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Volume 64, Issue 11, 01 June 1976

The transferability of molecular fragment canonical orbitals
View Description Hide DescriptionThe ability of certain canonical orbitals of isolated molecular fragments to transfer largely unchanged to the molecular environment is examined. The separation of fragment canonical orbitals from the total molecular electronic problem is compared with the more familiar separations of atomic core orbitals and fragment localized orbitals. The specific example of the carbonyl functional group in formaldehyde is examined in detail. These studies lead to a new concept of valence electron only calculations in which the molecular valence electrons are assumed to move in an effective field provided by frozen molecular fragment canonical cores. In addition, for the case of assumed fragment canonical orbital transfer, perturbation theory analysis is found to be an efficient method of assessing the quality of the approximate wavefunction, thus eliminating much of the uncertainty as new systems are studied. The methods developed in the course of these studies offer certain practical advantages for the construction of approximate wavefunctions for large molecules. The details of application of these concepts to existing molecular orbtial methods are also presented.

Antiferromagnetic coupling in ytterbium‐diluted dysprosium hexaborides
View Description Hide DescriptionA series of dysprosium hexaborides in which dysprosium was progressively replaced by ytterbium have been prepared by high temperature reaction between elemental boron and rare earth oxide. Magnetic susceptibility measurements have been performed by the Faraday method over the range 1.6–300 °K. In the interval 63–300 °K, the susceptibilities follow Curie–Weiss laws with an effective moment per dysprosium of 10.6±0.3 Bohr magnetons. The Weiss constants are relatively small, having values of −21.5, −18.5, −14.0, −11.5, and −7.5 °K in Dy_{ x }Yb_{1−x }B_{6} at x=1, 0.8, 0.6, 0.4, and 0.2, respectively. Below 60 °K, the materials show antiferromagnetism; Néel temperatures were observed to decrease in the sequence 21, 16, 8, and 2 °K for the first four of the above compositions. Interpretation of results via statistical analysis of two, three, and greater‐than‐three clusters indicates that when isolated magnetic ions are corrected for, the residual magnetism corresponds to a constant exchange energy J, independent of conduction electron concentration. There is no direct evidence that indirect exchange plays a role in the magnetic interaction.

Kinetic energy distributions from unimolecular decay: Predictions of the Langevin model
View Description Hide DescriptionThe kinetic energy released in a unimolecular decomposition is examined within the framework of quasiequilibrium theory. It is assumed that the motion is governed by the long‐range forces between the separating moieties. Explicit formulas are obtained for cases where the total angular momentum is either very low or very high. Comparison with experiment and with other formulations is made.

Excitation spectra of atoms and small molecules using effective valence shell Hamiltonians generated by canonical transformations
View Description Hide DescriptionThe canonical transformation–cluster expansion formalism is used to generate the effective valence shell Hamiltonian for carbon. Hydrogenlike orbitals defined by an effective nuclear charge parameter Z are used to span the core (K shell), valence (L shell), and excited (3⩽n⩽9) spaces. The effective Hamiltonian containing one‐ and two‐body interactions is diagonalized on the N _{ v }‐particle valence space to yield the low‐lying excitation spectrum. Considering alternative approximations to carry out the calculations, we indicate the importance of including the two‐body pair potential as well as the single particle operators in the generator of the canonical transformation. Upon doing this, good agreement with experiment is obtained for the lowest valence shell transitions over a wide range of Z. For certain physically reasonable Z the entire valence shell experimental excitation spectrum can be accurately reproduced. In contrast, a ’’zeroth order’’ effective Hamiltonian using only the ’’charge cloud’’ of the core to modify the one‐body potential and using e ^{2}/r _{12} for the two‐body potential fails to reproduce the spectrum for any choice of Z. We compare our effective Hamiltonian with those currently used in semiempirical calculations. We find the splitting in the 2s–2p orbital energies as well as the ’’strength’’ of the two‐body interaction to be substantially reduced from those corresponding quantities occurring in the zeroth order effective Hamiltonian. These results generally fulfill the semiempirical expectations. We thus consider the procedure as a method for obtaining the valence shell Hamiltonian for molecules. Preliminary results for ethylene are presented and discussed.

Measurement of the self‐diffusion constant of aqueous calcium nitrate solutions by an NMR spin–echo technique
View Description Hide DescriptionThe self‐diffusion constant of concentrated aqueous solutions of calcium nitrate has been measured using an NMR spin‐echo technique. Solutions with mole ratios of water to calcium nitrate of 4 (the fused tetrahydrate), 6, 8, and 10 were studied over an extensive temperature range including the supercooled regime. Diffusion data were also obtained on solutions with a water to salt mole ratio of 18.5, 55.5, and 222 over a narrower temperature range. The NMR ’’spin‐echo’’ diffusion measurement system which was designed and fabricated in this laboratory incorporated provision for both steady and pulsed gradient diffusion measurements. The system provides a method for improved stability of the widths and amplitudes of the magnetic gradient pulses compared to earlier instrumentation. The improved stability was accomplished with development of a special pulse generator and current control circuitry. The diffusion data were represented over its entire range by the empirical Vogel–Tamman–Fulcher (VTF) equation. The fitting parameters were determined and the values of T _{0D } were found to approach that of water for concentrations higher than R=4. For purposes of comparison with viscosity and conductivity data, fitting of the VTF equation was made for the data taken in the same temperature intervals. Results show an almost Arrhenius behavior for the diffusion process in contrast to the viscosity and conductivity. It appears, from these data, that the water has a mobility which at room temperature is about a factor of 3 higher than the mobility for the other transport properties and which does not tend to ’’freeze out’’ as fast as the glass transition temperature T _{ g } is approached. This high mobility may be attributed to either the motion of the entire water molecule independent of the cation hydration complex, or to the cooperative proton transport where the water is partially dissociated by the strong electrical field of the calcium ions (Grotthuss mechanism).

Evolution of the Clausius–Mossotti function of noble gases and nitrogen, at moderate and high density, near room temperature
View Description Hide DescriptionThe static dielectric constant of noble gases (excepting xenon) and nitrogen has been measured near room temperature in a large range of pressures (up to 12 kbar for He, Ne, Ar, and N_{2}). The Clausius–Mossotti function (C.M.) has been deduced, when density data are known, with a precision of 10^{−3} in the moderate pressure range and 3×10^{−3} above 1.0 kbar. Values of the first, second, and in some cases third dielectric virial coefficient have been determined. We have found, in agreement with previous results obtained at low pressure, that the light gases and the heaviest ones show a different behavior of their C.M. function in terms of the density. For He and Ne, the second dielectric virial coefficient is negative; for Ar, Kr, and N_{2} it is positive, but the C.M. function goes through a maximum and then decreases. The effect of density on the C.M. function of Ar and N_{2} is approximately a drop of 3.5% at 12 kbar. These results have been compared with the predictions of molecular theories of dielectric properties of nonpolar fluids in the case of a hard spheres model. We have found that the Kirkwood–Yvon theory based upon the DID approximation does not reproduce completely the results of experiments. By contrast, we have been able to show that the semiquantal theory of Heller and Gelbart which takes into account the influence of the electronic distortion is more in agreement for a wide range of densities. This is the case for Ne and Ar when the excess of the pair polarizabilitytensor of a diatom is computed within the electron–gas approximation, and for He only if it is deduced from the Hartree–Fock scheme.

Rate constants for the reactions of OH with ethane and some halogen substituted ethanes at 296 K
View Description Hide DescriptionAbsolute rate constants for the reactions of OH radicals with C_{2}H_{6} and twelve fluorine, chlorine, and bromine substituted ethane compounds are reported. The measurements are made at 296 K and pressures ranging from 100 to 1000 Pa (0.7–7 torr) using a discharge‐flow system and laser magnetic resonance detection of OH. The results are similar to those of an earlier work on a series of methane compounds and indicate that the reaction mechanism is the abstraction of an H atom. Thus, completely halogenated molecules are relatively inert. The hydrogen containing molecules react with rate constants ranging from about 3 to 400×10^{−15} cm^{3} molecule^{−1}⋅sec^{−1}.

Trigonal ligand field and zero field splitting diagrams for the d ^{5} configuration
View Description Hide DescriptionComplete trigonal ligand field, Coulombic repulsion, and spin–orbit interaction matrices have been computed for the d ^{5} configuration. The ligand field potential for D _{3} _{ d }, D _{3}, C _{3} _{ v } and a special case of C _{3} symmetry is expressed as a normalized spherical harmonic (NSH) potential. Ligand fieldenergy level diagrams for the quartet states, as well as zero field (spin–orbit) splitting diagrams for the ^{6} A _{1}(S) ground state of a six‐coordinate system, are presented. The advantages and limitations of the NSH formulation are discussed. The sign of the zero field parameter D is correlated with the sense of the trigonal distortion for six coordinate d ^{5} systems of D _{3} _{ d } symmetry, and two manganese(II) systems characterized by D _{3} _{ d } symmetry are specifically considered.

The electronic structure of tris(octamethylpyrophosphoramide)manganese(II) ion. Electronic absorption, emission, and excitation spectra of Mn(OMPA)_{3}(ClO_{4})_{2}
View Description Hide DescriptionSingle crystal absorption, emission, and excitation spectra of tris(octamethylpyrophosphoramide) ‐ manganese(II) perchlorate are reported. Crystal field calculations for D _{3} symmetry support assignments of the observed bands. Interelectron repulsion, normalized spherical harmonic (NSH) trigonal potential, and spin–orbit interaction parameters are fitted, with B=670, C=3620, D Q=26 291, D S I G=−2000, D T A U=2000, and λ=60 cm^{−1}. (The D Q, D S I G, and D T A U values correspond to the conventional crystal field parameter values of D q=836, Dσ=−239, and Dτ=−93 cm^{−1}.) Intensity borrowing mechanisms are discussed in light of the polarizations and splittings observed. The results are correlated with the previously reported zero field parameters.

Powder magnetic resonance spectra in the presence of planar rotational jumps
View Description Hide DescriptionThe effect on magnetic resonanceline shapes of powder due to inplane jumps and planar rotational diffusion is discussed. Two approaches are used to calculate the line shapes: (i) A group theoretical method developed previously is applied to describe the effect of discrete jumps about a principal axis of a nonaxial Hamiltonian. (ii) A formalism is developed which considers a continuous range of jump angles, distributed about a preferred angle. This formalism reduces to the discrete jump case or the planar diffusion case in the proper limits. Numerical results for some specific cases in which the jump process involves rotations by π/2 and π/3 are presented. It is shown that the discrete jumps lead in the intermediate rate region to the appearance of conspicuous features in the spectra typical of the jump process. When the jump angles are diffused these peaks broaden out and disappear completely in the rotational diffusion limit. Experimental results on the radical AsO^{4−} _{4} in powder samples of KH_{2}AsO_{4} which exhibit these predicted features are presented.

Distribution of vibrational populations of CO electronic states produced in CO_{2} photodissociation
View Description Hide DescriptionThe vibrational distributions of CO(d ^{3}Δ), CO(a′ ^{3}Σ^{+}), and CO(a ^{3}Π) states produced from CO_{2}photodissociation at various incident photonenergies are calculated using a quantum mechanical theory of poyatomic molecule dissociation and are compared with experiment. It is assumed that CO(d ^{3}Δ) and CO(a′ ^{3}Σ^{+}) are produced via direct photodissociation from the CO_{2}ground state to a repulsive electronic state. Agreement between theoretical and experimental distribution is obtained. The CO(a ^{3}Π) vibrational distribution calculated using the direct photodissociation assumption could not be made to agree with experiment. Evidence that the CO(a ^{3}Π) dissociation in the photonenergy range considered proceeds via a predissociative state of CO_{2} is given. Comparisons are made with other models of dissociation.

Comparison of the energy dependences and branching ratios of the reactions of Ar^{+} and N_{2} ^{+} with SO_{2}
View Description Hide DescriptionThe reactions of Ar^{+} and N_{2} ^{+} with SO_{2}, which have similar energetics due to the nearly equal ionization potentials of Ar and N_{2}, have been studied in a flow–drift tube from 0.04 to 3 eV relative kinetic energy. The energy dependences and product branching ratios of the two reactions are found to be almost identical. With increasing relative kinetic energy, the rate constants show a rather steep initial decline, followed by an equally steep increase. At the lower energies, both reactions yield only the charge‐transfer product SO_{2} ^{+}, and at the higher energies, both reactions yield predominately the dissociative charge‐transfer product SO^{+}.

Polarization of laser‐excited fluorescent lines from ^{85}Rb_{2} and ^{87}Rb_{2} molecules
View Description Hide DescriptionPolarization studies are made of the various fluorescent lines from the excited ^{85}Rb_{2}(C) state or the ^{87}Rb_{2}(C) state populated by the 4765 or the 4880 Å Ar ion laser lines. We conclude that the previous hypothesis that all these fluorescent lines are Q branches is incorrect.

Microwave spectra of deuterated forms of bicyclo[2.1.0]pentane and the complete molecular structure
View Description Hide DescriptionThe microwave spectra of six deuterium‐labeled species of bicyclo[2.1.0]pentane have been observed and analyzed. These data, along with previously published results for the heavy atoms, permit the evaluation of a complete molecular structure for this polycyclic system. Some pertinent structural parameters include: R (C_{1}H) =1.082±0.003 AÅR (C_{2}H, e x o) =1.085±0.007 AÅR (C_{2}H,e n d o) =1.097±0.009 AÅR (C_{5}H,e x o) =1.088±0.002 AÅR (C_{5}H, e n d o) =1.090±0.003 AÅ‖HC_{2}H=109.4°±0.3 °, and ‖HC_{5}H=116.7°±0.4°. In addition, all methylene groups have been found to be tilted in the e x o direction by nearly three degrees.

Species enrichment due to Mach‐number focusing in a molecular‐beam mass‐spectrometer sampling system
View Description Hide DescriptionThe analysis and measurements reported here emphasize the need to take into account species enrichments due to Mach‐number focusing when sampling gas mixtures using a molecular‐beam mass‐spectrometer sampling system. Depending upon source conditions and system geometry, the enrichment of a given species may vary from unity to a value which is of the order of magnitude of the ratio of the given‐species mass to the major‐species mass. Procedures for handling effects of Mach‐number focusing on species enrichments are presented. These procedures are more general than previous procedures in that they accommodate, as needed, (a) flow divergence upstream from the skimmer and (b) transition to free‐molecule flow (for one or more of the several species) upstream from the skimmer. The measurements support a procedure for handling effects of pressure diffusion near the sampling source which was suggested earlier. An empirical curve for handling modest effects of skimmer interference is included.

Multipole operators for an arbitrary number of spins
View Description Hide DescriptionBasis states and operators composed of n, in general, different nuclear spins of integer or half‐integer values are explicitly constructed. Various coupling schemes are discussed, and transformations between them derived. Following this, a complete set of irreducible tensor operators T ^{(k)} _{{V}} is constructed which can be used as a basis for expanding operators which depend on nnuclear spins. It is further shown that decomposition of the tensor’s components T ^{(k)} ^{ q } _{{V}} into a sum of products of two irreducible tensor components involves transformation matrices between different coupling schemes. Various properties and commutation relations of the T ^{(k)} ^{ q } _{{V}}’s are given along with a discussion of their reduced matrix elements.

The effect of an impurity on the critical point of a binary liquid system as a surface phenomenon
View Description Hide DescriptionAn impurity which is considerably more soluble in one of the components of a binary liquid system than the other raises the temperature of an upper critical (consolute) point. Since the interfacial tension vanishes at the critical temperature, this effect can be described as a surfaceeffect: The impurity raises the interfacial tension and is thus negatively adsorbed at the interface. The amount of impurity in the interface is assumed to be calculable by summing the dissolved amounts at all points of the interface, and can be seen to depend on the second derivative of the solubility as a function of concentration. These phenomena were treated thermodynamically with the help of the Gibbs adsorptionequation in earlier papers, before the nature of the singularities at a critical point were well understood. These ideas are now brought up to date by incorporating the more recent developments about critical points, and scaling laws are found for the solubility and the adsorption at the interface. Renormalization of exponents has been considered. Information about the interface thickness can be obtained by applying the theory to experimental data. Application is made to the cyclohexane–aniline system. The thickness has been found to be given as a function of the temperature T and the critical temperature T _{ c } by the formula 2.1 [(T _{ c }−T)/ T _{ c }]^{−0.62} Å. This is 4 or 5 times less than the thickness of the interface in the cyclohexane–methanol system determined by optical measurements. Part of the difference might be removed by use of better measurements of the solubility of water in cyclohexane–aniline.

Degenerate autoionization processes in the photoionization of molecular hydrogen
View Description Hide DescriptionThe contribution of both autoionization and direct ionization processes to the photoionization continuum of hydrogen has been examined experimentally in order to ascertain the relative importance of the above two processes, to determine the final state to which a particular autoionizing Rydberg state decays, and to see if there are any preferred routes for the two types of processes. Autoionization processes which produce electrons with energies in the range 0 to 0.003 eV, so‐called degenerate autoionization processes, have been studied here by means of a new type of threshold electron analyzer which has an identically zero transmission probability for energetic electrons. It was found that degenerate autoionization processes are not uncommon and that there is a preference in such autoionization processes for J=K between the ground state hydrogen molecule and the final state of the molecular ion. Direct ionization also appears to be favored for J=K. The detailed routes of several degenerate autoionization processes are examined and other inferences made.

Momentum eigenfunctions in the complex momentum plane. Local potential functions
View Description Hide DescriptionSingular points for one‐electron momentum functions in the complex momentum plane are located. The momentum functions are obtained from molecular orbitals which satisfy one‐electron Schrödinger equations with local potential functions. If the molecular orbitals are expressed as linear combinations of atomic orbitals which satisfy Schrödinger equations with single‐center local potential functions, then there are severe restrictions on the type of single‐center potential functions which are acceptable. The problem of obtaining single‐center potentials is discussed.

Rate constants for specific product channels from metastable Ar(^{3} P _{2,0}) reactions and spectrometer calibration in the vacuum ultraviolet
View Description Hide DescriptionThe product channels from interaction of metastable argon atoms (^{3} P _{2,0}) with a series of chlorine containing molecules (Cl_{2}, NOCl, ClO, HCl, CCl_{4}, PCl_{3}, and SnCl_{4}), as well as some other molecules (Br_{2}, N_{2}O, NO_{2}, H_{2}S, and COS), have been investigated by emission spectroscopy. The rate constants for product channels were established by comparison of the emission intensities from the excited state products to the emission intensities from excited state Kr atoms, which have known rate constants for excitation by metastable argon atoms. Comparison of the individual product rate constants with previously determined total quenching rate constants of Ar(^{3} P _{2,0}) gave the branching ratios for emitting product channels. Although our measurements include the wavelength range from 120–800 nm, emphasis is placed upon the vacuum ultraviolet region and upon the ArCl*, ArBr*, and ArO* product channels. The highest ArCl* yield, ∼50%, was obtained for Cl_{2} and ClO. Quenching mechanisms for the halogen containing reagents are discussed with an emphasis on analogy to reactions of alkali metal atoms with halogen containing molecules. The nature of the bound‐free ArCl* emission also is discussed. Since the spectral response of the monochromator in the vacuum ultraviolet is of critical importance for assignment of rate constant values, the molecular branching ratio method employed for the calibration of the optical system is carefully described.