Volume 60, Issue 2, 15 January 1974

Electronic structure and spectra of small rings. V Photoelectron and electron impact spectra of cyclopropenone
View Description Hide DescriptionThe photoelectron and electron impact spectra of cyclopropenone are presented and are interpreted with the aid of Gaussian orbital calculations of double‐zeta quality. The spectra and the calculations all lead to the conclusion that there is an unusually large interaction between both the pi and lone pair orbitals in the carbonyl portion of the molecule with the pi and sigma orbitals of the olefin portion. The first ionization potential (9.57 eV) involves ionization of an electron from the oxygen lone pair, whereas the second (11.19 eV) involves ionization of an electron from the olefin pi bond. The most vertical ionization is from the 7a _{1} MO (16.11 eV), the second lone pair orbital on oxygen. Rydberg series are observed in the electron impact energy loss spectrum converging upon each of these three ionization potentials.

Theoretical studies of H+H_{2} reactive scattering
View Description Hide DescriptionThe H + H_{2} reactive scattering problem was studied quantum mechanically in three dimensions by the close‐coupling technique. The ground vibrational state and a set of up to seven rotational states were included in the basis for both the initial and the final channels. The interaction of the three particles was described by the Porter‐Karplus surface in order to permit comparison with classical calculations. A method was developed for solving the sets of coupled integrodifferential equations that appear in the close‐coupling approach to rearrangement scattering. Transition probabilities for reactions involving the 0, 1, 2 rotational states of H_{2} were calculated for relative kinetic energies from 0.20 to 0.50 eV. Differential cross sections were estimated for the 0→1 rotational transition. The results were compared with three‐dimensional classical studies as well as other quantum mechanical results. A significantly lower threshold for reaction was obtained in the present work both with respect to the three‐dimensional classical results and a distorted wave Born calculation for reactive scattering from the same surface.

Dipole moments of the lowest excited singlet and triplet states of 2,4,5‐trimethylbenzaldehyde in a durene host crystal
View Description Hide DescriptionFrom Stark spectra, the differences in dipole moments between the ground state and the lowest singlet and triplet excited states of 2,4,5‐trimethylbenzaldehyde isolated in a durene host crystal are determined within a precise Lorentz local field approximation to be 1.65 ± 0.09 D and 1.05 ± 0.06 D, respectively, for the most prominent sites. Neither dipole moment change is parallel to the carbonyl axis, but the change for the singlet state has the largest component along this axis while that for the triplet state does not. These data are consistent with the assignment of these states as primarily ^{1} nπ* and ^{3}ππ*. The dipole moment of the ground state was determined to be 3.53 ± 0.05 D from dielectric constants of benzene solutions.

Exciton dynamics in molecular solids from line shape analysis: An assessment of the extent of line shape distortion resulting from use of real crystals
View Description Hide DescriptionFor crystal absorption systems, the line profile of the frequency dependence of the dielectricpermittivity ε(ω) contains information about the excitondynamics that may be studied by the autocorrelation function generated by the Fourier transformation of ε(ω) into the time domain. However, ε(ω) obtained through transforming normal incidence reflectance data R (ω) of a real crystal when the photon‐crystal eigenmodes are strongly coupled may be considerably distorted from ε(ω) of a perfect infinite crystal. In this paper, we consider the ways by which such distortions may arise and, by using a model for ε(ω) that might reasonably correspond to the 4000 Å b‐polarized 0–0 absorption system at low temperatures of crystalline anthracene probed on the (001) face, we illustrate the dependence of the extent of distortions on the line profile of ε(ω) upon the following number of factors, viz., (i) spatial dispersion of the exciton bands; (ii) use of an oblique angle of incidence as an approximation to normal incidence in determining R (ω); (iii) thickness of the crystal slab used to determine R (ω); (iv) extent of roughness on the crystal surface; (v) mole fraction of defects in the crystal; and (vi) mole fraction of impurities in the crystal. The treatment allows definition of the condition [real ε(ω) < 0] under which various quasiparticles (longitudinal excitons, surface excitons,excitons bound to impurities) may be excited in a particular crystal system. The methods employed in this paper are of general applicability to strongly absorbing crystal systems and will be of use in understanding excitondynamics in such systems. The data provide a firm foundation for interpreting reflectance data of a strongly absorbing crystal system, and thus we are able to discuss existing spectral data for anthracene crystals, especially narrow structure observed in low temperature reflection spectra, as well as suggest areas for both theoretical and experimental work.

Magnetic susceptibilities of trivalent lanthanide ions in an octahedral environment
View Description Hide DescriptionMagnetic susceptibilities for eight lanthanide ions in Cs_{2}NaLnCl_{6} were measured from 2.5 to [inverted lazy s] 80°K with a vibrating sample magnetometer. Computer fitting of the data for Cs_{2}NaCeCl_{6} gave g = 1.43 for the Γ_{7} ground level, and f ^{2} = 3.85 for the Γ_{8} excited level. These values are in good agreement with values calculated from first‐order wavefunctions. The ground crystal field level for Nd^{3+} in Cs_{2}NaNdCl_{6} was found to be a Γ_{8} level. Because of singlet ground levels and small crystal field splitting, no positive information on the ground crystal field levels was obtained for Pr^{3+}, Tb^{3+}, Dy^{3+}, Ho^{3+}, Er^{3+}, or Tm^{3+} compounds. Based on Nd^{3+} and Ce^{3+} results, the ratio was estimated to be about 20; , of the order of 10 cm^{−1}; and , of the order of 1 cm^{−1}.

Intermode vibrational energy transfer in laser excited CH_{3}Cl
View Description Hide DescriptionThe infrared fluorescence risetimes of the (ν_{1}, ν_{4}) and ν_{2} modes of CH_{3}Cl have been measured after pumping the ν_{6} mode with a Q‐switched CO_{2} laser. The rates of rise were found to be 214 ± 60 msec^{−1} · torr^{−1} for (ν_{1}, ν_{4}) and 160 ± 45 msec^{−1} · torr^{−1} for ν_{2}. Possible filling pathways for these modes are discussed, and infrared fluorescence rates for all modes in CH_{3}Cl are summarized. The results are compared with similar intermode vibrational transfer rates in CH_{3}F.

Transfer of functional group electronic structure representation between molecules: Ethane from methane
View Description Hide DescriptionPreviously developed analyses are coordinated into a viable scheme for effecting the transfer of electronic structure representation from one molecule to another. The scheme is sufficiently flexible to enable variational redetermination of portions of the electronic structure. Results are presented for a number of variants of transfer of methyl groups from methane to ethane. Comparison with the fully variational SCF calculation is made. The results are encouraging for expanding the scope of the approach.

Hopping of ions in ice
View Description Hide DescriptionThe effects of intermolecular tunneling by protons in ice and other protonic semiconductors on thermodynamic and transport properties are estimated on the basis of an idealized model. The model involves a simple tight‐binding Hamiltonian on the infinite‐dimensional set of molecular configurations in the generally proton‐bonded but otherwise disordered structure. The cycle‐poor topology of the state set is approximated by that of a cycle‐free Bethe lattice, i.e., an infinite, homogeneous Cayley tree. For coordination q and hopping matrix element V the distribution of energy levels is given by the function g(u) = g(E/V) = q[4(q − 1) − u ^{2}]^{1/2}/2π(q ^{2} − u ^{2}), where q = 3 for the set of hopping options available to an ion in ice. The thermal average of the group velocity v = [4(q − 1) − u ^{2}]^{1/2} V d / ℏ on the Bethe lattice with lattice spacings d determines a finite coefficient of diffusion in real three‐dimensional space, where paths on the Bethe lattice are represented by random walks in 3 space with only a finite measure of correlation between the directions of successive steps. These results agree with recent computations by Minagawa and with the results of various parallel efforts in the theory of electron tunneling. Some questions of principle are resolved by an analysis of the corresponding eigenvalue problem for a symmetrically constructed finite Cayley tree, and an effective upper bound for the error incurred by disregarding cycles is obtained from a computation for a periodic graph in three dimensions. While the ionic mobilities in ice are not yet well known, even the greatest claimed values of about 0.075 cm^{2}/V · sec are compatible with matrix elements somewhat smaller than 1 mV, which would entail tunneling corrections to the partition function for a hydrogen ion of less than 2% near the freezing point.

Temperature dependence of the isotopic liquid‐vapor fractionation factor for nitric oxide
View Description Hide DescriptionThe ^{15}N/^{14}N isotope fractionation factor between NO liquid and vapor has been determined in the temperature range 110–173°K. The results are in good agreement with the isotopic vapor pressure data of Clusius et al., which cover the range 110–121°K. The isotope fractionation data follow the T ^{−2} law up to 135°K. A refinement of the T ^{−2} law analysis of the isotopic vapor pressure data given by Bigeleisen in 1960 has been carried out by the harmonic oscillator cell model to include T ^{−1} and T ^{0} terms. It is shown that the T ^{−2} terms from the dimerization of the monomer in the liquid and the hindered translation and rotations of the dimer dominate the isotope fractionation factor. The falloff from the T ^{−2} law for the liquid‐vapor fractionation factor in NO is steeper than in argon. This is reconciled with the dissociation of the dimer in the liquid and the association of the monomer in the vapor at high temperatures.

Temperature dependence of vibrational energy transfer from DF (v = 1) to several diatomics
View Description Hide DescriptionThe V‐Venergy transfer rates from DF (v=1) to HCl, HBr, DBr, D_{2}, N_{2}, O_{2}, CO, and NO have been measured at temperatures from 295 to ∼ 800°K. The measurements were made behind reflected shock waves with the laser‐induced fluorescence technique. The rates for V‐V transfer to the infrared‐active molecules show an inverse temperature dependence near room temperature, characteristic of collisions dominated by attractive potentials. The rates for V‐V transfer to the homonuclear diatomics have positive temperature dependences, typical of short‐range repulsive potential interactions. Several rates of V‐R, T deactivation by DF were also obtained. The available data for the hydrogen halides show that P _{HY‐HX} > P _{HX‐HY} when P _{HX‐HX} > P _{HY‐HY}. HF and DF are equally efficient in deactivating HCl (v=1) and HBr (v=1).

Direct correlation function between charges and the equation of state of simple fluids
View Description Hide DescriptionA parallel drawn between classical correlation functions of molecular densities and correlation functions of charge densities arising in the quantum mechanical treatment of molecular fluids enables us to introduce the notion of a direct correlation function between charges, which can be used to derive an accurate equation of state that incorporates both the effect of the short‐range repulsion and the effect of additive and nonadditive many‐molecule dispersion forces.

Quantum mechanical perturbation expansion of the second virial coefficient and the Ursell‐Mayer function. II. The Heitler‐London linear polarizability model
View Description Hide DescriptionBy a modification of a previous method of quantum mechanical perturbation expansion, the Ursell‐Mayer function f(R) is obtained in the form 1 + f(R) = exp(−ΔE)(1 + βU _{1} + β^{2} U _{2} + ⋯) where ΔE is the Heitler‐London energy and U_{n} is at least of order 2n in the Coulomb interaction energy of the pair of molecules. The U_{n} 's depend on electron overlap integrals and distorted charge distributions. When electron overlap and charge distribution distortion are neglected the U_{n} 's become products of long range dispersion interaction potentials. Furthermore when the effect of nonlinear polarizabilities is neglected one obtains . The results are restricted to temperatures sufficiently low compared to the excitation energies of the two molecules.

Spontaneous decay of the state of Xe_{2}
View Description Hide DescriptionThe upper lasing level (first excited state) of molecular xenon is examined in the context of a particle‐hole model, with a view toward gaining insight into the electronic configuration and the electric dipole transition to the ground state. It is found that the spontaneous decay time of this lasing transition, reasonably independent of the form of the molecular binding, is in this model 23 ± 8 nsec.

Measurements of hyperpolarizabilities for some halogenated methanes
View Description Hide Descriptiondc Electric‐field induced optical second‐harmonic generation has been measured for CH_{4}, CH_{3}F, CH_{2}F_{2}, CHF_{3}, CF_{4}, CClF_{3}, and CBrF_{3}. For CH_{4} and CF_{4} the third order hyperpolarizability χ(−2ω; 0,ω,ω) is obtained directly. For the other (dipolar) molecules, a bond additivity estimate for χ(−2ω; 0,ω,ω) is used to extract the second order hyperpolarizability χ(−2ω;ω,ω).
Results are compared with various data from the literature: calculated hyperpolarizabilities, and measurements of optical harmonic generation, optical mixing and the Kerr effect. The degree of consistency of the experimental data with a bond additivity model is discussed.

Conformation of the −NH_{2} group in a single crystal of p‐chloroaniline as determined by combined Zeeman effects on the ^{35}Cl and ^{14}N nuclear quadrupole resonances
View Description Hide DescriptionThe Zeeman effect on the nuclear quadrupole resonance of both ^{35}Cl and ^{14}N nuclei in a single crystal of p‐chloroaniline has been studied at room temperature. A spectrometer was employed which was capable of working at the resonance frequency of either nucleus without altering the position of the crystal. Novel features of the spectrometer were both a frequency stabilizing apparatus working at the ^{14}N resonance frequency and the attachment of an electronic computer for direct and accurate ``on‐line'' determination of spectral parameters. The relative orientations of the electric field gradient tensors on both nuclei have been obtained. Furthermore, by studying the ^{14}N linewidth dependence on the static magnetic field orientation, information has also been gained about the position of the −NH_{2}protons in the electric field gradient tensor principal axes mainframe. Some remarkable experimental results can be interpreted theoretically when the treatment of the magnetic dipole interaction between ^{14}N and ^{1}H in the −NH_{2} group is pushed beyond first order. Analogous information has been gained by also studying a single crystal of p‐bromoaniline.

Electronic‐to‐vibrational energy transfer efficiency in the O(^{1} D)–N_{2} and O(^{1} D)–CO systems
View Description Hide DescriptionWith the aid of a molecular resonancefluorescence technique, which utilizes optical pumping from the v=1 level of the ground state of CO by A ^{1}Π‐X ^{1}Σ^{+}radiation, we have investigated the efficiency of E‐V transfer from O(^{1} D) to CO. O(^{1} D) is generated at a known rate by O_{2}photodissociation at 1470 Å in an intermittent mode, and the small modulation of the fluorescent signal associated with CO(v=1) above the normal thermal background is interpreted in terms of the E‐V transfer efficiency. The CO(v=1) lifetime in this system is determined mainly by resonance trapping of their fundamental band, and is found to be up to ten times longer than the natural radiative lifetime. For CO, (40 ± 8)% of the O(^{1} D) energy is converted into vibrational energy. By observing the effect of N_{2} on the CO(v=1) fluorescent intensity and lifetime, it is possible to obtain the E‐V transfer efficiency for the system O(^{1} D)–N_{2} relative to that for O(^{1} D)–CO. The results indicate that the efficiency for N_{2} is (83 ± 10)% of that for CO. In both cases the initial vibrational distribution remains unspecified. The relatively high efficiency of the O(^{1} D)–N_{2} reaction implies that it is the sole source of the N_{2} vibrational temperature in the earth's upper atmosphere.

Molecular beam reactions of potassium atoms with ZnCl_{2}, ZnI_{2}, CdI_{2}, HgBr_{2}, and HgI_{2}
View Description Hide DescriptionThe reactions of K atoms with ZnCl_{2}, ZnI_{2}, CdI_{2}, HgBr_{2}, and HgI_{2} have been studied in crossed molecular beams. Angular and velocity distributions of the potassium halide products were obtained over wide ranges. The angular distributions indicate that the reactions proceed through long‐lived complexes for some cases and through ``osculating complexes'' for others. The velocity distributions are compared to approximate results from phase space theories.

Effect of magnetic and electric fields on the transport properties of polyatomic gases. I. Formal theory
View Description Hide DescriptionThe changes in the coefficients of shear viscosity and thermal conductivity caused by a homogeneous external field are considered for a single‐component, dilute gas of spin‐zero, polyatomic molecules. The quantum mechanical equations for these Senftleben‐Beenakker effects are solved by an iterative technique which is especially suited to a series of restricted distorted wave approximations to the transition matrix. In this manner more rigorous and more physical reasons are found for the dominance of certain terms in the expansions usually employed to solve such equations. The final expressions for the Senftleben‐Beenakker effects are in terms of ``collision integrals'' which are greatly simplified by using group theoretical methods to completely and explicitly handle the m‐type quantum numbers.

Effect of magnetic and electric fields on the transport properties of polyatomic gases. II. The second order effect for rigid rotors in a magnetic field
View Description Hide DescriptionThe formal theory previously developed is applied to rotating, nonvibrating, diatomic molecules (i.e., rigid rotors) in a homogeneous magnetic field. It is shown that the approximations made in the formal theory are quite good. Nevertheless, a ``straightforward'' calculation of the Senftleben‐Beenakker effect which is of second order in the potential anisotropy does not agree with experiment. This effect is shown to be of some mixed or higher order in the anisotropy.

Effect of magnetic and electric fields on the transport properties of polyatomic gases. III. Mixed second order effect on the shear viscosity of rigid rotors in a magnetic field
View Description Hide DescriptionThe Senftleben‐Beenakker effect on the shear viscosity coefficients of a rigid rotor in a homogeneous magnetic field is treated in detail. Quantum and classical limit equations, valid for any intermolecular potential with a given functional dependence upon the angles between colliding molecules, are presented for this effect. Experimental measurements of this effect should lead, through the equations presented, to detailed information about anisotropicintermolecular potentials. As an example, calculations using a crude intermolecular potential to represent N_{2} are in reasonable agreement with experiment. The Senftleben‐Beenakker effect on shear viscosity is shown to be of mixed second order in the potential anisotropy.