Volume 57, Issue 2, 15 July 1972

Theory of Natural Optical Activity in Crystalline
View Description Hide DescriptionThe optical activity of crystalline is exclusively a property of the solid state, arising from a dissymmetric crystal environment. The rotatory strengths and dipole strengths associated with electronic transitions within the Ni^{2+} 3dmanifold of states are calculated to second order in perturbation theory. It is assumed that optical activity is induced in the ligand‐field bands of the octahedral NiO_{6} clusters by the perturbing influence of the neighboring crystal environment which has C _{2} symmetry. A crystal‐field representation is adopted so that the crystal perturber sites (the H atoms of the water ligands, and O and S atoms of the anions) are treated as point charges ``seen'' by the NiO_{6} chromophoric sites. The signs and relative magnitudes of the rotatory strengths calculated for the , and cubic transitions of Ni^{2+} are in substantial agreement with experiment. It is concluded that the CD spectrum of crystalline in the near infrared, visible, and near ultraviolet regions can be understood in terms of a model on which the optical activity is assumed to arise from dissymmetric perturbations of individual Ni^{2+} sites rather than from chiral exciton motion over the helically arranged clusters.

Quantitative Study of Luminescence in Aromatic and Heteroaromatic Molecules
View Description Hide DescriptionQuantum yields of fluorescence and phosphorescence were determined for about 20 organic compounds (and their deuterated analogs) using fluorescence yield of 9, 10‐diphenylanthracene as a reference standard. The emission yields so obtained are combined with appropriate phosphorescence lifetime data to deduce conclusions related to radiative and radiationless transitions in these molecules. Evidence is presented which indicates that the dominant singlet→triplet intersystem crossing is in benzene but in larger aromatic hydrocarbons. The results also indicate that deuteration of polycyclic hydrocarbons significantly increases the radiative lifetime of the lowest state, contrary to previously held views. Solvent and temperature dependence of fluorescence in nitrogen‐heterocyclic compounds and phosphorescence characteristics of aromatic carbonyl compounds are discussed in terms of vibronic interactions between nearby ππ^{*} and nπ^{*} states.

Anisotropic Self‐Diffusion in Erbium Single Crystals
View Description Hide DescriptionThe rate of self‐diffusion in single crystals of erbium has been studied over the temperature range from 1202 to 1412°C using a radioactive tracer (^{169}Er)‐sectioning (grinding) technique. The diffusion coefficients along the a axis (D_{a} ) and along the c axis (D_{c} ) of the close packed hexagonal structure are:By making use of Mullen's table for the diffusion of hcp metals by the vacancy mechanism, the ratio of jump frequencies is determined to be where ω_{ c } and ω_{ a } are frequency out of the basal plane and frequency in the basal plane, respectively.

Constant Acceleration Approximation in Collision‐Induced Absorption
View Description Hide DescriptionIn terms of the constant acceleration approximation, introduced by Oppenheim and Bloom in 1961, the line shapes occurring in collision‐induced absorption have a simple form that is suitable for numerical calculation. To test the reliability of the constant acceleration approximation in describing the appropriate time dependent distribution function, we compare a particular line shape in this approximation with the direct computer calculation of McQuarrie and Bernstein. A similar comparison with the experimental results of Bosomworth and Gush is also made. From both comparisons it follows that the constant acceleration approximation, as applied to a short range intermolecular interaction, is poor at all frequencies.

Calculated a ^{4}Σ^{−}, A ^{2}Δ, B ^{2}Σ^{−} States of CH
View Description Hide DescriptionAb initio CI calculations have been performed over a wide range of internuclear distances to obtain the potential curves for three low‐lying excited electronic states,a ^{4}Σ^{−}, A ^{2}Δ, B ^{2}Σ^{−}, of CH. With the computed potential curves, vibration‐rotational levels are obtained by numerical integration of the radial Schrödinger equations for the motion of the nuclei. The term values are analyzed to yield the conventional spectroscopic constants. Results, with known experimental values in parentheses, are , , ; , , and . The computed spectroscopic constants are found to be within 4% of known experimental values. A potential maximum of height 1600 cm^{−1} occurs in the computed potential curve of the B ^{2}Σ^{−} state. The a ^{4}Σ^{−} state, not known experimentally, is estimated to lie between 0.52 eV and 0.75 eV above the X ^{2}II ground state.

Vibrational Relaxation of the Bending Mode of Shock‐Heated CO_{2} by Laser‐Absorption Measurements
View Description Hide DescriptionThe vibrational relaxation characteristics of shock‐heated CO_{2} have been studied using a tuned CO_{2} laser absorption technique. Absorption‐coefficient histories were obtained for a single rotational state in each of the 10°0 and 02°0 levels over the temperature range from 500 to 2000°K, and for 21 rotational states of the 10°0 level at 1000°K. These histories have been combined with translational‐rotational temperature histories based on interferometermeasurements to calculate vibrational relaxation times for the bending mode. The results verify the mutual equilibrium of the bending and symmetric‐stretch modes due to Fermi resonance. The bending mode relaxation times are approximately 10% shorter than predicted from interferometer results using the ratio of specific heats. Furthermore, relaxation times based on measurements of different rotational states at 1000°K show a variation with quantum number J, indicating a possible rotational nonequilibrium during the vibration relaxation process.

Diagrammatical Method for Geminals. I. Theory
View Description Hide DescriptionA diagrammatical method, based on the second quantization formalism, time‐independent Wick's theorem and Feynman‐like diagrams, is developed for the calculation of arbitrary matrix elements of n‐particle spin‐independent operators between the states represented by antisymmetrized products of geminals of an arbitrary kind (i.e., strongly or weakly orthogonal, interacting, nonorthogonal or identical geminals). The method greatly facilitates any algebraic manipulation with geminal type functions, particularly when strong orthogonality is not assumed, and enables one to write down directly the algebraic expressions for the matrix elements of an arbitrary spin‐independent operator between the single antisymmetrized products of arbitrary geminals, solely on the basis of simple graphs, which are easily constructed.

Diagrammatical Method for Geminals. II. Applications
View Description Hide DescriptionThe diagrammatical method for the calculation of the matrix elements of an arbitrary spin‐independent operator in the basis of single antisymmetrized geminal products, developed in Part I, is applied to derive the overlap and energy mean value expressions for various types of geminal wavefunctions, namely for strongly and weakly orthogonal, nonorthogonal and identical geminals. The applications to other problems and the use of molecular symmetry in this formalism are also briefly discussed.

Convergence and First‐Order Approximation of the Fugacity Expansions for Physical Adsorption
View Description Hide DescriptionIntroducing a one‐dimensional Mayer‐type function for the absorptive potential, the cluster integrals are rewritten as finite sums. Approximating the cluster integrals by their leading terms, expressions are obtained for the specific amount of adsorption, the spreading pressure, and the local densities and pressures inside the surface and the adsorption layers. The equation of state inside the adsorption layer retains, in this approximation, the same form as in the case of the isolated gas. A criterion for the absolute and uniform convergence of the approximated fugacity expansions is obtained.

Formation of NO^{+} by the Reaction of O^{+} and Vibrationally Excited N_{2} in Crossed Molecular Beams
View Description Hide DescriptionThe cross sections for the reaction of vibrationally excited N_{2} with O^{+} (^{4} S) to form NO^{+} plus N over the O^{+} ion energy range 4–100 eV have been determined in modulated crossed molecular beams. The total effective cross section of N_{2} did not change by more than 15% in the temperature range 300–3000°K. The reaction cross section for N_{2} (v =1, 2, 3) did not vary by much more than a factor of 2 from the cross section for N_{2} (v =0) in this collision energy range.

Electronic Structure and Dynamic Jahn‐Teller Effect of Cobaltocene from EPR and Optical Studies
View Description Hide DescriptionIn order to determine quantitative information about chemical bonding in metallocenes, we investigated the electronic structure of the cobaltocene molecule by EPR and magnetic susceptibility measurements at 4.2°K and by optical spectroscopy at 77°K. Diamagnetic ruthenocene, weakly paramagnetic nickelocene, and paramagnetic cobaltocene single crystals as well as polycrystalline ferrocene served as host systems. From the poorly resolved optical spectra of pure cobaltocene, approximate ligand field parameters were determined. The magnetic properties (gtensor,cobalt hfs tensor) of the lowest Kramers doublet are explained in terms of the relative magnitudes of (a) spin‐orbit coupling, (b) static orthorhombic distortion, and (c) vibronic coupling (dynamic Jahn‐Teller effect) in the orbitally degenerate ^{2} E _{1g } ground state. From the analysis of the EPR data of cobaltocene‐doped ruthenocene, we conclude that covalency effects and vibronic interactions (``Ham effect'') are of comparable importance resulting in a drastic modification of the magnetic parameters compared to a free Co^{2+} ion in a static crystal field. In agreement with earlier qualitative and semiquantitative predictions, considerable covalency of the singly occupied orbital ( ligand, cobalt 3d character) was found. The strong change of the EPR parameters going from the ruthenocene to the ferrocene host lattice originates mainly in a strongly enhanced static orthorhombic splitting parameter in the tighter packed ferrocene environment. In cobaltocene single crystal, magnetic dipole‐dipole interactions broaden the EPR lines beyond detection even at 2°K. Nickelocene, an S =1 case with a large positive zero field splitting, behaves as a pseudodiamagnet at liquid helium temperature; exchange interactions with the cobaltocene dopant cause significant modifications of the g values but leaves the cobalt hfs tensor almost unaffected.

Many‐Body Effects and the Depolarization of Light by Simple Gases
View Description Hide DescriptionWe present a statistical mechanical description of the depolarized light scattering by simple gases which contains as a special case the well‐known binary collision result. For pressures greater than 50 atm, three‐and four‐particle correlations are shown to make important negative contributions to the experimental measurements.

Simple Model of the Dynamic Jahn‐Teller Effect in Six‐Coordinated Copper(II) Complexes
View Description Hide DescriptionA model potential is assumed for describing the vibrational degrees of freedom associated with the Jahn‐Teller effect in six‐coordinated copper (II) complexes. The pseudorotational limit is characterized by a potential that is constant in the region between two concentric cylinders, but becomes infinite elsewhere. The energy spectrum is obtained for both angular and radial excitations. A square‐well periodic angular potential is applied as a perturbation, yielding a localization of states. The results are used to describe the temperature dependence of the electron spin resonance spectra of copper (II) complexes with emphasis on the system NaCl:Cu(II) containing the hexachlorocuprate (II) complex.

Electric Resonance Spectrum of NaLi
View Description Hide Descriptiontransitions from the J =1, M_{J} =0 and the J =2, M_{J} =0 molecular rotational states of ^{23}Na^{7}Li have been observed by the molecular beam electric resonance method at 1–15 MHz. With an experimental linewidth of 7.5 kHz, the nuclear hyperfine pattern consisted of six unresolved doublets. In the beam, originating from a supersonic source, only one vibrational state was observed, which was shown to be the ground vibrational state by measurement of a ^{23}Na^{6}Li spectrum. The ground vibronic Stark coefficient and the molecular electric dipole moment μ_{0}, the equilibrium dipole moment μ_{e}, the molecular electric polarizabilities α_{ s } and α_{ a }, and the two nuclear electric quadrupole coupling constants eqQ were determined in ^{23}Na^{7}Li (using the reported rotational constant ) to be:

Statistical Mechanics of Adsorption from Dilute Liquid Solution
View Description Hide DescriptionFollowing the work of Hill, the McMillan‐Mayer theory of dilute solutions is used to derive an adsorption ``virial'' equation where the number of solute moles adsorbed is given by a power series in the liquid‐phase concentration. The virial coefficients are related to potentials of mean force. The theoretical analysis is used to reduce experimental data for adsorption on carbon for organic solutes from dilute aqueous solution. The adsorption virial equation is readily extended to multisolute systems.

Matrix ENDOR Linewidths of Trapped Electrons in Glassy Matrices at 77°K
View Description Hide DescriptionMatrix ENDOR lines of protons associated with trapped electrons in γ‐irradiated glassy matrices of 10M NaOH, methanol and 2‐methyltetrahydrofuran at 77°K have been observed. By analysis of the matrix ENDOR line shapes under comparable experimental conditions the linewidth has been related to the spatial extent of the ground statewavefunction of the trapped electron. These experimental results are compared with predictions of the semicontinuum model for trapped electrons and found to be in good agreement.

Theoretical Critical Configuration for Ethane Decomposition and Methyl Radical Recombination
View Description Hide DescriptionA theoretical critical configuration is described which yields calculated rate parameters in agreement with those measured for both the decomposition and recombination reactions in the ethane‐methyl radical system. It is shown that if structural effects in the molecule are considered as the reaction co‐ordinate is extended, this critical configuration is nearly identical to one determined by using the concept of minimum state density.

Excitation Transfer and Penning Ionization Reactions between Helium Metastables and Carbon Monoxide
View Description Hide DescriptionAbsolute intensity measurements have been made of the radiating states of the carbon atom and carbon monoxide ion produced in a flowing afterglow by the reaction,. These measurements coupled with absorption measurements of the He(2 ^{3} S) and CO densities are sufficient for calculating the rate constants for the production of the excited products mentioned above. It is found that of the total reaction rate between He(2 ^{3} S) and CO, 4% of this rate corresponds to the production of a dissociated CO molecule with the carbon atom in an excited state and, the remaining percentage of the total rate corresponds to Penning reactions into the three energetically available electronic levels of CO^{+} with about equal probabilities.

Self‐Consistent Procedures for Generalized Valence Bond Wavefunctions. Applications H_{3}, BH, H_{2}O, C_{2}H_{6}, and O_{2}
View Description Hide DescriptionMethods of efficiently optimizing the orbitals of generalized valence bond (GVB) wavefunctions are discussed and applied to LiH, BH, H_{3}, H_{2}O, C_{6}H_{6}, and O_{2}. The strong orthogonality and perfect pairing restrictions are tested for the X ^{1}Σ^{+} state of LiH, the X ^{1}Σ^{+}, a ^{3}π, and A ^{1}π states of BH, and the exchange reaction. The orbitals of H_{2}O and C_{2}H_{6} naturally localize into OH, CH, and CC bonding pairs. The nonbonding orbitals of H_{2}O are approximately tetrahedral but this description is only 2 kcal lower than the optimum description in terms of σ and π lone‐pair functions. The calculated rotational barrier for C_{2}H_{6} is 3.1 kcal, in good agreement with the experimental value (2.9 kcal). The description of the O_{2} molecule in the GVB approach is presented and the results of carrying out CI calculations using the GVB orbitals are discussed. The GVB orbitals are found to be a good basis set for configuration interaction calculations. The general features of GVB orbitals in other molecules are summarized.

Structure of Methylchlorosilyl Radicals
View Description Hide DescriptionThe ^{29}Si coupling constants a have been measured for methylchlorosily radicals in a number of solid matrices. The structure of these radicals deviates more and more from the planar one with the degree of CH_{3} substitution by a chlorine atom. Correlation found between the change in the value of a ^{29}Si coupling constant of a radical and the dipole moment of the molecules of the trapping matrix leads us to the hypothesis of a high value of a ^{29}Si_{pol} for the silyl radical.