bluuebunny/crossref_metadata_2025 huggingface dataset:
Calculation of DFT-GIAO NMR shifts with the inclusion of spin-orbit coupling
Authors: Wolff S. K. , Ziegler T.
Published: July 2002

A formulation for the calculation of nuclear magnetic resonance (NMR) shielding tensors, based on density functional theory (DFT), is presented. Scalar-relativistic and spin-orbit coupling effects are taken into account, and a Fermi-contact term is included in the NMR shielding tensor expression. Gauge-including atomic orbitals (GIAO) and a frozen-core approximation are used. This formulation has been implemented, and H1 and C13 NMR shifts of hydrogen and methyl halides have been calculated and show good agreement with experiment. C13 NMR shifts of 5d transition metal carbonyls have been calculated and show improved agreement with experiment over previous scalar-relativistic calculations. For the metal carbonyls it is shown explicitly that the combination of spin-orbit coupling and magnetic field mixes spin triplet states into the ground state, inducing a spin density that then interacts with the nuclei of the metal carbonyl via the Fermi-contact term. Results indicate that the Fermi-contact contribution to the C13 NMR of the metal carbonyl ions increases with increasing oxidation state of the ion. It is reasoned that as the oxidation state increases, π back bonding decreases and σ bonding increases, within the metal–carbon bond, thus facilitating a greater transfer of spin density from the metal to the carbon nucleus, and thus increasing the Fermi-contact contribution to the NMR shielding of the carbon.
Linear and sublinear scaling formation of Hartree–Fock-type exchange matrices
Authors: Ochsenfeld Christian , White Christopher A. , Head-Gordon Martin
Published: July 2002

We present a new method (LinK) to form the exact exchange matrix, as needed in Hartree–Fock and hybrid density functional theory calculations, with an effort capable of scaling only linearly with molecular size. It preserves the highly optimized structure of conventional direct self-consistent field (SCF) methods with only negligible prescreening overhead and does not impose predefined decay properties. Our LinK method leads to very early advantages as compared to conventional methods for systems with larger band gaps. Due to negligible screening overhead it is also competitive with conventional SCF schemes both for small molecules and systems with small band gaps. For the formation of an exchange-type matrix in coupled perturbed SCF theory our LinK method can exhibit sublinear scaling, or more precisely, independence of the computational effort from molecular size.
Smooth transformations of Kratzer’s potential in
N
dimensions
Authors: Hall Richard L. , Saad Nasser
Published: July 2002

We study smooth transformations V(r)=g(−1/r)+f(1/r2) of Kratzer’s potential −a/r+b/r2 in N⩾2 spatial dimensions. Eigenvalue approximation formulas are obtained which provide lower or upper energy bounds for all the discrete energy eigenvalues Enl and all N⩾2, corresponding, respectively, to the two cases that the transformation functions g and f are either both convex (g″⩾0) and f″⩾0) or both concave (g″⩽0 and f″⩽0). Detailed results are presented for V(r)=−a/r+b/rβ and V(r)=−(v/r)[1−ar/(1+r)]+b/r2.
Dynamic repulsion of surface steps during step flow etching: Controlling surface roughness with chemistry
Authors: Huang Yi-Chiau , Flidr Jaroslav , Newton Theresa A. , Hines Melissa A.
Published: July 2002

The development of surface roughness during step flow etching of vicinal one- and two-dimensional surfaces was investigated using kinetic Monte Carlo simulations. The two-dimensional simulations were performed on an unreconstructed Si(111) lattice and were designed to model aqueous silicon etching. In one dimension, the etching of a surface with noninteracting steps leads to a progressive roughening of the surface. In contrast, steps on a two-dimensional surface dynamically repel one another during etching, even when the steps are noninteracting. Dynamic step–step repulsion is the consequence of a feedback mechanism that is induced by step collisions and mediated by the morphology of the etching step and the presence of etch pits. The stability of this feedback mechanism to morphological perturbations is analyzed. During step flow etching, feedback can be enhanced either by increasing the roughness of the steps or the density of pits on the etched surface. Under certain conditions, etching can produce step distributions that are more regular than the corresponding equilibrium distribution. The implications of this observation on the production of very flat surfaces by etching are discussed.
Monte Carlo simulations of a simple model for the electrocatalytic CO oxidation on platinum
Authors: Koper M. T. M. , Jansen A. P. J. , van Santen R. A. , Lukkien J. J. , Hilbers P. A. J.
Published: July 2002

A simple lattice-gas model for the electrocatalytic carbon monoxide oxidation on a platinum electrode is studied by dynamic Monte Carlo simulations. The CO oxidation takes place through a Langmuir–Hinshelwood reaction between adsorbed CO and an adsorbed OH radical resulting from the dissociative adsorption of water. The model enables the investigation of the role of CO surface mobility on the macroscopic electrochemical response such as linear sweep voltammetry and potential step chronoamperometry. Our results show that the mean-field approximation, the traditional but often tacitly made assumption in electrochemistry, breaks down severely in the limit of vanishing CO surface mobility. Comparison of the simulated and experimental voltammetry suggests that on platinum CO oxidation is the intrinsically fastest reaction on the surface and that CO has a high surface mobility. However, under the same conditions, the model predicts some interesting deviations from the potential step current transients derived from the classical nucleation and growth theories. Such deviations have not been reported experimentally. Furthermore, it is shown that our simple model predicts different Tafel slopes at low and high potential, the qualitative features of which are not strongly influenced by the CO mobility. The comparison of our simulation results to the experimental literature is discussed in some detail.
Direct molecular simulation of gradient-driven diffusion
Authors: Thompson Aidan P. , Ford David M. , Heffelfinger Grant S.
Published: July 2002

Recent work in the active area of grand canonical molecular dynamics methods is first briefly reviewed followed by an overview of the dual control volume grand canonical molecular dynamics (DCV-GCMD) method, designed to enable the dynamic simulation of a system with a steady-state chemical potential gradient. A short review of the methods and systems used to prototype the DCV-GCMD method and its parallel implementation follows. Finally a new, novel implementation of the DCV-GCMD method that enables the establishment of a steady-state chemical potential gradient in a multicomponent system without having to insert or delete one of the components is presented and discussed.
Geometry and tunneling dynamics of CHD2 groups in aspirin: A single-crystal deuteron nuclear magnetic resonance study
Authors: Detken A. , Zimmermann H.
Published: July 2002

CHD 2 groups in aspirin are studied by single-crystal deuteron NMR at temperatures between 7 and 290 K. They perform stochastic reorientations which are governed by a rotational potential possessing three wells, two of which are almost equally deep whereas the third is significantly higher. The three minima of the rotational potential are separated by angles substantially different from 120°. Still, at least in the two lower wells, the geometry of the CHD2 groups is close to that of a symmetric rotor. By selective magnetization transfer experiments, the incoherent tunneling rate between the two lower potential wells is determined. At temperatures below 15 K, Raman processes are the dominating rotor-phonon coupling mechanism, while at higher temperatures, thermally activated processes with activation energies close to the total potential height prevail.
Cage substitution in metal–fullerene clusters
Authors: Branz W. , Billas I. M. L. , Malinowski N. , Tast F. , Heinebrodt M. , Martin T. P.
Published: July 2002

Photofragmentation mass spectra of metal–fullerene clusters C60Mx and C70Mx (M={Fe, Co, Ni, Rh}; x=0,…,30) reveal the existence of a reaction channel which yields clusters having the composition C59−2nM and C69−2nM (n=0,…,10). Enhanced abundances of clusters with 44, 50, and 60 atoms, as well as the presence of clusters containing almost exclusively an even number of atoms, indicate that one carbon atom of the fullerene cage is replaced by a transition metal atom. Additional tandem time-of-flight (TOF) experiments on mass selected C59M and C69M indicate that the initial fragmentation step of this new kind of substitutionally doped fullerenes is the loss of a neutral MC molecule. Measurements on preselected C70Rh3 and C70Ir2 were performed in order to monitor in detail their laser induced transformation into C69Rh and C69Ir.
Perturbation of local equilibrium by a chemical wave front
Authors: Lemarchand A. , Nawakowski B.
Published: July 2002

Microscopic simulations based on a direct simulation Monte Carlo method are performed to generate a reaction-diffusion wave front for reactions with or without activation energy. For fast reactions, the mean propagation speed of the front and its profile width differ from their predictions obtained from the standard reaction-diffusion equation. These discrepancies are related to the perturbation of equilibrium particle velocity distribution. To improve the analytical prediction of macroscopic front properties, we deduce from the Boltzmann equation the corrections to the macroscopic equation governing the evolution of concentrations of chemical species. In addition to these nonequilibrium effects, the discreteness of particle populations in the simulations induces deviations from the continuous description.
Line-mixing effects in N2O Q branches: Model, laboratory, and atmospheric spectra
Authors: Hartmann J.-M. , Bouanich J.-P. , Jucks K. W. , Blanquet Gh. , Walrand J. , Bermejo D. , Domenech J.-L. , Lacome N.
Published: July 2002

A model based on the energy corrected sudden approximation is used in order to account for line-mixing effects in N2O Q branches of Σ↔Π bands. The performance of this theoretical approach is demonstrated by comparisons with many (about 70) N2O–N2 and N2O–O2 laboratory spectra recorded in the 5 and 17 μm regions by three instrument setups; the Q branches of the 2ν20e–ν21f (near 579.3 cm−1), ν2 (near 588.8 cm−1), and ν2+ν3 (near 2798.3 cm−1) bands are investigated for different pressures (0.1–2.0 atm) and temperatures (200–300 K). The model is used to generate a set of line-mixing parameters for the calculation of the absorption by the ν2 Q branch under atmospheric conditions. These data are tested by comparisons between computed stratospheric emissions and values measured using a balloon-borne high resolution Fourier transform instrument. The results confirm the need to account for the effects of line mixing and demonstrate the capability of the model to represent the N2O absorption in a region which can be used for the retrieval of N2O5 mixing ratios.
New boron based nanostructured materials
Authors: Boustani Ihsan , Quandt Alexander , Hernández Eduardo , Rubio Angel
Published: July 2002

Based on a series of ab initio studies we have pointed out the remarkable structural stability of nanotubular and quasiplanar boron clusters, and postulated the existence of novel layered, tubular, and quasicrystalline boron solids built from elemental subunits. The present study illustrates and predicts qualitative structural and electronic properties for various models of nanotubular and layered boron solids, and compares them to well-known tubular and layered forms of pure carbon and mixed boron compounds.
Ab initio/interpolated quantum dynamics on coupled electronic states with full configuration interaction wave functions
Authors: Thompson Keiran , Martı́nez Todd J.
Published: July 2002

We present a new approach to first-principles molecular dynamics that combines a general and flexible interpolation method with ab initio evaluation of the potential energy surface. This hybrid approach extends significantly the domain of applicability of ab initio molecular dynamics. Use of interpolation significantly reduces the computational effort associated with the dynamics over most of the time scale of interest, while regions where potential energy surfaces are difficult to interpolate, for example near conical intersections, are treated by direct solution of the electronic Schrödinger equation during the dynamics. We demonstrate the concept through application to the nonadiabatic dynamics of collisional electronic quenching of Li(2p). Full configuration interaction is used to describe the wave functions of the ground and excited electronic states. The hybrid approach agrees well with full ab initio multiple spawning dynamics, while being more than an order of magnitude faster.
Solid-fluid equilibrium in molecular models of
n
-alkanes
Authors: Malanoski A. P. , Monson P. A.
Published: July 2002

We present a study of the solid-fluid phase equilibrium for flexible hard sphere site united atom models of n-alkanes using Monte Carlo computer simulation. We have considered models with different torsional potentials to examine the effect this has on the phase diagram. Extensive calculations of the fluid and solid phase equations of state have been made and solid phase free energies have also been determined. The initial solid phase structure used for each system was that which allows the chains to reach the highest density at close packing. The data for hard core chain models have been used as a reference system in a generalized van der Waals or mean field calculation of the n-alkane phase diagrams. This theory reproduces trends in the triple point temperature seen in experimental data. These trends are interpreted in terms of the changes in the close packed densities of the solids with chain length and the effect of the torsional energy on the relative stability of the fluid and solid phases.
First-order nonadiabatic coupling matrix elements using coupled cluster methods. I. Theory
Authors: Christiansen Ove
Published: July 2002

It is shown how first-order nonadiabatic coupling matrix elements can be calculated using coupled cluster electronic structure methods. The formalism is consistent with the coupled cluster response theory approach for calculation of excitation energies and adiabatic transition properties. Expressions are derived that are in the limit of a complete coupled cluster expansion give results equivalent to the full configuration interaction results. Computational tractable expressions are given for the first-order nonadiabatic coupling matrix in coupled cluster theory. The final expressions are quite similar to those employed in the implementation of the analytical calculation of molecular gradients.
Calculating the hopping rate for diffusion in molecular liquids: CS2
Authors: Gezelter J. Daniel , Rabani Eran , Berne B. J.
Published: July 2002

We extend the cage correlation function method for calculating the hopping rate in Zwanzig’s model of self-diffusion in liquids [R. Zwanzig, J. Chem. Phys. 79, 4507 (1983)] to liquids composed of polyatomic molecules. We find that the hopping rates defined by the cage correlation function drop to zero below the melting transition and we obtain excellent agreement with the diffusion constants calculated via the Einstein relation in liquids, solids, and supercooled liquids of CS2. We also investigate the vibrational density of states of inherent structures in liquids which have rough potential energy surfaces, and conclude that the normal mode density of states at the local minima are not the correct vibrational frequencies for use in Zwanzig’s model when it is applied to CS2.
A size-consistent state-specific multireference coupled cluster theory: Formal developments and molecular applications
Authors: Mahapatra Uttam Sinha , Datta Barnali , Mukherjee Debashis
Published: July 2002

In this paper we present a comprehensive account of a manifestly size-consistent coupled cluster formalism for a specific state, which is based on a reference function composed of determinants spanning a complete active space (CAS). The method treats all the reference determinants on the same footing and is hence expected to provide uniform description over a wide range of molecular geometry. The combining coefficients are determined by diagonalizing an effective operator in the CAS and are thus completely flexible, not constrained to preassigned values. A separate exponential-type excitation operator is invoked to induce excitations to all the virtual functions from each reference determinant. The linear dependence inherent in this choice of cluster operators is eliminated by invoking suitable sufficiency conditions, which in a transparent manner leads to manifest size extensivity. The use of a CAS also guarantees size consistency. We also discuss the relation of our method with the extant state-specific formalisms. Illustrative applications are presented for systems such as H4 in rectangular and trapezoidal geometries, the Be–H2 C2v insertion reaction path, the potential energy surface of Li2 and F2, and certain states of CH2 and C2 molecules with pronounced multireference character. The results indicate the efficacy of the method for obviating the intruders and of providing accuracy.
Microstructural changes in a colloidal liquid in the shear thinning and shear thickening regimes
Authors: Newstein Maurice C. , Wang Hao , Balsara Nitash P. , Lefebvre Amy A. , Shnidman Yitzhak , Watanabe Hiroshi , Osaki Kunihiro , Shikata Toshiyuki , Niwa Hirokazu , Morishima Yotaro
Published: July 2002

The structure of a colloidal suspension under shear flow was studied by in situ small angle neutron scattering (SANS). This suspension exhibited shear thinning at low shear rates and shear thickening at high shear rates. Under quiescent conditions, the SANS profiles were azimuthally symmetric and contained a well-defined scattering maximum. This is due to local, liquidlike correlations between neighboring particles. Increasing shear rate lead to changes in the interparticle correlations. These changes are quantified by obtaining the anisotropic structure factor of the suspension under shear flow. We found an increased probability for the formation of inter-particle clusters in the gradient-vorticity plane. This results in an increase in the low angle scattering intensity in the flow direction, and the scattering peak, observed under quiescent conditions, is reduced to a shoulder. We found no evidence for a shear-induced phase transition in our experimental window. At low shear rates (γ̇), the microstructure is relatively insensitive to shear rate. On the other hand, a pronounced shear rate dependence of microstructure is observed when γ̇≈1/τ, where τ is the characteristic time for the decay of concentration fluctuations. Dynamic light scattering was used to measure τ. The onset of shear thickening occurs when γ̇τ is of order unity suggesting an intimate relationship between quiescent dynamics, and shear-induced microscopic and macroscopic changes.
The spectroscopy and intramolecular vibrational energy redistribution dynamics of HOCl in the vOH=6 region, probed by infrared-visible double resonance overtone excitation
Authors: Callegari A. , Rebstein J. , Muenter J. S. , Jost R. , Rizzo T. R.
Published: July 2002

We use infrared-visible double resonance overtone excitation to promote HOCl molecules to single, well-characterized rotational levels of high OH stretching states just above the HOCl→HO+Cl dissociation threshold on the ground potential energy surface. Double resonance spectra are monitored by laser induced fluorescence detection of the OH dissociation products. We present here the results obtained in the 6ν1 region of HO35Cl where we have studied states with J ranging from 4 to 25, Ka from 0 to 5 and energy up to 300 cm−1 above the dissociation threshold. In the spectra for Ka=0–3 states, the zeroth-order (nOH,nθ,nOCl)=(6,0,0) level is split by mixing with a nearby dark state. Because the two states have very different A rotational constants, their separation increases with Ka, but the effects of the mixing remain observable in the spectrum up to Ka=3. Comparison with preliminary results from HO37Cl, together with analysis of the rotational constants, allows us to identify the perturbing state as (4,4,2). The lack of further strong perturbations compared to the average density of states allows us to infer that most of the matrix elements for couplings between the (6,0,0) bright state and other dark states are less than ∼0.1 cm−1. The average intramolecular vibrational energy redistribution (IVR) rate implied by these matrix elements (2.5×109 s) is two orders of magnitude longer than the predictions of statistical rate theory, indicating that IVR is likely to be the rate limiting step in the unimolecular dissociation process from (6,0,0). The present work provides the spectroscopic foundation for direct time-resolved studies of the unimolecular dissociation dynamics presented in a forthcoming paper.
Molecular dynamics study of vibrational energy relaxation of CN− in H2O and D2O solutions: An application of path integral influence functional theory to multiphonon processes
Authors: Shiga Motoyuki , Okazaki Susumu
Published: July 2002

Vibrational energy relaxation of a cyanide ion in the aqueous solutions has been investigated. Both the solute (CN−) and the solvent (H2O or D2O) were treated quantum mechanically based upon the path integral influence functional formalism assuming a harmonic oscillator bath. Single and multiphonon spectral densities were evaluated numerically from the normal modes of the solvent, i.e., the bath phonons, and the linear and nonlinear coupling constants between the C–N stretching coordinate and the phonons for 30 different quenched and instantaneous solvation structures generated by molecular dynamics calculations. The method combined with the normal mode analysis successfully presented not only the time constant of the relaxation but also information about what sorts of the solvent bath modes are responsible for the relaxation process. We show that two-phonon process caused by the nonlinear coupling between the C–N stretching mode and two bath phonons are shown to be mostly responsible for the present system. It is found, too, that the coupling of the system with two bath rotational libration modes and the coupling with a bath bending mode and a bath rotational libration mode are dominant in the relaxation process in an H2O solution, while, in a D2O solution, the coupling with the bath bending mode and bath rotational libration mode is most important. The normal modes that represent large motion of the water molecules inside the first and second solvation shells of the cyanide ion are particularly significant for the relaxation.
Topological effects due to conical intersections: A model study of two interacting conical intersections
Authors: Baer Michael , Varandas António J. C. , Englman Robert
Published: July 2002

A model is presented to study the (weak) interaction between two conical intersections (e.g., a dimer of two loosely bound molecules each characterized by a conical intersection). The model is an extension of a previous model for a single conical intersection formed by an electron housed by a vibrating molecule [Baer and Englman, Mol. Phys. 75, 293 (1992)]. The main result of this study is that the intermolecular coupling removes part of the degeneracy of the global system and in turn forms a new degeneracy, but will not affect the multivaluedness of the nuclear wave functions.
Theoretical study of the non-Arrhenius temperature dependence of thermal rate constants for the H+H2S→H2+SH reaction
Authors: Kurosaki Yuzuru , Takayanagi Toshiyuki
Published: July 2002

Thermal rate constants for the H+H2S→H2+SH reaction have been calculated over a temperature range of 100–2500 K using variational transition state theory combined with the multidimensional semiclassical tunneling correction. Potential energy curves for the reaction have been calculated using the spin-projected fourth-order Mo/ller–Plesset perturbation method and quadratic configuration–interaction method with the correlation-consistent polarized valence triple-ζ basis set. The calculated rate constants agree quite well with experiment over a wide range of temperature; in particular, excellent agreement with experiment is obtained around room temperatures. We have thus succeeded in quantitatively predicting the non-Arrhenius temperature dependence of thermal rate constants for the present reaction without adjusting any potential parameters, which has been observed recently by Yoshimura et al. [Chem. Phys. Lett. 189, 199 (1992)] and by Peng, Hu, and Marshall [J. Phys. Chem. 103, 5307 (1999)].
Femtosecond photoelectron spectroscopy of I2−(CO2)n clusters (n=4, 6, 9, 12, 14, 16)
Authors: Greenblatt B. Jefferys , Zanni Martin T. , Neumark Daniel M.
Published: July 2002

The photodissociation dynamics of I2−(CO2)n(n=4–16) clusters excited at 780 nm have been studied with femtosecond photoelectron spectroscopy (FPES). The range of cluster sizes spans the uncaged and fully-caged product limits for this reaction. We observe time scales for a variety of processes in these clusters, including dissociation of the I2− chromophore, solvation of the I− fragment, the onset of recombination on the ground state of I2−, vibrational relaxation, and solvent evaporation. In addition, substantial trapping in a “solvent-separated” state is seen for clusters with n⩾9; this state persists for at least 200 ps, the longest time delay probed here. Simulations of the spectra were performed in order to determine the time dependence of the electronic state populations, the I2− vibrational distribution, and the number of CO2 molecules in the cluster. Results are compared to previous experimental and theoretical studies of I2−(CO2)n photodissociation, and to a recent FPES study of I2−(Ar)n clusters.
Poiseuille flow of Lennard-Jones fluids in narrow slit pores
Authors: Travis Karl P. , Gubbins Keith E.
Published: July 2002

We present results from nonequilibrium molecular dynamics (NEMD) simulations of simple fluids undergoing planar Poiseuille flow in a slit pore only a few molecular diameters in width. The calculations reported in this publication build on previous results by including the effects of attractive forces and studying the flow at narrower pore widths. Our aims are: (1) to examine the role of attractive forces in determining hydrodynamic properties, (2) to provide clearer evidence for the existence of a non-Markovian generalization of Newtons law, (3) to examine the slip-stick boundary conditions in more detail by using a high spatial resolution of the streaming velocity profiles, (4) to investigate the significance of the recently proposed cross-coupling coefficient on the temperature profiles. The presence of attractive interactions gives rise to interesting packing effects, but otherwise, does not significantly alter the spatial dependence of hydrodynamic quantities. We find the strongest evidence to date that Newton’s Law breaks down for very narrow pores; the shear viscosity exhibits singularities. We suggest a method to test the validity of the non-Markovian generalization of Newton’s Law. No-slip boundary conditions are found to apply, even at these microscopic length scales, provided one takes into account the finite size of the wall atoms. The effects of any strain rate induced coupling to the heat flow are found to be insignificant.
Structure of electrorheological fluids
Authors: Dassanayake U. , Fraden S. , van Blaaderen A.
Published: July 2002

Specially synthesized silica colloidal spheres with fluorescent cores were used as model electrorheological fluids to experimentally explore structure formation and evolution under conditions of no shear. Using confocal scanning laser microscopy we measured the location of each colloid in three dimensions. We observed an equilibrium body-centered tetragonal phase and several nonequilibrium structures such as sheet-like labyrinths and isolated chains of colloids. The formation of nonequilibrium structures was studied as a function of the volume fraction, electric field strength, and starting configuration of the colloid. We compare our observations to previous experiments, simulations, and calculations.
Comparative dynamics of Cl(2P) and O(3P) interactions with a hydrocarbon surface
Authors: Garton Donna J. , Minton Timothy K. , Alagia Michele , Balucani Nadia , Casavecchia Piergiorgio , Gualberto Volpi Gian
Published: July 2002

The dynamics of the interactions of atomic chlorine with the surface of a saturated hydrocarbon liquid, squalane, were investigated and compared to the results of an earlier study on analogous oxygen-atom interactions. Beams of continuous supersonic chlorine atoms were directed onto a squalane surface, and the volatile products, Cl and HCl, were observed by mass spectrometry as a function of incident angle, final angle, and incident Cl-atom energy. Both the Cl and HCl time-of-flight (from the surface to the detector) distributions revealed thermal and hyperthermal interaction channels, in analogy to the dynamical behavior of the O and OH signals observed in the previous study. The thermal HCl product may arise from two mechanisms: (i) desorption of trapped HCl product and (ii) reaction of trapped Cl atoms to form thermal HCl, which subsequently desorbs. In contrast, the reaction of O atoms with squalane led to a thermal OH signal, which could only come from desorption of trapped OH. The hyperthermal HCl signal is the result of an Eley–Rideal direct-abstraction mechanism. An analogous reaction gave rise to hyperthermal OH products in O-atom reactions with squalane. The HCl and OH hyperthermal products were scattered preferentially in the specular direction in the laboratory frame. However, a kinematic analysis showed a propensity for scattering sideways or even backwards (with respect to the direction of the incident atomic beam) in the center-of-mass (c.m.) frame. The kinematic analysis also allowed the determination of the effective mass of the surface collision partner, the c.m. collision energy, and the final c.m. translational energy. Similar c.m. scattering dynamics have been observed in gas-phase reactions of O and Cl atoms with saturated hydrocarbons.
Contributions to the entropy of a glass and liquid, and the dielectric relaxation time
Authors: Johari G. P.
Published: July 2002

An analysis of the heat capacity data of 21 materials shows that a glass loses 17%–80% of its entropy on cooling from its Tg to 0 K, and that the entropy difference between a glass and crystal phase at Tg, ΔS(Tg), is 1.2 to 4.9 times the entropy difference at 0 K. This is contrary to the premise that the vibrational entropy of a glass is the same as the entropy of its crystal phase, or that ΔS(Tg) is equal to Sconf(Tg), the configurational entropy at Tg. The excess entropy of a glass over the crystal phase is attributed to (i) the relatively lower frequency and greater anharmonicity of lattice vibrations which contribute to their vibrational entropy, (ii) the kinetically unfrozen modes corresponding to the tail of the distribution of the α-relaxation times, which contribute to the configurational entropy, and (iii) localized relaxations of molecular groups which also contribute to the configurational entropy. These contributions vanish or become negligible at 0 K. Therefore, ΔS(Tg) cannot be used in place of Sconf(Tg) in the Adam and Gibbs equation. The finding puts into question the basis for the recent inferences [J. Chem. Phys. 108, 9016 (1998)] on molecular dynamics of supercooled liquids. An upper bound Sconf may be estimated at Tg by extrapolation of the vibrational entropy of a glass and used in the Adam and Gibbs equation to estimate roughly Sconf of a supercooled liquid from the dielectric relaxation time data.
A relationship between centroid dynamics and path integral quantum transition state theory
Authors: Jang Seogjoo , Voth Gregory A.
Published: July 2002

The theory of Feynman path centroid dynamics is applied to the calculation of quantum barrier crossing rates. The formulation starts from the exact definition of the quantum survival probability of the reactant state, and the reaction rate is then defined as the steady-state limit of the decay rate of the survival probability. A formulation is given in terms of exact centroid dynamics. Then, based on an approximation for the initial reactant state and the centroid molecular dynamics (CMD) approximation for the dynamics, a new approximate rate expression is obtained which is equal to the path integral quantum transition state theory (PI-QTST) expression multiplied by a transmission factor of order unity. This factor varies with the choice of the dividing surface in the low temperature limit, but it is invariant to that choice at higher temperatures. It is then shown that the PI-QTST rate expression results from the quadratic barrier approximation for the calculation of the transmission factor only. The potential to use the new rate expression as an improved version of the PI-QTST is also tested for model systems. For certain choices of the dividing surface, it is shown that the new reaction rate expression results in improvement over the PI-QTST results. The overall formulation also yields a better understanding of the barrier crossing dynamics viewed from the centroid perspective and the rigorous origin of the PI-QTST formula.
Depletion interactions in lyotropic nematics
Authors: van der Schoot Paul
Published: July 2002

A theoretical study of depletion interactions between pairs of small, globular colloids dispersed in a lyotropic nematic of hard, rodlike particles is presented. We find that both the strength and range of the interaction crucially depends on the configuration of the spheres relative to the nematic director, and on their size. The interaction is significantly stronger parallel than perpendicular to the director, explaining the emergence of stringlike aggregates observed in experiment.
Hydrolysis of sulfur trioxide to form sulfuric acid in small water clusters
Authors: Larson Laura J. , Kuno Mayuso , Tao Fu-Ming
Published: July 2002

The hydrolysis reaction of sulfur trioxide to form sulfuric acid in small water clusters is investigated using density function theory and ab initio methods. The equilibrium geometries for the reactant clusters that contain SO3 and one to four water molecules, SO3⋅(H2O)n, n=1–4, as well as the corresponding transition state and product clusters, are calculated at the levels of B3LYP/6-31+G*, B3LYP/6-311++G**, and MP2/6-311++G**. The relative energies of the reactant, transition state, and product are determined for each of the four clusters. The energy barrier required to form H2SO4 from the reactant cluster is found to decrease sharply with the number of water molecules in the cluster. Most significantly, the SO3⋅(H2O)4 cluster is found to be unstable and to form the ion pair HSO4− and H3O+ with little or no energy barrier. This work reveals the possibility of more pathways for the formation of sulfuric acid than have been previously considered.
Effect of basis set superposition error on the electron density of molecular complexes
Authors: Salvador Pedro , Fradera Xavier , Duran Miquel
Published: July 2002

The Chemical Hamiltonian Approach (CHA) versions of the Roothaan and Kohn–Sham equations, labeled CHA/F and CHA/DFT, respectively, have been used to obtain the basis set superposition error (BSSE)-corrected first-order electron density of the hydrogen fluoride dimer with several basis sets. We have analyzed the effect of BSSE in terms of the electronic relaxation, i.e., the redistribution of the electron density due to the inclusion of the CHA correction at a frozen geometry, along with the subsequent nuclear relaxation process. Critical points of the charge density have been located and characterized to compare the conventional, uncorrected first-order electron density against the BSSE-corrected density at each level of theory. Contour difference maps between BSSE-corrected and uncorrected densities on the molecular plane have also been plotted to gain insight into the effects of BSSE correction on the electron density.
On the second-order corrections to the quantum canonical equilibrium density matrix
Authors: Geva Eitan , Rosenman Efrat , Tannor David
Published: July 2002

We consider the equilibrium state of a quantum system weakly coupled to a quantum bath within second order perturbation theory. It was previously shown by Romero-Rochin and Oppenheim [Physica A 155, 52 (1989)] that the equilibrium state deviates from the canonical form, e−βHs/Zs (Hs is the free system Hamiltonian and Zs the canonical partition function). We reproduce this result via a different derivation, starting from the non-Markovian, rather than the Markovian, quantum Master equation. Our derivation sheds new light on the mechanism that stabilizes the deviation from the canonical form and shows that it involves an interplay between a static distortion to the equilibrium state and dynamical system–bath correlations. We show that this deviation is a necessary consequence of translational invariance and vanishes when the rotating-wave-approximation is applied. The deviation is also shown to vanish for a two-level system off-diagonally coupled to a heat bath or when the Lamb shifts are neglected. Two ways for numerically evaluating the second order deviations are described. Finally, the deviations from canonical equilibrium are given an illuminating geometrical interpretation in terms of the phase space Wigner distribution.
On the Cauchy problem for the nonlinear Boltzmann equation global existence uniqueness and asymptotic stability
Authors: Bellomo N. , Toscani G.
Published: July 2002

The analysis of the initial value problem for the nonlinear Boltzmann equation is considered in this paper. A theorem defining global existence and uniqueness for initial data which decay at infinity with an inverse power law is the main result of this work and is obtained by suitable application of fixed point theorems in Banach spaces. The theorem also defines the asymptotic stability of the solutions.
Automorphisms of algebraic varieties and Yang–Baxter equations
Authors: Maillard Jean-Marie
Published: July 2002

It is shown that commuting transfer matrix models in statistical mechanics are parametrized by algebraic varieties having a set of automorphisms deduced from the so-called ‘‘inversion relation.’’ In general this set of automorphisms is infinite: this shows that for algebraic varieties of dimension 1, the models are parametrized by algebraic curves of genus 0 or 1.
A new theory for scattering from a surface
Authors: Dashen Roger , Wurmser Daniel
Published: July 2002

A new formal approach to the problem of scattering from a rough surface is derived. The first ingredient of this approach is a formal statement of the composite model. This consists of an approximate expression for the change in the scattering amplitude corresponding to a perturbation of a reference surface. It is good to first order in the perturbation, and exact with respect to the reference surface. The derivation of this result makes use of the general asymptotic form of the scattering solution. The expression is simplified using the boundary conditions. When the formal composite model is applied to an unfinitesimal translation, a new representation of the scattering amplitude is obtained. Unlike the traditional representation, this expression depends on two full solutions to the wave equation, and it manifestly exhibits reciprocity. This article is the first in a series. Application of the results will be considered in future papers.
A bidirectional wave transformation of the cold plasma equations
Authors: Tippett Michael K. , Ziolkowski Richard W.
Published: July 2002

The bidirectional wave transformation developed for scalar equations is shown to have interesting extensions for first-order hyperbolic systems. Assuming a localized waveform of the solution gives an equation for the envelope of the localized wave. The type of the envelope equation depends on the characteristics of the original hyperbolic equations, and the speed of the localized wave. This method is applied to the cold plasma equations. In the general case integral representations are found for the fundamental solutions; and in a special case, exact solutions are constructed.
Stability conditions for method of self-similar approximations
Authors: Yukalov V. I.
Published: July 2002

A generalization for the method of self-similar approximations suggested recently by the author is given. Stability conditions for the method are formulated: first, the mapping multipliers for the self-similar recurrence relations have to be less than unity; second, the Lyapunov exponent for the differential form of the self-similar relations has to be negative. The fixed-point conditions defining the governing functions are analyzed from the point of view of stability. It is shown that the fixed-point condition expressed in the form of the principle of minimal sensitivity provides a contracting mapping contrary to the condition in the form of the principle of minimal difference. This explains why, in general, the former fixed-point condition yields more accurate results than the latter.
k-symplectic structures
Authors: Awane A.
Published: July 2002

The basic properties of k-symplectic structures are introduced and developed in analogy with the well-known symplectic differential geometry. Examples of such structures related to k-symplectic Lie algebras are given.
Canonical approximate quantum measurements
Authors: Ozawa Masanao
Published: July 2002

In order to generalize the Wigner formula for the joint probability distribution of successive canonical measurements of discrete observables to continuous observables, a mathematical model is investigated of a canonical approximate measurement of an arbitrary observable, which generalizes von Neumann’s model of measuring interaction and Davies’s covariant instrument for approximate position measurement. Calculations of two types of root-mean-square errors show that this model clears certain requirements for good approximate measurements. A modified Wigner formula for successive canonical approximate measurements of arbitrary observables is established. It is also shown that the canonical approximate measurement of a discrete observable is reduced to the conventional measurement satisfying the von Neumann–Lüders collapse postulate by a minor modification in the process of measurement.
On Schrödinger superalgebras
Authors: Duval C. , Horváthy P. A.
Published: July 2002

Using the supersymplectic framework of Berezin, Kostant, and others, two types of supersymmetric extensions of the Schrödinger algebra (itself a conformal extension of the Galilei algebra) were constructed. An ‘I-type’ extension exists in any space dimension, and for any pair of integers N+ and N−. It yields an N=N++N− superalgebra, which generalizes the N=1 supersymmetry Gauntlett et al. found for a free spin-1/2 particle, as well as the N=2 supersymmetry of the fermionic oscillator found by Beckers et al. In two space dimensions, new, ‘exotic’ or ‘IJ-type’ extensions arise for each pair of integers ν+ and ν−, yielding an N=2(ν++ν−) superalgebra of the type discovered recently by Leblanc et al. in nonrelativistic Chern–Simons theory. For the magnetic monopole the symmetry reduces to o(3)×osp(1/1), and for the magnetic vortex it reduces to o(2)×osp(1/2).
On the integrability of the inhomogeneous spherically symmetric Heisenberg ferromagnet in arbitrary dimensions
Authors: Daniel M. , Porsezian K. , Lakshmanan M.
Published: July 2002

The dynamics of an inhomogeneous spherically symmetric continuum Heisenberg ferromagnet in arbitrary (n-) dimensions is considered. By a known geometrical procedure the spin evolution equation equivalently is rewritten as a generalized nonlinear Schrödinger equation. A Painlevé singularity structure analysis of the solutions of the equation shows that the system is integrable in arbitrary (n-) dimensions only when the inhomogeneity is of inverse power in the radial coordinate in the form f(r)=ε1r−2(n−1)+ε2r−(n−2). This is confirmed by obtaining the associated Lax pair, Bäcklund transformation, and the solitonlike solution of the evolution equation. Further, calculations show that the one-dimensional linearly inhomogeneous ferromagnet acts as a universal model to which all the integrable higher-dimensional inhomogeneous spherically symmetric spin models can be formally mapped.
Polynomial deformations of osp(1/2) and generalized parabosons
Authors: Van der Jeugt J. , Jagannathan R.
Published: July 2002

We consider the algebra R generated by three elements A,B,H subject to three relations [H,A]=A, [H,B]=−B, and {A,B}=f(H). When f(H)=H this coincides with the Lie superalgebra osp(1/2); when f is a polynomial, we speak of polynomial deformations of osp(1/2). Irreducible representations of R are described, and in the case deg(f )≤2 we obtain a complete classification, showing some similarities but also some interesting differences with the usual osp(1/2) representations. The relation with deformed oscillator algebras is discussed, leading to the interpretation of R as a generalized paraboson algebra.
Nonsymmetric gravitational theory
Authors: Moffat J. W.
Published: July 2002

A nonsymmetric gravitational theory is presented which is free of ghost poles, tachyons, and higher-order poles and there are no problems with asymptotic boundary conditions. A static spherically symmetric solution in the long-range approximation is everywhere regular and does not contain a black hole event horizon. The information loss problem is resolved at the classical level.
Lorentzian metrics from characteristic surfaces
Authors: Frittelli Simonetta , Kozameh Carlos , Newman Ezra T.
Published: July 2002

The following issue is raised and discussed; when do families of foliations by hypersurfaces on a given four-dimensional manifold without further structure become the null surfaces of some unknown, but to be determined, metric gab(x). Explicit conditions for these surfaces are found, so that they do define a unique conformal metric with the surfaces themselves being characteristics of that metric. By giving an additional function (to be the conformal factor), full knowledge of the metric is determined. It is clear from these results that one can use these surfaces (and the conformal factor) as fundamental variables for describing any Lorentzian geometry and in particular for its use in general relativity.
Linearized Einstein theory via null surfaces
Authors: Frittelli Simonetta , Kozameh Carlos N. , Newman Ezra T.
Published: July 2002

Recently there has been developed a reformulation of general relativity (GR)—referred to as the null surface version of GR—where instead of the metric field as the basic variable of the theory, families of three-surfaces in a four-manifold become basic. From these surfaces themselves, a conformal metric, conformal to an Einstein metric, can be constructed. A choice of conformal factor turns it into an Einstein metric. The surfaces are then automatically characteristic surfaces of this metric. In the present paper we explore the linearization of this null surface theory and compare it with the standard linear GR. This allows a better understanding of many of the subtle mathematical issues and sheds light on some of the obscure points of the null surface theory. It furthermore permits a very simple solution generating scheme for the linear theory and the beginning of a perturbation scheme for the full theory.
Divergences in the moduli space integral and accumulating handles in the infinite-genus limit
Authors: Davis Simon
Published: July 2002

The symmetries associated with the closed bosonic string partition function are examined so that the integration region in Teichmuller space can be determined. The conditions on the period matrix defining the fundamental region can be translated to relations on the parameters of the uniformizing Schottky group. The growth of the lower bound for the regularized partition function is derived through integration over a subset of the fundamental region.