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Volume 71, Issue 4, 15 August 1979

Variationally deorthogonalized localized molecular orbitals
View Description Hide DescriptionThe Edmiston–Ruedenberg localized orbitals are shown to be solutions to the Hartree product of orthogonal orbital equations on the space of the occupied Hartree–Fock orbitals. The nonorthogonal Hartree orbitals on this space are thus a possible deorthogonalization of the localized orbitals. From the relationships of the Pauli principle to the orthogonality of the orbitals in the Hartree product wave function and to the full antisymmetry of the Hartree–Fock wave function, we propose an energy functional which imposes the Pauli principle on the Hartree product wave function without forcing the orbitals to be orthogonal. Minimization of this functional leads to the Pauli‐constrained Hartree equations. An algorithm is developed for their solution on the space of the Hartree–Fock orbitals. The results are called the variationally deorthogonalized Hartree product orbitals. This algorithm is then extended to apply to other localization functionals. Variationally deorthogonalized Edmiston–Ruedenberg orbitals are obtained by maximizing a function of the sum of the orbital self‐repulsions, and variationally deorthogonalized Boys localized orbitals are obtained by maximizing a function of the sum of the squares of the distances between orbital centroids. All three types of variationally deorthogonalized orbitals are obtained for H_{2}O, c i s‐ and t r a n s‐N_{2}H_{2}, C_{2}H_{2}, C_{2}H_{4}, eclipsed and staggered C_{2}H_{6}, BH_{3}, and B_{2}H_{6}. Comparisons are made in terms of the population distributions and the magnitudes and phases of the overlap integrals.

Gradient techniques for open‐shell restricted Hartree–Fock and multiconfiguration self‐consistent‐field methods
View Description Hide DescriptionFormulas for the analytical first derivatives of the potential energy have been derived for five specific cases of complexity beyond that of the closed‐shell single‐determinant self‐consistent‐field (SCF) approximation. The first four cases encompass most open‐shell systems of chemical interest, namely, the conventional restricted SCF wave functions for doublets, triplets, open‐shell singlets, and quartets. The final case considered is the two‐configuration SCF (TCSCF) wave function required to describe singlet diradicals and orbital symmetry forbidden reaction pathways. An explicit example of the latter procedure is provided by the least motion insertion of CH(^{2}Π) into H_{2} (^{1}Σ^{+} _{ g }) to yield the methyl radical. This doublet (S=1/2) TCSCF wave function is fairly typical of those required to theoretically explore problems in the physical chemistry of organic free radicals. Geometry optimization for the equilibrium structures of radical cations is illustrated by gradient calculations on H_{2}CO^{+}.

Carbon‐13 NMR of carbon monoxide. II. Molecular diffusion and spin–rotation interaction in liquid CO
View Description Hide DescriptionCarbon‐13 NMR was used to measure the molecular diffusion coefficient D and the spin‐rotation correlation time τ_{ s r } in liquid CO from its freezing point to about 110 K at several pressures up to 1.73 kbar. The behavior of D and τ_{ s r } is similar for liquid CO and N_{2}. Diffusion in CO at equilibrium vapor pressure takes place with an activation enthalpy of 2.9 kJ/mole and its pressure dependence leads to an activation volume which is a factor of 5 smaller than in the solid phase just below freezing. τ_{ s r } is nearly equal for CO and N_{2} at T?80 K and its variation with pressure for CO is smaller than that of D by almost a factor of 2. We also present a method for determining the magnetic field gradient used in the measurement of D which is free from many of the usual problems.

The reaction of ethanol with an aluminum oxide surface studied by inelastic electron tunneling spectroscopy
View Description Hide DescriptionInelastic electron tunnelingspectroscopy (IETS) has been employed to study the vibrational structure of ethanol reacting with a clean alumina surface as a function of temperature from 295 to 575 K. The spectra for the surface species up to approximately 450 K correspond to infrared spectra of aluminum ethoxide, Al(OC_{2}H_{5})_{3}. Between 450 and 475 K the structure changes from an ethoxide to an acetate, the most obvious spectral change being the appearance of a new peak at approximately 1585 cm^{−1} (197 meV) which is characteristic of the asymmetric OCO stretching mode of various inorganic acetates. No further changes are observed above 475 K. Above 370 K, there is also a significant increase in the total concentration of adsorbed species. This is due to a partial dehydration or dehydroxylation of the surface, thus freeing active sites which had previously been blocked by water or hydroxyl groups formed during the initial stages of ethanol adsorption. This dehydration or dehydroxylation of the surface is simultaneously accompanied by a transformation of the bulk aluminum oxide to aluminum hydroxide. While IETS has been applied successfully in the past to study a wide variety of adsorbate–adsorbent systems, here tunnelingspectroscopy is demonstrated explicitly to be effective in monitoring quantitatively the structural changes occurring in a reacting system at low pressures as a function of temperature.

Quantum‐mechanical calculation of three‐dimensional atom–diatom collisions in the presence of intense laser radiation
View Description Hide DescriptionA formalism is presented for describing the collision of fluorine with the hydrogen molecule in the presence of intense radiation. For a laser frequency on the order of the spin–orbit splitting of fluorine, the interaction of the molecular system with the radiation occurs at relatively long range where, for this system, the electric dipole is vanishingly small. Hence the interaction occurs due to the magnetic dipole coupling. Even so, at low collision energies a substantial enhancement of the quenching cross section is found for a radiation intensity of 10^{11} W/cm^{2}.

Electrical behavior of Se and Te to pressures of about 500 kbar
View Description Hide DescriptionUsing sintereddiamond tipped carbide piston apparatus, and techniques of temperature‐cycling the specimens while under pressure, the electrical resistance behavior of various kinds of Se specimens and of Te specimens has been explored as a function of pressure up to about 500 kbar. In general, earlier reported behavior to about 160 kbar was confirmed. New information includes: (i) Any type of initial Se goes to a stable metallic form above about 250 kbar. (ii) The ’’130 kbar metallic phase’’ of Se is probably the same as the ’’250 kbar metallic phase’’. (iii) The resistivity of metallic Se is very pressure sensitive, much more so than metallic Te. (iv) The activation energy of electrical conduction vs pressure results supports the earlier proposal that above 140 kbar Se goes into a high pressure semiconducting phase, which at about 250 kbar transforms to a metallic phase.

The effects of strong excitation‐phonon coupling on mixed crystal spectra: Diphenylmethylene in benzophenone
View Description Hide DescriptionWe present low temperature absorption and emission spectra of diphenylmethylene in benzophenone. Although the spectra are broad at temperatures greater than ∼20 K, considerable structure appears at lower temperatures. The spectra and their temperature dependence are readily explained by a large excitation‐phonon coupling which is expected for this type of mixed‐crystal system.

Laser magnetic resonance measurement of the 2 ^{3} P _{2}–2 ^{3} P _{1} splitting in atomic oxygen
View Description Hide DescriptionThe J=2→1 fine‐structure splitting in the ground state of atomic oxygen has been measured by laser magnetic resonance employing an intracavity dc glow discharge to generate the atom. The splitting, observed with the 63.1 μm laser line of ^{13}CH_{3}OH pumped by a CO_{2} laser, is 158.30298 (7) cm^{−1}.

A high‐density fluid‐perturbation theory based on an inverse 12th‐power hard‐sphere reference system
View Description Hide DescriptionA variational theory is developed that is accurate at normal liquid densities and densities up to 4 times that of the argon triple point. This theory uses the inverse 12th‐power potential as a reference system. The properties of this reference system are expressed in terms of hard‐sphere packing fractions by using a modified form of hard‐space variational theory. As a result of this ’’bootstrapping,’’ a variational procedure may be followed that employs the inverse 12th‐power system as a reference but uses the hard‐sphere packing fraction as the scaling parameter with which to minimize the Helmholtz free energy.

Thermochemical properties of the gaseous tantalum fluorides
View Description Hide DescriptionThe gaseous tantalum fluoride species TaF_{ n }, with n=1 to 5, were generated under equilibrium conditions by admitting SF_{6}(g) to a tantalum effusion cell at temperatures in the range 1000–2500 K. Mass spectrometry was utilized to establish the species identities and then to study several reaction equilibria. Reactionenthalpies were derived primarily by second law analysis, from which the standard enthalpies of formation at 298 K of TaF_{5} (−424.6 kcal/mol), TaF_{4} (−305.2 kcal/mol), TaF_{3} (−194.0 kcal/mol), TaF_{2} (−68.7 kcal/mol) and TaF (69.2 kcal/mol) were derived, all ±3 kcal/mol. Estimated thermodynamic functions of the Ta–F species, based on data for the neighboring tungsten fluorides, were found to be quite compatible with the equilibrium data. Equilibrium gas phase compositions in the Ta–F system, calculated over a range of temperatures for several pressures using the data reported here, correlate closely with kinetic data on the reaction of Ta with F atoms. The sharp decline in reaction rate above 2000 K can be accounted for on purely thermodynamic grounds.

ESR investigation of ScF_{2} isolated in rare gas matrices at 12 K
View Description Hide DescriptionThe radical molecule ScF_{2} has been produced at high temperature, trapped in argon and xenon matrices at 12 K and studied via electron spin resonance(ESR). Attempts to study the radical in neon matrices at 4 K and nitrogen at 12 K were unsuccessful. The observed ^{45}Sc and ^{19}F hyperfine splittings in an argon matrix were 220 and 28 MHz, respectively. The gtensor was not fully resolved; however, the most intense component had a g value of 1.995 (1) in argon. The magnetic parameters and electronic structure of ScF_{2} are compared to ScO, ScS, and TiF_{2} ^{+}. A nearly tenfold decrease in metal hfs is observed for ScF_{2} relative to ScO.

Direct measurements of the Gibbs free energy of OH using a cw tunable laser
View Description Hide DescriptionThis paper describes an absorption measurement for determining the Gibbs free energy of OH generated in a mixture of water and oxygen vapor. These measurements afford a direct verification of the accuracy of thermochemical data of H_{2}O at high temperatures and pressures. Our results indicate that values for the heat capacity of H_{2}O obtained through numerical computations are correct within our experimental uncertainty of 0.15 cal/mole °K.

Laser induced fluorescence, energy transfer and dissociation of Cs_{2}
View Description Hide DescriptionLaser induced fluorescences of Cs_{2} excited by the Ar^{+} laser lines have been studied. A series of lines with vibrational progression and the successive diffuse bands in the region down to 16 200 cm^{−1} were found to be polarized and identified as the resonancefluorescence. The diffuse fluctuation band with a maximum of intensity at 16 400 cm^{−1} consists of several bands at regular interval and it was independent on the line of excitation. By applying the theory on the role of kinetic energy in the Franck–Condon principle proposed by Mulliken, the band was identified as a transition from the internuclear distance of maximum kinetic energy in the vibrational level of the excited stateE ^{1}π_{ u }. All the other fluorescence bands of low frequency were observed to be depolarized completely, and the intensities increased when a foreign gas was added. These bands were identified as the fluorescence from the states which were populated by collision‐induced transitions from the E state. Atomic fluorescence 6p ^{2} P _{3/2}→6s ^{2} S _{1/2} is interpreted as the production of the excited atom Cs 6p ^{2} P _{3/2} by predissociation of Cs_{2} E ^{1}π_{ u } through interaction with, most probably, Cs_{2} B ^{1}π_{ u }.

Limiting slope of the generalized oscillator strength vs momentum transfer curve
View Description Hide DescriptionAlthough at the limit of zero momentum transfer, the generalized oscillator strength is equal to the Born value [E. N. Lassettre, A. Skerbele, and M. A. Dillon, J. Chem. Phys. 50, 1829 (1969)], it is found that the limiting slopes (d f/d K)_{ K=0} and (d f/d K ^{2})_{ K=0} do not obey the Born approximation. For dipole allowed transitions (d f/d K)_{ K=0} is nonzero but finite and (d f/d K ^{2})_{ K=0} becomes infinite at all finite incident energies. Also, the non‐Born correction to f _{0} deduced from zero angle data is just as important as the next higher multiple term in the Born approximation. Thus in the analytic fit of experimental data it is imperative to include odd power terms in K even when the Born approximation is apparently obeyed if the purpose is to deduce the limiting slope as well as the intercept. However, if only the intercept is needed and the measured f’s shows no apparent energy dependence, it is still possible to extrapolate to f _{0} using a series even in K. The relevance of the present result to a number of recent electron impact experiments is discussed.

An experimental study of multiple peak periodic and nonperiodic oscillations in the Belousov–Zhabotinskii reaction
View Description Hide DescriptionExperiments have been carried out on the Belousov–Zhabotinskii reaction in an isothermal continuous stirred tank reactor. The flow rate was varied from low values where simple single peak oscillations occur to large values where the reactor is in steady state. Several types of periodic multipeak oscillations were observed. Three regions of nonperiodic behavior were found, each of which occurred in a well defined range of flow rates bracketed by periodic oscillations.

Polarizability calculations with the SCF method. I. Linear and dynamic polarizabilities of conjugated hydrocarbons and aromatics
View Description Hide DescriptionWe calculate the static and dynamic linear electric polarizabilities of a group of aromatic and conjugated hydrocarbon molecules by means of a modified Pariser–Parr–Pople method. One purpose of the calculation is a comparison between various PPP results and previously obtained corresponding Hückel results. We calculate linear static polarizabilities and a contribution, the C term, to the third‐order nonlinear susceptibilities. The PPP values and Hückel values are not too different from each other except for those molecules that have unusually large susceptibilities. For the latter molecules the PPP results are significantly smaller than the Hückel results.

Statistical mechanics of helical wormlike chains. IX. Anisotropic light scattering
View Description Hide DescriptionThe anisotropiclight scattering by polymer molecules in dilute solution is studied on the basis of the helical wormlike chain on which optical polarizabilitytensors are arrayed with respect to its localized coordinate systems. The four independent components of the scattered intensity are evaluated as functions of scattering angle. It is facilitated by the use of irreducible (spherical) tensors with the expansion of the Green’s function in terms of the normalized Wigner functions. Rather detailed numerical results are presented. Evaluation is also carried out for the rigid rod, regular helix, random coil, and wormlike chain, which are the extreme cases of the helical wormlike chain. It is then noted that there are three possible types of anisotropic rods, and also of anisotropic wormlike chains, one of them being already well known as the one having cylindrically symmetric local polarizabilitytensors. A procedure for determining accurately the isotropic scattering function from observed scattered components is proposed on the basis of the numerical results. By a computer simulation, it is shown that the procedure does not involve an amplification of experimental errors in the individual components, except near the backward scattering angle. The mean‐square optical anisotropy determined from the depolarized component is also evaluated as a function of chain length. The ratio of it to chain length is shown to exhibit a maximum for some helical wormlike chains, and damped oscillation for one of the three types of rods with certain polarizabilities. An analysis of experimental data is made for polymethylene as an example.

Molecular dynamics of surface diffusion. I. The motion of adatoms and clusters
View Description Hide DescriptionThe motion of isolated adatoms and small clusters on a crystal surface is investigated by a novel and efficient simulation technique. The trajectory of each atom is calculated by molecular dynamics, but the exchange of kinetic energy with the crystal lattice is included through interactions with a ’’ghost’’ atom. This atom represents surface atoms of the lattice and is subjected to random and dissipative forces that are related by the fluctuation–dissipation theorem. The diffusion process is characterized by measurements of the velocity autocorrelation function, mean square displacement, directional correlations between hops, and the mean displacement per hop. In addition, the rate of evaporation of single adatoms and the rate of dissociation of clusters are discussed. The diffusion of an isolated adatom is found to be somewhat faster than that predicted by the classical rate theory for an activated process. This effect is a result of diffusion jumps of several atomic diameters that occur preferentially at high temperatures. But Arrhenius behavior is observed over the entire range of temperatures below the melting point. Dimers and larger clusters are found to diffuse more slowly than individual atoms, but with a smaller apparent activation energy. These results do not exhibit the high‐temperature anomalies that have been inferred from some experimental data on surfacemass transport. In a subsequent paper the method is extended to treat mass transport in the layer of adatoms and clusters that results from a dynamic equilibrium with the vapor phase.

A determination of adsite symmetry on surfaces via electron energy loss spectroscopy: Coadsorption of CO and NO on Ru(001)
View Description Hide DescriptionElectron energy loss spectroscopy has been used to study the vibrational energies of NO and CO coadsorbed on the Ru(001) surface.Adsorption of CO competes directly with adsorption of one of the two molecular states of NO. This is interpreted in terms of the geometry of the adsorption sites for CO and NO and is consistent with models proposed previously for adsorption of CO and NO separately on the Ru(001) surface.

Dynamics and ensemble averages for the polarization models of molecular interactions
View Description Hide DescriptionA family of ’’polarization models’’ has been generated for description of polarizable and deformable molecules in condensed phases. Within these models the intermolecular forces are not pairwise additive, but have a many‐body component that generalizes the polarizationinteractions present in conventional electrostatics. It is shown that the classical dynamical equations have a rather compact form, in spite of the many‐body interactions. Novel molecular distribution functions are introduced in terms of which the usual formulas of statistical thermodynamics can be expressed. Finally, the static dielectric constant is discussed for the polarization models, and it is related to fluctuating local moments in the system.