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Volume 63, Issue 9, 01 November 1975

Energy transfer in one‐dimensional molecular crystals: Direct and indirect energy exchange in the non‐Boltzmann regime
View Description Hide DescriptionDirect energy transfer between localized states via virtual coupling with the host states in one‐dimensional molecular solids is demonstrated experimentally using optical and optically detected electron spin coherence techniques. The relative importance of direct transfer versus indirect transfer (which is characterized by the phonon‐assisted promotion of the localized state to the band with the subsequent radiationless decay into a mobile exciton followed by retrapping) has been determined in isotopically mixed 1,2,4,5‐tetrachlorobenzene crystals over a temperature range where the thermal energy of the lattice is insufficient to establish Boltzmann equilibria between the localized and delocalized states (non‐Boltzmann regime). The results demonstrate that the transfer mechanisms between trap and host states are very sensitive to the trap concentration and the temperature of the lattice, and that direct exchange is dominant at high trap concentrations. Finally, the experimental results are compared with the theoretical expectations for excitation yields and trap‐to‐trap distances in the isotopically mixed crystals.

Metal‐isotope measurements of iron pentacarbonyl
View Description Hide DescriptionThe infrared spectra of ^{54}Fe(CO)_{5} and natural abundant Fe(CO)_{5} have been measured and compared in the 350 to 4000 cm^{−1} region. These measured shifts are compared to shifts calculated from three force fields.

Resonance Raman spectra and structure of some complex nitroaromatic molecules
View Description Hide DescriptionResonanceRaman spectra are reported for several biologically important nitroanilines and nitrophenols. The data provide new insight into intramolecular interactions in highly conjugated nitroaromatics. In certain o r t h o substituted compounds the data provide evidence for structural changes in going from the ground to the excited electronic state, or states, probed by the resonance Raman experiment. In each compound several Raman bands show variation of intensity with excitation wavelength. For N‐methyl‐o‐ nitroaniline excitation profiles for some isolated bands appear to peak at the maximum of the electronic absorption band at 442.0 nm. Experimental intensity profiles are compared to the presently available theories.

Self‐diffusion coefficients of a nematic liquid crystal via an optical method
View Description Hide DescriptionBy observing the textural changes caused when an enantiomer is allowed to diffuse into a racemic nematic liquid crystal of the substituted phenyl‐4‐benzoyloxybenzoate series, self‐diffusion coefficients can be directly evaluated in both the nematic and isotropic phases. The data obtained are shown to be consistent with other determinations by mass‐transport techniques, but inconsistent with relaxation methods, and the mechanistic factors causing these inconsistencies are discussed.

Theory of random walks with limited order of non‐self‐intersections used to simulate macromolecules
View Description Hide DescriptionA general theory of random walks subject to partial elimination of self‐intersections has been carried out. Specifically, the theory applies to so‐called self‐avoiding walks of order p, meaning that loops of p or less are forbidden while larger loops are allowed. All walks, used to represent macromolecules, are categorized by the configurations of their last p−1 steps. The theory deals with the successive addition of steps through use of transition matrices, together with their eigenvectors and eigenvalues, taking cognizance of the effect of symmetry. An exact solution is derived in general form and it is found that the mean square end‐to‐end separation of the walks becomes asymptotically linear in n, the number of steps. The slope of the asymptotic line increases with the order p, presumably without limit. All classes of walks, characterized by their different end configurations, asymptotically exhibit similar linear behavior with the same slope but with different intercepts.

Laser photoluminescence of TiO in Ne at 4 °K
View Description Hide DescriptionPseudo‐gas‐phase photoluminescence spectra of TiO isolated in Ne matrices at 4 °K have been obtained. Photoluminescence is induced by laser excitation from the X ^{3}Δ ground state to B ^{3}Π and C ^{3}Δ electronic levels using a cw tunable dye laser and a cw argon ion laser, respectively. Red emission from B ^{3}Π vibrational levels terminating in ground state levels is observed. In addition, the B ^{3}Π (v=0) and B ^{3}Π (v=1) levels have been found to undergo matrix‐induced intersystem relaxation into the b ^{1}Π state. Near‐infrared emission between excited states in the singlet manifold of TiO has been observed and identified as belonging to the δ (b ^{1}Π→a ^{1}Δ) and the φ (b ^{1}Π→d ^{1}Σ^{+}) band systems. Observed δ and φ emission bands are uniformly shifted by −93 cm^{−1} and +73 cm^{−1}, respectively, from observed or predicted gas phase bandheads. The line shape of the δ and φ emission in the solid is that of a sharp zero‐phonon line accompanied by a broad multiphonon sideband. An additional sharp zero‐phonon emission system, here labeled the ζ system, is found to overlap several broad multiphonon bands of the red γ′ (B ^{3}Π→X ^{3}Δ) emission. Evidence obtained supports the tentative conclusion that the ζ system is due to intercombination b ^{1}Π→X ^{3}Δ emission. From the assigned intercombination transition the energy of the low‐lying a ^{1}Δ state is determined to be 3500 cm^{−1} above the X ^{3}Δ ground state. The 3500 cm^{−1} value for the relative energy between the isoconfigurational a ^{1}Δ and X ^{3}Δ states is in qualitative agreement with theoretical expectations based on consideration of the bonding in the TiO molecule.

Low‐frequency vibrational spectra and ring puckering of cyclopentene‐d _{8}
View Description Hide DescriptionMore than 25 ring‐puckering transitions have been observed in the vapor‐phase Raman and far‐infrared spectra of cyclopentene‐d _{8}. The ring‐puckering potential energy function in reduced form was determined to be V=18.20(Z ^{4}−6.88 Z ^{2}) cm^{−1} which represents a barrier to inversion of 215 cm^{−1} (0.61 kcal/mole). The barrier differs from that of the undeuterated cyclopentene by 17 cm^{−1} owing to mixing of other motions (presumably CH_{2} rockings). The equilibrium value of the molecule is calculated to have a dihedral angle of 26°.

Cross section for single and double ionization of N_{2} and O_{2} molecules by electron impact from threshold up to 170 eV
View Description Hide DescriptionAbsolute ionization cross sections have been measured for the processes N_{2}+e→N_{2} ^{+}+2e, N_{2}+e→N_{2} ^{++}+3e, O_{2}+e→O_{2} ^{+}+2e, and O_{2}+e→O_{2} ^{++}+3e as a function of electron energy up to 170 eV in a crossed molecule–electron beam apparatus. The ionization cross section curve for producing the singly charged parent ions N_{2} ^{+} and O_{2} ^{+} is found to have at least one inflection of the type first observed by Lawrence for mercury. Using nth root extrapolation the following minimum ionization potentials were derived from the low energy cross section behavior: N_{2} ^{+}(X ^{2}Σ_{ g } ^{+}) =15.6±0.1 eV, N_{2} ^{++}(^{3}Π_{ u }) =42.9±0.3 eV, O_{2} ^{+}(X ^{2}Π_{ g }) =12.1±0.1 eV, and O_{2} ^{++}(X ^{1}Σ_{ g } ^{+}) =35.6±0.3 eV. From distinct breaks in the single ionization cross section curve the following excited states were observed; N_{2} ^{+}(B ^{2}Σ^{+} _{ u }) =18.8±0.2 eV, O_{2} ^{+}(a ^{4}Π_{ u }) =16.0±0.2 eV, and O^{+} _{2}(^{2}Σ^{−} _{ g }) =21.0±0.2 eV. In the double ionization cases, a square law was found from threshold up to some 20 eV above threshold. All results are compared with previous measurements if available.

Nonadiabatic effects in the collision of F(^{2} P) with H_{2}(^{1}Σ^{+} _{ g }). I. SCF interaction potentials for the 1 ^{2} A′, 2 ^{2} A′, and ^{2} A ^{″} states in the reactant region
View Description Hide DescriptionInteraction potentials for the 1 ^{2} A′, 2 ^{2} A′, and ^{2} A ^{″} states of the F+H_{2} system are computed in the self‐consistent field (SCF) approximation for a range of geometries suitable for the study of nonadiabaticinteractions at thermal energies. Notable features found for the energy surfaces are (a) dominance at long range of the quadrupole–quadrupole interaction, (b) strong repulsive forces at small F–H_{2} separations for the excited‐state surfaces, and (c) a pseudocrossing region with a conical intersection for the collinear nuclear arrangement at R (F–H_{2}) =5.2 a.u.

Comments on a new class of ionic materials
View Description Hide DescriptionWe consider the cohesion and electronic structures of a new class of ionic compounds including Na_{2}C_{18}H_{36}N_{2}O_{6} and NaC_{18}H_{36}N_{2}O_{6}I.

Bound‐state energies of the exponentially screened static and cosine Coulombic potentials
View Description Hide DescriptionBound state energies of the exponentially screened Coulomb potentials: V (r) =−Z e ^{−αr } cosεαr/r, static (ε=0) and oscillatory (ε=1), are obtained by a perturbation calculation on the basis of the Hulthén functions. Closed form expressions of the perturbative matrix elements as well as of the Hulthén functions, for ’’S’’ states and for l≠0 states (with an approximated rotational term), are obtained by the ladder operator method. When varying the values of the Hulthén parameter, the first order perturbed eigenvalues of the screened potentials are found to be close to the exact values. New results (l≠0) are given for the cosine case.

Modification of Glauber theory for dynamic scattering of electrons by polyatomic molecules
View Description Hide DescriptionIn its original form, Glauber scattering theory achieves a considerable simplification by neglecting several factors of modest consequence in atomic scattering but of importance in molecular scattering. These include, in particular, the spread of the shadow cast by a scatterer as a wave propagates downstream in the target. Although such effects do not matter in the original range of validity of the theory, the characteristic distances in molecules restrict the unmodified theory to an excessively small angular range. The present treatment introduces phase factors to take into account the distribution of scatterers in the incident direction and the propagation of the scattered waves in the target. This appreciably extends the formal range of applicability.

Experimental dipole moment function and calculated radiative lifetimes for vibrational transitions in carbon monoxide a ^{3}Π
View Description Hide DescriptionWe have used precision Stark effect data from a previously reported molecular beam electric resonance study of CO a ^{3}Π to determine the dipole moment operator as a function of the internuclear coordinate R for this state. The resulting experimental dipole moment function is well determined in the range 1.10 Å⩽R⩽1.35 Å, corresponding to the region sampled by the v=0–3 vibrational levels used for this analysis. With this dipole moment function we then calculate the spontaneous vibrational transition probabilities for the lower vibrational levels within CO a ^{3}Π. We obtain a lifetime for CO a ^{3}Π v=1→v=0 transition of 17 msec, approximately half the corresponding v=1→v=0 lifetime observed for ground state CO X ^{1}Σ^{+}. It is shown that vibrational radiative lifetimes are quite comparable to electronic radiative lifetimes in CO a ^{3}Π.

Studies in molecular dynamics. XV. High temperature description of the transport coefficients
View Description Hide DescriptionThe power series expansion of the transport coefficients in the attractive potential relative to the kinetic energy does not exist. However, the first term in this expansion appears to exist and is evaluated indirectly by molecular dynamics at various densities. For the diffusion coefficient this first term is predicted quantitatively at high density by the enhanced local density in the region of the attractive potential relative to that of the hard sphere system. Furthermore, since the enhanced density does not affect the kinetic contribution to the viscosity and thermal conductivity, these transport coefficients compare favorably with the predictions of the Boltzmann equation. An explicit calculation of the first term requires statistical mechanical averaging before expansion, a procedure unsuitable to molecular dynamics computations and which has as yet been unattained analytically at any finite density.

Influence of the Overhauser effect on ^{14}N PNQR T _{1} measurements on a single crystal of parachloroaniline
View Description Hide DescriptionSpin lattice relaxation measurements of ^{14}N by PNQR pulse experiments on a single crystal and powder of parachloroaniline are reported. In this compound, there are two symmetry related nitrogen sites in the unit cell. The dipolar interaction between nuclei in both sites affects the experimental results by an Overhauser‐type effect. This effect on various types of pulse experiments is analyzed. To simplify the analysis, the quadrupole Hamiltonian is expressed in terms of fictitious spin 1/2 angular momentum operators. The density matrix in this representation in the rotating frame of the quadrupole Hamiltonian is discussed, and the signal function for various types of pulse experiments is derived. The experimental results are in good agreement with theory.

Steric hindrance in the gas phase singlet electronic energy transfer: From naphthalene to the t r a n s‐azobutane isomers
View Description Hide DescriptionThe singlet intermolecular energy transfer rates from naphthalene (S _{1}, ∼91 kcal/mol) to the various t r a n s‐azobutane isomers have been measured in the gas phase. The first excited singlet states of these azobutane isomers lie below ∼70 kcal/mol. The rate constants for singlet collisional energy transfer (k _{ c }) are 30.3±2.6, 18.9±0.9, 12.6±1.0, and 3.2±0.3 in units of 10^{10} M ^{−1}⋅sec^{−1}, for the accepter series azo‐n‐butane, azoisobutane, azo‐s e c‐butane, and azo‐t e r t‐butane, respectively. The tenfold decrease in the rates of energy transfer through this series have been attributed to increasing steric inhibition of the electron exchange contribution to singlet–singlet electronic energy transfer.

Generalized x‐ray scattering factors in diatomic molecules
View Description Hide DescriptionGeneralized x‐ray scattering factors for atoms (pseudoatoms) in diatomic molecules are determined from a finite multipole expansion of the charge density about each nucleus. The Fourier–Bessel coefficients of the pseudoatom radial density functions are determined by a least squares fit to the molecular form factor. All molecular one‐center averages of the form 〈g (r _{ a }) P _{ j }(cosϑ_{ a }) 〉 are correctly given by the pseudoatom superposition whenever j?J, where J is the highest order multipole included in the a pseudoatom, regardless of the highest multipole order K for the b pseudoatom. To illustrate this property, a number of relationships between moments of the molecular charge distribution and of the pseudoatom are given. In addition, a sum rule relating the molecular form factor to the expectation values 〈r _{ a } ^{−(j+1)} P _{ j }(cosϑ_{ a }) 〉 and 〈r _{ b } ^{−(k+1)} P _{ k }(cosϑ_{ b }) 〉 is derived. For H_{2} the theoretical, coherent x‐ray scattering intensity is reproduced to about 1% for J=K=1 and to about 0.1% for J=K=2.

Diatomic generalized x‐ray scattering factors: Results from Hartree–Fock electron density functions
View Description Hide DescriptionGeneralized x‐ray scattering factors based on multipole representation of the atoms have been calculated from Hartree–Fock Roothaan one‐electron molecular density functions of first row diatomic hydrides (BH to FH) and the 14 electron series BF, N_{2}, (^{1}Σ)CO, and (^{3}Π)CO. The effect of different truncation of the mutipole expansions is discussed for NH. Results for the other molecules from expansions up to quadrupolar terms on each center are discussed. The monopole scattering factors are virtually the same as Hartree–Fock atomic form factors except at low sinϑ/λ values. The dipole and quadrupolescattering factors are rather specific to the particular molecule for the valence region, but core polarization features are similar. Static charge properties of the molecule are accurately given by the generalized scattering factors. However, charge properties associated with the individual pseudoatoms are strongly dependent on truncation of the multipole expansion. The coherent x‐ray scattering intensities of the molecule can be calculated from the generalized x‐ray scattering factors with a maximum relative error no larger than 4×10^{−5}.

Thermomagnetic torque in hydrogen isotopes
View Description Hide DescriptionThe thermomagnetic torque has been measured in parahydrogen and ortho and normal deuterium for pressures from 0.10 to 2.0 torr and temperatures from 100 to 370 K. Since the torque depends on the precession of the molecular rotational magnetic moment around the field direction, coupling of the molecular nuclear spin to the rotational moment can affect the torque. Evidence of spin coupling effects is found for the torque in both deuterium modifications. In para hydrogen the torque at all temperatures and pressures exhibits behavior expected of a gas of zero nuclear spin molecules. Additionally, earlier data for hydrogen deuteride and for normal hydrogen from 105 to 374 K are evaluated and discussed. The high pressure limiting values of torque peak heights and positions for all these gases are compared with theory.

Direct transitions among the allotropic forms of boron nitride at high pressures and temperatures
View Description Hide DescriptionThe direct transition behavior among the graphitic (hBN), wurtzitic (wBN), and zincblende (zBN) crystal forms of boron nitride is investigated as a function of temperature for pressures up to 130 kbar. At pressures in the 45 to 70 kbar range, direct transformation of both the hBN and wBN forms to the zincblende form are observed and at higher pressures (85 kbar and above) direct transformation of hBN to wBN is also observed. A pressure/temperature phase diagram is presented for pressures up to 130 kbar. In this pressure range, the thermodynamically stable solid phases are hBN and zBN, the experimental behavior indicating that wBN is not thermodynamically stable over this range. From temperature/time data, the activation energy for both the hBN to zBN and wBN to zBN transitions is estimated to be about 200 kcal/mole. From these high activation energies it is concluded that the direct conversion processes essentially require disruption of the hBN and wBN lattices before the atoms can re‐form into the zincblende structure.