Index of content:
Volume 66, Issue 11, 01 June 1977

Reduced Green’s functions and coupled perturbed Hartree–Fock calculations. II. Application to the static dipole polarizability of the helium isoelectronic sequence
View Description Hide DescriptionThe reduced free‐particle Green’s function formulation of the first‐order coupled perturbed Hartree–Fock theory is applied to the calculation of the static dipole polarizability for the helium atom and for two‐electron ions as a test of the formulation and to demonstrate a power‐moment method of solution. The power‐moment method reduces the first‐order coupled perturbed Hartree–Fock (FO‐CPHF) integral equation to a set of simultaneous linear equations tailored to fit the problem. The formalism facilitates a consistent treatment of three approximations to the coupled perturbed method, depending upon the potential from which the unoccupied states (appearing in the corrected Green’s function) are derived. In each case the occupied (hole) states are accurate series solutions to the zero‐order Hartree–Fock equations. Results in agreement with previous calculations are reported for the helium isoelectronic sequence.

Viscous liquids and the glass transition. VI. Relaxations in simple molecule glasses in the 4–77 K range
View Description Hide DescriptionPrevious dielectric studies from our laboratory have shown that a secondary relaxation β, usually attributed to molecular flexibility, occurs as often, with the same strength, and in the same place (0.75 T _{ g } for 1 kHz measuring frequency) in glasses made of simple rigid molecules. We concluded that the β relaxation is a universal feature of amorphous packing. We have now extended our previous studies on molecular and fused salt glasses to the 4–77 K temperature range, and found relaxations at about 0.2–0.5 T _{ g } in seven of 16 substances examined. These low temperature relaxations appear in some rigid molecule and in some flexible molecule glasses, but not all. We conclude flexibility is not a necessary condition for a low temperature relaxation, but feel the evidence that such relaxations are also characteristic of amorphous packing is weak. Four alcohols studied gave evidence of an additional loss peak below 4 K. We suggest this peak may be related to the well‐known very low temperature anomalies common to most glasses. A general explanation of secondary relaxations in glasses in terms of the amorphous cluster model of glass structure is proposed.

Theory of thermal unimolecular reactions at low pressures. I. Solutions of the master equation
View Description Hide DescriptionThe master equation for a thermal unimolecular reaction in gases at low pressures is formulated. Steady‐state solutions are derived in analytical form with an exponential model of collisional transition probabilities, (i) for vibrational energy transfer in molecules with variable densities of states, and (ii) for combined rotational and vibrational energy transfer in molecules with variable heights of the centrifugal barriers. Other models of transition probabilities are treated numerically. The diffusion limit of energy transfer is discussed. In all cases, the nonequilibrium populations of excited states and the weak collision efficiency factors β_{ c } are calculated.

Theory of thermal unimolecular reactions at low pressures. II. Strong collision rate constants. Applications
View Description Hide DescriptionTheoretical expressions for the strong collision rate constants of thermal unimolecular reactions at low pressures k _{0} ^{sc} are discussed. The rate constant is split up into various factors: a basic expression for a simplified harmonic oscillator model, a factor accounting for anharmonicity effects, a factor accounting for the energy dependence of the density of states, an overall rotation factor accounting for the effects of centrifugal barriers, and an internal rotation factor accounting for the barriers of hindered rotors. Simplified and easily applicable expressions for these factors are derived. The theory is applied in detail to many practical examples. The comparison with experimental results demonstrates the large importance of the weak collision effects which have been treated in part I of this article. Empirical values for the weak collision efficiencies β_{ c } are derived and compared with predicted values.

Variation of the polarizability of noble gases with density
View Description Hide DescriptionDensity data for helium and neon up to 10 kbar at 25 °C are reported. The earlier experimental results for the Clausius–Mossotti function have been extended to higher densities for the whole noble gas series (i.e., up to reduced density ρ*?1). These results, combined with the machine calculation of the dipole–induced‐dipole contribution with respect to density for a Lennard‐Jones fluid, allow the determination of the mean individual atomic polarizability of noble gases as a function of density. In an appropriate system of units, the values of the mean polarizability fall on a single universal curve for all the reduced temperatures investigated.

Determination of the absolute energy levels of organic molecules in the gas phase and in condensed media. I. Solution and gas phase ionization energies and electron affinities of substituted pyridine‐N‐oxides
View Description Hide DescriptionThe basic principle for the determination and interrelation of the absolute energy levels of organic molecules in the gas phase and condensed media are discussed. The electrochemical and gas phase data for a series of substituted pyridine‐N‐oxides were used to examine the validity of Born’s formula, which approximate the chemical solvation energies of ions. A linear free‐energy relationship between the gas phase ionization potentials (I.P.) and the electrochemical half‐wave oxidation potentials (E ^{ox} _{1/2}) for substituted pyridine‐N‐oxides was found. This relationship was utilized to predict the ionization potentials of other heterocyclic amine‐N‐oxides whose I.P.’s have not been measured. The estimated effective ionic radius r _{eff} for pyridine‐N‐oxide derivatives was found to be highly dependent on the nature of the substituent and linearly related to the electrophilic substituent constant σ^{+}. Substituted pyridine‐N‐oxides have moderately low ionization energies and form stable positive radical cations. Their use as hole traps when immersed in insulating fluid in contact with photoconductors will be discussed.

Thermochemistry of gaseous UF_{5} and UF_{4}
View Description Hide DescriptionThermochemical data for gaseous UF_{5} and UF_{4} were obtained from equilibrium and electron impact measurements made by high temperature mass spectrometry. Equilibrium measurements yielded for the gaseous reaction Ag+UF_{5}=AgF+UF_{4} the enthalpy change ΔH _{298}=16.9±1.5 kcal by second law analysis. Additionally, the sublimation of UF_{4}(s) was studied by the torsion–effusion method, leading to ΔH _{298}(sub) =76.2±0.5 kcal/mol. These results were combined with auxiliary thermochemical data to derive the standard heats of formation ΔH f °_{298}(UF_{5}, g) =−460.6±3.4 kcal/mol and ΔH f °_{298}(UF_{4}, g) = −377.8±0.6 kcal/mol, and the bonddissociation energiesD _{0}(F_{5}U–F) =68.3±3.5 kcal and D _{0}(F_{4}U–F) =101.0±3.4 kcal. Threshold energies for formation of UF_{5} ^{+} and UF_{4} ^{+} by dissociativeionization of UF_{6} were determined along with the ionization potentials of UF_{6}(14.00 eV), UF_{5} (11.29 eV), and UF_{4} (9.96 eV), leading to the BDE values D _{0}(F_{5}U–F) =68.0±3.2 kcal and D _{0}(F_{4}U–F) =102.4±3.2 kcal, in agreement with the equilibrium data. Uncertainties associated with the measurements and the interpretation of the data are discussed. The entropy of UF_{5}(g) inferred from the equilibrium measurements was used in a third law treatment of published UF_{5}sublimation data, giving thermochemical results in good agreement with the above. The UF_{4}sublimation measurements lead to a vapor entropy that seems more compatible with a molecular configuration of lower symmetry than the obvious tetrahedral structure.

Extension of Koopmans’ theorem. IV. Ionization potentials from correlated wavefunctions for molecular fluorine
View Description Hide DescriptionUncorrelated (Hartree–Fock) a b i n i t i o calculations have proven unable to predict the energy ordering of 3σ_{ g } and 1π_{ u } molecular orbitals as observed in electron spectroscopy experiments on fluorine (F_{2}). The correct ordering was obtained, however, by applying an extension of Koopmans’ theorem [J. Chem. Phys. 62, 113 (1975)] to an MC–SCF correlated wavefunction for F_{2} which contained only one configuration beyond the one used in Hartree–Fock. With the addition of still further configurations to the wavefunction for the neutral molecule, the ordering of the extended Koopmans’ valence orbital energies was maintained and the correspondence improved between those and the experimental values.

Excited state spectroscopy, subpicosecond predissociation, and solvation of diatomic XeO in solid rare gas hosts
View Description Hide DescriptionTime, wavelength, and polarization resolved fluorescence techniques are used to investigate the photophysics of weakly bound diatomic XeO following frequency doubled dye laser excitation near 2200 Å. Photoselection experiments prove that the ’’Green bands’’ contain both E ^{1}Σ→C ^{1}ΣΠ and E ^{1}Σ→B ^{1}Σ fluorescences. The B ^{1}Σ state, which correlates with O(^{1} D)+Xe, is at least three vibrational quanta deeper than previously thought. An isotopic reversal of linewidths between Xe^{16}O and Xe^{18}O in the E ^{1}Σ→B ^{1}Σ spectra is interpreted in terms of subpicosecond homogeneous predissociation of B ^{1}Σ. Solid phase homogeneous predissociationtheory is discussed, and the isotopic sensitivity of the appropriate Franck–Condon factors is numerically investigated. The C ^{1}Π and B ^{1}Σ potentials are unambiguously deeper and more harmonic in solid Ar than in vacuum. This change in potential curve shape appears to reflect increased admixture of charge transfer (Xe^{+}O^{−}) components in the solid phase electronic wavefunctions.

Carbon‐13 NMR of carbon monoxide. I. Pressure dependence of translational motion in β‐CO
View Description Hide DescriptionActivation parameters for self‐diffusion of carbon monoxide molecules have been studied in the hexagonal beta phase of CO as a function of pressure and temperature. The carbon‐13 nuclear transverse relaxation timeT _{2}, which is proportional to the average molecular jump rate τ^{−1}, was measured by the Carr–Purcell Meiboom–Gill method. The activation enthalpy increases from 13 to 16 kJ/mole between 0 and 1.75 kbar and the activation volume is 44±5 cm^{3}/mole, which corresponds to 1.5 molar volumes. The results indicate a single diffusion mechanism in this P–T range; most probably the diffusion takes place by migration of monovacancies.

Hartree–Fock electron affinity of the CN radical
View Description Hide DescriptionSelf‐consistent‐field calculations on CN(X ^{2}Σ^{+}) and CN^{−}(X ^{1}Σ^{+}) have been performed at several internuclear separations. The estimated Hartree–Fock limit value for the adiabatic electron affinity of CN is 3.29±0.05 eV as compared with the observed value of 3.82±0.02 eV. A qualitative explanation has been proposed for the large electron affinity of CN.

Variable temperature ^{31}P and ^{19}F NMR studies of Fe(CO)_{3}(PF_{3})_{2} and Fe(CO)_{2}(PF_{3})_{3}
View Description Hide Description^{31}P and ^{19}F NMRspectra for the compounds Fe(CO)_{3}(PF_{3})_{2} and Fe(CO)_{2}(PF_{3})_{3} were studied in the temperature range +25 °C down to −100 °C. The four spin–spin coupling constants ^{1} J _{PF}, ^{3} J _{PF′}, ^{2} J _{PP′}, and ^{4} J _{FF′} were evaluated as a function of temperature. Owing to the fast intramolecular exchange of axial with equatorial ligand groups in these compounds, the observed spectra are time‐averaged. The magnitude of the observed time‐averaged ^{2} J _{PP′} coupling constant can be accounted for by the experimentally determined mole fractions for the various isomers and the t r a n s, c i s and v i c i n a l phosphorus–phosphorus coupling constants ^{2} J ^{ t r a n s } _{PP′}, ^{2} J ^{ c i s } _{PP′} and ^{2} J ^{ v i c i n a l } _{PP′}, respectively. An angular correlation of the phosphorus–phosphorus coupling constant is attempted. These results are compared to variable temperature ir and ^{13}C NMR studies of these compounds. The usefulness of studying ir or Raman spectra in addition to the NMRspectra for certain nonrigid molecules which fall in the ’’very fast exchange’’ category where no temperature coalescence of NMRspectral lines can be observed, is demonstrated. The simultaneous fitting of both the time‐averaged NMRspectra on the one hand and the separate ir spectra on the other is the best way to study such molecules. 151

Molecular calculations with the MODPOT, VRDDO, and MODPOT/VRDDO procedures. II. Cyclopentadiene, benzene, diazoles, diazines, and benzonitrile
View Description Hide DescriptionA procedure for carrying out nonempirical LCAO–MO–SCF calculations on large molecules is outlined. Use is made of an approximation for neglecting some one‐ and two‐electron integrals proposed by Wilhite and Euwema. The differential overlap between a pair of basis functions is set to zero if the pseudo‐overlap is less than the adjustable threshold. We refer to this method as variable retention of diatomic differential overlap (VRDDO). In addition, only the valence electrons may be explicitly considered. The influence of the core electrons is taken into account by using the model potential (MODPOT) Hamiltonian suggested by Bonifacic and Huzinaga. The two methods can be used together resulting in the MODPOT/VRDDO procedure. VRDDO, MODPOT, and MODPOT/VRDDO calculations are reported for cyclopentadiene, benzene, pyrazole, imidazole, pyridazine, pyrimidine, pyrazine, and benzonitrile. The accuracy of the VRDDO calculations is very good. Orbital energies and gross atomic populations differ from the reference values by only 0.001–0.002 a.u. The maximum error in the total energy is 0.0024 a.u. and in the dipole moment is 0.009 a.u. Valence electron‐only calculations with the MODPOT and MODPOT/VRDDO procedures yield orbital energies and charge densities that the quite good in comparison with the a b i n i t i o calculations taking all electrons into consideration. Orbital energies and gross atomic populations differ from the reference values b by 0.001–0.011 a.u. The maximum error in the dipole moment is 0.018 a.u. For benzonitrile, the largest molecule studied, introduction of the VRDDO procedure results in a 25% saving in computer time. The MODPOT calculation is three times faster than the a b i n i t i o reference calculation, while the MODPOT/VRDDO calculation is four times faster.

Determination of potassium ion–rare gas potentials from total cross section measurements
View Description Hide DescriptionIncomplete total cross sections have been measured for K^{+} scattered by He, Ne, Ar, Kr, and Xe in the range EΘ_{ R }=2–100 eV deg. Here E is the energy of the K^{+} beam, and Θ_{ R } is the nominal resolution angle of the apparatus. The cross sections have been analyzed to obtain estimates of the potentials in the region of the attractive well. The results are compared with other theoretical and experimental work on these systems.

Infrared spectra of isotopically mixed CO_{2} crystals
View Description Hide DescriptionInfrared spectra are reported for ^{12}C^{16}O_{2}/^{13}C^{16}O_{2}, ^{12}C^{16}O_{2}/^{12}C^{18}O_{2}, and ^{12}C^{18}O_{2}/^{13}C^{16}O_{2} mixed crystals throughout their complete concentration ranges. The changes with concentration in both the frequencies and the line shapes are in reasonable agreement with current theories of the effects of impurities on exciton states. An apparent exception is an anomalously rapid broadening with concentration in impurities whose transition energies are larger than that of the host. Effects due to interference between guest and host spectral bands, reflection, and possibly particle shape are observed. An analysis of the frequencies of dilute impurities indicates that the ν_{2} vibrational exciton band has a highly asymmetric density of states with a second moment of about 30 cm^{−2} and a total spread of about 22 cm^{−1}.

Experimental study on the nucleation of water vapor sulfuric acid binary system
View Description Hide DescriptionThe formation of aerosols in a gaseous mixture of water and sulfuric acid was studied experimentally. The formation of particles having been demonstrated during previous experiments, an experimental device was developed which would make it possible to determine the rate of nucleation for different values of partial pressure of water vapor and sulfuric acid. These results were compared with the numerical values given by Mirabel and Katz on the one hand, and by Kiang and Stauffer on the other hand; it was found that the most satisfactory correlation is obtained when the value of 3.5×10^{−4} torr is adopted for the pressure of the sulfuric acid saturating vapor at a temperature of 20 °C.

CNDO/S studies on the electronic structure of carbazoles. I. The parent molecule
View Description Hide DescriptionA semi‐empirical molecular orbital calculation, using the CNDO/S spectral parameterization of Del Bene and Jaffe, has been carried out for carbazole. The ground state occupied orbital eigenvalues are used to provide an orbital assignment of the photoelectron spectrum of carbazole. A limited configuration interaction procedure, utilizing the lowest 60 singly excited configurations, is subsequently carried out to determine the energies of excited singlet and triplet states of carbazole. Agreement between theoretical calculations and experimental results for the lower lying electronic transitions of carbazole is such as to allow higher lying transitions to be assigned with a degree of confidence.

Orbital level splitting in octahedral symmetry and SF_{6} rotational spectra. I. Qualitative features of high J levels
View Description Hide DescriptionThe interesting qualitative features of octahedral symmetry splitting of orbital levels with large angular momentum are derived using a simple quantum mechanical model. The clustering of certain octahedral group representations which has recently been observed in high resolution SF_{6}spectra is explained in detail. Semiquantitative formulas for splitting of the clusters are derived. An analogy with electron energy bands and Bloch waves is shown. The groundwork is laid for a quantitative theory which is given in the following article.

Orbital level splitting in octahedral symmetry and SF_{6} rotational spectra. II. Quantitative treatment of high J levels
View Description Hide DescriptionWe give a quantitative analysis for the clusters of octahedral terms which appear in the high resolution rotational spectra of SF_{6} for large angular momentum. We derive approximate expressions for the cluster energies and the splittings within each cluster which obviate the diagonalization of the octahedral deformation potential.

Many‐body calculations on molecules with second‐row atoms: H_{2}S and H_{2}CS
View Description Hide DescriptionThe ionization potentials of H_{2}S and H_{2}CS are calculated by a many‐body Green’s function method. Correlation energy changes in the diffuse part of the charge cloud require an extension of the polarization function basis compared to the first row atoms. When f‐type functions are included all calculated ionization potentials of H_{2}S agree with the experimental values to within 0.1 eV. The ionization potentials of H_{2}CS agree satisfactorily with the recently determined experimental values except for the fourth band where possibly predissociation occurs. The ordering of the ionic states is the same for H_{2}CS as for H_{2}CO. The vibrational structure in the photoelectron spectrum of H_{2}CS is computed.