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Volume 67, Issue 5, 01 September 1977

Frequency‐dependent multipole polarizabilities and reduced Green’s functions. I. The ground state hydrogen atom
View Description Hide DescriptionThe reduced free‐particle Green’s function formalism is applied to the calculation of frequency‐dependent multipole polarizabilities for the ground state hydrogen atom. A new modified polynomial fitting procedure is developed which yields satisfactory results for the polarizabilities well into the anomalous dispersion region and locates a rather large number of the excitation frequencies to high accuracy.

Effects of magnetic field on triplet state of Pt–phthalocyanine single crystal
View Description Hide DescriptionZeeman effect of the first excited triplet state in Pt–phthalocyanine single crystal is studied in the magnetic field up to 100 kG by observing the phosphorescence emission at 4.2 K. Phosphorescence peaks are observed at the wave numbers 10 289.1 and 10 297.6 cm^{−1} in the zero magnetic field at 1.7 K (zero field splitting). The zero field splitting coefficients of the triplet state are estimated from the Zeeman study to be D=−7.8±0.2 cm^{−1} and ‖E‖=0.7±0.2 cm^{−1}. The decay time of the emission peak of 10 289.1 cm^{−1} decreases with increasing magnetic field from 7 μsec at 0 G to 3 μsec at 100 kG. Z component of spin level has the largest decay rate of 3.3×10^{5} sec^{−1} at zero magnetic field. Dependence of the phosphorescence intensity and the energy shift of their peaks on the direction of the magnetic field referred to the crystal axis are also measured and compared with the theoretical calculations.

Laser fluorescence detection of nascent product state distributions in reactions of Sc and Y with O_{2}, NO, and SO_{2}
View Description Hide DescriptionThe reactions of Y and Sc with O_{2}, NO, and SO_{2} have been investigated by the laser‐induced fluorescence method. The excitation spectra are reported for metal oxide products formed under single‐collision conditions in a beam–gas arrangement. Possible systematic errors which arise in deducing the internal state distributions from the spectra are discussed. The relative vibrational populations of metal oxides for all reactions are close to unbiased statistical distributions (in the sense of the information theoretic approach). Although the rotational distributions from the reactions with NO and SO_{2} also follow statistical behavior, those from the reactions with O_{2} peak significantly lower than the statistical ones. Radiative lifetimes are reported for the A and B states of YO and ScO, and the B and C states of LaO.

Low temperature vibrational spectroscopy. I. Hexachlorotellurates
View Description Hide DescriptionFar infrared and Raman spectra of six hexachlorotellurate (IV) salts have been obtained at ∼100 K for the first time. In the rubidium, cesium, ammonium, and tetramethylammonium salts the Raman active T _{2g } cation lattice translatory mode was found. In the monoclinic K_{2}[TeCl_{6}] a number of low frequency lattice modes were observed and interpreted in terms of a phase transition near 165 K, similar to transitions in other K_{2}[MX_{6}] salts. The cubic tetramethylammonium hexachlorotellurate salt undergoes a phase transition of supposed first order at a temperature near 110 K, corresponding to transitions known in analogous uranium and tin compounds. Possible reasons for the transitions are discussed. In the low temperature phases the ν_{4} and ν_{6} bendings of [TeCl_{6}]^{2−} have been identified with bands near ∼130 and ∼110 cm^{−1}. No evidence seemed to favor any stereochemical distortion due to the lone pair of electrons present in hexachlorotellurates.

A hydrodynamic theory of light scattering in ionic solutions
View Description Hide DescriptionA linearized hydrodynamic description of concentration fluctuations in ionic solutions is formulated and is used to provide a phenomenological theory of light scattering. Our formulation takes ionic effects into account and using model calculations we are able to show that Rayleigh scattering from charge fluctuations in simple 1–1 ionic solutions should be negligible in the usual light scatteringexperiments. This then justifies the previous treatment of an electrolyte as a single nonionic solute species in comparisons with light scattering and explains the failure to detect Rayleigh scattering from charge fluctuations in these experiments. This approach is extended to calculate Rayleigh‐to‐Brillouin intensity ratios and we find that for NaCl the neglect of charge fluctuations is within experimental error. We expect this to be less satisfactory for LiCl. For 2–2 salts the neglect of ionic effects is clearly inadequate and our study indicates the appropriate theoretical description. Our estimates of the ionic contributions exhibit some improvement in comparisons to experiment but more detailed calculations await theoretical characterization of appropriate modelelectrolyte systems.

Theoretical study of the anion of lithium hydride
View Description Hide DescriptionThe potential energy curves of the ground state of LiH and LiH^{−} have been obtained by accurate a b i n i t i oconfiguration interaction calculations. The bond length, dissociation energy, and spectroscopic constants obtained from the potential curve of LiH are within 1% of corresponding experimental values. The results for LiH^{−} are R _{ e } =3.15±0.03a _{0}, D _{ e }=2.10±0.02 eV, D _{0}=2.03±0.02 eV, and ω_{ e }=1179±11 cm^{−1}. The calculated adiabatic electron affinity of LiH is 0.32 eV with an estimated error limit of ±0.02 eV. A semiempirical method for calculating diatomic molecular electron affinities is proposed. A detailed comparison of the current CI calculation with a previous equations‐of‐motion calculation is presented.

Isotopic effects on the electronic properties of H_{2}O and D_{2}O in the vacuum uv
View Description Hide DescriptionOptical and dielectric functions of liquid H_{2}O and D_{2}O at 25 °C were obtained in the 2–9.2 eV region of photon energy. The reflectance was measured for several angles of incidence at a liquid–semicylindrical‐window interface. The refractive indexn and absorption coefficientk were obtained by a least‐squares fit of calculated to experimental reflectance. The principle difference observed was the contraction of the D_{2}O spectra due to the mass effect of the heavier isotope.

Oscillations and runaway states in a closed illuminated system
View Description Hide DescriptionUsing a modelreaction mechanism we show that in a closed illuminated system one may find limit cycle oscillations and runaway states involving unbounded increase in temperature (until new physical processes become important). The model is a simplification of that used by Prigogine and Lefever to demonstrate oscillations in an open system. For our model we show that there exists an upper and lower bifurcation point for oscillation and that in the vicinity of parameter values (light intensities) for which the runaway states may occur the typical Hopf bifurcation is masked. Under conditions of multiple time scales the oscillation consists of a sequence of short time scale ’’explosions’’. The model presents itself as an ideal system for statistical mechanical studies because when the optical pathlength is short the system may be treated as a homogeneous ensemble, unlike earlier open model systems.

A model for unimolecular reaction of sulfur hexafluoride
View Description Hide DescriptionThe thermal dissociation data for SF_{6} has been re‐evaluated using RRKM unimolecular reaction rate theory and was found to be consistent with a higher value for the sulfur–fluorine bond strength (92 kcal/mole). A model based on a rate equation formalism has been developed that includes unimolecular dissociation, collisional energy transfer (V–T processes), and absorption and emission of laser radiation. The model was designed to test theories of absorption of laser radiation for laser‐induced chemical reaction in SF_{6} that are amenable to a rate equation formalism. It was found that the thermal reaction and vibrational relaxation data could be adequately reproduced. Sample calculations of laser‐induced chemical reactions are performed.

Numerical Hartree–Fock calculations for N_{2}, FH, and CO: Comparison with optimized LCAO results
View Description Hide DescriptionThe restricted Hartree–Fock equations for the ground states of N_{2}, FH, and CO were solved numerically in prolate spheroidal coordinates. The series expansions employed converge rapidly, the maxium error in our orbitals being about 10^{−5} or less. The errors in our energies are smaller than 5×10^{−4} hartree. Comparisons of the energies, dipole quadrupole moments, and cusp ratios of our wavefunctions with the best available matrix LCAO results are presented. Our solutions, in most cases, significantly improve the cusp ratios and for N_{2} and CO lower the total energies by more than 10^{−3} hartree. Orbital density difference plots indicate the existence of significant errors in the LCAO orbitals, which are most apparent in the internuclear region.

Direct determination of non‐Boltzmann vibrational level populations in electric discharges by CARS
View Description Hide DescriptionThe direct measurement of nonequilibrium vibrational level populations of N_{2} at the center of an electric discharge has been demonstrated by a new diagnostic technique: coherent anti‐Stokes Raman spectroscopy(CARS). On the assumption of a Boltzmann equilibrium among only the l o w e s t vibrational levels, a method has been developed and utilized for the direct determination of vibrational populations of all other levels, even in the case of extreme deviations from a Boltzmann equilibrium. Limitations of the method are discussed and illustrated.

Piecewise polynomial electronic wavefunctions
View Description Hide DescriptionPiecewise polynomials are examined as basis functions for electronic wavefunctions. The spline function method is a special case, which is shown to be less accurate, for a fixed set of mesh points, than a method based directly on Hermite’s interpolation formula. The determination of a suitable mesh is discussed both inductively and deductively, and a logarithmic formula for the 1s orbital of helium is ’’derived.’’ The accuracy is shown to depend on the number of points N+1 and on the polynomial order 2s+1, approximately according to the formula, δE∼N ^{−4s−2}, for appropriate meshes. A striking result is the possibility for systematically increasing the accuracy of the energy by systematically increasing the number of points, without encountering linear dependence problems, is demonstrated by calculations on the helium atom. With a 16‐point theoretically derived mesh, and with seventh order polynomials, we obtain a Hartree–Fock energy for helium of −2.8616799956122 a.u.

On entropy production in a stochastic model of open systems
View Description Hide DescriptionTwo expressions for the entropy production of a system arbitrarily far from equilibrium are considered for a stochastic model. The two expressions result from the consideration of two different definitions of the nonequilibrium entropy: the Gibbs form and the generalized form suggested by the Brussels–Austin group. The entropy principle is established briefly for isolated and then, in detail, for open systems, and the origin and form of the entropy flow is discussed.

Theoretical studies of photoionization cross sections and angular distributions for the hydrogen molecule
View Description Hide DescriptionTheoretical studies of photoionization cross sections and angular distributions are reported for the ground state of the hydrogen molecule in the photonenergy range 20–40 eV. Results are obtained using an integral equation technique recently developed by Chapman and Hayes. The method employs a partial wave expansion for the continuum wavefunction to generate a set of coupled equations which are solved exactly using an integral equation technique. Single center expansions are used for the initial and final electronic wavefunctions and exchange is treated iteratively. The results agree rather well with earlier studies of Kelly, of Ritchie, and of Hirota. Studies of the dependence of the differential cross section on molecular orientation are reported. These studies are of potential interest as a simple model for photoionization of a molecule adsorbed on a surface.

A method for the calculation of the distribution functions of dielectric relaxation times, using a deconvolution technique, applied to simulated experimental spectra
View Description Hide DescriptionThe authors use the deconvolution technique for research into distribution functions of the relaxation times of a substance. They propose a new method of smoothing and of interpolation and extrapolation of the experimental data. They recommend the use of a rectangular integration window which allows the acquisition of a good resolving capacity while taking into account experimental errors. The method of calculation used enables also the differentiation of the different types of distribution (Debye, Cole and Cole, and Cole and Davidson). The advantages of this method are illustrated by numerous examples.

Raman intensities, depolarization ratios, and polarizability derivatives: Matrix notation, relation to other molecular constants and simple isotopic rules
View Description Hide DescriptionNew matrix relations for the Raman intensities I _{ i }, the polarizability derivatives (∂?/∂Q _{ i })^{2} as well as (∂γ/∂Q _{ i })^{2}, and the depolarization ratios ρ_{ i } are presented. These matrix formulations have been utilized to relate the Raman data to other molecular constants such as the mean square amplitudes of vibration, Coriolis constants, etc. In order to serve as a check on quantum mechanical calculations the extremal properties of the derivatives of the polarizability components with respect to the symmetry coordinates S _{ i } are derived. The Jacobians related to the Raman intensities are presented with a view to study the sensitivity of the force constants to the Raman intensities. Based on the first order perturbation theory a new isotopic rule involving the change in each I _{ i }, (∂?/∂Q _{ i })^{2}, and (∂γ/∂Q _{ i })^{2} is presented to study the isotopic substitution of heavy atoms in general.

Exciton scattering processes in (1,4)‐dibromonaphthalene
View Description Hide DescriptionThe dephasing of optically prepared k?0 triplet excitons in crystalline (1,4) ‐dibromonaphthalene (DBN) has been investigated by measurement of the temperature dependence of the absorption line shape. At temperatures below 10 K the dephasing is due to scattering of the exciton by impurities or lattice defects. We show that the naturally occurring ^{13}C containing DBN molecules can make a significant contribution to this linewidth. Above 10 K the excitons are scattered by optical phonons. The most likely exciton–phonon scattering process is shown to involve a single phononscattering of the exciton between the two crystallographically inequivalent sites.

A theoretical study of the optical absorption band shape for xenon hexafluoride
View Description Hide DescriptionThe classical Franck–Condon approximation is used together with the Monte Carlo integration technique to calculate the optical absorption band shape arising in xenon hexafluoride from the pseudo‐Jahn–Teller active t _{1u } bending mode. The potential energy function for this mode has the Devonshire form for the hindered rotational motion of a diatomic molecule in a cubic site and is characterized by three parameters. Results are presented using values of these parameters as determined by Pitzer and Bernstein for the ^{1} A _{1g } electronic ground state and as estimated by us from the crystal‐field model of Wang and Lohr for the ^{1} T _{1u } and ^{3} T _{1u } electronic excited states.

Rate measurements of reactions of helium metastable species at atmospheric pressures. II. He_{2} (2 ^{3}Σ^{+} _{ u }) in pure afterglows
View Description Hide DescriptionUsing resonance absorption spectrometry the rates of the reactions He_{2}(2 ^{3}Σ^{+} _{ u })+He_{2}(2 ^{3}Σ^{+} _{ u }) →products and He_{2}(2 ^{3}Σ^{+} _{ u })+Ne→products have been measured in the afterglow period of electron beam excited discharge plasmas in helium at atmospheric pressures. The reported rate for the first reactions at (1.3±0.3)10^{−10} cm^{3} sec^{−1} is an order of magnitude lower than previously reported values. A value for the inverse transition probability of the 3 ^{3}Π_{ g }←2 ^{3}Σ^{+} _{ u } electronic transition has also been established.

An a b i n i t i o study of the phosphorescence and intersystem crossing of the lowest triplet state of pyrazine
View Description Hide DescriptionSinglet–triplet spin–orbit matrix elements have been estimated for pyrazine using molecular wavefunctions obtained by an a b i n i t i o configuration‐interaction method and minimal basis sets of Gaussian atomic orbitals. The computed radiative lifetime (10.2 ms) of the short lived component of the lowest ^{3} B _{3u } state is in good agreement with the experimental value. For the next excited triplet state (^{3} B _{1u }) a radiative lifetime is found similar to that of azine molecules in which the lowest triplet state is of ππ* nature. The spin–orbit matrix elements governing the rate constants of the T _{1}→S _{0} and S _{1}→T _{1} nonradiative processes have been evaluated.