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Volume 63, Issue 3, 01 August 1975

Dissociative excitation of H_{2} by electron impact: Translational spectroscopy of long lived high Rydberg fragment atoms
View Description Hide DescriptionElectron impact excitation of H_{2} leads to three distinguishable groups of high Rydberg fragment atoms. High Rydberg molecules are also detected. The measurements consist of (1) excitation functions and (2) time of flight distributions which are transformed to fragment translational energy distributions. For high Rydberg fragments from molecular high Rydberg states converging to the repulsive wall of the H^{+} _{2}ground state, the measured and calculated kinetic energy distributions agree, in accordance with the prediction of the core ion model of high Rydbergdissociation. The remaining high Rydberg fragments result from dissociation of states of H_{2} with both electrons excited to low principal quantum numbers rather than from dissociation of molecular high Rydberg states.

Continuum radiation and potentials of Na–noble gas molecules
View Description Hide DescriptionThe normalized emission spectra resulting from the perturbation of Na atoms by 1–1000 Torr of noble gas have been measured in the range 10–150 nm about the 589 nm resonance line. This spectrum, due to the A–X and B–X transitions of the Na–noble gas molecules, was measured with 1.5 nm resolution. The Na, in a cell at a temperature of 417±5 °K, was optically pumped to the 3 ^{2} P _{1/2} and 3 ^{2} P _{3/2} states by resonance radiation. The resulting emission was measured at several Na densities to obtain the normalized emission spectra in the limit of zero radiation entrapment. Using the Franck–Condon principle, or equivalently the quasistatic theory of line broadening, and density factors, the A ^{2}Π_{1/2,3/2} and X ^{2}Σ_{1/2} state potentials for NaAr, NaKr, and NaXe have been obtained from the pressure dependence of the spectra. Continuum absorption and emission coefficients for these molecules, obtained by application of the same theories, are also presented. The analysis identifies the low pressure limit of the spectrum as due to free collision states above the angular momentum barrier. The population factors corresponding to quasibound, orbiting resonances are evaluated and used in this analysis.

A Raman spectral study of amorphous solid water
View Description Hide DescriptionRaman spectra of amorphous solid H_{2}O, [H_{2}O(as)], D_{2}O(as), and 12% H_{2}O in D_{2}O(as) were measured over a temperature range from 30 to 120 °K. The spectra of H_{2}O(as) resemble those of liquid water more than they do those of ice lc or ice lh. The spectra suggest that the water molecules are located in two or three types of distinguishable environments depending on the details of the assignment. No structural changes were observed between 30 and 120 °K, but at ∼160 °K the amorphous samples transformed rapidly and irreversibly to ice lc.

Extrinsic photoemission and diffusion of ’’free’’ excitons in solid xenon
View Description Hide DescriptionExtrinsic photoemission from pure solid rare gases at energies below the direct photoemission threshold is assigned to the diffusion of ’’free’’ mobile excitons (prior to exciton trapping) to the gold (emitter) substrate followed by exciton‐enhanced electron ejection from the electrode. From a semiquantitative study of the extrinsic photoemission yield of solid Xe as a function of the film thickness we get the diffusion length l?300 Å, for exciton migration on the time scale of 10^{−11}–10^{−12} sec.

ESR, ENDOR, and double ENDOR at 300 °K of DL‐serine x irradiated at 340 °K, a new radical species
View Description Hide DescriptionWhen DL‐serine single crystals are x rayed at 300 °K or below, two stable radicals are observed at room temperature. One of these, IV, is of greater intensity than the other, V, and was previously identified. By irradiating at a slightly elevated temperature, ∼340 °K, the concentration of V becomes more intense than IV. In this work we report on a detailed study of V using ESR,ENDOR, and double ENDOR, all at room temperature. We have determined that V is and have obtained five hyperfine tensors representing one α‐H, two β‐H’s, the rotating amino H’s, and a fourth H which is probably in a neighboring molecule. We have also observed the ENDOR transition of the nitrogen. The α‐H tensor is somewhat unusual in that the isotropic term (−41.3 MHz) is considerably less than for a 2ρπ electron and of the same sign, but the anisotropic term is approximately the same (+31.9, +3.5, −35.4 MHz). This is consistent with our model since the bonding to the α‐carbon is strained and would not be expected to be pure s p ^{2}.

Argon matrix infrared spectra of CF_{3}OOF and CF_{3}OOOCF_{3} and their photolysis products. Spectroscopic evidence for the CF_{3}OO radical
View Description Hide DescriptionUltraviolet photolysis of fluoroperoxytrifluoromethane, CF_{3}OOF, in argon matrices at 8 °K produced CF_{4} and a new species, tentatively identified as the CF_{3}OO radical, with infrared absorptions at 1173.7 and 1094.1 cm^{−1}. This species was also produced, along with CF_{4}, CF_{3}OCF_{3}, and COF_{2}, by photolysis of bistrifluoromethyl trioxide, CF_{3}OOOCF_{3}, at wavelengths below 300 nm. In the latter case, extensive isotopic labeling experiments with CF_{3} ^{16}O^{16}O^{16}OCF_{3}, CF_{3} ^{16}O^{18}O^{16}OCF_{3}, CF_{3} ^{18}O^{16}O^{18}OCF_{3}, and CF_{3} ^{18}O^{18}O^{18}OCF_{3} led to the observation of four distinct isotopic absorptions for the O–O stretching vibration (1094.1 cm), thus confirming the nonequivalent oxygen atom structure of CF_{3}OO.

Elastic and rotationally inelastic H–H_{2} and H–D_{2} collisions
View Description Hide DescriptionThe coupled‐states approximation in the body‐fixed coordinate system is applied to the study of elastic and rotationally inelastic H–H_{2} and H–D_{2}collisions. For both systems, integral and differential cross sections are computed in the collisionenergy range 0.5–1.5 eV. The isotope effect in the integral cross sections for j=0→j ′ (j ′=0,2,4,6) is found to be more pronounced for increasing j ′. In addition, as the ratio of rotational energy transferred to kinetic energy, i.e., ΔE/E, decreases, the differential cross sections shift from backward to forward peaked.

Evidence for predissociation in the C ^{2}Σ^{+} state of NS
View Description Hide DescriptionIn a series of emission, absorption, and fluorescence experiments on the C ^{2}Σ^{+} state of NS it is shown that the intensities of bands originating from v′=1 and 2 levels are less (relative to v′=0 band intensities) than is expected on the basis of Franck–Condon factors. This weakening is attributed to predissociation and an upper limit of 45 380 cm^{−1} is obtained for D _{ e }, the ground statedissociation energy. Correlations of NS states with those of NO are made and possible mechanisms of predissociation discussed.

Towards a molecular theory of freezing
View Description Hide DescriptionThe subject of this article is the fluid–solid transition and, in particular, an analysis of crystallization in terms of quantities which describe the average local arrangements of molecules in a fluid. We determine whether it is possible to predict the existence of crystalline solutions for the local molecular density from a Hamiltonian which is invariant under all translations and rotations. Crystallization is studied using the singlet probability density, the pair correlation function, and the intermolecular potential energy. An integral equation is obtained for these quantities, and we pursue the existence of crystalline (i.e., periodic but nonconstant) solutions for the singlet probability which branch from the fluid (i.e., constant) solution which is the number density. The phenomenon of crystallization, that is, the existence and determination of these solutions, can then be represented as a nonlinear eigenvalue problem. The analysis is applied to hard sphere systems in one, two, and three dimensions. Crystallization to close‐packed lattices is found in two and three dimensions when the isotropic media are overcompressed by amounts which depend on the structures to which the fluids crystallize. That is, the fluid persists into a portion of the metastable region. The nature of the crystalline solutions is analyzed in the neighborhood of the branching eigenvalues, and the relation between these special eigenvalues and equilibrium freezing points is discussed. The stability of these crystalline solutions is determined by comparing the values of a free energylike functional on these solutions with its value for the fluid.

Variational principles which are functionals of electron density
View Description Hide DescriptionThe Ritz variational principle, ordinarily written as a functional of the ground‐state wavefunction, is rewritten in such a way that only one‐electron functions are included as variables. Three different such variational formulas are derived explicitly based on the formula given by Hohen Kohn. They constitute variational expressions of the integrated Hellmann–Feynman theorem, integral Hellmann–Feynman theorem, and virial theorem. These variational formulas are exact within the Born–Oppenheimer approximation, and when applied, they give the same results as does the conventional Ritz variational principle. However, they still have the defect that they require knowledge of the correct density function associated with a suitably chosen reference potential. Some applications are given for one‐electron systems. A new formula for the kinetic energy plus electron–electron repulsion energy is obtained from the integrated Hellmann–Feynman theorem.

Decay mechanisms of CH_{3} in 3‐methylpentane and 3MP‐d _{14} glasses at 77 °K as indicated by methane yields
View Description Hide DescriptionThe isotopic methane yields from γ irradiation of 3‐methylpentane, 3MP–1%CH_{3}I, 3MP‐d _{14}–1%CH_{3}I, and 3MP‐d _{14}–1%CD_{3}I glasses confirm recent evidence from decay kinetics that thermal CH_{3} radicals can abstract H from C–H bonds in hydrocarbon glasses at 77°K (plausibly by tunneling) and show that similar abstraction does not occur from C–D bonds. Also, in 3MP‐d _{14} the CH_{3} (formed by the CH_{3}I+e ^{−} → CH_{3}+I^{−} process) does not decay by radical combination processes (CH_{3}+CH_{3} or CH_{3}+C_{6}D_{13}), implying that decay is by geminate recombination with the I^{−} partner. In the γ irradiation of 3MP‐d _{14}–1%CH_{3}I irradiated at 77°K, G (CH_{3}D) from hot abstraction by CH_{3} is 0.7; thermal CH_{3} and CD_{3} radicals are able to abstract H from low concentrations of C–H bond isotopic impurities; and the yields of scavengeable electrons and of radicals are substantially different than in 3MP‐h _{14}.

Yield of singlet and triplet excitons from x‐ray and ruby laser excitation of anthracene single crystals
View Description Hide DescriptionA new method for determining the singlet:triplet yields for x‐ray and ruby laser excited anthracene crystals is described. It was found that the ratio is higher than has been reported for x‐ray excitation and lower than reported for ruby laser excitation. X‐ray excitation produces roughly equal numbers of triplets and singlets. Ruby laser excitation indicates that the intersystem crossing rate from the first excited singlet is 1.5±0.5×10^{7} sec^{−1}, which is larger than had been reported, but still smaller than for anthracene molecules in solution. The greater triplet yield produced by x irradiation is related to efficient spin–lattice relaxation in highly excited electronic states and neither spin–spin nor spin–lattice relaxation in the electron and hole ground states is important in the short time involved in geminate recombination.

Laser pumped magnetophotoselection in triplet dyes
View Description Hide DescriptionSome observations have been made on the Δm=±2 and Δm=±1 ESRspectra in rhodamine (type R), fluorescein (type F), and acridine (type A) dyes, important laser active media, during laser excitation at 77 K. The results have revealed that the spectra and the lifetimes of the dyes in the T _{1} states in ethanol are affected significantly by the chromophoric structure. The root‐mean‐square value of zero‐field splitting parameters (ZFSP), D*, and the triplet‐state lifetime, τ_{ T }, increase in the order type R < type A < type F and type F < type R < type A, respectively. By the method of magnetophotoselection, the Δm=±1 absorption lines of acridine orange and fluorescein disodium salt dyes are assigned to three directions along the molecular axes. Furthermore, the ZFSP values and the polarization results show that the π‐electron distribution is most strongly polarized along the long axis of the chromophore in the case of type F dyes.

Thermochemical properties of gaseous ZrO and ZrO_{2}
View Description Hide DescriptionThe dissociation energy of gaseous ZrO, D _{0}° (ZrO), and the heat of atomization of gaseous ZrO_{2} have been measured using a high temperature mass spectrometer. A number of equilibria were studied and the following results were derived: Δ_{ f } H (ZrO,g,298.15 K) =83±12 kJ/mol, D _{0}° (ZrO) =761±15 kJ/mol) (or 7.89±0.15 eV), Δ_{ f } H (ZrO_{2},g,298.15K) =−298±30 kJ/mol, and D _{0}° (ZrO_{2}) =1386±30 kJ/mol (or 14.4±0.3 eV). The ionization potentials of ZrO and ZrO_{2} were derived from the measured appearance potentials. In the case of ZrO it was necessary to make corrections for the thermal populations of low‐lying electronic states. The derived values are I.P.(ZrO) =6.0±0.2 eV, I.P.(ZrO_{2}) =9.4±0.2 eV. These measurements are discussed in relation to other studies. Uncertainties in the derived thermochemical quantities owing to uncertainties in the spectral data are discussed. The chemical bonds in ZrO and ZrO_{2} are briefly discussed.

Study of the sensitivity of coupled reaction systems to uncertainties in rate coefficients. III. Analysis of the approximations
View Description Hide DescriptionIn Parts I and II of this series [J. Chem. Phys. 59, 3873, 3879 (1973)] we developed a new method of sensitivity analysis for large sets of coupled nonlinear equations with many parameters. In developing this theory and in carrying out the computer calculations involved in this analysis we made a number of approximations. We present here a quantitative analysis of these approximations and, where applicable, develop rigorous error bounds. Our analysis shows that we can specify the approximations which enter into our theory so as to obtain sensitivity measures of known accuracy. On this basis we feel that the techniques developed in this series of papers provide a useful and efficient method of sensitivity analysis of large systems with many parameters.

The excitation and quenching of N(^{2} P)
View Description Hide DescriptionThe rate coefficients for quenching N(^{2} P) by N, O, NO, CO, H_{2}, O_{2}, N_{2}O, and CO_{2} have been measured by following the decay of emission from N(^{2} P) excited in a Tesla discharge by energy transfer from N_{2}(A ^{3}Σ^{+} _{ u }). Some of these results differ considerably from those in the literature.

Hartree–Fock and Gordon–Kim interaction potentials for scattering of closed‐shell molecules by atoms: (H_{2}CO,He) and (H_{2},Li^{+})
View Description Hide DescriptionThe Gordon–Kim (GK) electron gas model for calculating the forces between closed‐shell atoms and molecules is applied to the He–H_{2}CO and Li^{+}–H_{2} systems. GK interaction energies are computed following the original theory and also including the self‐energy correction suggested by Rae. GK interaction energies, neglecting correlation, are found to be in qualitative accord with Hartree–Fock (HF) interaction energies for the two systems. However, quantitative discrepancies are noted which are possible sources of error if GK potential energy surfaces are used to compute accurate scattering cross sections.

Debye temperatures and cohesive properties
View Description Hide DescriptionValues of crystalline‐solid Debye temperatures depend both on the method and temperature of measurement. Simple relationships between Debye temperatures and such cohesive properties as compressibility and melting point were derived over 60 years ago by Madelung, by Einstein, and by Lindemann. Debye temperatures Θ_{XR} of a number of piezoelectricsemiconductors with chalcopyrite structure have been determined at room temperature by x‐ray diffraction. A new series of heat capacitymeasurements over the temperature range 1.2–40 °K, for four chalcopyrites, give Θ_{ D } values at 0 °K. A common proportionality is found between each of these Θ_{XR} and Θ_{ D } values and microhardness, and also melting point: Acceptable reproducibility is given for the A ^{I} B ^{III} C ^{VI} _{2} chalcopyrites and, separately, the A ^{II} B ^{IV} C ^{V} _{2} compounds. Values of Θ are predicted for 15 additional chalcopyrites. Excellent proportionality between Θ_{elastic} and compressibility is found for the europiumchalcogenides, based on the data of Shapira and Reed.

Path integral representation of the reaction rate constant in quantum mechanical transition state theory
View Description Hide DescriptionFeynman’s path integral representation of the Boltzmann operator e ^{−βH } is used to express the rate constant of a recently formulated quantum mechanical version of transition state theory. By evaluating the path integral in two separate stages, one is able to interpret the result as a generalization of a model suggested several years ago by Johnston and Rapp for handling the nonseparable aspect of tunneling in transition state theory. A Fourier series expansion of the path integral is also developed, and this approach has promise for direct numerical evaluation of the quantum rate expression.

Translational excitation of the molecular beam reaction K+HCl→KCl+H
View Description Hide DescriptionThe translational energy dependence of the reaction K+HCl→KCl+H has been studied in crossed beams in the c.m. energy range 2.1–12.1 kcal/mole (0.09–0.53 eV). Beams of HCl were generated at different translational energies by hydrodynamic expansion of various H_{2}/HCl mixtures and the laboratory energy of the HCl was measured by time‐of‐flight techniques. Angular distributions of the product were measured and integrated for each energy and the total reactive cross section was found to increase monotonically with energy. The functional form of the energy dependence is well approximated by the traditional line‐of‐centers relation. Although the cross section increases with energy, translational excitation is n o t as effective as vibrational excitation and modest extrapolation of the data suggests that still larger amounts of translational energy will be similarly ineffective. The cross section might be expected to depend upon the number of states which are accessible to the products. But this number grows rapidly as the reagent energy is increased and the influence upon the cross section of this large statistical effect can obscure any subtle dynamic effects due to the nature of the potential surface. In order to remove this statistical bias, it is convenient to express the results in terms of the average state‐to‐state transition rate ?, the experimental rate constant divided by the density of possible product states. Even though the detailed product state distribution is not known, the density of p o s s i b l e product states can be calculated from the conservation laws and molecular properties of the asymptotic products. The state‐to‐state transition rate so obtained is found to decay exponentially with the square root of the energy in excess of the thermodynmic threshold: ?=A exp[−β (E′)^{1/2}]. An extrapolation to energies higher than those studied predicts an eventual decrease in the reaction cross section.