Index of content:
Volume 70, Issue 3, 01 February 1979

On the contribution of angular momentum polarization to gas phase thermal conductivity
View Description Hide DescriptionThe qualitative theory of the Senftleben effects [Coope and Snider, J. Chem. Phys. 57, 4277)], as applied here to the thermal conductivity, is used to stress the generality with which the contribution of angular momentumpolarization to the thermal conductivity can be determined from the field dependence of the thermal conductivity.

Diffusion and relaxation kinetics in stochastic models for crystal growth
View Description Hide DescriptionThe combined influence of relaxation and diffusion processes on the dynamic behavior of stochastic models for crystal growth is systematically investigated. The models are the kinetic Ising model, the discrete Gaussian model, and the SOS–Kossel model. The relaxation kinetics are introduced by single‐site transition probabilities to account for adsorption and evaporation. The diffusion kinetics are introduced by two‐site transition probabilities to account for nearest‐neighbor exchange. The kinetic equations are studied by Monte Carlo simulation, quasichemical(pair) approximation (QCA), and high temperature expansion. The diffusion is found to generally enhance the growth rate of the crystal. In the range of validity of the QCA, i.e., outside the nucleation regime, the results are in very good quantitative agreement with previous Monte Carlo simulations. In the limit of infinite diffusion speed the growth rate approaches the Wilson–Frenkel rate. The local roughness or surface energy is reduced if surfacediffusion occurs. The relative influence of diffusion on the response of the system to a chemical potential difference between the two phases depends significantly upon the particular type of transition probability. For the homogeneous Glauber–Ising chain no influence of the diffusion upon the dynamic behavior could be detected.

Ionic clusters isolated in a metal matrix: The structure and vibrational frequencies of Rb_{9}O_{2} and Cs_{11}O_{3} clusters in alkali metal suboxides
View Description Hide DescriptionThe stable configurations of Rb_{9}O_{2} and Cs_{11}O_{3} clusters are determined by minimizing the total energy assuming purely ionic, two particle interactions. The calculated interatomic distances and angles are found to correspond very closely with those which have been determined from a crystallographic study of alkali metal suboxides. Raman spectra are reported for Rb_{9}O_{2}, Cs_{11}O_{3}, Cs_{7}O, and Rb_{7}Cs_{11}O_{3} and a comparison made with vibrational frequencies calculated using the same ionic model. The agreement is good. These results offer further evidence that the crystalline alkali metal suboxides may be thought of as composed of independent ionic clusters isolated in a metallic environment.

The orthogonal gradient method. A simple method to solve the closed‐shell, open‐shell, and multiconfiguration SCF equations
View Description Hide DescriptionA new, simple and efficient method of solving closed‐shell, open‐shell, and multiconfiguration SCF orbital equations is presented. It is based on the orthogonal gradient approach introduced originally in conjunction with the maximum overlap principle. Semiempirical test calculations show that the method converges rapidly.

Numerical SCF method for the calculation of static polarizabilities and hyperpolarizabilities for atoms, He through Ne
View Description Hide DescriptionThe static polarizabilities and hyperpolarizabilities for the ground states of first row atoms, helium through neon, have been calculated solving the SCF equations of an atom in an electric field by numerical integration of coupled one dimensional differential equations using the Numerov method in matrix form. The calculated polarizabilities agree within 2% with the values obtained by basis function methods. Heretofore only the hyperpolarizabilities of helium, lithium,beryllium, and neon have been calculated. For helium the hyperpolarizability is in good agreement with previous calculations, whereas for beryllium and neon the values obtained by basis function methods are scattered and significantly lower than the values we obtain. Comparison with experimental results for neon indicates that the Numerical Hartree Fock (NHF) method leads to a better representation of polarized orbitals than the use of basis function methods, which require tedious nonlinear optimization of large basis sets.

Resonance fluorescence, Raman spectra and relaxation of single vibronic levels in the condensed phase: Azulene in naphthalene
View Description Hide DescriptionResonancefluorescence and Raman spectra for excitation of single vibronic levels of the first excited singlet state of azulene in a naphthalene mixed crystal at 2 K are described. The intensity distributions for the resonanceemission spectra were used to verify and in some cases reassign previously proposed correlations of the ground and excited state a _{1} modes. Relaxed fluorescence from levels populated via vibrational relaxation from the resonant vibronic level was observed and measurements of the population ratios for the vibronic levels relative to the zero‐point level are given. From these ratios the following two conclusions were made. (1) In addition to the zero‐point level, only strongly absorbing nearby vibronic levels are significantly populated through vibrational relaxation from the resonantly pumped level for excitations up to ≈1560 cm^{−1} above the zero‐point level. This suggests that there is little cascading within the S _{1} vibrational manifold and that vibrational relaxation occurs largely by V–V energy transfer to the naphthalene host modes. (2) The measurements of the population ratios indicate that the vibrational relaxation times of most of the pumped levels are longer than the mean nonradiative decay time for the levels into which their relaxation occurs. When the nonradiative decay time is taken as 2.6 ps, the following values for the total vibrational relaxation times of the lower a _{1} vibronic levels were found: 8.7 (384), 7.4 (665), 10.8 (856), 1.3 ps (912). Comparison of the relative intensities of the Raman scattering and relaxed fluorescence from the zero‐phonon level upon excitation of the phonon sideband of the 0–0 transition led to a value of ≈0.2 ps for the phonon relaxation lifetime. Spectral distinctions between resonanceRaman scattering and fluorescence were examined through the temperature dependence of the spectrum of the emission onto the 825 cm^{−1} ground state vibrational level over the range 4.2–35 K. The total dephasing decay constant T _{2} was calculated from the ratio of the contributions of the fluorescence and Raman scattering to the emission and from the fluorescence linewidth at various temperatures. The values ranged from ≈5.4 ps at 4.2 K to ≈1.5 ps at 35 K and were similar at a given temperature for both methods of calculation indicating that the same dephasing mechanisms are responsible for both effects. The temperature dependence of the fluorescence linewidth and frequency shift is consistent with mechanisms of dephasing involving phonons of either a single mode or all thermally accessible modes. Finally, vibrational and electronic dephasing are compared.

First‐order diffusive effects in the coagulation of colloidal suspensions
View Description Hide DescriptionSolutions to an infinite system of reaction–diffusion equations associated with colloidal coagulation are obtained by incorporating first‐order diffusive effects into restricted diffusion‐free initial value problemsolutions. It is shown that this method of approximation yields explicit asymptotically exact solutions for sufficiently small values of time. In addition, the diffusion‐corrected solutions are recast in closed form by assuming that the diffusivity of the m‐fold aggregates is given by D _{ m }=D _{ m } ^{−δ}, where D and δ are positive constants.

Electron spin resonance of polyacetylene and AsF_{5}‐doped polyacetylene
View Description Hide DescriptionThe results of an electron spin resonance(ESR) study of trans‐polyacetylene, before and after doping with AsF_{5}, are reported. The undoped polymer exhibits a Lorentzian line (g=2.00263) indicative of motional narrowing from a mobile unpaired electron species. Measurement of the intensity indicates a Curie law susceptibility with approximately one unpaired electron per 3×10^{3}carbon atoms in agreement with earlier studies. From these results and comparison with earlier data on the c i spolymer, it is suggested that the ESR signal arises from a mobile defect in the π system. Utilizing an apparatus which allows i n s i t u AsF_{5}doping of a polyacetylene sample in the microwave cavity, we have monitored the ESR signal during the doping process. The spin resonance line narrows and increases in intensity, with no detectable g shift, as the doping proceeds. At high doping levels the line becomes asymmetric with a characteristic Dysonian line shape consistent with metallic behavior.

The temperature dependence of electron attachment to N_{2}O in the gas phase
View Description Hide DescriptionThe temperature dependence of electron attachment to N_{2}O has been measured in the gas phase for pure N_{2}O and N_{2}O–C_{2}H_{6} and N_{2}O–neopentane mixtures. The rate constant found for e ^{−}+N_{2}O→N_{2}+O^{−} can be expressed as 2.2×10^{−7} exp(−5.18×10^{3}/T) cm^{3}/molecule⋅sec while that for e ^{−} +N_{2}O→N_{2}O^{−*} is 4.2×10^{−9} exp(−2.65×10^{3}/T) cm^{3}/molecule⋅sec. The corresponding activation energies are 0.44 and 0.23 eV. The latter value is discussed by reference to recent calculations on the N_{2}O^{−} energy surface. Formation of N_{2}O^{−*} with such an activation energy seems possible. The temperature dependences of other reactions in the overall mechanism are also determined. Certain rate constants increase with a decrease in temperature. Formation of negative ion complexes is suggested to account for the observation.

Electron escape depths of organic solids. II. The energy dependence of naphthacene and perylene films
View Description Hide DescriptionThe energy dependence of the electron escape depth of naphthacene and perylene depositedfilms has been measured by an overlayer technique. Energy distribution curves of transmitted electrons through deposited organic layers were obtained by differentiating the I–V characteristic curves, and the electron escape depths classified by their kinetic energies were obtained from the above results. Presently obtained escape depth is between 8 and 15 nm for naphthacene and between 30 and 37 nm for perylene. They differ from our previous results, and the reason for this discrepancy is discussed.

Rate constant for the reaction of atomic chlorine with formaldehyde from 200 to 500 K
View Description Hide DescriptionThe absolute rate constant for the reaction of atomic chlorine with formaldehyde has been measured from 200 to 500 K using the flash photolysis–resonance fluoresence technique. The results were independent of substantial variations in [H_{2}CO], total pressure (Ar) and flash intensity (i.e., initial [Cl]). The rate constant was shown to be invariant with temperature, the best representation for this temperature range being k _{1}= (7.48±0.50) ×10^{−11} cm^{3} molecule^{−1} s^{−1}, where the error is one standard deviation. This result is compared with the only previous determination of k _{1}, which was a relative value obtained at 298 K. The rate constant is theoretically discussed and the potential importance of the reaction in stratospheric chemistry is considered.

Series solutions and the variational principle
View Description Hide DescriptionThe B matrix method of Frost for solution of nonseparable Schrödinger equations is used in combination with the upper bound theorem for linear variation functions to show that series solutions are possible in the general case without explicit evaluation of integrals. The procedures are illustrated with calculations on the hydrogen‐molecule ion, with some discussion of the helium atom.

Electron attachment to perfluorocarbon compounds. I. c‐C_{4}F_{6}, 2‐C_{4}F_{6}, 1,3‐C_{4}F_{6}, c‐C_{4}F_{8} and 2‐C_{4}F_{8}
View Description Hide DescriptionElectron attachment rates αw, as a function of the pressure‐reduced electric fieldE/P _{298} and mean electron energy <ε≳ have been measured for trace amounts (<10^{−3} Torr) each of c‐C_{4}F_{6} (perfluorocyclobutene), 2‐C_{4}F_{6} (perfluoro‐2‐butyne), 1,3‐C_{4}F_{6} (perfluoro‐1,3‐butadiene), c‐C_{4}F_{8} (perfluorocyclobutane), and 2‐C_{4}F_{8} (perfluoro‐2‐butene) in mixtures with N_{2} (pressures 500–2000 Torr) and Ar (pressures 500–1500 Torr) at T=298°K. The thermal attachment rates for these molecules were found to be 4.89×10^{9}, 1.77×10^{9}, 4.26×10^{9}, 4.05×10^{8}, and 1.56×10^{9} sec^{−1} Torr^{−1}, respectively. From the αw (<ε≳) data, the attachment cross sections σ_{ a }(ε) as a function of electron energy ε have been determined using the swarm‐unfolding technique and are reported. For all five perfluorocarbon molecules, σ_{ a }(ε) are very large. They exhibit three distinct negative ion resonances with maxima at: ∼0.0, 0.19, and 0.80 eV for 2‐C_{4}F_{6}; ∼0.0, 0.17, and 1.04 eV for 1,3‐C_{4}F_{6}; ∼0.0, 0.22, and 0.48 eV for c‐C_{4}F_{8}; and ∼0.0, 0.18, and 0.59 for 2‐C_{4}F_{8}. For c‐C_{4}F_{6}, only a shoulder with a possible maximum at ∼0.14 eV was observed, in addition to the maxima at ∼0.0 and 0.71 eV. Although the positions of the maxima in σ_{ a }(ε) vary only slightly among these compounds, the magnitude of σ_{ a }(ε) depends strongly on structure.

Electron attachment to perfluorocarbon compounds. II. c‐C_{5}F_{8}, c‐C_{6}F_{10}, c‐C_{6}F_{12}, C_{7}F_{8}, and C_{8}F_{16}: Relevance to gaseous dielectrics
View Description Hide DescriptionElectron attachment rates αw as a function of the pressure‐reduced electric field have been measured for c‐C_{5}F_{8} (perfluorocyclopentene), c‐C_{6}F_{10} (perfluorocyclohexene), c‐C_{6}F_{12} (perfluoro‐1,2,‐dimethylcyclobutane), C_{7}F_{8} (perfluorotoluene), and C_{8}F_{16} (perfluoro‐1,3‐dimethylcyclohexane). The thermal values (αw)_{ther} of the attachment rate for these compounds are 12.8, 12.9, 5.0, 9.2, and 2.4×10^{9} sec^{−1} Torr^{−1}, respectively. The electron attachment cross sections σ_{ a }(ε) as functions of the electron energy ε have been determined using the swarm‐unfolding technique; they show distinct structure at ε<1.5 eV. The electron attachment properties for the perfluorocarbons (PFCs) studied in this and the preceding paper depend strongly on the molecular structure. Thus (i) open‐chain saturated PFCs do not attach electrons as efficiently as the unsaturated PFCs; (ii) for saturated PFCs an increase in molecular size (chain length) increases αw; (iii) the presence of multiple bonds in the molecule dramatically increases the magnitude of αw for the saturated open‐chain PFCs, but it has only a small effect for cyclic PFCs; (iv) the cyclic nature of the PFCs seems to increase greatly σ_{ a }(ε); and (v) for single‐bonded cyclic PFCs, substitution of CF_{3} groups for F atoms increases (αw)_{ther} more than does an increase in molecular size; in double‐bonded cyclic compounds increase in ring size increases σ_{ a }(ε) at thermal energies. The PFCs studied in this and the preceding paper have higher dielectric strengths than SF_{6}. This improvement in dielectric strength can be attributed to their large σ_{ a }(ε) over a wider energy range (to ∼1.5 eV). Their use as unitary gases and/or as additives to multicomponent gas mixtures is discussed.

Valence and Rydberg excited states of H_{2}S: An SCF‐Xα‐SW molecular orbital study
View Description Hide DescriptionSCF‐Xα‐SW calculations have been performed for H_{2}S in the ground state, in ionic states resulting from the vertical removal of a valence electron, and in 36 singlet and triplet excited states resulting from the vertical excitation of an electron from the 2b _{1} or the 5a _{1} molecular orbitals to various virtual orbitals. Excellent agreement for the transition energies is found both with the experimental ultraviolet and photoelectron spectra and with recent large‐scale configuration interaction calculations. The average absolute difference between the Xα‐SW and CI results for the 26 cases where both exist is only 0.24 eV. The intrinsic advantages of the Xα‐SW method over the traditional LCAO or one‐center approaches for the treatment of Rydberg states are delineated. Contour plots of the excited orbitals have been generated and these are used to illustrate some of the conceptual problems related to the Rydberg‐valence distinction. Finally, a brief speculative discussion of the possible photochemical implications of the character of the two excited orbitals involved in the first absorption band is given.

Infrared laser photochemistry of silane
View Description Hide DescriptionThe infrared photochemistry of silane has been investigated using CO_{2} TEA laser excitation. Energy deposition measurements show that only 1.5 photons/molecule are absorbed at a pressure of 1 Torr and a P (20) fluence of 0.8 J/cm^{2}, while at 10 Torr 7.5 photons/molecule are absorbed. The visible luminescence that accompanies the dissociation of silane is due to molecular and atomic hydrogen. The thresholds for both luminescence and dissociation increase sharply as the pressure drops below 5 Torr, indicating that dissociation is a collisional process. Silane d _{1} and d _{2} have been produced by irradiating silane–deuterium mixes.

Limiting behavior of ^{2}H spin lattice relaxation in molecules with multiple internal rotations
View Description Hide DescriptionExpressions for the dependence of deuteron relaxation times for CD bond vectors on the number of internal rotations, N + 1, in polymeric chains and side chains of micelles and phospholipid vesicles have been derived for large N. The expressions are valid for molecules in which : (i) the diffusiontensors have ellipsoidal symmetry,(ii) all angles between successive pairs of internal rotation axes are equal, and (iii) the internal rotations are independent and all diffusion coefficients for internal rotation are equal. For molecular entities with spherically symmetric rotational diffusiontensors, the asymptotic relation simplifies to the following relation: where D _{ O } is the rotation diffusion coefficient, D the diffusion coefficient for internal rotation, ω_{0} is the magnetic resonance frequency, and Q _{ D } is the quadropole coupling constant for the CD bond vector. For hydrocarbon chains the relaxation rate is within 10% of its asymptotic value for relatively small N (about 6) and converges rapidly to the asymptotic relaxation rate as N is increased.

Lattice vibrational motion in tetracyanoquinodimethane (TCNQ): A ^{14}N nuclear quadrupole resonance study
View Description Hide DescriptionThe mean square angular amplitudes of motion are obtained from the analysis of the ^{14}N nuclear quadrupole resonance thermal averaging in pure TCNQ. The temperature dependence of the mean square angular amplitudes is given. The results are compared with those found at room temperature by x ray by Long e t a l. [Acta Cryst. 18, 932 (1965)].

On the calculation of polyatomic Franck–Condon factors: Application to the ^{1} A _{1g }→^{1} B _{2u } absorption band of benzene
View Description Hide DescriptionTwo methods for calculating polyatomic Franck–Condon integrals are reported. The first method uses a coordinate transformation on the normal coordinates of both the ground and excited electronic states. This transformation effectively removes any Duschinsky mixing and allows the multidimensional Franck–Condon integral to be written as a sum of integrals each of which is a product of one‐dimensional harmonic oscillator overlap integrals. The second method uses contact transformationperturbation theory to construct a representation of the vibrational wavefunctions. With this representation, the calculation of a polyatomic Franck–Condon integral involves evaluation of matrix elements exclusively within the ground electronic state vibrational manifold. Application of both methods is made to the A ^{0} _{ n } vibronic series of the ^{1} A _{1g }→^{1} B _{2u } symmetry‐forbidden electronic transition of benzene. Relative intensities calculated by either method agree well with observed values. However, the computational efficiencies of the two methods are found to be markedly different, with the perturbation method being the least efficient.

Kinetics of swelling of gels
View Description Hide DescriptionWe present a theory of the kinetics of the swelling of a gel. The characteristic time of swelling is proportional to the square of a linear dimension of the gel and is also proportional to the diffusion coefficient of the gel network, which is defined as D=E/f where E is the longitudinal bulk modulus of the network, and f is the coefficient of friction between the network and the gel fluid. This constitutes an essential difference between the present theory and the previous theory which is based on the assumption that the swelling time is determined by the diffusion coefficient of the fluid molecules. Experimental data are shown for spheres of 5% polyacrylamide gels and are analyzed using the present theory. The value of the diffusion coefficient obtained from the macroscopic swelling experiments shows excellent agreement with that obtained microscopically using laser light scatteringspectroscopy.