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Volume 66, Issue 12, 15 June 1977

Infrared absorption spectra of gaseous HD. IV. Analysis of the collision‐induced fundamental band of the pure gas
View Description Hide DescriptionStudies of the infrared absorption spectra of the HD fundamental band in the pure gas, reported for the room temperature in Paper I of this series, have now been extended to temperatures 77 and 196 K. The spectra of the band were recorded for a number of gas densities up to 50 amagat. In addition to the usual collision‐induced broad features of the infrared fundamental band of a symmetric diatomic gas, these spectra at 77 and 196 K show the dipole‐allowed sharp R _{1}(0) and R _{1}(1) transitions owing to the individual molecules. Derived binary absorption coefficients of the collision‐induced band are (1.15±0.06) ×10^{−35} and (1.71±0.07) ×10^{−35} cm^{6} s^{−1} at 77 and 196 K, respectively. An analysis of the absorption profiles of the band at 77 and 196 K and those of the band at 298 K reported in Paper I was carried out, and the characteristic half‐width parameters δ_{ d } and δ_{ c } of the short‐range overlap‐induced transitions and δ_{ q } (and δ_{ q′}) of the long‐range quadrupole‐induced transitions are derived. The contributions of the overlap‐ and quadrupolar‐interactions to the absorption intensity of the band are separated by the method of profile analysis. The magnitude parameter λ and the range ρ of the overlap‐induced dipole moment for the HD–HD collision pairs are determined by obtaining the best fit of the calculated overlap part of the binary absorption coefficient as a function of temperature to the experimental values. Derived overlap parameters are λ=5.60×10^{−3}, ρ=0.25 Å, and μ (σ) (the overlap‐induced dipole moment at the Lennard–Jones intermolecular diameter σ) =3.1×10^{−2} ea_{0}.

Absolute coverage determination of CO on Ni(111)
View Description Hide DescriptionThe adsorption of CO on Ni(111) has been studied using LEED and calibrated Auger measurements in order to determine the absolute amount of adsorbed CO molecules. At room temperature and CO pressures of up to 1.3×10^{−3} Pa a saturation coverage of ϑ_{CO}?0.28, corresponding to 5.2×10^{14} molecules per cm^{2}, has been obtained. This is contrary to the commonly accepted opinion that the saturation coverage of nondissociated CO on various transition metals should always amount to about 1×10^{15} molecules per cm^{2} irrespective of the underlying substrate structure.

Molecular beam Zeeman effect and dipole moment sign of ClF
View Description Hide DescriptionMolecular beam electric resonance spectroscopy has been used to observe hyperfine, Stark, and Zeemanproperties of chlorine monofluoride. The dipole moment from Zeeman data is 0.85(15), −FCl+, in agreement with the known magnitude. The sign obtained here is the opposite of earlier, less precise, Zeeman results but agrees with calculations and van der Waals molecule experiments. Hyperfine, Stark, and Zeemanproperties for ^{35}ClF and ^{37}ClF are reported, including polarizabilityanisotropy, α_{∥}−α_{⊥}=1.32(8) Å^{3}, molecular quadrupole moment, ϑ_{∥}=1.54(7) ×10^{−26} esu⋅cm^{2}, and the chlorine quadrupole coupling constant derivative, d e Q q/d R=−90(20) MHz/Å.

Stark and Zeeman properties of ozone from molecular beam spectroscopy
View Description Hide DescriptionStark and Stark–Zeeman transitions within single J states of ozone have been studied using molecular beam electric resonance spectroscopy. Results include dipole moment, μ; dipole moment of the first excited bending mode, μ (010); polarizabilityanisotropies, α_{ a a }−α_{ b b } and α_{ a a }−α_{ c c }; rotational magnetic moments,g _{ a }, g _{ b }, g _{ c }; magnetic susceptibility anisotropies, χ_{ a a }−χ_{ b b } and χ_{ a a }−χ_{ c c }; and quadrupole moment components, ϑ_{ a a }, ϑ_{ b b }, ϑ_{ c c }. μ=0.5337(1) D, μ (010) =0.5261(1) D, α_{ a a }−α_{ b b }=2.82(1) Å^{3}, α_{ a a }−α_{ c c }=2.63(4) Å^{3}, g _{ a a }=2.98933(8), g _{ b b }=−0.22919(3), g _{ c c }=−0.07623(b), χ_{ a a }−χ_{ b b }=5.91(2) KHz/kg^{2}, χ_{ a a } −χ_{ c c }=12.05(4) KHz/kg^{2}, ϑ_{ a a }=−1.4(2) ×10^{−26} esu⋅cm^{2}, ϑ_{ b b }=−0.7(2) ×10^{−26} esu⋅cm^{2}, ϑ_{ c c }=2.1(3) ×10^{−26} esu⋅cm^{2}.

The optical absorption spectrum of stoichiometric neodymium nitrate hexahydrate
View Description Hide DescriptionThe optical absorptionspectrum of single crystals of neodymium nitrate hexahydrated with the stoichiometric composition (that is, without analytical excess of nitrogen) was recorded at 4.2 K between 10 000 and 33 000 cm^{−1}. The theoretical analysis was undertaken through a computer program which takes into account free‐atom classical operators, including two‐ and three‐body operators, as well as a crystal‐field operator written in the approximate C _{3v } symmetry of the truncated icosahedron which makes the tencorners coordination polyhedron. The Hamiltonian was applied on the basis of the 364 ‖S L J M _{ J }〉 kets in the 4f ^{3} configuration, that is, including J mixing. The experimental sequence of 98 Stark levels from 28 ^{2 S+1} L _{ J } levels was reproduced with a mean square deviation of 30 cm^{−1} out of an 18 adjustable parameters fit (12 free‐atom parameters and six crystal‐field ones).

Electron spin resonance study of the radical Ph_{2}Ṡb trapped in a single crystal matrix
View Description Hide DescriptionA radical formed by x‐irradiation of a single crystal of triphenylantimony is identified as Ph_{2}Ṡb. Its ESRspectral parameters (for ^{121}Sb)g _{1}=1.9804, g _{2}=2.1044, g _{3}=1.9959, T _{ x }=1270 MHz, T _{ y }=−752 MHz, T _{ z }=−699 MHz corrected for nuclear spin–orbit interactions and decomposed into isotropic (−60.3 MHz) and anisotropic (1330.3, −691.7, −638.7 MHz) components, and the nuclear quadrupole coupling constants e ^{2} Q q _{x}=−101 MHz, e ^{2} Q q _{ y }=−205 MHz, e ^{2} Q q _{ z }=306 MHz, have been interpreted in terms of the radicals’s electronic structure and indicate that, like the analogous Ph_{2}Ṗ and Ph_{2}Ȧs radicals, the unpaired electron is localized on the 5p _{π} valence orbital of the antimony atom and that the radical is strongly bent, ∠CSbC≃98°.

Velocity distribution of H(2s) resulting from the electron impact dissociation of H_{2}
View Description Hide DescriptionWe have calculated the velocity distribution of the fast, metastable hydrogen and deuterium atoms which result from the dissociation of the ^{1}Π_{ u }(2pπ_{ u }, 2sσ_{ g }) autoionizing states of H_{2} and D_{2}. The present model uses the previously computed potential energy curve and autoionization width of this doubly excited ^{1}Π_{ u } state. The model treats the competition between ionization and dissociation into neutral fragments classically. In calculating the laboratory velocity distribution we take into account the thermal motion of the target molecules and the recoil due to the scattered electron. The effect of momentum transfer is important, as the calculated laboratory speed distribution depends sensitively on the angle of detection. The comparison of the experimental and the theoretical velocity distributions shows a significant discrepancy among the three measurements which have been reported to date.

Effect of collision‐induced phase shifts on the linewidths and line shifts of rotational spectral lines
View Description Hide DescriptionA more general theory of the width and shift of microwave absorption lines is developed under the impact approximation with the effect of elastic as well as inelastic collisions being considered in a more rigorous way. Previous formulations (Anderson and Murphy–Boggs) are shown to be limiting cases of this treatment. The theory is applied to pure rotational transitions of the OCS–OCS, OCS–He, and OCS–Ar systems and the results compared with experiment. The agreement is very satisfactory for the quantum number dependence and temperature dependence of the linewidths and for the approximate magnitude of the pressure‐induced line shift.

Predissociation linewidths and level shifts for double‐curve crossing models
View Description Hide DescriptionAn analytic scattering model is applied to the problem of double‐curve crossings in predissociation. Analytic expressions are obtained for the energy shift ΔE and linewidth Γ by searching for poles in the scattering matrix. The validity of perturbation expressions for these parameters is examined by comparing numerical calculations of these expressions to our results. It is found that contributions from individual crossings are not always additive owing to interference effects.

Internal energy of CH^{+} produced by the C^{+}(H_{2},H)CH^{+} reaction
View Description Hide DescriptionThe energy spectrum of CH^{+} from the reaction C^{+}(H_{2},H)CH^{+} was measured with a tandem mass spectrometer with improved energy resolution as a function of projectile kinetic energy. These spectra indicate the presence of the three lowest electronic states of CH^{+} and product vibrational excitation was observed in favorable cases. The internal energy distribution in the CH^{+} product was in satisfactory agreement with published results of phase space theory calculations for this reaction.

^{14}N PNQR investigation of the effect of pressure on phase transition in malononitrile
View Description Hide DescriptionThe ^{14}N pure nuclear quadrupole resonance frequencies in the molecular crystal malononitrile were measured as a function of hydrostatic pressure up to 5.6 kbar. Above T=21.55°C, the second order phase transition previously studied by Zussman and Alexander was observed at high pressures. Above the transition pressure p _{ c }, each resonance line splits into two. The splittings Δν along an isotherm at 23°C were fitted to the equation Δν=B (p−p _{ c })^{β} and the critical exponent β was found to be close to 0.5. The variation of T _{ c } with pressure was measured to 2 kbar and the line of transition could be described by the linear equationT _{ c }(p) = 21.51+16.5734p. The present results for the variation of Δν along an isotherm were compared with previous results obtained along an isobar.

The monomeric character of xenon hexafluoride vapor. The mass spectroscopy of noble gas binary fluorides and xenon oxide tetrafluoride
View Description Hide DescriptionPositive ion mass spectra have been obtained for KrF_{2}, XeF_{2}, XeF_{4}, XeF_{6}, and XeOF_{4} using 60 or 70 V electron impact ionization and a molecular beamsource designed especially for reactive fluorides. Flight time distribution measurements have been made for neutral XeF_{6}. Both these and the mass spectrometric fragmentation pattern indicate monomeric species in the saturated vapor. Associated (dimer) molecules can be obtained by isentropic expansion of XeF_{6}; these are detected as dimer ions at one part in 10^{4} of the monomeric ions in the mass spectrum. Electric deflection measurements on XeF_{6} vaporizing from inlets at temperatures from −19 to 40 °C showed no focusing effect.

Optically detected magnetic resonance spectra of the lowest triplet states of benzophenone, ^{13}C‐benzophenone, and three 4,4′‐dihalobenzophenones
View Description Hide DescriptionWe describe measurements of the complete angular dependence of the optically detected magnetic resonance(ODMR)spectra of the lowest triplet states of benzophenone, carbonyl‐^{13}C‐benzophenone, 4,4′‐difluorobenzophenone, 4,4′‐dichlorobenzophenone, and 4,4′‐dibromobenzophenone in 4,4′‐dibromodiphenylether host crystals at liquid helium temperatures. The principal axes and values of D (including the absolute signs) and g are reported and used to evaluate the spin–spin and spin–orbit contributions to the fine‐structure tensor of the parent molecule. It is found that the dipolar contributions to D in ^{3}(n,π*) benzophenone are at least a factor of 2 less than recent a b i n i t i o estimates of the spin–spin contributions to D in ^{3} A _{2} formaldehyde. Carbon‐13 hyperdfine splittings have been observed in the ODMRspectra of ^{13}C‐benzophenone; an analysis of these yields estimates of the orbital spin densities ρ_{2s } ^{C(O)}?0.008 and ρ_{2p } _{ x } ^{C(O)}?0.14 and suggests that the C_{1}–C(O) –C_{1}′ fragment is planar. The fine‐structure parameters of triplet benzophenone are strongly influenced by halogen atoms in the p a r a ring positions. The ODMRspectra of the 4,4′‐difluoro and 4,4′‐dibromo derivatives also exhibit ring halogen atom hyperfine structure from which the estimate ρ_{2p } _{ π } ^{C} ^{ 4 }?0.10 is obtained. Taken together, the results of this investigation suggest that as much as 50% of the total spin density in the lowest triplet state of benzophenone itself resides on the aromatic rings, thereby accounting for the reduction in the dipolar contributions to D in the parent molecule and for the changes in the principal values (and directions) of D which occur in its heavy‐atom substituted derivatives.

Level‐anticrossing and cross‐relaxation effects in oriented molecular triplet states. ^{3}(n,π*) benzophenones in 4,4′‐dibromodiphenylether
View Description Hide DescriptionThis paper reports the observation and analysis of magnetically induced changes in the phosphorescence intensities of triplet state benzophenone, carbonyl‐^{13}C‐benzophenone, and three 4,4′‐dihalobenzophenones in single crystals of 4,4′‐dibromodiphenylether at 1.6°K. The signs, magnitudes, field positions, and widths of these changes can be interpreted in terms of two effects, anticrossings of two different electron–nuclear spin manifolds of the guest molecule and cross relaxation between the spin system of the guest and that of the host. At fields where anticrossings occur, the mixing between the spin states is strong and no hyperfine structure is observed. However, by comparing the results for the different molecules in the same host, it is shown that secular terms of the hyperfineinteraction play a key role in determining the minimum spectral widths of the ’’transitions’’. At fields where cross relaxation predominates, the mixing between the spin states is weak and hyperfine and quadrupole splittings of both the guest and host can be resolved. The magnetic and optical parameters obtained by fitting the ’’spectra’’ are in excellent agreement with those determined by ODMR techniques [J. A. Mucha and D. W. Pratt J. Chem. Phys. 66, 5339 (1977), preceding paper]. Thus, experiments of this type can be utilized to provide information about the fine‐structure, g, hyperfine, and quadrupoletensors of emitting paramagnetic species in the complete absence of perturbing radiofrequency or microwave fields. Moreover, the systems described herein offer considerable promise in future studies of spin relaxation mechanisms in molecular solids by optical detection methods.

An analytically soluble model for the penetration of a two‐dimensional barrier: Quantal and semiclassical treatment
View Description Hide DescriptionThe reflection and transmission of a wave on a two‐dimensional barrier is studied quantum mechanically and semiclassically. The simple model consists of two degrees of freedom. One of them contains a barrier (of the Eckart type); the second allows only a bound motion in discrete quantum states. These two degrees of freedom are coupled. The transition probabilities for transitions between the different quantum states can, in the model considered here, be evaluated analytically, both quantum mechanically and semiclassically. Several of the so called uniform semiclassical approximations and also the initial value integral representation for the semiclassical transition amplitudes are considered and compared to the exact quantum mechanical results. Some new insight on the semiclassical treatment of the tunneling process is gained, specially concerning the proper choice of the integration path for the initial value integral representation of the transition amplitudes.

Depolarized Rayleigh scattering in 10M amorphous and liquid KOH aqueous solutions
View Description Hide DescriptionAn interpretation of the low frequency Raman scattering in all disordered systems including liquids is suggested in terms of phononlike excitations damped by anharmonicity and by structural relaxations. In principle, owing to the disorder‐induced breakdown of the k vector selection rule, all of these excitations are allowed to participate to the scattering process. An a d h o c simplified model is also proposed to calculate the low frequency Raman scattering, and it is found to reproduce at least qualitatively the main features of the depolarized spectrum in amorphous solid and liquid 10M KOH watersolutions at different temperatures.

Dynamic effects in the scattering of electrons by small clusters of atoms
View Description Hide DescriptionDynamic scattering corrections were calculated for 40 kV electronsdiffracted by randomly oriented fcc clusters of argon and of gold atoms ranging in size from 13 to 135 atoms. Computations were carried out according to several variants of two limiting theoretical approaches, namely, the direct summing up of atomic contributions calculated through single–single and single–double scattered waves by modifications of Glauber theory, and the extrapolation to limitingly small crystallites of conventional dynamic theory in the Blackman and Fujimoto formulations. For the small clusters studied, integrated intensities of diffractionrings (through single–double scatterings) calculated for three dimensional crystallites differ insignificantly from Glauber theory intensities calculated by projecting atomic potential energies onto a plane perpendicular to the mean direction of the incident and scattered wave vectors. The fractional dynamic correction increases with cluster size very nearly as N ^{2/3} in both the Glauber and Blackman–Fujimoto limiting treatments. For crystalline clusters 8–20 Å in diameter, the dynamic effect calculated by summing single–double scatterings is a n o r d e r o f m a g n i t u d e larger than that according to Blackman–Fujimoto theory. For argon clusters the dynamic effect is not serious; but according to our direct sums, dynamic corrections for 16 Å spheres of gold are surprisingly large, exceeding 25% for 111 reflections. Since the direct sums have been verified experimentally for several vapor‐phase molecules, the present work indicates that, in the limit of very small scatterers, extrapolations from conventional two‐beam dynamic theory may seriously underestimate the magnitude of dynamic effects.

Molecular motions in compressed liquid heavy water at low temperatures
View Description Hide DescriptionThe NMR deuteron spin–lattice relaxation timesT _{1}, self‐diffusion coefficients D, and shear viscosities η have been measured as a function of pressure in the temperature interval −15 to 10°C. The low‐pressure extreme of the measurements is Ice I, whereas Ice V represents the high‐pressure boundary of the experiments. In analogy with anomalous motional behavior in compressed liquid water, the initial compression of liquid D_{2}O in the temperature interval studied results in higher motional freedom of D_{2}O molecules so that T _{1} and D dependences with pressure exhibit a maximum and shear viscosity shows a minimum. This is a result of distortion and weakening of the hydrogen bond network owing to compression. Further compression hinders molecular motions as a result of increased repulsive interactions due to higher packing. This study also enables us to test the applicability of hydrodynamic equations at the molecular level for liquid heavy water. Analysis of the relaxation and shear viscosity data show that the Debye equation fails to describe the density effects on reorientation of D_{2}O molecules. It appears that the success of the Debye equation to describe temperature effects on reorientation of H_{2}O and D_{2}O molecules at 1 bar is accidental. However, the data show that the deuteron relaxation rate (1/T _{1})_{D} is proportional to η/T under isochoric conditions. The fact that the slope of the (1/T _{1})_{D} vs η/T plot diminishes with increasing density indicates that compression leads to diminished coupling between rotational and translational motions of water molecules. The shear viscosity and self‐diffusion data show that the Stokes–Einstein equation does not represent the relationship between D and η in liquid heavy water. A brief discussion of the isotope effects on shear viscosity in liquid D_{2}O and H_{2}O is presented.

Diagrammatic perturbation theory: Many‐body effects in the X ^{1}Σ^{+} states of first‐row and second‐row diatomic hydrides
View Description Hide DescriptionDiagrammatic many‐body perturbation theory is employed in a study of the X ^{1}Σ^{+} states oif first‐ and second‐row diatomic hydrides at their respective equilibrium nuclear separations. All two‐, three‐, and four‐body terms are determined through third‐order in the energy within the algebraic approximation (i.e., parameterization of state functions by expansion in a finite basis). Padé approximants to the energy are constructed. From the first‐order wavefunction rigorous upper bounds to the expectation value of the electronic energy are obtained from the Rayleigh quotient. Two different zero‐order Hamiltonians are used, and the convergence properties of the resulting perturbation expansions are compared. In both schemes three‐ and four‐body terms are significant, having a magnitude that is as much as 24% of the sum of the second‐ and third‐order terms.

The potential energy curves of the X ^{1}Σ^{+} and A ^{1}Σ^{+} states of LiH
View Description Hide DescriptionAs an important intermediate step in a long‐term project to fully understand the spectroscopy of the three lowest singlet states of LiH, (X ^{1}Σ^{+}, A ^{1}Σ^{+}, and B ^{1}Π), we have constructed accurate hybrid potential energy curves for the X ^{1}Σ^{+} and A ^{1}Σ^{+} states to complement earlier work on the B ^{1}Π state. In each case the known Rydberg–Klein–Rees (RKR) for low vibrational levels was joined to the long‐range region of the potential (represented by new C _{6}, C _{8}, and C _{10} coefficients reported herein) fixed by the accurately known dissociation limits. The joining was obtained by scaling slightly the a b i n i t i o results of Docken and Hinze in the region of interpolation. Extrapolation to smaller distance was also done using a b i n i t i o results.