of representing nonadditive effects in terms of powers of the overlap integrals is shortly discussed.

Fokker–Planck equations for simple non‐Markovian systems
View Description Hide DescriptionExact generalized Fokker–Planck equations are derived from the linear Mori–Kubo generalized Langevin equation for the case of Gaussian but non‐Markovian noise. Fokker–Planck equations which generate the momentum and phase space probability distribution functions (pdf’s) for free Brownian particles and the phase space pdf for Brownian oscillators are presented. Also given is the generalized diffusionequation for the free Brownian particle pdf in the zero inertia limit. The generalized Fokker–Planck equations are similar in structure to the corresponding phenomenological equations. They, however, involve time‐dependent friction and frequency functions rather than phenomenological constants. Explicit results for the frequency and friction functions are given for the Debye solid model. These functions enter as simple multiplicative factors rather than as retarded kernels. Further the phase space Fokker–Planck equations contain an extra diffusive term, a mixed phase space second partial derivative, not occurring in the phenomenological equations. For short times the generalized Fokker–Planck equations reduce to the appropriate Liouville equations. For systems with long time tail decay, e.g., the hydrodynamical Brownian particle and an oscillator in a harmonic lattice, the generalized equations do not asymptotically reduce to the phenomenological equations since these latter predict exponential decay. Moreover the exact generalized equations are not equivalent to the familiar approximate generalized Fokker–Planck equations with retarded kernels except when both types of equations reduce to the phenomenological form. The value of the approximate equations with retarded kernels as an improvement upon the phenomenological equations is thus subject to question.

Some similarities between ionic states and excited states in the reaction potential surface
View Description Hide DescriptionRecent a b i n i t i o calculations on the Li+He interaction potential by Krauss e t a l. show that the interaction between the excited Li atom in its ^{2} P state and the ground state He atom is attractive and quite similar to the interaction potential between the cation Li^{+} and He. The idea of similar potential curves between a σ→π* type excited system and an ionic system is further applied to the ketone system for a qualitative study of the relative activation barriers for n,π* and π,π* states towards enolization reactions. The breakdown of the concepts of net charge dependence of the reaction activity and the deficiency of the CNDO method for the present type of interaction potential are discussed.

Electron spin relaxation of di‐tertiary‐butyl nitroxide in supercooled water
View Description Hide DescriptionThe linewidths and line shapes of electron spin resonance spectra of dilute solutions of di‐t‐butyl nitroxide in supercooled water were analyzed at temperatures ranging from 15 to −33 °C. The electron spin relaxation is mainly due to the motional effect of anisotropic magnetic interactions. The rapidly increasing linewidths at temperatures below 0 °C reflect a large temperature dependency of the viscosity of supercooled water.