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Volume 64, Issue 3, 01 February 1976

A comprehensive parametrization and computational program for the analysis of MCD and absorption data
View Description Hide DescriptionA tractable method is presented for separating vibronic and static effects, which does not require extensive vibrational analysis of each molecule. The parameters so obtained can be expressed in terms of explicit matrix elements for a computation using only equilibrium position geometry and orbitals. The behavior of these vibronic quantities can provide an extremely sensitive means for studying the effects of substitution on the transition density matrix. This paper has been designed with sufficient flexibility in both the phenomenological and computational formalism to indicate how results of one procedure suggest appropriate modifications in the other. Benzene and its derivatives provide a fitting example for summarizing the procedure.

Ion cyclotron resonance studies of endothermic reactions of UF^{−} _{6} generated by surface ionization
View Description Hide DescriptionIon cyclotron resonancespectroscopy is used to investigate endothermic reactions of UF^{−} _{6}. At temperatures below those required for electron emission, UF^{−} _{6} is formed by negative surface ionization on a directly heated rhenium filament. The reactant ion is accelerated to a known energy and traverses the source region of the ICR cell in the direction of the magnetic field. Slow products from reactive and nonreactive encounters are confined in the trapping well and detected in the usual manner. The formation of UF^{−} _{7}, UF^{−} _{6}, UF^{−} _{5}, and UF^{−} _{3} from the reaction of UF^{−} _{6} with UF_{6} is studied over the energy range 0–40 eV in the center of mass. The cross section for UF^{−} _{7} formation exhibits a threshold at a relative kinetic energy of 2.7 eV. Reaction of UF^{−} _{6} with BF_{3} leads to formation of BF^{−} _{4} with a threshold of 1.6 eV in the center of mass. From these thresholds, E.A.(UF_{6}) =4.9±0.5 eV is deduced and the bond dissociation energies D (UF_{5}–F^{−}) =108±6 kcal/mole and D (UF_{6}–F^{−}) =46±10 kcal/mole are calculated. The endothermic reaction of UF^{−} _{6} with SF_{6} to produce SF^{−} _{6} is also investigated, the cross section for the process exhibiting a gradual onset at ∼7.5 eV, considerably above the thermodynamic threshold. The experimental techniques for using ion cyclotron resonancespectroscopy to study endothermic reactions of positive and negative ions formed by surface ionization are considered in detail.

Paramagnetic relaxation reagents as a probe for translational motion of liquids
View Description Hide DescriptionUse of the paramagnetic relaxation reagent t r i s‐ (acetylacetonato) chromium(III) [Cr(acac)_{3}] proves capable of probing the solution structure of organic liquids. The theory describing the relaxation effects of this chelate is presented, wherein it is assumed that the nuclear spin–lattice relaxation mechanism is due to the modulation of the electron–nuclear dipole–dipole interaction. The electronic relaxation timeT ^{ e } _{1} (or τ_{ s }) and the mutual translational motion of the paramagnetic species and the solvent molecules, in our case carbon tetrachloride, are considered the only causes of this modulation. Since for the paramagnetic molecules it is possible to calculate the electronic relaxation times, such systems are well defined for the description of translational diffusion. It is found that a jump diffusion model for translational motion explains the experimental data with jump distances comparable to the diameter of the solvent molecules.

Inelastic collisions between an atom and a diatomic molecule. III. Comparison of approximation methods as applied to the H+H_{2} rotational excitation
View Description Hide DescriptionThe close coupling method is used to calculate the rotational excitation cross sections of H+H_{2}collisions. On the potential surface suggested by Chu and Dalgarno, close coupling results are compared with results of distorted wave Born approximation and of effective close coupling approximation. On the potential surface suggested by McGuire and Krüger, close coupling results are compared with results of DWBA and of J _{ z }‐conserving coupled states approximation. The simple DWBA is generally adequate for this system, and in some cases, it is much better than other approximation methods. A third potential based on the experimental V _{0} of Gegenbach, Hahn, and Toennies and the nonempirical V _{2} of Norbeck, Certain, and Tang is also used. The excitation cross sections are smaller by orders‐of‐magnitude than the ones determined on the other two surfaces.

SPIN–CIPSI calculations on H_{2}CO
View Description Hide DescriptionThe efficiency of configuration interaction by perturbation with spin eigenfunctions is discussed in the case of ground and excited states of formaldehyde in its ground state equilibrium conformation. Two extensive configuration interactions using for every excited state more than 40 000 configurations eigenfunctions of spin, including six open shells, is carried out using the spincip program, spin‐symmetry‐adapted generalization of cipsi.

Atomic and molecular calculations with the model potential method. IV
View Description Hide DescriptionResults of model potential calculations are reported for the ground state of transition metal elements, Sc through Zn. We also present satisfactory results of calculations on both the ground and selected excited states of Fe, Fe^{++}, Ni, and Ni^{++} with the model potential method. The model potentials were constructed to replace the 1s ^{2} 2s ^{2} 2p ^{6} 3s ^{2} 3p ^{6} core, and also the 1s ^{2} 2s ^{2} 2p ^{6} 3s ^{2} core, thus including 3p electrons as the ’’valence’’ electrons.

Magnetic linear dichroism in S _{4} symmetry: Experimental evidence for complex coefficients in wavefunctions for Nd^{3+} in SrMoO_{4}
View Description Hide DescriptionA detailed calculation of magnetic linear dichroism (MLD) is performed in the case of S _{4} symmetry for ions with an odd number of active electrons, using perturbation theory. First it is shown that MLD anisotropy provides reliable assignments of the symmetry of the excited states. Then, in case of sinusoidal variation of the MLD amplitude, it is demonstrated that the complex part of the wavefunctions coefficients introduces phase differences between the signals associated to different transitions. This shows unambiguously that the use of six parameters to account for S _{4} symmetry instead of five in the simplifying assumption of D _{2d } symmetry does not reduce simply to the adjunction of one more adjustable parameter but is of prime physical importance. Experiments confirm the theoretical predictions. In addition, for the example of Nd^{3+} in SrMoO_{4}, the evaluation of MLD amplitude using the wavefunctions calculated by Karayianis from experimental absorption data are shown to be in quantitative agreement with experiment.

Energy bands in reactive collisions. I. H+H_{2} on the collinear SSMK surface
View Description Hide DescriptionThe collision of H+H_{2} on the collinear Shavitt, Stevens, Minn, and Karplus (SSMK) surface is studied for incident energies of 0–2 eV. By assuming a fixed zero‐point energy for H_{2}, and systematically varying the incident energy of the atom and the vibrational phase angle of the molecule, the trajectories divide into a continuous series of reactive (R) and unreactive (U) bands. At the R–U boundary, trajectory times and product vibrational energies reach a maximum. From the bands, the reaction probability may be obtained with a high degree of precision. Band continuity is shown clearly by means of linear and polar plots. The reaction probabilities obtained from the band plots are discussed and compared to other quasiclassical and quantum‐mechanical studies.

Self‐consistent‐field wavefunctions using a symmetry‐restricted annihilation of single‐excitations procedure
View Description Hide DescriptionThe form of Brillouin’s theorem appropriate for restricted Hartree–Fock calculations is used to determine rigorous self‐consistent‐field wavefunctions for the ^{3} A _{1}, ^{3} E, ^{3} A _{2}, ^{1} A _{2}, and ^{1} E states of the ... 2e ^{3} 3emanifold of CH_{3}CO^{+}, a manifold for which traditional Fock operator techniques are unsuitable. The results of an approximate method previously reported are compared with these exact results are found to be in quite good agreement.

Some consequences of molecular symmetry in the theory of photoelectron angular distributions
View Description Hide DescriptionThe molecular photoelectron angular distribution is treated by regarding the ionization process as a coherent superposition of component transitions, each having specific molecular symmetry transformation properties. The symmetry‐related properties of the resulting contributions and the selection rules that govern their occurrence in some specific ionization models are examined, and a generally applicable rule is obtained requiring interferences between ionization components with appropriate molecular symmetry transformation properties to vanish identically. Application of molecular symmetry methods to the angular momentum transfer formulation leads to the development of methods for generating angular‐momentum‐transfer selection rules. These methods are applied to direct ionization in an orbital approximation for 40 symmetries and for the general case of an n‐fold rotational symmetry, and meaningful restrictions on the allowed values of the angular momentum transfer are shown to apply even to some low symmetry systems.

Formation of nitrous oxide in the reaction of O(^{1} D _{2}) atoms with nitrogen
View Description Hide DescriptionThe quantum yields of N_{2}O (φ_{N} _{ 2 } _{O}) formed in the reaction of O(^{1} D _{2}) atoms with N_{2} have been determined in the gas phase at 23°C and at pressures between 25 and 115 atm and, for comparison, in liquid phase at cryogenic temperatures. Extrapolation of the gas phase results indicates for φ_{N} _{ 2 } _{O} at 1 atm the very low value of 3×10^{−7}, which precludes direct observation of N_{2}O formation at 1 atm in laboratory experiments by the currently employed analytical techniques. With increasing pressure φ_{N} _{ 2 } _{O} increases but does not show the simple dependence on [N_{2}] predicted by the generally used mechanism based on the ’’strong collision’’ assumption. The results show instead a linear dependence of 1/φ^{1/2} _{N} _{ 2 } _{O} on 1/[N_{2}], which can be rationalized in terms of two alternative mechanisms. Although both mechanisms invoke a two stage deactivation of the energy rich initial adduct (N_{2}O*), they differ in some important respects. The effects of additions of O_{2} and Ar have been also studied and can be explained well by the same two mechanisms but do not differentiate between them within the range of experimental conditions employed.

A contribution to the thermodynamics of the interstitial solid solution of hydrogen in metals
View Description Hide DescriptionA basic physical model has been proposed for the statistical thermodynamics of the interstitialsolid solution of hydrogen in metals where the behavior of not only the solute hydrogen but also of the parent metal is considered. The solid phase was represented as a superposition of the metal and hydrogen assemblies. The interaction energy between both the assemblies, which is partitioned into each assembly in an amount just large enough to cancel each other according to the rule of action and reaction, was expressed as a function of the hydrogen content with the aid of the theory of elasticity. The absolute activity for each component was derived from the respective grand partition function. The energy part in the state equation obtained was given in a quadratic expression with respect to the hydrogen content, unlike a linear expression in Lacher’s equation. It has been established that the energy associated with the parent lattice expansion is sufficient to cause the occurrence of two solid phases which coexist in a region of the hydrogen content, as suggested by various investigators. The critical condition, and the relation between the parent lattice expansion coefficient and the interaction energy among nearest‐neighbor hydrogen atoms were determined. For simplicity, Hooke’s equation was used to calculate the strain energy, and the results obtained are subject to the limitations of validity of this constitutive equation.

Thermodynamic properties of the system polystyrene‐t r a n s‐decalin
View Description Hide DescriptionOsmotic pressure measurements were performed on solutions of polystyrene in t r a n s‐decaline in the temperature range from 20° to 90 °C and in concentrations of segment fraction φ_{2} ranging from 0.06 to 0.26. The cloud‐point curves for this system were observed for samples of molecular weights from 3.7 to 270×10^{4}. Values of the interaction parameter χ obtained from osmotic pressure data were compared with those calculated from the new Flory theory for liquid mixtures. The behavior of χ was well represented by the simple relation: χ= (127.1+72.6φ_{2}+48.7φ^{2} _{2})/T +(2.32×10^{−4}+2.07×10^{−4}φ_{2}) T, where the terms proportional to temperature and to reciprocal temperature were found to be ascribed mainly to the difference of the liquid properties of the respective components and the exchange energy, respectively. Behaviors of the cloud‐point curves were well explained by the above expression for χ.

Volta effect and liquidlike layer at the ice surface
View Description Hide DescriptionThe Volta potential difference between Ih icesingle crystals and different metals has been measured as a function of the temperature by using the vibrating electrode technique. Reproducible results have been obtained with ice–gold and ice–copper contacts, indicating that in these cases the equilibrium has been attained. At temperatures below −30 °C the dependence is linear, and we think that this is the effect of the impurity content on the ice Fermi level. At higher temperatures a term which is logarithmic in (T _{ m }−T), where T _{ m } is the melting temperature of ice, is added. This additional pd has proved to be localized at the icesurface and ranges from 0 to 150 mV; it can be directly related to the appearance and thickening of the polarized, liquidlike layer predicted by N. H. Fletcher, if we assume that a constant electric field exists in the layer interior. The preferred dipole orientation turns out to be that with the oxygens outwards. We also obtained the approximate value of 4.3 eV for the ice work function.

Collision dynamics of three interacting atoms: Stripping reactions of Ar^{+}+H_{2} and of K+I_{2}
View Description Hide DescriptionEquations for stripping reaction cross sections, obtained from a multiple‐collision expansion for triatomic systems, are applied to Ar^{+}+H_{2} → ArH^{+}+H and its isotopic substitutions, and to K+I_{2} → KI+I. The equations involve the momentum distributions of reactant and product molecules, and are considered for mechanisms where stripping begins either before or after electron transfer, for both systems. Calculations of forward velocity distributions, product angular and energy distributions, isotope ratios, and total cross sections for Ar^{+}+H_{2} are in over‐all agreement with experiments and indicate that stripping begins after electron transfer in these systems. Comparison with experiment of calculated product angular and energy distributions and forward velocity distrubutions for K+I_{2} favors a mechanism where a vertical electron transfer occurs first, with simultaneous partial vibrational relaxation of I^{−} _{2}, followed then by stripping. Discrepancies remain however for K+I_{2}, suggesting some contribution from other mechanisms.

Infrared determination of the orientation of molecules in stearamide monolayers
View Description Hide DescriptionThe orientation of molecules in the monomolecular stearamide monolayers has been studied by infrared linear dichroism. By comparing the transmission absorption spectra carried out at different angles of incidence with the reflection absorption spectra obtained by depositing the monolayers on a metal substrate, the orientation of the dipole transition moments for a great number of normal vibration modes of the molecules may be determined to within a few degrees accuracy. Given certain assumptions, the orientation of the molecules themselves can then be deduced.

On the theory of diffraction of Maxwellian atomic beams by solid surfaces
View Description Hide DescriptionIn the context of diffraction of Maxwellian (thermal) atomic beams by solid surfaces, the usual assumption that the angular position of the maximum in a diffractedbeam corresponds to the diffraction angle of atoms with the most probable de Broglie wavelength is examined, and compared with other possible criteria and with the correct result. It is concluded that, although this criterion may be the best simple one available, it is certainly bad in some situations; the reasons why, and the conditions under which, it is expected to be good are discussed. Also, it is shown that considerable care must be taken when shapes of diffractedbeams and when angular positions of their maxima are calculated, because certain physical effects (which are always present) may change these shapes and positions in unexpected ways. The theory is compared with two sets of relatively modern experimental data, one set for which the fit is good, and another set for which a fit is impossible.

The reaction of nitric oxide with vibrationally excited ozone. II
View Description Hide DescriptionThe reaction of nitric oxide and vibrationally excited ozone was studied using a CO_{2} TEA laser to excite O_{3}(001) and a photomultiplier tube to measure the decay of the NO_{2}* chemiluminescence. In experiments with <1% O_{3}, a single, rapid rise rate was observed, suggesting that for ozone lean mixtures the laser‐induced signal is caused primarily by the two stretching modes of ozone, with comparatively little V–V transfer to the bending mode. The linear dependence of the NO_{2}* peak height on the laser intensity and background reaction indicates that second order effects do not contribute appreciably. Using a simple model which includes only contributions from the stretching modes and the ground state, the rate constantsk _{3a }(308 °K) =4.3±0.7×10^{9} and k _{3b }(308 °K) =5.4±0.7×10^{10} cm^{3} mole^{−1}⋅sec^{−1} were obtained for the laser‐enhanced luminescent and nonluminescent reactions, respectively. In addition the rate constants for V–T relaxation of O_{3}(001) by nine buffer gases were measured. It was found that the laser enhancement of the luminescent reaction is less than the thermal enhancement that would be obtained if one quantum of energy (3.0 kcal/mole) were distributed statistically among all reagent degrees of freedom, while for the nonluminescent reaction the laser and thermal enhancements are about equal.

Topological index as applied to π‐electronic systems. III. Mathematical relations among various bond orders
View Description Hide DescriptionMathematical relations among the Coulson (p ^{C} _{ l }), Ham and Ruedenberg (p ^{HR} _{ l }), Pauling (p ^{P} _{ l }), and topological (p ^{T} _{ l }) bond orders have been derived by combining the enumeration technique of the graph theory and the complex integral developed by Coulson and Longuet‐Higgins. If one defines a function F _{ G,l }(y) for bond l of graph G as F _{ G,l }(y) =Δ_{ r,s }(i y)/Δ (i y)(l=) the following relations are proved for alternant hydrocarbons: p ^{C} _{ l }=2/πF^{∞} _{0} F _{ G,l }(y) d y, p ^{HR} _{ l }=p ^{P} _{ l }=F _{ G,l }(0), p ^{T} _{ l }=F _{ G,l }(1) for tree graphs, p ^{T} _{ l }=F _{ G,l }(1) for nontree graphs. Linear relationship p ^{C} _{ l }∝p ^{T} _{ l }+A p ^{P} _{ l } (A≪1) is also proved. Abnormal bond orders for 4n‐membered ring systems are discussed. Graphical methods for decomposing determinants and adjuncts are proposed.

The linear electric field effect for low spin ferric heme compounds
View Description Hide DescriptionWe have measured the linear electric field induced g shifts for a series of low spin ferric heme compounds. Measurements were made by the electron spin echo method on noncrystalline samples at liquid helium temperatures. Some of these samples consisted of proteins and protein derivatives; others were made from heme reacted with small ligand molecules. Analytic expressions relating the observed changes in spin echo amplitude to certain of the g ^{2}‐shift coefficients B _{ i j } have been derived for the case where the Zeeman field H _{0} is set at either end of the electron paramagnetic resonance(EPR) spectrum. Elsewhere in the spectrum the observations can be described in terms of a shift parameter σ which is obtained by noting the time integral of the applied field E required to cause a 50% reduction in the echo amplitude. This shift parameter is approximately equal to the mean value of ‖δg/g‖ +E. In order to illustrate qualitatively the way in which σ depends on the values of the B _{ i j } and on the H _{0} setting, numerical computations of the mean value of ‖δg/g‖ have been made for a typical set of g values and for unit values of the B _{ i j }. Computations have been made for the two cases of E∥H_{0} and E⊥H_{0}. A simplified crystal field model has been used to interpret the data. The results suggest the presence of extensive back bonding between the Fe^{3+} ion and the axial ligands of the heme complex, this back bonding being several times larger for an RS^{−} ligand than for ligands involving nitrogen. The results also suggest that myoglobin hydroxide is characterized by a crystal field which is exceptionally low for the S′= (1/2) ferric heme group of compounds.