Index of content:
Volume 64, Issue 7, 01 April 1976

Isotope effects in superionic conductors
View Description Hide DescriptionA quantum mechanical calculation of the conductivity of a simple model of a superionic conductor which considers short range interactions betweetn the mobile ions is p’resented. This model yields results which depend strongly on the nuclear spin on the mobile ion. In principle, this isotope dependent conductivity could lead to isotope separation. In practice, ignored interactions between the mobile ions and the nonmobile ions in the lattice could mask this effect.

Studies on the charge transfer spectrum of Co^{++} in KCl
View Description Hide DescriptionSystematic experimental measurements have been carried out on the crystal field and charge transfer spectra for divalent cobalt ions in a series of alkali halide crystals. The influence of divalent lead ions on these spectra has also been investigated. Additionally, the spectrum of Co^{++} in acetone with LiCl has been studied and the charge transfer band is found to be absent. The analysis of these measurements and earlier data indicate that the interstitial model for the cobalt complex in KCl proposed in the literature is unsatisfactory. An alternate model involving regions in which double salts (such as M_{2}CoCl_{4}) are present is shown to successfully explain the available data.

Influence of molecular nonrigidity on the infrared absorption and Raman scattering line shape in dense media
View Description Hide DescriptionStarting from the well‐known infrared absorption and Raman scattering line shape expressions, the two situations where a complete frequency degeneracy (unresolved isotropic Raman band) is or is not present (absorption band, anisotropic Raman band, and resolved isotropic Raman band) are examined. Thus the influence of the nonrigidity of the interacting molecules on the line shape is studied. The physical mechanisms responsible for the dependence of the profiles upon the internal molecular vibrations are carefully analyzed. An application to the spectra of a diatomic molecule trapped in a rare gas crystal is made and the vibrational broadening of HCl and CO embedded in Ar, Kr, and Xe crystal is calculated.

The interaction of ions with nonpolar neutrals: The collision broadening of ion cyclotron resonance lines of ions in hydrogen and methane
View Description Hide DescriptionThe motion of ions in an ion cyclotron resonance cell is considered, and measurements of ion cyclotron resonancelinewidths are described. The connection between cyclotron resonancelinewidths and kinetic parameters is developed. Mobilities and collision frequencies of CH_{5} ^{+}, C_{2}H_{5} ^{+}, C_{3}H_{7} ^{+}, C_{4}H_{9} ^{+}, and Na^{+} in methane and H^{+}, H_{3} ^{+}, H_{3}0^{+}, CH_{5} ^{+}, C_{2}H_{5} ^{+}, C_{3}H_{7} ^{+}, and Na^{+} in hydrogen are determined from the linewidth measurements. Resulting mobilities of H^{+}, H_{3} ^{+}, and Na^{+} in H_{2} are found to agree well with drift tube measurements, in contrast to previous cyclotron resonancelinewidth determinations. The mobilities are interpreted in terms of three model ion molecule interaction potentials. The mobilities are found to be in general consistent with both a three term 12–6–4 potential and an acentric potential but not with the simple polarization potential. Potential parameters consistent with binding energies from the literature and the present mobility measurements are reported for H_{3} ^{+}–H_{2}, CH_{5} ^{+}–CH_{4}, and C_{2}H_{5} ^{+}–CH_{4}.

An electron paramagnetic resonance study of methylene
View Description Hide DescriptionThe present paper is a detailed account of the study of the methylene molecule trapped in matrices at 4.2 °K by electron paramagnetic resonance spectroscopy. The methylene is generated by photolysis of its diazirine precursor dissolved in the matrix material. Besides verifying that the methylene ground electronic state was a spin triplet, the first observation of the EPRspectrum revealed that the molecule was nonlinear. Through assumptions concerning the amounts of spectral averaging owing to molecular motion and the relationship of the zero‐field splitting parameters D and E with each other through an s–p hybrid model of the electronic structure, other workers showed the bond angle to be substantially bent. This was later confirmed by ourselves and others with a measurement of the isotropic carbon‐13 hyperfine interaction. Using 90.5% carbon‐13 enrichment in the present work, a more precise determination of the isotropic carbon‐13 hyperfine interaction was found to be 239 MHz. The increased resolution also permits a measurement of the anisotropic carbon‐13 hyperfine interaction from which a bond angle of 134° can be derived. All three methods of bond angle determination are in substantial agreement. Chemical trapping of the products of the photolysis with a 100% mass balance accounting for all substances supplement the EPR of the isotopically substituted species to show conclusively that the trapped paramagnetic species is methylene. Experiments in a nonnuclear magnetic matrix show that the linewidths are not due to hyperfine interactions with matrix nuclei. In addition to xenon matrices, experiments in krypton and xenon–krypton mixtures are reported where the observed zero‐field splitting parameters are modified by molecular motion and interaction with the trapping matrix. The present work also verifies that the heat of formation of methylene is 91.9±1.0 kcal/mole.

Nonrandomization of energy at high pressures in photochemical systems
View Description Hide DescriptionA general mechanism which explains the effects of high pressures on photochemically induced unimolecular reactions is proposed. As an example, the photochemically induced unimolecular decomposition of cycloheptatriene is discussed in great detail. It is shown that if both random and nonrandom channels for decomposition are postulated, the caluclated results show the leveling off behavior found in the experimental Stern–Volmer plot.

Theoretical study of the binding of an electron to a molecular dipole: LiCl^{−}
View Description Hide DescriptionAb initio calculations are carried out to determine the nature of the binding of the LiCl anion. The extra electron.is found to be in a predominantly nonbonding orbital on the lithium end of the molecule and the calculations predict an electron affinityu of LiCl of 0.54 eV. This is in good agreement with the experimental value of 0.61 eV, which has been recently determined by Carlsten, Peterson, and Lineberger. The ab initio results are discussed in light of the finite dipole model.

Absolute elastic differential electron scattering cross sections in the intermediate energy region. III. SF_{6} and UF_{6}
View Description Hide DescriptionA recently developed technique has been used to measure the ratios of elastic differential electron scattering cross sections (DCS) for SF_{6} and UF_{6} to those of He at electron impact energies of 5, 10, 15, 20, 30, 40, 50, 60, and 75 eV and at scattering angles of 20° to 135°. In order to obtain the absolute values of DCS from these ratios, He DCS of McConkey and Preston have been employed in the 20° to 90° range. At angles in the 90° to 135° range the recently determined cross sections of Srivastava and Trajmar have been utilized. From these DCS, elastic integral and momentum transfer cross sections have been obtained.

An eigenfunction expansion method for the analysis of exponential decay curves
View Description Hide DescriptionA method is developed for the analysis of data composed of random noise, plus an unknown constant ’’baseline,’’ plus a sum (or an integral over a continuous distribution) of exponential decay functions. It is based on the expansion of the solution of a Fredholm integral equation of the first kind in the eigenfunctions of the kernel. In contrast to the Fourier transformsolution [Gardner e t a l., J. Chem. Phys. 31, 978 (1959)], the finite time range of the data is exactly accounted for, and no extrapolation or iteration is necessary. A computer program is available for the analysis of sums of exponentials. It is completely automatic in that the only input are the data (not necessarily in equal intervals of time); no potentially biased initial estimates of either the number or values of the amplitudes and decay constants are needed. These parameters and their standard deviations are decided with a linear hypothesis test corrected approximately for nonlinearity. Tests with simulated two‐, three‐, and four‐component data containing pseudorandom errors indicate that the method has a wide range of applicability.

A note on semiclassical bound states and correspondence principles
View Description Hide DescriptionSemiclassical bound statetheory is considered from the viewpoint of the phase space representations of quantum mechanics. In the small h/ limit, within a representation defined by the ordering chosen for the noncommuting position and momentum operators, we obtain: (1) equations of motion, which need not be classical and (2) correspondence principles in action‐angle variables, regarded as those initial conditions on the equations of motion which dominate in the small h/ limit. The Weyl ordering is seen to generate the classical equations of motion and the normal correspondence result. Possible evaluation of semiclassical bound state energies is discussed by means of the eigenvalue approach to classical mechanics used by Prigogine and co‐workers.

Internal coordinate formulation for the vibration–rotation energies of polyatomic molecules
View Description Hide DescriptionThe vibration–rotation energies of polyatomic molecules are obtained under the assumption of small oscillations using curvilinear internal coordinates for the vibrational degrees of freedom. The use of curvilinear coordinates introduces anharmonic terms into the vibrational kinetic energy and gives second derivative terms for the moments of inertia that include the motion of an atom along its natural curved path during vibration. Coordinate transformation of the intramolecular potential energy is unnecessary. Perturbation expansion is used to obtain all of the vibration–rotation coefficients, α^{ i } _{ k }, χ_{ k k }, χ_{ k k′}, χ_{l} _{ s l } _{ s }, χ_{l} _{ s l } _{ s }, for linear, symmetric top, and asymmetric top molecules. Vibration–rotation constants are given for the linear X_{2}Y and XYZ and nonlinear X_{2}Y molecules in terms of the molecular structure.Analysis is made of the vibration–rotation and anharmonic vibrational coefficients using previously determined anharmonic force constants for CO_{2} and H_{2}O. Partial analysis of vibration–rotation coefficients is made for additional molecules.

A new approach to time‐dependent perturbation theory
View Description Hide DescriptionA time‐dependent perturbation theory for the solution of the time‐dependent Schrödinger equation is developed and is applied to systems having two states with pulse and Lorentzian types of perturbations. It is shown in the case of the pulse perturbation that the expression corresponding to the Nth order of the perturbation theory converges to the exact solution when N tends to infinity. The results obtained from this perturbation theory, the Magnus approximation, and the time‐dependent perturbation theory developed by Dirac are compared with the exact results. This theory is found to be good for larger values of the perturbations and for larger intervals of time.

Dynamic corrections for neutron scattering from molecular fluids
View Description Hide DescriptionThe Placzek corrections for neutron scattering from atomic systems have been generalized to include molecular fluids. The correction terms include spherical Bessel functions of the zeroth and second order. As a consequence, the dynamic corrections for molecular systems show sizeable oscillations with a period determined by the internuclear distances within a molecule. These results are compared with neutron diffraction data for liquid carbon tetrachloride.

Large perturbations and nonexponential decays in spin relaxation. Applications of the memory function theory
View Description Hide DescriptionOur memory function theory of time correlation functions [J. Chem. Phys. 62, 2098 (1975)] is applied to two problems which are met in the theory of protonrelaxation in aqueous solutions of Ni^{++}. In this system the modulation of the zero‐field splitting (zfs) which drives the electron spin relaxation is neither small enough nor fast enough for the usual second‐order perturbation calculation to be accurate or for the relaxation to obey Bloch’s equations. Here the perturbation series for the memory function is rearranged to give a new series which converges rapidly even when the perturbation is large. This result is exact for a particular model for the modulation process and for vanishing external magnetic field. It is applicable as an approximation method more generally. When the Solomon–Bloembergen equations are used to calculate the relaxation rates of the protons due to interaction with the electron spins, and the latter do not obey Bloch’s equations, then we show how the electron spin relaxation times and Larmor frequency are to be replaced by ’’effective’’ parameters which now depend upon the modulation of the proton–electron spin interaction as well as on the field and the parameters of the zfs interaction. Finally, calculations for protonrelaxation rates based on the new theory are compared with those done in a standard way for the case of interest.

Studies of molecular motions of CH_{2}Br_{2} in the liquid state by depolarized Rayleigh and Raman scattering
View Description Hide DescriptionWe have obtained from the concentration dependent depolarized Rayleigh scatteringexperiment (using a Fabry–Perot interferometer) the single particle reorientation relaxation time τ_{ s } of CH_{2}Br_{2} to be 3.4±0.2 psec at 20 °C. This time is a factor of 2.0 greater than the Raman correlation time τ_{ m } obtained for the ν_{2}(A _{1}) Raman band. Moreover, the Raman correlation times τ_{ m } obtained for the other A _{1} bands do not have the same values as that obtained for the ν_{2} band. This difference is due to the fact that the nonreorientational correlation functionsC _{iso}(t) and C _{β}(t) do not have the same time dependence, hence making the usual Raman line shape analysis difficult to apply to CH_{2}Br_{2}. From depolarized Rayleigh scattering, we have found in neat CH_{2}Br_{2} that the classical Stokes–Einstein relation for rotational diffusion does not apply, despite the fact that τ_{Ray} was found to vary linearly with η/T. However, when using the slip boundary condition and modeling CH_{2}Br_{2} as an ellipsoid, we have found reasonable agreement between theory and experiment. This work is the first temperature dependent study of molecular motion in simple liquids involving the joint use of the Rayleigh and Raman scattering techiques. We have shown that by combining results from temperature and concentration dependent Raman and depolarized scatteringexperiments, significantly more information concerning molecular motions can be obtained than is possible from either technique alone.

A collinear analytic model for atom–diatom chemical reactions
View Description Hide DescriptionA collinear analytic model for atom–diatom chemical reactions is developed in a systematic fashion from the exact quantum mechanical formulas. All the approximations involved were outlined and their range of validity indicated. The products’ vibrational distributions of 12 chemical reactions as well as isotope effects were calculated and shown to agree well with numerical collinear calculations, experimental results, and classical trajectory studies (when available). The factors influencing a reaction’s outcome were analyzed and the mass and isotope effects extensively explored; two types of behavior corresponding to the light atom and heavy atom regions were quantitatively mapped. It is hoped that similar results can be obtained from this model via spectroscopic data of the separate diatomics without ever having to precalculate a triatomic potential surface.

Associative ionization in collisions between metastable helium and atomic nitrogen and oxygen
View Description Hide DescriptionAbsolute and relative cross sections were obtained for the associative ionization (AI) reactions He*+N→HeN^{+}+e and He*+O→HeO^{+}+e by a merging‐beams technique from nominally 0.01 to 1.5 eV for the first reaction and 0.01 to 0.2 eV for the second. The He* represents a composite of He(2 ^{1} S) and He(2 ^{3} S), and the N and O represent composites of ground and metastable states. Although the observation of AI between two excited reactants is rare, evidence is presented for such an observation between excited He and excited N.

Atomic recombination dynamics on a solid surface: H_{2}+W(001)
View Description Hide DescriptionA model potential to describe the interaction of a diatomic molecule with a rigid solid surface has been described previously. Using this interaction potential, a series of classical trajectory calculations have been carried out, designed to simulate the recombination dynamics of two hydrogen atoms initially adsorbed on a tungsten (001) solid surface to form a gas‐phase hydrogen molecule. The vibrational and rotational state distributions of the desorbed hydrogen molecules are discussed in terms of a simple statistical model. The angular and speed distributions for the desorbed atoms and molecules are presented. The angular distributions are found to be substantially noncosine in form and peaked towards the surface normal, in qualitative agreement with experiment.

Chemical pumping of the water vapor laser. I
View Description Hide DescriptionFlash photolysis of mixtures of O_{2}/H_{2}O/O_{3} leads to lasing at 357.53 cm^{−1}. Emission at this wavenumber coincides with that of the strongest line that is observed from both the pulsed and cw water vapor discharge laser. Accordingly it is assigned to the (001)6_{33}– (020)5_{50} transition in water. The pumping scheme O_{3}→^{ hν}O(^{1} D)+O_{2}(^{1}Δ_{ g }), (1); O(^{1} D)+O_{2}(^{3}Σ^{−} _{ g }) →O_{2}(^{1}Σ^{+} _{ g })+O(^{3} P), (2); O_{2}(^{1}Σ^{+} _{ g })+H_{2}O→O_{2}(^{1}Δ_{ g })+H_{2}O^{†}, (3), where H_{2}O^{†} subsequently lases, is consistent with all the experimental observations. Computer modeling of this sequence of reactions reproduces both the observed pulse’s profile and its onset delay after flash initiation.

Chemical pumping of the water vapor laser. II
View Description Hide DescriptionLaser emission at 273.03, 262.33, and 590.24 cm^{−1} has been observed from flash photolysis of H_{2} and O_{3} mixtures, in addition to that at 285.55 cm^{−1}, which was previously reported. All four lines are assigned to laser transitions arising from the (100)13_{1,12}– (010)13_{11,2} resonance in H_{2}O. This lasing has been shown to be pumped by the reaction sequence O_{3}→^{ hν} O(^{1} D)+O_{2}(^{1}Δ_{ g }), (1); O(^{1} D)+H_{2}→OH^{†}+H, (2); H+O_{3}→OH^{†}+O_{2}, (3); OH^{†}+H_{2}→H_{2}O^{†}+H, (4b), where H_{2}O^{†} subsequently emits. The vibrational excitation of OH^{†} is effective in overcoming the activation energy barrier of Reaction (4b).