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Volume 61, Issue 2, 15 July 1974

Ham effect in the ^{2} T _{2u } charge‐transfer excited state of octahedral
View Description Hide DescriptionThe allowed ligand‐to‐metal charge‐transfer bands in octahedral ral which correspond to the excitation t _{2u }(π)→t _{2g }(d) show a highly resolved complex vibronic pattern over the region 22 900 – 24 500 cm^{−1} at liquid helium temperature. In this paper, it is shown that this spectrum can be interpreted in detail on the basis of a strong Jahn‐Teller effect in the t _{2g } molecular mode. The treatment is carried out in a basis spanning all vibronic functions through the first 11 quanta of the undisplaced t _{2g } harmonic oscillator functions. All matrix elements involving both the first order Jahn‐Teller Hamiltonian and spin‐orbit coupling are included in a complete diagonalization. A large Ham effect quenches the spin‐orbit coupling so that the no‐phonon lines of the two spin‐orbit components ( and U′ _{ u }) are separated by ∼5–6 cm^{−1} rather than the expected value of ∼(3/4)ζ_{Cl}≈440 cm^{−1}. The calculated results explain semiquantitatively the over‐all band spectrum in both absorption and MCD as well as the behavior of the no‐phonon lines as a function of magnetic field (up to ∼70 kG) and temperature. There is additional low energy vibrational structure, undoubtedly due to lattice vibrations, the most important of which is probably Jahn‐Teller active. The e_{g} molecular vibration appears weakly, if at all. An alternative treatment assuming a strong Jahn‐Teller effect in the e_{g} mode does not satisfactorily account for the observed spectrum. Arguments are suggested to account for t _{2g } rather than e_{g} Jahn‐Teller activity.

Effect of changes in the potential on atom‐solid elastic scattering
View Description Hide DescriptionThe relative intensity appearing in various diffraction peaks for the elasticscattering of an atom from a solid surface is studied as aspects of the interaction potential are varied. It is observed that the detailed relationship between the flat portion of the potential V _{0}(z) and the (x,y)‐dependent part on the repulsive wall (in the general region of the classical turning point) most strongly affects the diffraction properties. The scattering is relatively insensitive to the long range behavior of the flat part of the potential V _{0}(z) and the long range behavior of the (x,y)‐dependent parts.

Infrared laser enhanced reactions: Spectral distribution of the NO_{2} chemiluminescence produced in the reaction of vibrationally excited O_{3} with NO
View Description Hide DescriptionVibrationally excited ozone, produced by CO_{2} laser radiation, was found to react significantly faster with NO than does thermal O_{3}. The emission spectrum of the laser enhanced chemiluminescence from this reaction was measured from 520 to 810 nm. The lowest lying 1^{2} B _{2} state was identified as the primary source of NO*_{2} emission in the NO+O_{3}reaction. One quantum of vibrational excitation in the reactant O_{3} was found to introduce one quantum of vibrational energy in the product NO_{2} (1^{2} B _{2}). The rate enhancement of the reaction channel producing NO_{2}(1^{2} B _{2}) as a result of vibrational excitation of O_{3} was 5.6±1.0. Thus, only about 50% of the available vibrational energy is used to enhance this reaction.

Scaled particle theory of hard spherocylindrical fluids
View Description Hide DescriptionFor a system of spherocylindrical particles, an integral equation in the singlet angular distribution function is obtained. The integral equation is solved analytically by an expansion in the reduced density. Two nontrivial solutions appear, one corresponding to a nematic phase where the long axes of the molecules tend to align parallel, and one corresponding to a nonstable pseudonematic phase where the short axes tend to align parallel. The transition from the isotropic to the nematic phase is first order, whereas the transition to the pseudonematic phase is second order. None of the ordered phases can exist for reduced densities below a certain value, which is found as a simple function of the length to width ratio of the molecules.

Molecular constants of some bent symmetrical XY_{2} molecules
View Description Hide DescriptionOn the basis of a revised set of symmetry coordinates, all the force constants (General Quadratic Valence Force Field) of 16 bent symmetrical XY_{2} type of molecules have been evaluated afresh by the Wilson's F‐Gmatrix method using the Raman and infrared spectral frequencies. Certain simplifying considerations involving molecular dynamics have been made use of in solving the secular equation. The mean amplitudes have also been calculated at 298.16° K by Cyvin's method using the present values of the force constants.

Far infrared optical phonons of some two‐dimensional layer compounds
View Description Hide DescriptionThe far infrared transmission spectra of the layer structure compounds of the type (C_{ n }H_{2n+1}NH_{3})_{2} MCl_{4}, n = 1,2,3, ···, (M=Cu, Cd) have been measured in the region of 10–400 cm^{−1} at 1.2 K. The rather involved spectra of all the compounds investigated can be interpreted in terms of the normal lattice modes of the layers alone. From these far infrared data, the contribution of the optical phonons to the specific heat has been estimated. A comparison with the result for this contribution obtained by Bloembergen, Tan, Lefevre, and Bleyendaal [J. Phys. (Paris) Suppl. 32, 874 (1971)] from a fit of the measured total specific heat leads to the conclusion that the absorption lines that we observed at wavenumbers lower than ∼40 cm^{−1} are probably due to multiphonon processes.

Reactions of recoil ^{13}N atoms in the gas phase
View Description Hide DescriptionRecoil reactions of ^{13}N atoms in CO_{2}, N_{2}, O_{2}, N_{2}O, and NO were studied. Recoil nitrogen atoms were generated by the ^{12}C(d, n)^{13}N reaction using CO_{2} as the target molecule. The only products observed were ^{13}NN and ^{13}NNO. Other products sought but not detected were NO, NO_{2}, and CN radicals. The ^{13}NN formation with added N_{2} is attributed to an exchange reaction involving translationally excited nitrogen atoms with nitrogen molecules. The ^{13}NNO yield is independent of CO_{2} concentration; however, it increases rapidly with the addition of O_{2}. This increase, along with an equal decrease in the ^{13}NN yield, is explained by the reaction of excited nitrogen molecules (^{13}NN*) with O_{2}. It is concluded that recoil ^{13}N atoms do not react directly with CO_{2}.

Alignment of molecules in gaseous transport: Alkali dimers in supersonic nozzle beams
View Description Hide DescriptionFrom measurements of the degree of polarization of the molecular fluorescence, it is shown that one can determine the coefficients of the first three even‐ordered Legendre polynomials in the expansion of the spatial distribution of J vectors (M_{J} population), n(θ)=1 + a _{2} P _{2}(cosθ) + a _{4} P _{4}(cosθ), where θ is the angle between the angular momentum vector J of the molecule and the beam direction. This method is applied to determine the alignment of Na_{2} molecules in a supersonic nozzle beam generated by expansion of sodium vapor through a converging nozzle (throat diameter = 0.375 mm and channel length = 0.750 mm) with stagnation temperature (oven temperature) up to ∼1015°K, corresponding to stagnation pressures (oven pressures) up to ∼155 torr. The 4880 Å line of a cw argon‐ion laser is used to excite the transition (ν″=3, J″=43 → ν′=6, J′=43) in the band system of Na_{2} molecules and the degree of polarization of a single line of the resulting fluorescence series (Q series) is measured as a function of (1) stagnation pressurep _{0} and (2) the angle θ_{0} between the electric vector of the exciting laser light and the molecular beam direction. A decrease in the degree of polarization from its isotropic value of 0.50 for θ_{0}=0 to a value of 0.44 at a stagnation pressure of 155 torr is found, showing increasing alignment of dimer molecules with their angular momenta preferentially pointing perpendicular to the beam direction. At the stagnation pressure of 155 torr the coefficients of the Legendre polynomials are found to be a _{2}=−0.203±0.006 and a _{4}=−0.14±0.03. For this distribution the ratio of molecules with angular momentumJ parallel and perpendicular to the beam axis is ∼2:3. Classical models involving the nonreactive collisions between hard spheres (atoms) and ellipsoids of revolution (molecules) and the chemical exchange between atoms and dimers predict the production of alignment in qualitative agreement with experiment.

Infrared and Raman spectra of polyethylene oxide in the low frequency region
View Description Hide DescriptionThe far infrared and Raman spectra of polyethylene oxide (PEO) between 5 and 150 cm^{−1} has been measured for three crystalline samples with different degrees of polymerization. Lines are observed at 37, 52, 81, and 107 cm^{−1} in the infrared and at 37, 56, and 78 cm^{−1} in the Raman spectrum. Theoretical calculations show that the 81 and 107 cm^{−1} lines are assignable to the torsional motion of the PEO helical chain about the C–O bond. The absorptions at 37 and 52 cm^{−1} have not been previously reported or predicted by any normal mode calculations of the isolated 7/2 helix although they seem to arise from intramolecular rather than lattice vibrations.

Theoretical equations for photoionization cross sections of polyatomic molecules in plane‐wave and orthogonalized plane‐wave approximations
View Description Hide DescriptionThe general polyatomic molecule in a closed‐shell electronic state with nuclei fixed according to the Born‐Oppenheimer approximation is photoionized to form a final singlet state in which one electron is excited into the continuum. All bound orbitals are assumed identical in the initial and final states. The unbound orbital is approximated either by a plane‐wave or by a plane‐wave orthogonalized to all occupied bound orbitals. Formulations are given for cases in which bound orbitals are expressed as linear combinations of Slater‐type orbitals, orthogonalized Slater‐type orbitals, Cartesian Gaussian‐type orbitals, or Gaussian‐lobe functions. General equations are derived for the photoionization cross section of randomly oriented polyatomic molecules as a function of angle between the polarization vector of the photonbeam and the propagation vector of photoejected electrons. Also derived is the photoionization cross section of the same sample as a function of angle between an unpolarized photonbeam and the propagation vector of photoejected electrons.

Calculated photoionization cross sections and relative experimental photoionization intensities for a selection of small molecules
View Description Hide DescriptionThe general equations for calculating photoionization cross sections of polyatomic molecules in the plane‐wave and orthogonalized plane‐wave approximations have been programmed for the electronic computer. Applications are described for the molecules H_{2}, CH_{4}, N_{2}, CO, H_{2}O, H_{2}S, and H_{2}CCH_{2} for incident photon energies from threshold to 1500 eV. Relative experimental photoionization band intensities for the above molecules are measured using NeI, HeI, and HeII resonance radiation. A simplified analysis of the intensities derived from electrostatic deflection analyzers is presented. The ^{2} P _{3/2}:^{2} P _{1/2} intensity ratios of the rare gases are determined with the three modes of excitation mentioned above. An analysis of the resolution capabilities of an electrostatic deflection spectrometer as a function of electron kinetic energy is presented. Relative experimental photoionization band intensities for the above molecules obtained by ionization with the three uv sources and MgK_{a} and A1K_{a} x‐ray sources are compared with computed differential cross sections. Variations in computed cross sections as a function of the kinetic energy of the photoelectrons are discussed and possible interpretations are proposed.

Calculated angular distributions of photoelectrons using the orthogonalized plane‐wave approximation
View Description Hide DescriptionThe general equations for calculating angular distributions of photoelectrons within the orthogonalized plane‐wave approximation have been programmed for the electronic computer. Applications are described for the molecules CH_{4}, H_{2}O, and N_{2} with incident photon energies from threshold to 1254 eV. Computed values of the asymmetry parameter β are compared to experimentally determined β values using HeI excitation. Large variations in β as a function of photon energy are obtained; possible interpretations are proposed.

Dipolar hard spheres: A Monte Carlo study
View Description Hide DescriptionThe paper reports Monte Carlo computations for fluids of hard spheres with embedded point dipoles, at two densities and for a range of dipole moments. The results are compared with the predictions of the mean spherical and Onsager models and those of thermodynamic perturbation theory; the last appears to be most successful.

Matrix isolation infrared spectrum and vibrational potential function of sulfur monochloride
View Description Hide DescriptionInfrared spectra of sulfur monochloride in various solid matrices were taken at 12°K. The sharpness of the band seen at 550 cm^{−1} compelled its assignment as the S–S stretching mode. Enrichment of samples with ^{37}Cl led to the identification of the chlorine isotopic splittings on the two S–Cl stretching modes observed near 450 cm^{−1}. A normal coordinate analysis was performed; on the basis of the best frequency fit, the band observed at 457.5 cm^{−1} was assigned to the symmetric S–Cl stretching mode and that at 449.0 cm^{−1} to the asymmetric mode. The force field derived from the normal coordinate analysis shows a weaker S–Cl bond than in SCl_{2}, but essentially the same S–S bond strength as H_{2}S_{2}.

Study of the structure of molecular complexes. VI. Dimers and small clusters of water molecules in the Hartree‐Fock approximation
View Description Hide DescriptionThe analytical fit to a large number of Hartree‐Fock computations for the water‐water interaction has been reanalyzed and used to study small clusters of water molecules. With the analytically fitted Hartree‐Fock potential, thousands of possible configurations for the dimers, trimers, tetramers, pentamers, hexamers, heptamers, and octamers of water have been compared in order to determine the configuration of lowest energy (maximal stabilization energy). For the dimer two possible stable configurations are found, corresponding to an open form and a cyclic form, with the open form being more stable. For the trimers and tetramers the cyclic forms are somewhat more stable than the open structures. For the larger clusters it is concluded that it is rather meaningless to consider a single structure, but what is physically relevant is the statistical distribution of different configurations, since many configurations with significantly different geometry have nearly the same energy. The comparison of the stabilization energy per molecule of the different clusters with the corresponding value for liquid water does not support the mixture‐model theories of the structure of liquid water.

Statistical mechanics of polar systems: Dielectric constant for dipolar fluids
View Description Hide DescriptionThe Hemmer‐Lebowitz‐Stell‐Baer formalism is used to derive an exact expression for the dielectric constant ε of a polar (nonpolarizable) system. The Kac inverse‐range parameter γ is then introduced into the dipole‐dipole potential, and it is shown that in a ``mean‐field'' limit γ→0, the Clausius‐Mosotti expression is recovered in the same way that a van der Waals‐like theory has been previously recovered for simple fluids, a Debye‐Hückel‐like theory has been obtained for ionic fluids and the Weiss and Bragg‐Williams theories have been recovered for lattice systems. In this limit the zero‐field free energy reduces to the free energy of the same system at zero dipole moment. The relation this work bears to other formalisms and developments is discussed. In particular we show that our general expression and quite different‐looking earlier expressions give the same ε. We have avoided the approximations made in earlier treatments by Nienhuis and Deutch and by Ramshaw, and our work helps to clarify the status of those treatments.

Hydrates in supersaturated binary sulfuric acid‐water vapor
View Description Hide DescriptionPortions of the free energysurface giving the reversible work W required to form a droplet containing n _{1} molecules of H_{2}O and n _{2} molecules of H_{2}SO_{4} from an initially homogeneous vapor have been calculated for a variety of relative humidities and H_{2}SO_{4} vapor concentrations. These surfaces are displayed as three dimensional perspective plots. The surfaces predict the existence of stable H_{2}SO_{4} hydrates in the vapor phase, and the number of hydrates, N_{h} , with h molecules of H_{2}O per hydrate has been calculated for three different values of the relative humidity. The results of these calculations indicate that virtually all the H_{2}SO_{4} present, especially for relative humidities greater than 100%, exists in hydrate form. As the relative humidity is increased (i.e., greater than 200%), the distribution of hydrate sized agrees well with that found by Giauque et al. for solid H_{2}O–H_{2}SO_{4} mixtures. Hydrate formation can exert an appreciable effect on the process of vapor phase nucleation in H_{2}O–H_{2}SO_{4} mixtures, and must be considered in any theory of nucleation rate.

Excess energy dependence of radiationless transitions in naphthalene vapor: Competition between internal conversion and intersystem crossing
View Description Hide DescriptionExperimental and theoretical evidence for effective internal conversion to the ground state from highly vibrationally excited states is presented for naphthalene‐h _{8} and ‐d _{8}. The evidence is based upon both the variation of the deuteron effect and strong exponential increase of the nonradiative decay rate as observed in the excess energy region between 10 000 and 18 000 cm^{−1}. The calculations are only consistent with the experiments if it is assumed that the excess energy does not redistribute completely according to the statistical weighting among the normal modes but rather stays in the class of strongly accepting modes.

Photoelectron spectroscopy of high temperature vapors. V. HeI spectra of GaX_{3} and InX_{3} (X = Cl, Br, I)
View Description Hide DescriptionThe HeI (584 Å) photoelectron spectra of GaX_{3} and InX_{3} (X=Cl, Br, I) are reported. All peaks are classified and the results are compared with spectra of the boron trihalides to bring out systematic variations caused by substituting different halogens and central atoms. A revision of the classification of the outermost e′ and e″ peaks in the spectra of BBr_{3} and BI_{3} is suggested. The spectra of GaI_{3} and InI_{3} exhibit splitting of the band due to ionization from an e″ MO (in D _{3h } symmetry), which suggests that either the neutral ground state or the first excited ^{2} E″ state of the ion is pyramidal.

Decomposition of K and T matrices for inelastic scattering using variational principles
View Description Hide DescriptionA family of related approximate equations for K and T matrices applicable to inelastic scattering are derived from a variational principle using operator decompositions and projection operators. These approximations utilize the computational simplicity of first and second Born integrals but have the character of a resummed series such as to extend the usefulness of perturbation theory to stronger interactions and to provide information on multiquanta transitions. The approximations can be viewed as a reorganization of perturbation theoryinformation to yield high‐order nonperturbative results. The size of the matrices that enter the decomposition formulation is controlled by the states included in the projection operator. Coupling between these states is included to all orders and is not restricted to transitions between states coupled directly by the potential. The remaining degrees of freedom are treated in a renormalized Born approximation. The formulations can be developed for K or T, either fully off‐shell, half off‐shell, of fully on‐shell, and the final approximations are rational in the potential strength. The approximations to the K matrix are Hermitian so that the resulting S matrix is unitary.