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Volume 66, Issue 6, 15 March 1977

Medium perturbations of atomic extravalence excitations
View Description Hide DescriptionIn this paper we present the results of an experimental study of the lowest ^{1} S _{0}→^{3} P _{1} extravalence electronic excitation of atomic xenon in dense supercritical and subcritical fluid argon over the density range 0.1–1.4 g⋅cm^{−3}, spanning the temperature region 80–300°K. Solvent perturbations were characterized in terms of the spectral shift, the linewidth and the first and the second moments of the absorption band. These energetic parameters exhibit a weak temperature sensitivity and a strong density dependence. The experimental data were analyzed in terms of the semiclassical theory of line broadening extended to account for guest–host and host–host correlations and incorporating realistic pair potentials in the ground and in the excited electronic states. The semiclassical theory results in manageable expressions for the first and for the second moments of the absorption band which are expressed in terms of a difference guest–host interaction potential together with the solute–solvent and the solvent–solvent radial distribution functions. The theory provides a semiquantitative account for the weak temperature dependence and for the marked density dependence of the energetic parameters specifying solvent perturbations and was utilized to extract quite reliable information concerning the excited state Xe(^{3} P _{1})+Ar(^{1} S _{0}) potential.

Electron tunneling, charge transfer, and the intermolecular forces between two H_{2} molecules
View Description Hide DescriptionThe spherically averaged van der Waals potential for the system H_{2}–H_{2} has been calculated using a nonorthogonal CI method based on SCF orbitals for the individual molecules. With suitable restrictions on the CI calculation we have isolated various contributions to the van der Waals potential, and have found that charge transfer and dispersion effects are comparable to distances corresponding to the potential minimum. The charge transfer contribution is further discussed in terms of a mechanism involving electron tunneling through the intervening space between the molecules. Our calculation gives a spherically averaged van der Waals well depth of 2.96 meV at 3.49 Å. Experimental values are 3.00 meV at 3.49 Å.

The semiconductor model of electric conductivity applied to the supercritical mercury vapor
View Description Hide DescriptionThe semiconductormodel of electric conductivity in dense metallic vapors is modified and applied to the hard‐sphere fluid with hard spheres preserving electronic properties of mercury atoms. This fluidmodels the supercritical mercury vapor in low density limit of the semiconductor regime. Supplementary calculations of the total scattering cross section of slow electrons on mercury atoms are described. The calculated activation energy of the electric conductivity and the values of electric conductivity are in a qualitative accord with the existing experimental data for supercritical mercury vapors.

Statistical mechanics of nonspherical molecules. VIII. Hard‐core models
View Description Hide DescriptionCalculations of some properties of systems composed of nonspherical hard‐core molecules are presented. The intermolecular interactions are modeled by representing each molecule as an assemby of overlapping hard spheres. The specific cases treated include: triangles; planar squares; and linear arrays composed of three, four, and five spheres. The basic statistical property computed is exp(−potential energy/k T) for various values of separation distance and molecular orientation; the results are presented by calculating the distance dependence of the coefficients in the expansion of this quantity in a set of orthogonal functions of the Eulerian orientation angles for each molecule. A number of average properties are calculated with the aid of this function, including: second virial coefficients; the angular correlation contribution to the depolarized light scattering of dilute gases; and the deviation from the Clausius–Mosotti equation (for the dielectric constant of nonpolar fluids) that is linear in density. The properties of these fluids at high density are also calculated by invoking the blip‐function theory, as adapted to nonspherical molecules, to calculate molecular pair corrleation functions and the equation of state. Comparisons are made with the scaled‐particle equation of state for nonspherical hard‐core molecules, and the pair correlation functions are used to calculate angular correlations, depolarized light scattering, and one of the terms contributing to the deviation from the Clausius–Mosotti equation for dense fluids.

Thermotransport of ^{85}Sr and ^{54}Mn in potassium chloride single crystals
View Description Hide DescriptionThe thermotransport of ^{85}Sr and ^{54}Mn tracers in single crystals of KCl was measured in the temperature range 950–1025 K, by means of Soret effectmeasurements. The mean value of the impurity heat of transport was −3.18±0.09 eV for Sr in pure or Sr‐doped crystals, and was −5.45±0.83 eV for Mn in pure or Mn‐doped crystals. There was no significant difference between values from pure and doped crystals for Sr, but for Mn this may not be the case. A discussion of the experimental and theoretical limitations of such measurements as a source of information about the heats of transport for individual jumps was given, and a comparison made with earlier thermotransport measurements in simple ionic solids.

Reaction rate of electrons with scavengers in nonpolar liquids
View Description Hide DescriptionThe reaction rate of electrons with scavengers in nonpolar liquids is formulated using the time‐dependent perturbation theory. The rate constant is expressed in terms of the electron attachment spectrum of the scavenger, which is experimentally obtainable. The correlation of the rate constant with so‐called V _{0}, which has been experimentally observed, is satisfactorily explained by the present theory.

ESR study of molecular jumps of manganese(II) impurity in single crystals of Cs_{2}HfCl_{6} and Cs_{2}ZrCl_{6}
View Description Hide DescriptionElectron spin resonancespectra at 35 and 9.3 GHz of Mn^{2+} impurity ions in single crystals of Cs_{2}HfCl_{6} and Cs_{2}ZrCl_{6}, from 12 to about 400 K are reported. Below ∼60 K the spectrum consists of a superposition of a number of anisotropic subspectra due to crystallographically equivalent Mn^{2+} species. Each subspectrum consists of five fine structure bands, due to the different (m−1↔m) transitions, split into six hyperfine components. The spin Hamiltonian of the Mn^{2+} species in this temperature range is characterized by isotropic g and hyperfinetensors (g=2.004, A=77.0 G) and an almost axially symmetric zero field splitting (ZFS) tensor (D=470 G and E=3 G). It is suggested that the Mn^{2+} impurity that gives rise to these subspectra consists of MnCl^{3−} _{5} ions with nearly tetragonal symmetry. The various subspectra correspond to MnCl^{3−} _{5} ions whose principal ZFS tensor components point along different crystallographic axes. As the temperature is raised above 60 K conspicuous changes occur in the spectrum over an extremely wide range of temperatures: The m≠1/2 fine structure components first broaden and eventually disappear in the noise, while the m=1/2 transitions, due to the different sites, coalesce to give a singly, slightly anisotropic,hyperfine sextet. At high temperatures the full intensity of the spectrum emerges again to give a sharp isotropic sextet. The temperature dependence of the spectrum over the whole temperature range studied can be quantitatively interpreted in terms of a dynamic model in which the major ZFS tensor axis undergoes random jumps between the three crystallographic cubic directions. A general theory for the ESR line shape in the presence of such a process is derived for the case that the ZFS interactions is small compared to the Zeeman energy. Simple and explicit equations are derived for the linewidth and frequency shift in the slow jump limit for the m≠1/2 as well as the m=1/2 fine structure bands. For the fast jump limit the appropriate relaxation matrix is also derived. This theory is then used for a quantitative analysis of the experimental spectra in the CsHfCl_{6} and CsZrCl_{6} crystals, and values for the jump rate and the magnetic parameters as function of temperature are derived. It is found that as the temperature is raised from 60 to about 400 K the g value changes from 2.004 to 2.006 and D decreases monotonically from 470 to 330 G. In this temperature range the jump rate changes by about four orders of magnitude and it can be characterized by an Arrhenius plot with the following kinetic parameters: (1.τ)(300 K) =3.5×10^{11} s^{−1}, ΔE=1.4 kcal/mol. Possible mechanisms for the jump process are discussed.

Electron paramagnetic resonance of Ag^{2+} dimers in Na_{2}Zn(SO_{4})_{2}⋅4H_{2}O single crystals
View Description Hide DescriptionElectron paramagnetic resonance studies have been made on Ag^{2+} ion in Na_{2}Zn(SO_{4})_{2}⋅4H_{2}O single crystals at 300 K. Ag^{2+} is obtained by the xirradiation of Ag^{+}doped samples at ambient temperature and is found to be stable over a period exceeding one year. The EPR spectra indicate the presence of dimeric divalent silver species with the hyperfine structure with two inequivalent silver nuclei. The Ag–Ag has a singlet ground state concluded from the spectra vanishing around 100 K. The major contribution to the fine structure tensor is found to be from spin–orbit coupling.

The Raman spectrum of the ordered phase of NH_{4}Cl and ND_{4}Cl: Dipole and polarizability derivatives
View Description Hide DescriptionThe polarized Raman spectra of NH_{4}Cl and ND_{4}Cl have been observed at temperatures of the order of 25–35 K such that the crystal is in the ordered T _{ d } phase. The transverse, longitudinal frequency separations for modes ν_{3}, ν_{4}, ν_{5} (the lattice translation) and the Fermi resonant combination ν_{2}+ν_{4} in NH_{4}Cl have been used to deduce the infrared intensity parameters ∂μ/∂Q. Then, using these quantities together with an estimate of the electronic contribution to the nonlinear susceptibility, and measurements of the r e l a t i v e intensities of longitudinal, transverse Raman line pairs, we calculate ∂α/∂Q _{ j } for j=3, 4, 5. Since only the mode j=5 is well determined by this procedure, the final values of the polarizability derivatives are based upon mode 5 as an internal standard along with the intensities of the other modes relative to 5. The theory is developed on the assumption of additive molecular polarizabilities, and the ∂α/∂Q _{ j } values reported are those for vanishing local field. Both the ∂μ/∂Q and ∂α/∂Q _{ j } parameters appear to satisfy simple isotopic intensity rules. The value found for ∂α/∂Q _{1} is about 0.4 of the corresponding value in gaseous CH_{4}. Several combination and overtone bands are partially analyzed using polarization, and the components of 2ν_{6} are shown to be in excellent agreement with theory.

Statistical phase space theory of polyatomic systems: Rigorous energy and angular momentum conservation in reactions involving symmetric polyatomic species
View Description Hide DescriptionClassical formulas for the sum and density of rotational and rotational–orbital states pairs of polyatomic molecules are derived using a geometrical approach that rigorously conserves energy and angular momentum. The pair combinations considered include a spherical top in combination with either a linear, spherical, or symmetric top molecule. With the formulas presented here it is possible to perform exact classical statistical phase space theory calculations for bimolecular reactions involving polyatomic molecules. In suitable limits our results reduce to well‐known classical expressions for rotational state densities and sums or to equations previously derived by Klots using an aprroximate phase space approach. Calculations are given that demonstrate the distortions produced in the system phase space by molecular oblateness and prolateness are usually small.

Dynamics of adsorption on covered surfaces
View Description Hide DescriptionA previous model for the interaction of a diatomic molecule with a solid surface is extended to allow the treatment of three atoms interacting with the solid. The effect of an adsorbed atom on the diatom–solid surface potential is examined. The dynamics of adsorption of a hydrogen molecule in the presence of an adsorbed hydrogen atom is studied. For the potential function used, the dissociative sticking probability of the incident molecule decreases for closer collisions with the adsorbed atom.

Effect of a dissolved gas on the homogeneous nucleation pressure of a liquid
View Description Hide DescriptionAn isothermal decompression technique has been used to measure the pressure at which homogeneous nucleation of bubbles occurs in solutions of nitrogen in ethyl ether. Droplets of the ethyl ether–nitrogen solution were suspended in a host liquid by flowing the host liquid at a rate which just countered the buoyancy of the droplets. The system was then decompressed until nucleation occurred. The presence of the dissolved nitrogen in the ethyl ether was observed to raise the pressure at which nucleation occurred. The extent of the increase corresponds closely with that which has been previously predicted.

Approximate natural orbitals via the biorthogonal valence bond method
View Description Hide DescriptionA method is introduced for determining an initial approximation to the first‐order density matrix and natural orbitals of a molecular system within the valence bond formalism. The nonorthogonality problem usually associated with these calculations is avoided by using a dual biorthogonal basis set. Results of test calculations are presented and the feasibility of using this method in large‐scale natural orbital CI calculations is discussed.

Theoretical studies of atmospheric triatomic molecules: Accurate SCF vertical spectrum for valence, mixed character, and Rydberg states of CO_{2}
View Description Hide DescriptionAn accurate SCF vertical spectrum is computed for CO_{2}. Orbital sizes, electric quadrupole moments, and quantum defects are reported for the excited states. The Rydberg MO expectation values are found to be highly transferable. Spectral assignments are made for the Rydberg states based on the closeness of agreement with observed spectroscopic data.

Theoretical studies of atmospheric triatomic molecules: A b i n i t i o equations of motion excitation energies for valence states of the configuration 1π^{3} _{ g }2π^{1} _{ u } in CO_{2}
View Description Hide DescriptionPolarized and unpolarized basis set equations‐of‐motion vertical spectra are presented for the five lowest valence states of CO_{2}. In addition to the traditional solution method, an iterative diagonalization scheme is used to solve the renormalized matrix equations. The equations‐of‐motion methods depend on the basis set in much the same fashion as conventional SCF, MCSCF, and CI methods. The iterative diagonalization changes the excitation energies by ∼0.2 eV. The final polarized basis spectrum is the most accurate available for CO_{2}.

Effects of pressure on Raman‐active phonons and distortion of [ZnCl_{4}]^{2−} ions in the Cs_{2}[ZnCl_{4}] crystal
View Description Hide DescriptionPressure dependences of frequencies and Raman intensities of the zone center metal–ligand modes in Cs_{2}[ZnCl_{4}] crystal have been measured and are discussed on the basis of the results from the approximate frequency and intensity calculations. The pressure effect on the distortion of the [ZnCl_{4}]^{2−} ions and the mode anharmonicities have also been studied. The main conclusions are given in Sec. IV of the paper.

Nuclear magnetic resonance in a two‐dimensional system
View Description Hide DescriptionThe NMRtheory for a two‐dimensional (2D) system of spins coupled by dipolar interaction and undergoing diffusive motion is presented. The correlation functions (c.f.) of the dipolar coefficients are split in two parts: a ’’slow’’ one and a ’’fast’’ one. The c.f. are also written in a form which allows easy prediction of the angular dependence of the relaxation rates. It is demonstrated that, owing to the diffusion process, the slow part decays at long times as t ^{−1} and the fast one as t ^{−2}. Measurements of T _{2}, T _{1}, T _{1ρ} on the protons of nitric acid intercalated in graphite have been performed in the temperature range −153 °C,+18 °C. The prediction of the model was checked both in the solid phases (where ω_{0}τ_{ D }≫1 with τ_{ D }= diffusionalcorrelation time) and in the ’’liquid’’ phase (above −20 °C). The measurements at room temperature prove, over several decades of frequency, the logarithmic divergence of the slow part‐spectral density for ω→0. Also in the solid phases, the 2D‐diffusive model interprets the measurements. Using the experimental results, we can illustrate the angular dependence of the relaxation rates that are predicted by the theory for planar systems in different dynamical situations. The information given by NMR on graphite nitrate are also discussed.

Determination of exchange parameters of Cr^{3+} pairs in MgAl_{2}O_{4} by optical measurements
View Description Hide DescriptionThe emission and luminescence excitation spectra of nearest‐neighbor Cr^{3+} pairs in spinel MgAl_{2}O_{4} have been studied. Analyses of these spectra yield the (^{4} A _{2}, ^{4} A _{2}) ground statelevel splittings. They are described by −JS̄_{1}⋅S̄_{2}+j (S̄_{1}⋅S̄_{2})^{2}, with S _{1}=S _{2}=3/2, J=−(29±3) cm^{−1}, and j=−(3±2) cm^{−1}. A couple of transitions to the first excited pair state (^{4} A _{2}, ^{2} E) have been observed in the excitation spectrum; however, the data are insufficient to determine the parameters describing the exchange splittings of the excited state.

Comparison of final state approximations in the calculation of total and differential photoemission cross sections of neon
View Description Hide DescriptionDifferential photoemission cross sections for the 1s, 2s, and 2p shells of neon were calculated by several different approximations for photon energies up to 2000 eV. Specifically, plane wave (PW), orthogonalized plane wave (OPW), and Hartree–Fock functions (with and without consideration of relaxation in the final ionic state) were used to compute transition matrix elements in both velocity and length approximations. Plane wave and orthogonalized plane wave continuum functions were found to have very limited applicability to cross section calculations, with both approximations giving spurious local minima and incorrect angular distributions. The reasons for these failures were analyzed, and limits were set on the n, l, and z values for which the PW model yields qualitatively correct total cross sections. Calculations using Hartree–Fock continuum functions agree very well with experiment, emphasizing the necessity of considering atomic potentials explicitly in photoemission processes. Further, the effects of relaxation in the final bound system were investigated. They were small for valence electrons and only slightly more important for Ne 1s core electrons. Applications of these findings to photoemission from molecules and absorbates are discussed briefly.

Anomalous emission in the blue wings of sodium and rubidium lines
View Description Hide DescriptionAbsorption spectroscopy of the high temperature shock heated vapors of Rb and Na has shown that certain lines of these metals may appear partly in absorption and partly in emission. The lines concerned are the 5890/5896 Å doublet of Na, and the Rb lines at 6298, 6206, 6160, 6071 Å. In all cases the anomalous emission arises in the blue ’’wing’’ of the line. Mechanisms to account for this phenomenon are put forward.