Volume 60, Issue 12, 15 June 1974

Time autocorrelation functions for harmonic solids from Gaussian quadratures
View Description Hide DescriptionGaussian quadratures determine time autocorrelation functions (TAF's) of harmonic solids from modified moments of the phonondensity of states. The quadratures determine the TAF's with great precision out to times more than twice those at which the Taylor series expansion in time ceases to be accurate. The quadratures provide rigorous bounds to the TAF's over most of this range in time. Moreover, a single set of abscissas and weights determines the quadratures for both position and momentum TAF's. The method can determine TAF's to long times, so that the asymptotic behavior can be examined for a simple model solid.

Mechanism of condensation. II. Condensation of molecular beams of sodium chloride on clean and contaminated surfaces of oriented single crystals of NaCl
View Description Hide DescriptionWith large supersaturation ratios, unit coefficients have been measured for condensation of normal‐incident molecular beams of sodium chloride on clean (100) oriented single crystalsurfaces of NaCl. Since α=1 for the composite molecular beam, individual coefficients for condensation of NaCl(g) and Na_{2}Cl_{2}(g) must have unit values under the conditions of these experiments. Over the range investigated, α is independent of molecular beam flux and surface temperature. A large flux of nitrogen on the surface during molecular beam deposition has no effect on α. Nonunit values of α correlate with the presence of relatively small amounts of hydrocarbons in the residual gas. The results of the present work on condensation on clean surfaces under ultrahigh vacuum differ from those previously reported for condensation of sodium chloride under high vacuum. A mechanism of condensation is proposed. Discrepancies between the present and previous results for condensation of sodium chloride are discussed.

Ionization in liquid hydrocarbons: γ radiolysis yields and electron range distribution functions
View Description Hide DescriptionThe use of an exponential distribution of initial separation distances in thermalized electron‐ion pairs in γ irradiated liquid hydrocarbons leads to the calculation of total ionization yields of G _{tot} = 5–6. The distribution possesses a power function tail (y ^{−3}) at large initial separations (y). The concepts of ionization and excitation in a liquid are briefly dicussed.

Theoretical analysis of the vibrational structure of the electronic transitions involving a state with double minimum: E, of H_{2}
View Description Hide DescriptionIt is shown that the convergence problem encountered in the numerical integration of the vibrational Schrödinger equation for an electronic state with a double‐minimum potential does not exist in the analytical expansion method. For the , C ^{1}π_{ u }, and E, states of H_{2}, the expansion method gives consistently and progressively better energy eigenvalues than the numerical integration. method. Franck‐Condon factors for the transitions and were computed, and the vibrational structure of the case is discussed in some detail.

EPR investigations of Eu^{2+} in orthorhombic sites of NaCl
View Description Hide DescriptionSpin‐Hamiltonian parameters describing the EPR spectrum of Eu^{2+} in orthorhombic sites of NaCl single crystals have been determined at 77 and 300 K. Previously undetermined absolute signs of the parameters were deduced from observations of relative line intensities at liquid helium temperatures. The sign of the second‐order spin‐Hamiltonian parameter b _{2} ^{0} was found to be positive and is therefore in agreement with the sign reported by Nair et al. for Eu^{2+} in KCl. Previously proposed models for the orthorhombic Eu^{2+}defects in alkali halides are discussed.

Application of the variational least squares method to inelastic scattering
View Description Hide DescriptionThe anomalyfree, minimumnorm, and variational least squares methods for algebraic variational inelastic quantum mechanical scattering calculations are all applied to the same example. The zeroorder variational least squares method, which is completely free of spurious singularities, is found to be an accurate and useful method. Some alternative versions of the variational least squares method are pointed out.

Rate constant of OH + OH = H_{2}O + O from 1500 to 2000 K
View Description Hide DescriptionIt was shown several years ago that concentration profiles of the OH radical in the shock‐initiated combustion of lean ([H_{2}]/[O_{2}] = 0.1) hydrogen‐oxygen‐argon mixtures at low pressures (≃ 30 kPa) and high temperatures (1200–2000 K) exhibit transient maxima prior to attainment of partial equilibrium. At that time, the maxima could not be accounted for quantitatively in terms of the accepted mechanism of the H_{2}–O_{2}reaction. The profiles have been reanalyzed utilizing more sophisticated computational techniques and increased knowledge of the reaction mechanism. The occurrence of maxima at temperatures above 1500 K was found to depend upon the ratio of the rate constants of the elementary reactions O+H_{2}→OH+H and OH+OH→H_{2}O+O. Using the rate constant expression 1.6×10^{14} exp(−56.6 kJ/R T) cm^{3} mol^{−1} s^{−1} for the former reaction, the rate constant expression for the latter was found to be 5.5×10^{13} exp(−29 kJ/R T) cm^{3} mol^{−1} s^{−1}. This latter expression does not extrapolate linearly on an Arrhenius plot to the available room temperature data. The effect of boundary layer growth on the data analysis is discussed.

^{127}I Mössbauer studies of some fluorosubstituted organo iodine compounds
View Description Hide DescriptionFrom the measured ^{127}I Mössbauer spectra, we have determined the isomer shift, quadrupole coupling constant, and recoilless fraction for CH_{3}I, CF_{3}I, C_{6}H_{5}I, o‐, m‐, and p‐C_{6}H_{4}FI, and C_{6}F_{5}I. From relative intensities of the peaks, there is evidence for either orientation or Goldanskii‐Karyagin effects in CH_{3}I, CF_{3}I, and φI. The isomer shifts and quadrupole coupling constants give values for the numbers of p and s holes, from which the charge and hybridization of iodine in these compounds is calculated. Except for C_{6}F_{5}I, the charges correlate well with the pK_{ a } of corresponding carboxylic acids. It is suggested that the anomalous behavior of this compound arises from the formation of a charge transfer complex in the solid. From a comparison of NQR and Mössbauer data for CI_{4} and CF_{3}I, an explanation is suggested for the anomalous decrease of chlorine NQR frequencies in the series of compounds CF_{ n } Cl_{4−n } (n = 0→3). The problem of deriving meaningful Mössbauer parameters from complex spectra taken with thick absorbers is discussed.

Precision neutron diffraction structure determination of protein and nucleic acid components. XV. Crystal and molecular structure of the amino acid L‐valine hydrochloride
View Description Hide DescriptionA neutron diffraction study of L‐valine · HCl has been carried out: space group P2_{1}, a = 10.382(2), b = 7.066(1), c = 5.4407(9) Å, β = 91.40(2)°, Z = 2. The structure has been refined by full‐matrix least‐squares techniques with anisotropic temperature factors for all atoms and with a Type II anisotropicextinction correction, leading to a conventional R value of 0.031. All hydrogen atoms have been located with a precision of 0.005 Å. The structure is stabilized by a three‐dimensional network of one O–H … Cl and three N–H … Cl hydrogen bonds, one for each hydrogen atom that is expected to participate in hydrogen bonding. The potential energy barrier for torsional motion of the ammonium group is estimated to be 6.4 kcal mole^{−1}, or about 3 times larger than those found for the methyl groups. This difference reflects the effects of hydrogen bonding.

Scattering of alkali halides by electrons. I. CsF
View Description Hide DescriptionThe scattering of CsF by 0.69–6.81 eV electrons has been measured with the molecular beam recoil technique. A novel kinematicanalysis is used to fit center of mass differential cross section models to the data. Absolute total cross sections determined in this fashion are a factor of 2 smaller than first Born approximation predictions at low energies. Absolute momentum transfer cross sections are an order of magnitude smaller than theory.

Kinematics of small angle scattering
View Description Hide DescriptionIn beam‐recoil measurements of the scattering of molecules by electrons or photons, deflected molecules are observed at very small angles, comparable to the angular divergences of the observed and crossing beams. A kinematic analysis is presented that explicitly includes the effects of these divergences. Distinguishing features of the analysis include the transformation to apparatus fixed vs ``laboratory'' coordinates and the calculation of the integrals over a finite detector in center of mass coordinates. The latter feature permits a simple recipe for inversion of laboratory observations to obtain a center of mass differential cross section.

Adsorption of CO on a Ni(111) surface
View Description Hide DescriptionCarbon monoxide adsorbed on Ni(111) forms around θ = 1/3 an ordered √3 × √3/R 30^{c} structure whose unit cell is continuously compressed upon further increasing the coverage until at saturation (θ=0.53 corresponding to 1 × 10^{15} molecules/cm^{2}) a densely packed layer is reached. The work function increases by 1.31 eV. At θ=1/3 the adsorption energy decreases from its value of 26.5 kcal/mole by 3 kcal/mole. CO adsorption causes the appearance of two peaks at 6 and 14 eV in the electron energy loss spectra, which are ascribed to excitations of electrons from chemisorption levels. The sticking coefficient remains nearly constant up to medium coverages which can be described by a ``precursor'' state model. The results show close similarities with those reported for other nickelsurfaces.

Simple basis sets for molecular wavefunctions containing atoms from Z = 2 to Z = 54
View Description Hide DescriptionThe double‐zeta orbital exponents for Slater‐type functions have been reoptimized for the ground state functions of the atoms with Z = 2 to the atoms with Z = 36, and accurately computed for the ground statewavefunctions of the atoms with Z = 37 to the atoms with Z = 54. Thus the entire series of basis sets for accurate double‐zeta functions for the atoms from He(^{1} S) to Xe(^{1} S) are now available for molecular computations.

Annihilation of positrons in gaseous and liquid NH_{3} and in NH_{3}–Ar and NH_{3}–Ne mixtures
View Description Hide DescriptionThe lifetime spectra of positrons annihilating in gaseous NH_{3}, in NH_{3}–Ar and NH_{3}–Ne gas mixtures, and in liquid NH_{3} have been measured as a function of density and temperature. The annihilation rate of slow positrons in NH_{3} gas, λ_{NH3 }, has a strong nonlinear dependence on gas density and temperature, indicating a complex positron‐ammonia interaction. A Z _{eff}/Z ratio of 1860 was observed for 22.5°C NH_{3} gas at 2.4×10^{−4} g/cm^{3}. Above gas densities of about 0.0015 g/cm^{3} at 22.5°C, λ_{NH3 } is found to be equal to the value measured in liquid NH_{3} at 0.607 g/cm^{3}. λ_{NH3 } is additionally found to be independent of the partial density of Ar or Ne in the gas mixtures. ^{1} Z _{eff} for orthopositronium annihilation in NH_{3} has a temperature independent value of 0.60±0.03 throughout the gaseous and liquid density range investigated.

VUV dissociative excitation cross sections of H_{2}O, NH_{3}, and CH_{4} by electron impact
View Description Hide DescriptionAbsolute excitation functions for excited fragments resulting from electron bombardment of H_{2}O, NH_{3}, and CH_{4} by low energy electrons (0–300 eV) have been measured in the VUV (1100–1950 Å). The predominant emission for each molecule was the H Lyman‐α line while the OI, NI, CI, and C_{II} emissions were at least an order of magnitude weaker. Absolute cross sections at 100 eV are given along with the appearance potential of the various processes and the possible dissociative‐excitation channels through which such processes proceed.

Corrections to the Born‐Oppenheimer approximation and electronic effects on isotopic exchange equilibria. II
View Description Hide DescriptionIf nonadiabaticeffects are neglected (the adiabatic approximation), the potential energy for the motions of the nuclei of a molecule is the sum of the Born‐Oppenheimer electronic energy and the adiabatic correction (diagonal nuclear motion correction). This adiabatic correction has been evaluated at the experimental equilibrium internuclear separation for a number of first‐ and second‐row diatomic hydrides and deuterides. The electronic wavefunctions which have been used in these calculations are LCAO MO SCF functions which range in quality from so‐called minimum basis set functions to so‐called near‐Hartree‐Fock functions. The explicit R dependence of the LCAO coefficients has been taken into account. The adiabatic corrections to the electronic energy are functions of the nuclear masses. With the assumption of the distance independence of the adiabatic correction, the calculations here can be used to evaluate the effect of the adiabatic correction on the equilibrium constants for the isotopic exchange reactions HX+HD=DX+H_{2}. For the HX systems on which calculations were done here, these correction factors range, with good single configuration wavefunctions, from 0.963 to 1.113 at 300°K.

Shifts in vibrational constants from corrections to the Born‐Oppenheimer approximation: Effects on isotopic exchange equilibria
View Description Hide DescriptionThe adiabatic correction to the Born‐Oppenheimer approximation has been evaluated as a function of internuclear separation for the diatomic molecules in the isotopic exchange reaction HX+HD=DX+H_{2}, where X=D, Li, or Cl. The sum of the isotope‐dependent adiabatic correction and the isotope‐independent Born‐Oppenheimer electronic energy is the effective potential energy for nuclear motion if nonadiabaticeffects are neglected. The resulting shifts, from the Born‐Oppenheimer values, of the equilibrium internuclear separations and of other vibrational constants are calculated. It is found that these shifts are so small that they have negligible effect on calculated values of the isotopic exchange equilibrium constants. The only important contribution of the adiabatic correction to the equilibrium constants arises from the fact that the ΔE of the isotopic exchange reactions between translationless, rotationless, vibrationless reactants and corresponding products no longer equals zero.

Raman spectral shifts relevant to electron delocalization in polydiacetylenes
View Description Hide DescriptionThe extent of π electron delocalization in solid‐state polymerized diacetylenes is derived from observed Raman vibrational frequencies. Raman intense C=C and C≡C vibrations indicate that the polymer backbone is best represented by (=C–C≡C–C=)_{ n }. However, v _{C=C} is linearly correlated with v _{C≡C} over a wide frequency range and both frequencies increase with decreasing phase perfection. This suggests a significant fractional contribution δ from the mesomeric structure (–C=C=C=C–)_{ n }, which decreases the π bond order of C=C to 1‐δ and C≡C to 2‐δ. Both v _{C=C} and v _{C≡C} are calculated as a function of δ and compared with observed frequencies for variously substituted polydiacetylenes in different physical states. Resulting Δv _{C=C}/Δv _{C≡C} values obtained using two different bond‐length to bond‐order approximations are in good agreement with the observed value (1.19±0.12).

Molecular photodissociation
View Description Hide DescriptionIn this paper we present a quantum mechanical model for direct photodissociation and for predissociation of polyatomic molecules in terms of a sequential decay scheme involving multiple coupled continua, where each continuum corresponds to a different internal vibrational state of the fragments. The coupling matrix elements between the ``initial'' state and the continuum states are in general determined by the appropriate vibrational overlap factors for the polyatomic radical, while intercontinua coupling for a triatomic molecule occurs only between adjacent vibrational continua. The time evolution of the system was handled by the Green's function method. Explicit theoretical expressions for the final vibrational distribution of the fragments in the photofragmentation of linear triatomic molecules were derived, which are determined by the initial coupling to the different continua and by a wave matrix which couples the various dissociative channels. The wave matrix was evaluated for some simple realistic models for the intercontinua coupling. The available experimental data for the vibrational distribution of the CN(B^{2}Σ) radical resulting from photodissociation and predissociation of XCN molecules are well accounted for in terms of our theory.

Hall mobility measurements in HF doped ice
View Description Hide DescriptionHall measurements on HF doped water ice crystals showed no signals comparable with those reported by Bullemer and Riehl on pure crystals. This may either be due to the considerably different techniques of their dc method compared to our double frequency method or it may be a result of the different nature of the samples. We find a small signal which can only be removed from the noise by extended runs that indicates a mobility of +4.2±2.8×10^{−3} cm^{2}/V·sec at − 5°C. The sign is characteristic of positive charge carriers. This is of the same order of magnitude as the drift mobility reported in the literature.