bluuebunny/crossref_metadata_2025 huggingface dataset:
Rare gas clusters: Solids, liquids, slush, and magic numbers
Authors: Beck Thomas L. , Jellinek Julius , Berry R. Stephen
Published: July 2002

Simulations by constant energy molecular dynamics have been performed for numerous clusters in the size range N=7–33. Detailed investigations have been conducted on the portions of the caloric curves in which the transition between rigid and nonrigid behavior occurs, to study the N dependence of the solid–liquid phase change. Clusters of several sizes display a coexistence of forms, each with a characteristic mean temperature, over a well-defined energy range in the transition region, as had been observed for the Ar13 cluster. Within the coexistence region, the high temperature form is solid-like and the low temperature form behaves in a liquid-like fashion. The caloric curves of state for these clusters take on two-valued forms when averages are calculated for each of the two ‘‘phases’’ separately; the two branches are smooth extensions of the curves from the single phase regions. Clusters of other sizes do not display this clear coexistence of phases, but appear to pass through a ‘‘slush-like’’ state during the melting transition. The coexistence behavior is not a smooth function of N. The clusters Ar13 and Ar19, and to a certain extent Ar7, display high stability properties indicative of magic number behavior.
Dielectric friction and the transition from adiabatic to nonadiabatic electron transfer in condensed phases. II. Application to non-Debye solvents
Authors: Sparpaglione Massimo , Mukamel Shaul
Published: July 2002

Outer sphere electron transfer rates in polar media are analyzed for non-Debye solvents whose dielectric function contains a few relaxation times (e.g., linear alcohols) or has a continuous distribution of relaxation times (e.g., the Cole–Davidson form for glycerol). The activation free energy and the preexponential factor are calculated and related to the solvent polarity and dielectric relaxation. The conditions for observing a fractional power dependence of the rate on the solvent time scale are analyzed.
Deduction of the Guldberg–Waage mass action law from Gyarmati’s governing principle of dissipative processes
Authors: Lengyel Sándor
Published: July 2002

It is shown that the Gyarmati–Li generalized reciprocal relations are satisfied in chemical kinetic systems of elementary reactions in continuous media provided that the rates of all forward and reverse reactions are considered as the complete set of independent fluxes together with the De Donder forward and reverse affinities of a complete set of stoichiometrically independent reactions as forces. This choice obviously differs from the usual one where net reaction rates and van’t Hoff affinities play the role of fluxes and forces, respectively. The corresponding nonlinear dissipation functions are constructed and the consistency of chemical kinetics with thermodynamics demonstrated.
Chain entanglements. I. Theory
Authors: Fixman Marshall
Published: July 2002

A model of concentrated polymer solution dynamics is described. The forces in a linear generalized Langevin equation for the motion of a probe chain are derived on the assumption that all relaxation of the forces is due to motion of the surrounding matrix. Vicinal chain displacements are classified as viscoelastic deformation, reptation, and minor residual fluctuations. The latter provide a torsional relaxation of the primitive path that minimizes the significance of transverse forces on the probe chain. All displacements of vicinal segments are assumed proportional to the forces that they exert on the probe chain. In response to an external force, the displacement of the probe chain relative to a laboratory frame is increased by viscoelastic deformation of the matrix, but reptative diffusion relative to the deforming matrix is slowed down. The net effect on translational diffusion is negligible if the probe and vicinal chains have the same chain length N, but the friction constant for reptative motion is increased by a factor N1−xs. xs=1/2 if Gaussian conformational statistics applies during the disengagement process, while xs =0.6 if excluded volume statistics applies. The translational friction constant is βp ∼N2, as in reptation theory, but the viscosity is η∼N4−xs . The persistence of entanglements during the translational diffusion of the probe chain across many radii of gyration is rationalized pictorially in terms of correlated reptative motion of the probe and vicinal chains.
Hexamethylbenzene as a sensitive nuclear magnetic resonance probe for studying organic crystals and glasses
Authors: Jansen-Glaw B. , Rössler E. , Taupitz M. , Vieth H. M.
Published: July 2002

Deuterated hexamethylbenzene (HMB) is used as a probe molecule for 2H NMR studies of the crystalline state of hexachlorobenzene and of several organic glasses. By measuring the spin–lattice relaxation and the line shape in the temperature range of 4–300 K the dynamical parameters of the molecular reorientation are investigated. For the system HMB/hexachlorobenzene, we find exponential relaxation and for the corresponding T1 an increase of its activation energy by a factor of 2 in comparison to the neat HMB. A homogeneous mixing of the guest and host molecules is found at least for guest concentrations up to 7%. In contrast, nonexponential spin–lattice relaxation is characteristic for all glass matrices, indicating motional heterogeneities. A log–Gauss distribution for the corresponding motional correlation times gives a good fit of the data. Its width parameter decreases linearly with temperature, while the mean correlation times are described by an Arrhenius law. The mean activation energy is reduced by a factor of about 3.5 as compared to neat HMB, demonstrating a loose packing of the molecules in the glass matrices.
Simulation of aggregating colloids in shear flow
Authors: Doi M. , Chen D.
Published: July 2002

Computer simulation is carried out for the kinetics of aggregating colloids in shear flow. The colloidal particles are assumed to form a cluster when they touch. The clusters can deform, rupture, and aggregate with other clusters. The motion of the clusters is determined by solving the equation of motion of individual particles. Cluster size and macroscopic viscosity are calculated as a function of shear rate and particle concentration. It is found that (i) at low concentration the particles form compact clusters, while at high concentration they form loose networks, and that (ii) despite the change in the cluster type, the steady state viscosity obeys the same power law for all concentrations. These results suggest that the key structural parameter governing the macroscopic viscosity is not the size of the clusters, but the size of the flowing unit which is a rigid block in the cluster.
General contraction of Gaussian basis sets. II. Atomic natural orbitals and the calculation of atomic and molecular properties
Authors: Almlöf Jan , Taylor Peter R.
Published: July 2002

Our recently proposed scheme for using natural orbitals from atomic configuration interaction wave functions as a basis set for linear combination of atomic orbitals (LCAO) calculations is extended for the calculation of molecular properties. For one-electron properties like multipole moments, which are determined largely by the outermost regions of the molecular wave function, it is necessary to increase the flexibility of the basis in these regions. This is most easily done by uncontracting the outermost Gaussian primitives, and/or by adding diffuse primitives. A similar approach can be employed for the calculation of polarizabilities. Properties which are not dominated by the long-range part of the wave function, such as spectroscopic constants or electric field gradients at the nucleus, can generally be treated satisfactorily with the original atomic natural orbital sets.
Fourth adiabatic ensemble
Authors: Ray John R. , Graben H. W.
Published: July 2002

The statistical mechanics of a new adiabatic ensemble, which allows volume and particle fluctuations, is presented. Characteristic fluctuation formulas and suitable response functions are derived.
Transformation of the Hamiltonian in excitation energy calculations: Comparison between Fock-space multireference coupled-cluster and equation-of-motion coupled-cluster methods
Authors: Meissner Leszek , Bartlett Rodney J.
Published: July 2002

A use of the transformed form of the Hamiltonian in excitation energy calculations is discussed and a comparison between methods using this form is performed. It is shown that use of a similarity-transformed Hamiltonian can lead to separation of the ground state and excited state eigenvalue problems. Then standard approaches for determination of excited state energies can be used. Since these energies are usually quasidegenerate, it is convenient to use the effective Hamiltonian scheme. For different approximate methods, various advantages and disadvantages referring to desirable features of a ‘‘theoretical model chemistry’’ are discussed.
Hydrogen bonding and the static dielectric constant in liquid water
Authors: Sprik Michiel
Published: July 2002

The static dielectric constants of several models for water are compared. These models have in common that they all give a good description of the energetics and structure of the hydrogen bonding in the liquid. Despite this similarity, the average molecular dipole moments vary over a range of 50% and the dielectric constants can differ by as much as a factor of 6. This observation verifies that the average dipole moment is a crucial parameter for the dielectric properties. On the other hand, this quantity seems of less importance for the stability of the hydrogen bonded network, which is largely determined by the details of the electrostatic and atom–atom interactions at short range. Applying this analysis we construct a polarizable model for liquid water with an average dipole moment of 2.6 D and a dielectric constant of 85. The structure and self-diffusion coefficient are in good agreement with experiment, and the value of the dimer binding energy in the gas phase is also acceptable.
Infrared spectra of molecular B(OH)3 and HOBO in solid argon
Authors: Andrews Lester , Burkholder Thomas R.
Published: July 2002

Anhydrous B(OH)3 was pressed into a pellet and sublimed at room temperature under vacuum to give molecular B(OH)3 for argon matrix infrared study. The spectrum showed sharp fundamentals without the effect of hydrogen bonding observed in the solid. Fermi resonances were characterized for two fundamentals. The observed frequencies for B(OH)3 and the three deuterium substituted molecules are in agreement with values from self-consistent field/double zeta plus polarization (SCF/DZP) calculations allowing for appropriate scale factors. The major thermal decomposition products from pulsed laser evaporation of B(OH)3 were H2O, B2O3, and HOBO. Molecular HOBO was characterized by a strong 2020 cm−1 fundamental, which was confirmed by SCF/DZP calculations.
On the intersection of potential energy surfaces in charge transfer reactions: A crossing seam for two states of the same symmetry in the reaction H++NO(X 2Π)→H(2S)+NO+(X 1Σ+)
Authors: Manaa M. Riad , Yarkony David R.
Published: July 2002

An actual crossing seam of two potential energy surfaces of the same symmetry relevant to the charge transfer reaction H++NO(X 2Π)→H(2S)+NO+(X 1Σ+) is reported. This crossing seam occurs for general Cs geometries. It represents the intersection of the 1,2 2A′ potential energy surfaces which correlate asymptotically with H(2S)+NO+(X 1Σ+) and H++NO(X 2Π), respectively. A portion of the seam is exoergic relative to the reactant channel, H++NO(X 2Π), asymptote. The present results complement a previous determination of two allowed crossing seams in C∞v symmetry, and provide, for the first time, an example of a system for which both allowed and actual conical intersections exist. Since the actual crossing seam occurs for geometrical configurations quite distinct from the allowed crossing seams previously considered these results have important implications for the rotational–vibrational energy distribution in the products of the charge exchange process.
Potential curves for the ground and excited states of the Na2 molecule up to the (3s+5p) dissociation limit: Results of two different effective potential calculations
Authors: Magnier S. , Millié Ph. , Dulieu O. , Masnou-Seeuws F.
Published: July 2002

Theoretical calculations for the ground state and for 83 excited states of the Na2 molecule are presented in the framework of two independent approaches. The electron–core interaction is represented either by a pseudopotential or by a model potential, and a core polarization potential is introduced in both cases. The basis set contains either Gaussian orbitals or two-center generalized Slater orbitals. The two methods appear to give similar results, one being more accurate for the ground and first excited states, the other being better adapted to the intermediate Rydberg states. A very good agreement is obtained with the experimental spectroscopic constants determined for 26 states, the mean deviation being ΔRe=0.05a0, Δωe=0.86 cm−1, and ΔDe=57 cm−1.
Dynamics of small molecules in dense polymers subject to thermal motion
Authors: Gusev Andrei A. , Suter Ulrich W.
Published: July 2002

A new transition-state theory model has been proposed that is based on the concept that the dynamics of small molecules dissolved in dense polymers is coupled to the elastic thermal motion of dense polymers but can be treated separately from their structural relaxation. The model has been used to study the dynamics of light gases dissolved in atomistic microstructures of poly(isobutylene) and bisphenol-A-polycarbonate. Short-time scale MD runs have been used to characterize the elastic thermal motion of the host matrix. This information on mobility is then used for a stochastic simulation of solute dynamics up to approximately 10 μs. Three time regimes have been observed: a short-time, high-mobility domain, a time domain of anomalous diffusion, and a diffusive regime at long times. From the long-time data diffusion coefficients for He, H2, Ar, O2, and N2 have been estimated. Comparison with experimental data has resulted in satisfactory agreement indicating that the mechanisms of the motion of small gases in glassy and rubbery polymers are the same.
Small angle neutron scattering near Lifshitz lines: Transition from weakly structured mixtures to microemulsions
Authors: Schubert K.-V. , Strey R. , Kline S. R. , Kaler E. W.
Published: July 2002

We have studied the phase behavior, wetting transitions, and small angle neutron scattering (SANS) of water, n-alkane, and n-alkyl polyglycol ether (CiEj) systems in order to locate the transition between weakly structured mixtures and microemulsions, and to provide a measure for the transition. We first determined the wetting transition by macroscopic measurements and then measured the location of the Lifshitz lines by SANS. Starting with well-structured mixtures (exhibiting nonwetting middle phases and well-expressed scattering peaks, features that qualify them as microemulsions) the wetting transition was induced by increasing the chain length of the alkane or by changing the oil/water volume ratio, and then the Lifshitz line was crossed. Further, starting with systems past the disorder line (weakly structured mixtures that display wetting middle phases and no scattering peaks), local structure was induced by either increasing the surfactant concentration or decreasing the oil/water volume ratio or the temperature. In each case a Lifshitz line was crossed. Analyzing the scattering experiments quantitatively, allows determination of the amphiphilicity factor, which is a measure of the strength of the surfactant. The results suggest there is a sequence of roughly parallel surfaces within the three-dimensional composition-temperature space. As the amphiphilicity factor increases, first a disorder surface is encountered, then a Lifshitz surface, and finally a wetting transition surface. How and to what extent these surfaces move in the one-phase region toward smaller surfactant concentrations, and intersect there with the body of heterogeneous phases, depends on a number of factors that are discussed in some detail.
Pressure-induced disappearance of the in-plane lattice distortion in layered cupric chloride: (C2H5NH3)2CuCl4
Authors: Moritomo Y. , Tokura Y.
Published: July 2002

Effects of hydrostatic pressure on Raman scattering and electronic absorption spectra have been investigated in layered cupric chloride (C2H5NH3)2CuCl4, consisting of strongly Jahn–Teller (JT) deformed CuCl4 layers. We observed selective deactivation of the Cu–Cl stretching modes at a pressure above ∼4 GPa, and interpreted the phenomena in terms of disappearance of the in-plane lattice distortion of the CuCl4 layer. The pressure-induced structural change reduces the charge-transfer (CT)-type gap from the ligand (Cl3p) to metal (Cu3dx2−y2) sites by ∼0.4 eV, and perhaps produces the two-dimensional electronic states analogous to that of the parent compounds for the cupric superconductors.
Magic numbers for classical Lennard-Jones cluster heat capacities
Authors: Frantz D. D.
Published: July 2002

Heat capacity curves as functions of temperature for classical atomic clusters bound by pairwise Lennard-Jones potentials were calculated for aggregate sizes 4≤N≤24 using Monte Carlo methods. J walking (or jump walking) was used to overcome convergence difficulties due to quasiergodicity in the solid-liquid transition region. The heat capacity curves were found to differ markedly and nonmonotonically as functions of cluster size. Curves for N=4, 5, and 8 consisted of a smooth, featureless, monotonic increase throughout the transition region, while curves for N=7 and 15–17 showed a distinct shoulder in this region; the remaining clusters had distinguishable transition heat capacity peaks. The size and location of these peaks exhibited ‘‘magic number’’ behavior, with the most pronounced peaks occurring for magic number sizes of N=13, 19, and 23. This is consistent with the magic numbers found for many other cluster properties, but there are interesting differences for some of the other cluster sizes. Further insight into the transition region was obtained by comparing rms bond length fluctuation behavior with the heat capacity trends. A comparison of the heat capacities with other cluster properties in the solid-liquid transition region that have been reported in the literature indicates partial support for the view that, for some clusters, the solid-liquid transition region is a coexistence region demarcated by relatively sharp, but separate, melting and freezing temperatures; some discrepancies, however, remain unresolved.
Statistical distribution and stochastic resonance in a periodically driven chemical system
Authors: Dykman M. I. , Horita Takehiko , Ross John
Published: July 2002

The probability density distribution is studied analytically and by Monte Carlo simulations for a periodically driven chemical bistable system, described by a master equation, for the case of low-frequency driving. The quasistationary distribution about the stable states is well approximated by the solution of the master equation in the eikonal approximation for large volumes of the system. For a one-component system both the exponent and the prefactor of the steady distribution are obtained in explicit form, for an arbitrary strength of the driving and for an arbitrary interrelation between the frequency of the driving and the probabilities of transitions between the stable states. The results of the simulations are in good agreement with analytical results. We demonstrate the onset of stochastic resonance for the driving frequency close to the probabilities of fluctuational transitions between the states.
Perturbative triple excitation corrections to coupled cluster singles and doubles excitation energies
Authors: Christiansen Ove , Koch Henrik , Jo/rgensen Poul
Published: July 2002

The contributions from various excitation levels to excitation energies calculated within a coupled cluster framework are analyzed in terms of order in the fluctuation potential. In particular, the role of triple excitations is considered, focusing on their importance for describing excitations of single and double replacement dominated character. Several noniterative triples corrections to the coupled cluster singles and doubles (CCSD) excitation energies are proposed. In the CCSDR(3) approach, which is a noniterative analog to the recently proposed iterative CC3 model, single replacement dominated excitations are correct through third order in the fluctuation potential, and double replacement dominated excitations are correct through second order. The performance of CCSDR(3) is compared to other noniterative and iterative triples models in benchmark calculations on CH+, Ne, BH, and CH2.
The effect of a model environment on the S2 absorption spectrum of pyrazine: A wave packet study treating all 24 vibrational modes
Authors: Worth G. A. , Meyer H.-D. , Cederbaum L. S.
Published: July 2002

The absorption spectrum of pyrazine to the S2 electronic state can be usefully described by a 4-mode system interacting with a 20-mode bath. In this paper wave packet propagation techniques, using the multiconfiguration time-dependent Hartree approach, are used to study this problem. The investigation was made in stages so as to study the nature of the wave function needed to correctly describe various properties of this multimode problem: the absorption spectrum; the energy exchange between the system and the bath; and the rate of inter-state crossing. It was found that, despite the relatively weak system–bath coupling, a multiconfigurational wave function was necessary to describe the interaction between the two parts of the problem. While it was not possible to treat the full 24-mode problem with such a wave function, the spectrum for a 14-mode system, which includes all the important bath modes, has been calculated in this way. The results, in agreement with the path integral calculations of Krempl et al. [J. Chem. Phys. 100, 926 (1994)], show that the effect of a model bath linearly coupled to the system is to reduce the vibrational structure of the spectrum, so as to produce a broad envelope analogous to that observed experimentally. The details of the spectrum are however different for the two methods. The effect of introducing anharmonicity to the bath was also studied, with the result that this leads to a yet broader spectrum.
Coupled Q-oscillators as a model for vibrations of polyatomic molecules
Authors: Bonatsos Dennis , Daskaloyannis C. , Kolokotronis P.
Published: July 2002

The system of two Q-deformed oscillators coupled so that the total Hamiltonian has the suQ(2) symmetry is proved to be equivalent, to lowest order approximation, to a system of two identical Morse oscillators coupled by the cross-anharmonicity usually used empirically in describing vibrational spectra of triatomic molecules. The symmetry also imposes a connection between the self-anharmonicity of the Morse oscillators and the cross-anharmonicity strength, which can be removed by replacing the Q-oscillators by deformed anharmonic oscillators. The generalization to n oscillators is straightforward. The applicability of the formalism to highly symmetric polyatomic molecules is discussed.
Simulation of many-spin system dynamics via sparse matrix methodology
Authors: Dumont Randall S. , Jain Shashi , Bain Alex
Published: July 2002

A sparse-matrix-based numerical method is constructed to simulate NMR spectra of many-spin systems, including the effects of chemical exchange and/or relaxation. The associated computational demands are predicted to scale like O(22n), as the number of spins n increases. This is vastly superior to the inevitable O(26n) scaling of conventional Householder-based methodology. The improved scaling is verified via numerical computations of simple isomerization systems with four to nine spins. The new method is based on splitting the propagator and use of Chebyshev polynomial expansion of the exponential function.
Short-range attractions between two colloids in a lipid monolayer
Authors: Sintes T. , Baumgärtner A.
Published: July 2002

Two mobile cylinders embedded in a lipid monolayer exhibit two types of short-range attractions, a depletion-induced attraction in the range r<σL, where σL is the diameter of a lipid and r is the distance between the surfaces of the two cylinders, and a fluctuation-induced attraction in the range 1<r/σL<4. Using Monte Carlo methods we have calculated the force between the cylinders for various diameters σP. Evidence is given that the strength of attraction increases with decreasing curvature of the cylinders.
Macromolecular clusters in poor-solvent polymer solutions
Authors: Raos Guido , Allegra Giuseppe
Published: July 2002

We apply our previously proposed “Gaussian cluster” model [J. Chem. Phys. 104, 1626 (1996)] to the study of macromolecular association and aggregation, under poor-solvent conditions (T<Θ). The properties of the macromolecular clusters are studied as a function of the number of chains ν=2,3,4,…, of the attractive two-body excluded-volume parameter z and of the repulsive three-body parameter K1. In the temperature window between its upper stability temperature and the coil-globule transition temperature for the single chains, a cluster of 2÷10 chains can have a smaller radius of gyration than an isolated polymer chain, provided K1 is sufficiently small. We suggest that this parameter may be estimated by considering the relative separations between the Θ, the critical and the collapse temperatures. We compute the equilibrium distribution of the chains in a dilute solution among all possible cluster sizes (including ν=1, the isolated chains); population of the clusters ν⩾2 increases with K1, but is generally rather small. Below the coil–globule transition temperature, anywhere on the dilute side of the two-phase region of the phase diagram, there is no free-energy barrier to polymer aggregation and precipitation: a single collapsed chain is a “critical nucleus” and the spinodal practically coincides with the binodal.
Determination of local structure in solid nucleic acids using double quantum nuclear magnetic resonance spectroscopy
Authors: Gregory D. M. , Mehta M. A. , Shiels J. C. , Drobny G. P.
Published: July 2002

A theoretical analysis of dipolar recoupling with a windowless multipulse irradiation (DRAWS) is presented. Analytical expressions that describe the degree to which the DRAWS pulse sequence recouples the dipolar interaction as a function of offset and spinning rate are derived using Floquet theory. Numerical methods are used to assess the performance of DRAWS in the preparation and detection of multiple quantum coherence. Simulations indicate that the mutual orientation of two or more CSA tensors can be obtained with high accuracy from double quantum spectra prepared and detected by DRAWS irradiation (DQDRAWS). These expectations are born out by experiment and in particular, the mutual orientation of three 13C CSA tensors in selectively labeled 2-deoxythymidine are determined from DQDRAWS data. The results of the DQDRAWS analysis of CSA tensor orientation in 2-deoxythymidine are shown to be in excellent agreement with results obtained by conventional methods. Using these CSA tensor orientations and an independent measurement of internuclear distance, a practical strategy is proposed and executed for deriving the mutual orientation of purine and pyrimidine bases in a DNA dodecamer from DQDRAWS data. The DQDRAWS method for determining the mutual orientation of rigid bodies in macromolecules is compared and contrasted to distance-based methods.
Probing the intermolecular hydrogen bonding of water molecules at the CCl4/water interface in the presence of charged soluble surfactant
Authors: Gragson D. E. , Richmond G. L.
Published: July 2002

The molecular structure and hydrogen bonding of water molecules at the CCl4/water interface in the presence of a charged soluble surfactant has been explored in this study using vibrational sum frequency generation. By examining OH stretching modes that are highly sensitive to the local hydrogen bonding environment it is found that water molecules at the CCl4/water interface both in the presence and absence of a charged soluble surfactant are predominantly in a tetrahedral arrangement much like the structure of ice. Isotopic dilution studies have been employed to further characterize this icelike interfacial structure. A blueshift of approximately 120 cm−1 of the icelike OH stretching mode is observed upon dilution with D2O. The first vibrational spectra of the OH stretching mode from uncoupled HOD molecules at the CCl4/water interface is also reported.
Magnetic coupling in ionic solids studied by density functional theory
Authors: Illas Francesc , Martin Richard L.
Published: July 2002

Magnetic coupling in ionic solids is studied using a density functional theory, DFT, approach applied to suitable cluster models representing KNiF3, K2NiF4, and La2CuO4. A mapping between eigenstates of the exact nonrelativistic and spin model Hamiltonians allows us to obtain the magnetic coupling constant J and to compare the DFT values with either experiment or previous theoretical studies based on the use of accurate wave functions. In the present work different correlation and exchange functionals are explored. Numerical results show that it is possible to reach very good agreement with experiment. Surprisingly, it is shown that the difficulty of the local spin density approximation in describing the antiferromagnetic behavior of these compounds lies not in the correlation but in the exchange part of the density functional. Hybrid functionals, which include a component of the full, nonlocal, “exact” exchange interaction yield qualitatively and semiquantitatively correct magnetic interactions. The origin of this behavior is discussed from the point of view of the adiabatic connection formula.
Energies and analytic gradients for a coupled-cluster doubles model using variational Brueckner orbitals: Application to symmetry breaking in O4+
Authors: Sherrill C. David , Krylov Anna I. , Byrd Edward F. C. , Head-Gordon Martin
Published: July 2002

We describe an alternative procedure for obtaining approximate Brueckner orbitals in ab initio electronic structure theory. Whereas approximate Brueckner orbitals have traditionally been obtained by mixing the orbitals until the coefficients of singly substituted determinants in the many-electron wave function become zero, we remove singly substituted determinants at the outset and obtain orbitals which minimize the total electronic energy. Such orbitals may be described as variational Brueckner orbitals. These two procedures yield the same set of exact Brueckner orbitals in the full configuration interaction limit but differ for truncated wave functions. We consider the simplest variant of this approach in the context of coupled-cluster theory, optimizing orbitals for the coupled-cluster doubles (CCD) model. An efficient new method is presented for solving the coupled equations defining the energy, doubles amplitudes, and orbital mixing parameters. Results for several small molecules indicate nearly identical performance between the traditional Brueckner CCD method and the variational Brueckner orbital CCD approach. However, variational Brueckner orbitals offer certain advantages: they simplify analytic gradients by removing the need to solve the coupled-perturbed Brueckner coupled-cluster equations for the orbital response, and their straightforward extensions for inactive orbitals suggests possible uses in size-extensive models of nondynamical electron correlation. Application to O4+ demonstrates the utility of variational Brueckner orbitals in symmetry breaking cases.
Monte Carlo simulation of an ion-dipole mixture as a model of an electrical double layer
Authors: Boda Dezső , Chan Kwong-Yu , Henderson Douglas
Published: July 2002

Canonical Monte Carlo simulations were performed for a nonprimitive model of an electrical double layer. The ions and the solvent molecules are modeled as charged and dipolar hard spheres, respectively, while the electrode as a hard, impenetrable wall carrying uniform surface charge. We found that the ion-dipole model gives a reasonable description of the double layer for partially charged ions with small to moderate dipole moments, or equivalently for an “effective” dielectric constant. Density, polarization and mean electrostatic potential profiles are reported. Strong layering structure, and at higher charges, charge inversion in the second layer were found. With appropriate choices of charge and solvent parameters, states corresponding to the primitive or the solvent primitive model can be produced, and the results agreed well with literature data. At higher effective charges and dipole moments, the dipolar solvent has difficulties in preventing the ions from clustering. More realistic models of water and other solvents are necessary to study the double layer.
Microcanonical Monte Carlo simulation of thermodynamic properties
Authors: Lustig Rolf
Published: July 2002

A rigorous sampling procedure in configurational phase space is used to simulate any thermodynamic property in the microcanonical ensemble. It is shown how two classical choices of W in Boltzmann’s S=kB ln W differ for small systems and become numerically equivalent in the thermodynamic limit. The same holds true for the comparison with classical molecular dynamics simulations. A comparison with the best empirical equations of state for the Lennard-Jones system shows that this Monte Carlo method is as accurate and reliable as any other simulation technique.
Analytical free energy second derivatives with respect to nuclear coordinates: Complete formulation for electrostatic continuum solvation models
Authors: Mennucci B. , Cammi R. , Tomasi J.
Published: July 2002

We present the theory and the implementation of analytical free energy second derivatives with respect to nuclear displacements for a molecular solute described within the framework of the polarizable continuum model. The formulation applies to a cavity with an accurately modeled molecular shape and it permits a complete consideration of all aspects of the solvation model. In particular, the implementation uses the recently proposed method known as the integral equation formalism (IEF), and it can be applied to Hartree–Fock and to density functional calculations. The analysis of both formal and technical features is reported as well as some numerical applications to solvatochromic shifts in IR vibrational frequencies and to transition state searches for reactions in solutions.
Electron spin-lattice relaxation of silver nanoparticles embedded in SiO2 and TiO2 matrices
Authors: Mitrikas G. , Trapalis C. C. , Kordas G.
Published: July 2002

Metallic silver nanoparticles were prepared by the sol-gel method in amorphous SiO2 and crystalline TiO2 matrices. The metal particles were monodispersed in size and their mean diameters varied between 1 and 10 nm, depending upon the processing conditions. The spin-lattice relaxation (SLR) times were investigated by pulsed electron paramagnetic resonance (EPR) spectroscopy in a temperature range between 4 K and 300 K. The spin echo recoveries were slow enough (of the order of some ms), and demonstrated a biexponential character. This study showed that for silver nanoparticles in the SiO2 matrix, the temperature dependence of T1 can be described by the relation (1/T1)∝Tn, where 0.4<n<1. Contrary to this behavior, the temperature dependence of T1 has a Raman-type character (1/T1∝T2) for silver nanoparticles in the TiO2 matrix. The unusual behavior for the SiO2 samples is attributed to the amorphous phase of the SiO2 matrix. The results are discussed in terms of possible relaxation mechanisms suggested by Khaliullin and Khusainov taking into account the energy levels correlation functions. This study showed that the spin relaxation due to static defects is in agreement with our results. In addition, a satisfactory agreement between theory and experiment can only be obtained in the case of repulsion between the energy levels indicative for the quantum size effect.
Phase changes in 38-atom Lennard-Jones clusters. II. A parallel tempering study of equilibrium and dynamic properties in the molecular dynamics and microcanonical ensembles
Authors: Calvo F. , Neirotti J. P. , Freeman David L. , Doll J. D.
Published: July 2002

We study the 38-atom Lennard-Jones cluster with parallel tempering Monte Carlo methods in the microcanonical and molecular dynamics ensembles. A new Monte Carlo algorithm is presented that samples rigorously the molecular dynamics ensemble for a system at constant total energy, linear and angular momenta. By combining the parallel tempering technique with molecular dynamics methods, we develop a hybrid method to overcome quasiergodicity and to extract both equilibrium and dynamical properties from Monte Carlo and molecular dynamics simulations. Several thermodynamic, structural, and dynamical properties are investigated for LJ38, including the caloric curve, the diffusion constant and the largest Lyapunov exponent. The importance of insuring ergodicity in molecular dynamics simulations is illustrated by comparing the results of ergodic simulations with earlier molecular dynamics simulations.
A small angle x-ray scattering study of the droplet–cylinder transition in oil-rich sodium bis(2-ethylhexyl) sulfosuccinate microemulsions
Authors: Svergun D. I. , Konarev P. V. , Volkov V. V. , Koch M. H. J. , Sager W. F. C. , Smeets J. , Blokhuis E. M.
Published: July 2002

A method for nonlinear fitting of x-ray scattering data from polydisperse mixtures was developed. It was applied to the analysis of the structural changes in the droplet phase of oil-rich water-in-oil (w/o) sodium bis(2-ethylhexyl) sulfosuccinate (AOT) microemulsions with increasing temperature or upon addition of salt. Data were collected at different temperatures (15 to 60 °C) and salt concentrations (up to 0.6% NaCl) within the one-phase region of the L2 phase (w/o microemulsion) for different droplet sizes (water/AOT molar ratio wo=25 to 56) and concentrations (droplet weight fraction cw=2% to 20%). This allowed us to distinguish between contributions from individual scattering particles, e.g., droplets and cylinders to the total scattering intensity. The complete data set containing over 500 scattering curves could be interpreted by fitting the scattering of weighted sums of AOT covered water droplets, long cylinders, and inverse AOT micelles containing bound water only, to the experimental scattering curves. The polydispersity of the droplets and cylinders is described by Schulz distributions and the interactions between the droplets are calculated using a sticky hard-sphere potential in the Percus–Yevick approximation. The volume fractions of the components, their average sizes and polydispersity, and the stickiness of the water/AOT droplets are determined by a nonlinear fit to the experimental data.
The range of quantum probability
Authors: Pitowsky Itamar
Published: July 2002

The set of all pair (and in fact higher-order) distributions that are representable in quantum mechanics is characterized and compared with the classical range. Various interference phenomena yield pair distributions that are not classical; a few examples are discussed. These results shed light on some fundamental problems concerning the interpretation of quantum mechanics, in particular it is demonstrated how the ‘‘quantum logic’’ of Birkhoff and Von Neumann can be naturally interpreted in terms of truth values. Finally, the possibility of interpreting quantum probability in a realistic ‘‘quasiclassical’’ way is explored.
Spontaneous symmetry breaking and the Higgs mechanism for quaternion fields
Authors: Nash C. , Joshi G. C.
Published: July 2002

In the context of quaternion valued fields spontaneous symmetry breaking and the Higgs mechanism are investigated. In particular, for the potential −(μ2/2)φ̄φ−(λ/4)(φ̄φ)2, Goldstone’s theorem is studied and, for the gauge theory of automorphisms of the quaternions, a Higgs mechanism investigated.
Wiener measures for path integrals with affine kinematic variables
Authors: Daubechies Ingrid , Klauder John R. , Paul Thierry
Published: July 2002

The results obtained earlier have been generalized to show that the path integral for the affine coherent state matrix element of a unitary evolution operator exp(−iTH) can be written as a well-defined Wiener integral, involving Wiener measure on the Lobachevsky half-plane, in the limit that the diffusion constant diverges. This approach works for a wide class of Hamiltonians, including, e.g., −d2/dx2+V(x) on L2(R+), with V sufficiently singular at x=0.
On identically closed forms locally constructed from a field
Authors: Wald Robert M.
Published: July 2002

Let M be an n-dimensional manifold with derivative operator ∇a and let B(M) be an arbitrary vector bundle over M, equipped with a connection. A cross section of B defines a field φ on M. Let α be a p-form on M (with p<n) which is locally constructed from φ and finitely many of its derivatives (as well as, possibly, some ‘‘background fields’’ ψ and their derivatives) such that dα=0 for all cross sections φ. Suppose further that α=0 for the zero cross section, φ=0. It is proven here that there exists a (p−1)-form β that also is a local function of φ,ψ and finitely many of their derivatives, such that α=dβ. A number of applications of this result are described. In particular, gauge invariance is established for the charges and the total fluxes derived from gauge-dependent conserved currents, and severe limitations are established on the the possibilities for gravitational analogs of magnetic charges.
Generalized Gel’fand invariants and characteristic identities for quantum groups
Authors: Gould M. D. , Zhang R. B. , Bracken A. J.
Published: July 2002

The generalized Gel’fand invariants for an arbitrary quantum group are explicitly constructed, and their eigenvalues in any irreducible representation are computed. These invariants enable one to develop characteristic identities for the quantum group, and as a natural application, these identities are used to construct projection operators for tensor products of representations. To illustrate the general theory, the quantum group Uq(gl(m)) is studied in detail.
Symmetry groups and similarity solutions of MHD equations
Authors: Fuchs J. C.
Published: July 2002

A similarity analysis of the nonlinear nonstationary real MHD equations is presented. For several cases of real MHD the complete Lie algebra of infinitesimal symmetries is calculated. Using subalgebras of this Lie algebra, reduced systems for similarity solutions can be obtained. Some similarity solutions of the ideal MHD equations are discussed.
Constraints of the Kadomtsev–Petviashvili hierarchy
Authors: Cheng Yi
Published: July 2002

For the Kadomtsev–Petviashvili (KP) hierarchy constructed in terms of the famous Sato theory, a ‘‘k constraint’’ is proposed that leads the hierarchy to the nonlinear system involving a finite number of dynamical coordinates. The eigenvalue problem of the k-constrained system is naturally obtained from the linear system of the KP hierarchy, which takes the form of kth-order polynomial coupled with a first-order one, thus we are able to derive the correspondent Lax pair, recursion operator, bi-Hamiltonian structures, and conserved quantities. The constraints for the BKP hierarchy are also sketched.
General solutions of Maxwell–Dirac equations in 1+1-dimensional space–time and a spatially confined solution
Authors: Das A.
Published: July 2002

The most general solution of the system of massless Maxwell–Dirac equations in 1+1-dimensional space–time (or classical Schwinger theory) is obtained in terms of four arbitrary functions and one arbitrary constant. A particular example is furnished for which the Dirac wave function vanishes completely outside a finite spatial range. Maxwell–Dirac equations for a nonzero mass parameter are reduced to a single, real, fourth-order, nonlinear partial differential equation. A particular class of solutions for this complicated equation is provided.
On a model of a relativistic particle with curvature and torsion
Authors: Nesterenko V. V.
Published: July 2002

A new version of the model of a relativistic particle with curvature and torsion considered in V. V. Nesterenko [J. Math. Phys. 32, 3315 (1991)] is investigated. Two integrals along the world trajectory of its curvature and torsion are added to the standard action for the pointlike spinless relativistic particle. Since here the three-dimensional space–time is considered at the beginning, the torsion of the world curve is defined with a sign in contrast to the previous consideration. Upon obtaining a complete set of constraints in the phase space a generalized Hamiltonian description of a new version of the model is constructed. This enables one to quantize the model canonically and to derive exactly the relation between the spin and mass of the states.
Justification of the zeta function renormalization in rigid string model
Authors: Nesterenko V. V. , Pirozhenko I. G.
Published: July 2002

A consistent procedure for regularization of divergences and for subsequent renormalization of the string tension is proposed in the framework of the one-loop calculation of the interquark potential generated by the Polyakov–Kleinert string. In this way, a justification of the formal treatment of divergences by analytic continuation of the Riemann and Epstein–Hurwitz zeta functions is given. A spectral representation for the renormalized string energy at zero temperature is derived, which enables one to find the Casimir energy in this string model at nonzero temperature very easy.
Entropic integrals of hyperspherical harmonics and spatial entropy of D-dimensional central potentials
Authors: Yáñez R. J. , Van Assche W. , González-Férez R. , Dehesa Jesús S.
Published: July 2002

The information entropy of a single particle in a quantum-mechanical D-dimensional central potential is separated in two parts. One depends only on the specific form of the potential (radial entropy) and the other depends on the angular distribution (spatial entropy). The latter is given by an entropic-like integral of the hyperspherical harmonics, which is expressed in terms of the entropy of the Gegenbauer polynomials. This entropy is expressed in terms of the values of the quadratic logarithmic potential of Gegenbauer polynomials Cnλ(t) at the zeros of these polynomials. Then this potential for integer λ is given as a finite expansion of Chebyshev polynomials of even order, whose coefficients are shown to be Wilson polynomials.
Design of guide vanes for minimizing the pressure loss in sharp bends
Authors: Sahlin Alexander , Johansson Arne V.
Published: July 2002

A guide-vane section was designed with the aim of minimizing the pressure drop for flow in a 90° corner. A central part of the design process was to use potential flow calculations in order to obtain a vane geometry such that the velocity distribution on the suction side replicates that of a chosen single airfoil (Wortmann FX60-100) at the angle of attack for maximum lift/drag in a straight free stream. The choice was based on proven good drag characteristics at low Reynolds numbers. For the design of the pressure-side velocity distribution advantage was taken of the expansion in the middle part of the cascade to obtain a high pressure coefficient on the pressure side, as compared to the single airfoil case. Vanes were built and tested in a special-purpose wind tunnel. The two-dimensional pressure-loss coefficient, as measured downstream of a five-vane corner, was found to be as low as 0.036, which is about one-fifth of that for traditional (1)/(4) -circle-shaped vanes.