ALBERT

Notes: The exact (bosonic) ground state and a class of excited states are obtained for several Calogero-type N-body problems in D dimensions when the N bodies are also interacting via an N-body potential of the form −e2/Σri2. © 1999 American Institute of Physics.

Notes: In this paper we study the eigenvalue problems for the Ginzburg–Landau operator with a large parameter in bounded domains in R2 under gauge invariant boundary conditions. The estimates for the eigenvalues are obtained and the asymptotic behavior of the associated eigenfunctions is discussed. These results play a key role in estimating the critical magnetic field in the mathematical theory of superconductivity. © 1999 American Institute of Physics.

Notes: For the hydrogenlike atom, with central potential −Z/r, partial differential equations exist for the Slater sum Z(r,β) [β=(kBT)−1] and for its s-wave (l=0) component Z0(r,β). It is shown that Z can be eliminated, to lead to a result in which Z(r,β) is solely characterized by Z0(r,β). A similar situation is exhibited for the three-dimensional isotropic harmonic oscillator, for which closed forms of both Z(r,β,ω) and Z0(r,β,ω) can be obtained explicitly. Finally, a third central field problem is considered in which independent electrons are confined within a sphere of radius R, but are otherwise free. We are able to derive explicitly for this model the s-wave component Z0(r,β,R). The full Slater sum Z(r,β,R) then is also analyzed in some detail. © 1999 American Institute of Physics.

Notes: A theory of stochastic flows over the algebra of observables of a dynamical system is presented in which the main objective is to ensure that the overall canonical/symplectic structure on the algebra is preserved. We study both classical and quantum systems and the importance of physical interpretation in the Stratonovich interpretation is stressed. We find the natural formulation of quantum dissipative systems to be given in terms of quantum stochastic calculus. This treatment allows for a physically meaningful treatment of both constant and nonlinear dissipation. As an application, we quantize a mechanical system with the same nonlinear damping mechanism as the van der Pol oscillator. © 1999 American Institute of Physics.

Notes: Euler–Kirchhoff filaments are solutions of the static Kirchhoff equations for elastic rods with circular cross sections. These equations are known to be formally equivalent to the Euler equations for spinning tops. This equivalence is used to provide a classification of the different shapes a filament can assume. Explicit formulas for the different possible configurations and specific results for interesting particular cases are given. In particular, conditions for which the filament has points of self-intersection, self-tangency, vanishing curvature or when it is closed or localized in space are provided. The average properties of generic filaments are also studied. They are shown to be equivalent to helical filaments on long length scales. © 1999 American Institute of Physics.

Notes: A standard classical model of a so-called rigid two-body collision that employs the dynamic Coulomb friction law to model friction is studied. For arbitrary object geometries and initial conditions it is known that the direction of the relative sliding velocity continuously changes during the impact. A (new) exact analytical solution for the relative sliding speed utr of the two objects in terms of initial conditions and sliding direction is derived. This solution is formulated in terms of a first integral, which is used to rigorously prove that the dynamic Coulomb friction law does not allow either instantaneous sticking or stable sticking to evolve from an initially nonzero utr, except for certain very special cases. The first integral also yields a new procedure for accurately and efficiently computing the final center of mass velocity and the final angular velocity of each of the objects in the model two-body collision. Accurate solutions such as these are essential for analyzing and controlling impacts, which is important, for example, in robot manipulation. Efficient solutions are critically important for producing real-time simulations of rigid two-body collisions. © 1999 American Institute of Physics.

Notes: Using the correspondence between a stationary space–time and a curved three-dimensional space with a static magnetic field and a conservative field of force, the Maxwell equations in a stationary space–time are expressed in terms of fields associated with the corresponding three-dimensional geometry. The Maxwell equations take a form analogous to the one they have in flat space–time. The Ricci tensor of the space–time is also written in terms of the three-dimensional fields. © 1999 American Institute of Physics.

Notes: The diffusion equation in physical space–time for a Brownian particle driven by an external force field has been derived by Smoluchowski in the two particular cases where the external field is uniform or varies linearly with position (elastic force). In more general cases, correction terms must be added to the Smoluchowski equation. We show here how to use a multi-scale Chapman–Enskog expansion to obtain, in the hydrodynamic limit, the first corrective terms to the Smoluchowski equation, without any restriction on the friction coefficient, and for any sufficiently small position-dependent constant force field. We also compare our approach with the works of Wilemski, Titulaer, and van Kampen. © 1999 American Institute of Physics.

Notes: We analyze spectral properties of a class of integral-difference collision operators arising in some nonequilibrium statistical physics models. We present analytical estimates and numerical results for the operators defined on finite intervals and corresponding to the truncated Gaussian equilibrium distribution function. Some conclusions are drawn about the spectrum of operators on whole axis. Physical limitations for these kinds of models are discussed. © 1999 American Institute of Physics.

Notes: This paper studies Manin–Radul supersymmetric Kadomtsev–Petviashvili hierarchy (MR-SKP) in three related aspects: (i) We find an infinite set of additional ("ghost") symmetry flows spanning the same (anti)commutation algebra as the ordinary MR-SKP flows. (ii) The latter are used to construct consistent reductions SKPr/2,m/2 of the initial unconstrained MR-SKP hierarchy which involves a nontrivial modification for the fermionic flows. (iii) For the simplest constrained MR-SKP hierarchy SKP〈fraction SHAPE="CASE"〉12,〈fraction SHAPE="CASE"〉12 we show that the orbit of Darboux–Bäcklund transformations lies on a supersymmetric Toda lattice being a square root of the standard one-dimensional Toda lattice, and also we find explicit Wronskian-ratio solutions for the super-tau function. © 1999 American Institute of Physics.

Notes: Hamiltonian formalism for the nonlinear Schrödinger equation in physical space–time is developed. Owing to the fact that the equation involves the second partial derivative with respect to time, the canonical variables are shown to be u, u¯, −u¯t, and −ut. The first Lax equation and its variations with respect to canonical variables are very complicated, but the Poisson brackets of transition coefficients are shown to be simple, and thus the Hamiltonian formalism in terms of action-angle variables has been achieved. A peculiarity is that the continuous spectrum consists of real λ as well as pure imaginary λ. In the case of pure imaginary λ the full Jost solutions shall tend to be infinite or vanish as |t|→∞. This problem needs further investigation. © 1999 American Institute of Physics.

Notes: The classical Boussinesq–Burgers hierarchy is decomposed into two systems of solvable ordinary differential equations with the help of the Lax representations of stationary evolution equations, from which the finite-band solutions of the higher-order classical Boussinesq–Burgers equations are obtained. © 1999 American Institute of Physics.

Notes: The nonlinear Schrödinger equation on the half line with mixed boundary condition is investigated. After a brief introduction to the corresponding classical boundary value problem, the exact second quantized solution of the system is constructed. The construction is based on a new algebraic structure, which is called in what follows boundary algebra and which substitutes, in the presence of boundaries, the familiar Zamolodchikov–Faddeev algebra. The fundamental quantum field theory properties of the solution are established and discussed in detail. The relative scattering operator is derived in the Haag–Ruelle framework, suitably generalized to the case of broken translation invariance in space. © 1999 American Institute of Physics.

Notes: We derive an asymptotic solution of the Einstein field equations which describes the propagation of a thin, large amplitude gravitational wave into a curved space–time. The resulting equations have the same form as the colliding plane wave equations without one of the usual constraint equations. © 1999 American Institute of Physics.

Notes: A study of Hamiltonian structures associated with supersymmetric Lax operators is presented. Following a constructive approach, the Hamiltonian structures of Inami–Kanno super-KdV hierarchy and constrained modified super-KP hierarchy are investigated from the reduced supersymmetric Gelfand–Dickey brackets. By applying a gauge transformation on the Hamiltonian structures associated with these two nonstandard super-Lax hierarchies, we obtain the Hamiltonian structures of generalized Manin–Radul super-KdV and constrained super-KP hierarchies. We also work out a few examples and compare them with the known results. © 1999 American Institute of Physics.

Notes: The author showed previously that there are several equations that "directly linearize" the Korteweg de Vries equation. They may give different classes of solutions and they correspond either to generalized Gelfand Levitan or generalized Marchenko inversion equations. The idea is developed here with a precise goal: solving by linear methods the "other Cauchy problem" for KdV, i.e., the boundary value problem where the solution is known at fixed x, together with its two first derivatives. After several new direct linearization equations are given and analyzed, the one that solves the problem is eventually obtained. It also corresponds to a new inverse spectral problem, whose scalar equations are fourth order, and that is first studied in the Gelfand Levitan form, and then studied and completely solved in the Marchenko form. The methods given here can be extended probably to most nonlinear integrable equations, and suggest several new problems. © 1999 American Institute of Physics.

Notes: A four-index tensor is constructed with terms both quadratic in the Riemann tensor and linear in its second derivatives, which has zero divergence for space–times with vanishing scalar curvature. This tensor reduces in vacuum to the Bel–Robinson tensor. Furthermore, the completely timelike component referred to any observer is positive, and zero if and only if the space–time is flat (excluding some unphysical space–times). We also show that this tensor is the unique one that can be constructed with these properties. Such a tensor does not exist for general gravitational fields. Finally, we study this tensor in several examples: the Friedmann–Lemaître–Robertson–Walker space–times filled with radiation, the plane–fronted gravitational waves, and the Vaidya radiating metric. © 1999 American Institute of Physics.

Notes: It has recently been shown [W. Rudnicki, Phys. Lett. A 224, 45–50 (1996)] that a generic gravitational collapse cannot result in a naked singularity accompanied by closed timelike curves. An important role in this result plays the so-called inextendibility condition, which is required to hold for certain incomplete null geodesics. In this paper, a theorem is proved that establishes some relations between the inextendibility condition and the rate of growth of the Ricci curvature along incomplete null geodesics. This theorem shows that the inextendibility condition may hold for a much more general class of singularities than only those of the strong curvature type. It is also argued that some earlier cosmic censorship results obtained for strong curvature singularities can be extended to singularities corresponding to the inextendibility condition. © 1999 American Institute of Physics.

Notes: It is shown that when a first integral of a R3 vector field X is known, instabilities are induced on the equilibrium points of X. © 1999 American Institute of Physics.

Notes: We construct a nondegenerate symmetric bilinear form on quantized enveloping algebras associated to Borcherds superalgebras. With this, we study its center and its universal R matrix. © 1999 American Institute of Physics.

Notes: In general, Picard–Fuchs systems in N=2 supersymmetric Yang–Mills theories are realized as a set of simultaneous partial differential equations. However, if the quantum chromodynamics (QCD) scale parameter is used as a unique independent variable instead of moduli, the resulting Picard–Fuchs systems are represented by a single ordinary differential equation (ODE) whose order coincides with the total number of independent periods. This paper discusses some properties of these Picard–Fuchs ODEs. In contrast with the usual Picard–Fuchs systems written in terms of moduli derivatives, there exists a Wronskian for this ordinary differential system and this Wronskian produces a new relation among periods, moduli, and QCD scale parameter, which in the case of SU(2) is reminiscent of the scaling relation of prepotential. On the other hand, in the case of the SU(3) theory, there are two kinds of ordinary differential equations, one of which is the equation directly constructed from periods and the other is derived from the SU(3) Picard–Fuchs equations in moduli derivatives identified with Appell's F4 hypergeometric system, i.e., Burchnall's fifth-order ordinary differential equation published in 1942. It is shown that four of the five independent solutions to the latter equation actually correspond to the four periods in the SU(3) gauge theory and the closed form of the remaining one is established by the SU(3) Picard–Fuchs ODE. The formula for this fifth solution is a new one. © 1999 American Institute of Physics.

Notes: A novel realization of the classical SU(2) algebra is introduced for the Dirac relativistic hydrogen atom defining a set of operators that allow the factorization of the problem. An extra phase is needed as a new variable in order to define the algebra. We take advantage of the operators to solve the Dirac equation using algebraic methods. A similar path to the one used in the angular momentum case is used; hence, the radial eigenfunctions so calculated comprise nonunitary representations of the algebra. One of the interesting properties of such nonunitary representations is that they are not labeled by integer nor by half-integer numbers, as occurs in the usual angular momentum representation. © 1999 American Institute of Physics.

Notes: Well known methods of measure theory on infinite dimensional spaces are used to study physical properties of measures relevant to quantum field theory. The difference of typical configurations of free massive scalar field theories with different masses is studied. We apply the same methods to study the Ashtekar–Lewandowski (AL) measure on spaces of connections. In particular we prove that the diffeomorphism group acts ergodically, with respect to the AL measure, on the Ashtekar–Isham space of quantum connections modulo gauge transformations. We also prove that a typical, with respect to the AL measure, quantum connection restricted to a (piecewise analytic) curve leads to a parallel transport discontinuous at every point of the curve. © 1999 American Institute of Physics.

Notes: We construct a new family of boson coherent states using a specially designed function which is a solution of a functional equation dε(q,x)/dx=ε(q,qx) with 0≤q≤1 and ε(q,0)=1. We use this function in place of the usual exponential to generate new coherent states |q,z〉 from the vacuum, which are normalized and continuous in their label z. These states allow the resolution of unity, and a corresponding weight function is furnished by the exact solution of the associated Stieltjes moment problem. They also permit exact evaluation of matrix elements of an arbitrary polynomial given as a normally-ordered function of boson operators. We exemplify this by showing that the photon number statistics for these states is sub-Poissonian. For any q〈1 the states |q,z〉 are squeezed; we obtain and discuss their signal to quantum noise ratio. The function ε(q,x) allows a natural generation of multiboson coherent states of arbitrary multiplicity, which is impossible for the usual coherent states. For q=1 all the above results reduce to those for conventional coherent states. Finally, we establish a link with q-deformed bosons. © 1999 American Institute of Physics.

Notes: We examine three overlapping problems in the application of five-dimensional (5D) manifolds to physics. First, we linearize the 5D theory along the lines of the four-dimensional (4D) theory, using the harmonic gauge condition. The resulting wave equations have sources, and can in principle describe gravitons and scalar particles with finite masses, but the natural choice of gauge parameters makes both massless. Second, we generalize the 5D metric by including separate conformal factors on its 4D and extra parts. Then the 5D harmonic gauge gives back the 4D harmonic gauge of gravitational waves and the Lorentz gauge of electromagnetic waves, but both particles are massless. Third, we again take a conformally rescaled metric, but rewrite the field equations in a novel manner. This allows us to interpret the finite masses of ordinary particles in terms of the wavelengths associated with 4D spaces embedded in a 5D space. © 1999 American Institute of Physics.

Notes: An algebraic structure related to discrete zero curvature equations is established. It is used to give an approach for generating master symmetries of the first degree for systems of discrete evolution equations and an answer to why there exist such master symmetries. The key of the theory is to generate nonisospectral flows (λt=λl, l≥0) from the discrete spectral problem associated with a given system of discrete evolution equations. Three examples are given. © 1999 American Institute of Physics.

Notes: We show that the algebra of functions on the Grassmann supergroup Grq(1|1) has a (graded) Hopf algebra structure related to GLq(1|1). © 1999 American Institute of Physics.

Notes: Applying the harmonic map ansatz we find new classes of SU(N) and SO(N) chiral fields. We write the corresponding one-dimensional subgroups of SU(N) and SO(N) chiral fields in terms of one and two harmonic maps and the corresponding two-dimensional subgroups in terms of SU(2) and SO(3) chiral fields. In other words, we reduce the SU(N) and SO(N) chiral equations to harmonic maps in one- and two-dimensional spaces. © 1999 American Institute of Physics.

Notes: We obtain connection coefficients between q-binomial and q-trinomial coefficients. Using these, one can transform q-binomial identities into q-trinomial identities and back again. To demonstrate the usefulness of this procedure we rederive some known trinomial identities related to partition theory and prove many of the conjectures of Berkovich, McCoy and Pearce, which have recently arisen in their study of the φ2,1 and φ1,5 perturbations of minimal conformal field theory. © 1999 American Institute of Physics.

Notes: A simple approach to phase-space representation of quantum state vectors using the displacement-operator formalism is presented. Although the resulting expressions for the fundamental operators (position and momentum) are equivalent to those obtained by other methods, this approach provides both alternative mathematical foundation as well as physical interpretation of phase-space representation of quantum state vectors. © 1999 American Institute of Physics.

Notes: Rate constants for vibrational energy exchange in CO collisions have been calculated for normal CO and two isomers. The calculations have been carried out using a semiclassical collision model in which translational and rotational motions are treated classically. The vibrational degrees of freedom are quantized. The theoretical predicted rates agree well with recent experimental data. © 1999 American Institute of Physics.

Notes: Rhomboidal SiC3, a planar ring with C2v symmetry and a transannular C–C bond, was detected at centimeter wavelengths in a pulsed supersonic molecular beam with a Fourier transform microwave (FTM) spectrometer, and was subsequently observed in a low-pressure dc glow discharge with a free-space millimeter-wave absorption spectrometer. The rotational spectrum of SiC3 is characterized by large harmonic defects and large splitting of the K-type doublets. Lines in the centimeter-wave band were very strong, allowing the singly substituted isotopic species to be observed in natural abundance. Measurements of the normal and five isotopically substituted species with the FTM spectrometer provided conclusive evidence for the identification and yielded an experimental zero-point (r0) structure. Forty-six transitions between 11 and 286 GHz with Ka≤6 were measured in the main isotopic species. Three rotational and nine centrifugal distortion constants in Watson's A-reduced Hamiltonian reproduce the observed spectrum to within a few parts in 107 and allow the most intense transitions up to 300 GHz to be calculated with high accuracy. The spectroscopic constants confirm that SiC3 is a fairly rigid molecule: the inertial defect is comparable to those of well-known planar rings and the centrifugal distortion constants are comparable to molecules of similar size. The number of SiC3 molecules in our supersonic molecular beam in each gas pulse is at least 3×1011, so large that electronic transitions may be readily detectable by laser spectroscopy. © 1999 American Institute of Physics.

Notes: Photodissociation of the H2S molecule at 157.6 nm was studied experimentally using the Rydberg tagging technique. Translational energy distributions of the H-atom product from the H2S photodissociation were measured, and the SH(X 2Π)+H(2S) channel was found to be the dominant dissociation process. Spin-orbit and rovibrational state distributions were also obtained for the SH product, which was found to be both vibrationally and rotationally excited. An intriguing bimodal rotational distribution in the lowest two vibrational states, v=0 and 1, has been clearly observed for the SH product, indicating that there are two distinctive dissociation mechanisms involved in the photodissociation of H2S at 157 nm excitation. © 1999 American Institute of Physics.

Notes: Rotationally resolved S1←S0 electronic spectra of the van der Waals complexes indole-Ar and N-deuterated-indole-Ar in the gas phase are described. Both spectra exhibit inertial axis reorientation. A comparison of the parameters derived from fits of the two spectra with those obtained from a previous study of the bare molecule [Berden et al., J. Chem. Phys. 103, 9596 (1995)] shows that the Ar atom in indole-Ar is attached above the indole plane, displaced toward the N atom in the five-membered ring, in both electronic states. However, the measured center-of-mass coordinates of the Ar atom in the principal axis frames of indole in the two states are different, leading to the observed axis reorientation in the high resolution spectra. The S1 state in indole itself is shown to be the 1Lb state, which has a different electronic distribution from that of the ground state. Thus, the Ar atom "moves" when the photon is absorbed because there are significant differences in the intermolecular potential energy surfaces of the two states. © 1999 American Institute of Physics.

Notes: The infrared spectrum of the iron dicarbonyl radical Fe(CO)2 produced in a supersonic jet expansion by the excimer laser photolysis of iron pentacarbonyl Fe(CO)5 was observed by time-resolved infrared diode laser spectroscopy. About 170 transitions, each split into one or two fine structure components, were assigned to the ν3 (CO antisymmetric stretch) band of Fe(CO)2. The assignment was greatly facilitated by spectral simplification caused by rotational as well as vibrational cooling in the supersonic jet. It was observed that lines are missing at alternate J quantum numbers in each spin component, which confirmed that Fe(CO)2 is a linear molecule with D∞h symmetry and that the electronic ground state is of 3Σg− symmetry. The rotational and centrifugal distortion constants in the ground state were determined to be B0=1414.675(46) MHz and D0=0.3077(74) kHz, respectively. The spin–spin interaction constants obtained, λ0=655.3(42) GHz, is comparable with that of the FeCO radical, λ0=684.470(51) GHz. The ν3 band origin was determined to be 1928.184335 (82) cm−1. The figures in parentheses are uncertainties (1σ) in units of the last digit. © 1999 American Institute of Physics.

Notes: The coupling of two large amplitude motions, the internal rotation of the methyl group and the intramolecular proton transfer, has been investigated for jet-cooled 5-methyltropolone, 5-methyltropolone–OD, and the 5-methyltropolone–(H2O)1 1:1 hydrogen-bonded complex by measuring the fluorescence excitation, dispersed fluorescence, and hole-burning spectra in the S1–S0 region. The vibronic bands in the excitation spectrum of 5-methyltropolone consist of four components originating from the transitions between the sublevels in the S1 and S0 states. The intensity of the bands, the frequencies, and the change in the stable conformation of the methyl group upon photoexcitation have been analyzed for 5-methyltropolone–(H2O)1 by calculating the one-dimensional periodic potential function, which provides the correlation between the internal rotational levels of 5-methyltropolone–(H2O)1 and the sublevels of 5-methyltropolone. It has been shown that the electronic transitions between the sublevels within the same symmetry are allowed in 5-methyltropolone. The tunneling splitting of the zero-point level in the S1 state is 2.2 cm−1 for 5-methyltropolone. The corresponding splitting for 5-methyltropolone–OD is less than 0.5 cm−1. A drastic decrease of the tunneling splitting for 5-methyltropolone as compared to that for tropolone (19.9 cm−1) is ascribed to a strong coupling between the two large amplitude motions in the S1 state. The existence of a similar coupling has been suggested in the S0 state of 5-methyltropolone. The excitation of the sublevel in the S1 state considerably promotes proton tunneling. This effect has been explained by the delocalization of the wave function of the internal rotation of the methyl group. The two-dimensional potential energy surface along the proton transfer coordinate and the rotational angle of the methyl group has been calculated to explain the effects of the coupling on proton tunneling. © 1999 American Institute of Physics.

Notes: We investigate the depletion induced phase separation in mixed suspensions of colloidal spheres with diameter σ and colloidal rods with length L and diameter D. Using an extension of the free volume method developed by one of us [H.N.W. Lekkerkerker and A. Stroobants, Physica A 195, 387 (1993)], we calculate the phase diagrams for L≤σ and various L/D ratios. For long thin rods, the volume fractions of rods needed to induce phase separation scale as D2/Lσ. Good agreement with recent experimental results is obtained. © 1999 American Institute of Physics.

Notes: The reorientational relaxation of CS2 in solution in CCl4 and its dependence on both concentration and temperature is investigated with the use of the optical Kerr effect (OKE). The comparison of the single-particle reorientational relaxation time extracted from OKE data and obtained by Raman spectroscopy supports the hypothesis that the vibrational and reorientational relaxation processes for CS2 are not correlated. It is shown that the reorientational dynamics of CS2 is influenced by the solvent configuration around the solute molecule (cage effect), and that it is also influenced by the pair orientational correlation between solute molecules, even in dilute solutions. © 1999 American Institute of Physics.

Notes: The two-exciton wave functions of conjugated dendrimers with fractal geometries are calculated using the Frenkel-exciton model. Self-similarity and the high degree of symmetry make it possible to express the two-photon spectra of these chromophore aggregates in a compact form using irreducible representations of optical excitations, single-exciton states, and an effective two-exciton transition dipole moment. The explicit calculation of the complete manifold of two-exciton states which involves an expensive l3×l3 diagonalization, l being number of generations, is totally avoided. A real space analysis shows that the two-exciton states and resonances are dominated by periphery chromophores due to their exponentially large number. © 1999 American Institute of Physics.

Notes: Six analytical expressions (four of which have been published recently) for the equation of state of a hard sphere system, together with two different expressions for the molecular diameter, have been tested in order to reproduce molecular dynamics results for pressure and potential energy of the Weeks–Chandler–Andersen reference system for the Lennard-Jones potential. The best choices for the combination of equations of state and molecular diameters in the calculation of those properties are given. It is shown how that choice may differ for different ranges of temperatures and densities, and how there is not a direct relation between the simplicity or complexity of the analytical expressions and their accuracy. © 1999 American Institute of Physics.

Notes: We present high resolution (∼0.01 cm−1) infrared absorption spectra of the ν4 band of methane doped parahydrogen (CH4/pH2) solids produced by two different techniques: gas condensation in an enclosed cell at T(approximate)8 K, and rapid vapor deposition onto a T(approximate)2 K substrate in vacuum. The spectrum of the rapid vapor deposited solid contains a novel progression of single peaks with (approximate)5 cm−1 spacing, superimposed over the known spectrum of CH4 molecules trapped in sites of D3h symmetry in hexagonal close-packed (hcp) solid pH2. New theoretical calculations of the rovibrational transitions of a tetrahedral molecule in an external field of Oh symmetry permit the assignment of this new progression to CH4 molecules trapped in crystalline face centered cubic (fcc) regions of the pH2 solid. Annealing of the rapid vapor deposited samples to T(approximate)5 K decreases the intensities of the CH4/pH2(fcc) absorptions, and results in intensity changes for parallel and perpendicularly polarized CH4/pH2(hcp) transitions. We discuss these phenomena, and the narrow (0.01–0.04 cm−1 full width at half-maximum) absorption linewidths, in terms of the microscopic structure of the pH2 hosts. © 1999 American Institute of Physics.

Notes: Ultraviolet/visible absorption and fluorescence spectroscopies at different temperatures and pressures were applied to investigate the microscopic solvent structures of subcritical and supercritical methanol using 4-nitroanisole, ethyl-(4-dimethylamino)benzoate, Reichardt's dye, and anthracene as the probe molecules. It was found that at temperatures higher than 150 °C the long winding chains of sequentially hydrogen-bonded methanol molecules were probably broken, but the small hydrogen-bonded aggregates possibly existed in methanol even at higher temperature. It was also found that the solvation process of the anthracene molecule in the S0-ground state obeyed the Langmuir adsorption model. However, in the case of fluorescence measurements in supercritical methanol, we detected deviations from the simple Langmuir adsorption model. These deviations were explained in terms of preferential solvation of the solvent molecules around photoexcited anthracene. Judging from the experimental results, it was concluded that the local density augmentation of the supercritical methanol around the nonpolar solute was a short-ranged effect, which did not correspond directly to the large isothermal compressibility of fluid near the critical point. © 1999 American Institute of Physics.

Notes: We study theoretically the harmonic light scattering (HLS) of centrosymmetric molecules in solution. Since HLS is inherently absent for centrosymmetric molecules, the intensity and line shape are obtained by taking into account two distinct physical processes: solute vibrational transition and solvent effective field contribution. The intensity is expressed in each case as the Fourier transform of the relevant time correlation functions. The implications for experiments, which use HLS to determine the first hyperpolarizability β of optically interesting molecules, are discussed. © 1999 American Institute of Physics.

Notes: In this paper we examine, within simple models, different approaches to computing tunneling probabilities in super-exchange models of electron transfer. The relationship between tunneling calculations that use scattering theory type formalisms and approaches based on standing waves, which are more closely related to electron transfer between bound donor and acceptor states, is established. Transmission probabilities computed by using truncated basis representations are compared to exact analytical or numerical results for one- and two-dimensional models. We find that while resonance tunneling is well approximated by truncated basis approaches, computing deep tunneling using such basis sets can lead to large errors. Implications for calculations of bridge assisted electron transfer are discussed. © 1999 American Institute of Physics.

Notes: The noisy dynamic behavior of a surface catalytic reaction model to describe the oxidation of carbon monoxide is investigated when the control parameter is perturbed by external noise near a supercritical Hopf bifurcation point. Noise induced coherent oscillation (NICO) is observed and the NICO strength goes through two maxima with the increment of the noise intensity D from zero, characteristic of the occurrence of stochastic multiresonance without external signal. The frequency of the NICO also increases with the increment of D. © 1999 American Institute of Physics.

Notes: The structural, dynamical, and electronic properties of solid HBr at high pressure are investigated using the ab initio constant pressure molecular dynamics method. A detailed analysis of the orientational distribution, and the reorientational and vibrational dynamics of the disordered phase I at ambient temperature showed that this phase can be described as a rotator phase with fluctuating hydrogen bonds up to pressures well over 10 GPa. We predict that the disorder at higher densities leads to cooperative proton-transfer dynamics. The approach to hydrogen-bond symmetrization is studied in phase I and the high pressure ordered phase III. The simulation results for phase III also indicate that this phase develops dielectric instabilities at high density. At pressures over 40 GPa we observe spontaneous formation of H2 with rearrangement of the Br lattice from fcc to hcp. The chemical reactivity is rationalized in terms of the electronic structure under conditions of near symmetrical hydrogen bonding. © 1999 American Institute of Physics.

Notes: The effect of attractive interactions on the behavior of polymers between surfaces is studied using Monte Carlo simulations. The molecules are modeled as fused sphere freely rotating chains with fixed bond lengths and bond angles; wall–fluid and fluid–fluid site–site interaction potentials are of the hard sphere plus Yukawa form. For athermal chains the density at the surface (relative to the bulk) is depleted at low densities and enhanced at high densities. The introduction of a fluid–fluid attraction causes a reduction of site density at the surface, and an introduction of a wall–fluid attraction causes an enhancement of site density at the surface, compared to when these interactions are absent. When the wall–fluid and fluid–fluid attractions are of comparable strength, however, the depletion mechanism due to the fluid–fluid attraction dominates. The center of mass profiles show the same trends as the site density profiles. Near the surface, the parallel and the perpendicular components of chain dimensions are different, which is explained in terms of a reorientation of chains. © 1999 American Institute of Physics.

Notes: Supra-valence electron transfer from surface Cs-doped MoS2(0002) to electron acceptor adsorbates was investigated by high resolution x-ray photoelectron spectroscopy (HRXPS) in the valence band region and above the valence band maximum (VBM). Deposition of a sub-monolayer amount of Cs onto the basal plane of MoS2 introduced a new electron density of states at ca. 1.25 eV above VBM. Angle-resolved HRXPS and theoretical analysis located this electron density in the MoS2 layer. Upon the reaction with Cl2, this Cs-induced photoelectron almost completely disappeared and the Cs 3d and Cl 2p core levels indicated the formation of a surface Cs-chloride species. The Cs-covered MoS2(0002) surface also reacted with O2 to form surface peroxides and superoxides, as evidenced by two distinct binding energies of the O 1s core level peaks. However, the reaction with water proved to be more difficult: Exposure of the Cs-covered MoS2(0002) surface to H2O at 10−5 Torr did not result in electron transfer reaction, but the Cs/MoS2(0002) surface exposed to H2O at 1 Torr showed a substantial decrease in the density of states above VBM as well as formation of a surface-hydroxide, indicated by the O 1s core level position. Theoretical calculations using a full-potential linearized augmented plane wave density functional theory (FLAPW-DFT) confirm the conclusion based on experimental intensity anisotropy of the new peak: the Cs 6s electron transfers into the MoS2 substrate, forming the Cs/MoS2 electron donor–acceptor complex with Csδ+. In addition, all phenomena observed during the adsorption of electron donor–acceptor molecules are quantitatively accounted by the theory. © 1999 American Institute of Physics.

Notes: Previous pulsed-field gradient (PFG) nuclear magnetic resonance (NMR) measurements on different sorbate–zeolite systems suggest that there exist at least five different types of dependence of self-diffusivity of the sorbate, D, on the concentration, c, of the sorbate. Sorbate–zeolite systems have been modeled as a two-dimensional lattice gas and studied by carrying out Monte Carlo simulations under different conditions. Among the different factors that have been varied are the arrangement of adsorption sites, hop length, nature and strength of the sorbate-sorbate interaction, and the degree of confinement. Surprisingly, even the simple 2-D lattice gas model could yield more than one type of D vs c dependence. The present study provides insight into the possible reasons for a given type of D vs c dependence. © 1999 American Institute of Physics.

Notes: The electronic states in conjugated organic materials are usually characterized either by quantum-chemical approaches relying on a molecular picture, or by solid-state band structure models requiring infinite periodicity of the chains. In this contribution we present calculations showing that a band structure like character is inherent also in molecular systems and discuss the gradual evolution of a full band structure upon increasing the number of repeat units in oligomer molecules. The main feature of a band structure approach is the description of the electronic eigenstates in momentum space. We have therefore developed a method to describe momentum dependent excitation processes in conjugated organic materials based on a post-Hartree–Fock approach including electron–electron correlation effects. The results of the simulations performed for oligo(phenylene)s of different chain lengths agree very well with experimental electron energy loss spectroscopy (EELS) data. © 1999 American Institute of Physics.

Notes: The microscopic diffusional dynamics of H and D on Pt(111) have been studied over length scales between 3 and 14 Å by quasielastic helium atom scattering. Data taken over a wide range of parallel wave vectors (0.3 Å−1≤|ΔK|≤3.1 Å−1) in the surface temperature range 140 K≤Ts≤250 K and at coverages 0.05 ML≤aitch-thetaH≤0.66 ML, provide evidence for an isotropic single jump mechanism with an activation energy of 68±5 meV and a pre-exponential factor of D0=1.1±0.5×10−3 cm2 s−1 at low coverages. The diffusion coefficient is 2 to 3 orders of magnitude higher than found in an earlier laser induced desorption experiment, whereas the dependence on coverage is similar. © 1999 American Institute of Physics.

Notes: The statistical rate theory approach is used to describe far-from-equilibrium diffusion of carbon monoxide on a stepped Pt(111) surface at low total coverages. Under nonequilibrium conditions, migration of adsorbates from terraces to steps, where adsorbates are more strongly bound, can occur. An expression for the molecular transport rate between terraces and steps is derived in terms of an equilibrium exchange rate, and the instantaneous chemical potentials of the molecules adsorbed on the terraces and along the steps. The theory contains no free parameters. Both the equilibrium exchange rate and the chemical potentials are obtained in the framework of a lattice gas model. The time evolution of the populations of steps and terraces is calculated and used to fit the available experimental data in order to evaluate the activation barrier of diffusion on terraces and the associated prefactor. © 1999 American Institute of Physics.

Notes: Inelastic neutron scattering was used to probe the nature of the boson peak in atactic polypropylene (aPP), head-to-head polypropylene (hhPP), polyisobutylene (PIB) and a 1/1 mass ratio hhPP/PIB blend. Atactic polypropylene is among the most "fragile" of glass formers and was found to have a shoulder rather than the distinctive peak exhibited by the other three polymers. This difference is already apparent at 15 K where relaxations are not expected to occur. The results suggest that the fragility of hhPP is intermediate between aPP and PIB. Within this group of polymers which have similar chemical structures the position of the boson peak appears to correlate with the glass transition temperature and the cohesive energy density. The possibility of a correlation with chain stiffness as expressed by the characteristic ratio is also discussed. © 1999 American Institute of Physics.

Notes: Rheological properties and the equilibrium colloidal phase behavior of concentrated dispersions of a temperature sensitive microgel were investigated. The temperature sensitive hydrogel particles consist of poly (N-isopropylacrylamid) (PNiPAM) chemically crosslinked with N,N′ methylenbisacrylamid (BIS). With increasing temperature the microgel particles decrease in size (hydrodynamic radius 142 nm at 10 °C and 58 nm at 35 °C) and with it the effective volume fraction, which leads to dramatic changes in rheology—vanishing yield stress and decreasing viscosity and elastic properties. The relative zero-shear viscosity and the plateau modulus at different temperatures superpose to mastercurves when plotted vs the effective volume fraction. The monodisperse hydrogel particles form colloidal crystals and glasses in concentrated solution but at higher effective volume fractions as compared to model hard sphere suspensions. Comparison of the experimental freezing point with soft sphere computer simulations indicate a repulsive interaction potential of the order 1/r12. The frequency independent shear modulus exhibited a power law concentration dependence which also agrees with the soft sphere behavior. © 1999 American Institute of Physics.

Notes: We study the nematic–isotropic transition in model colloidal systems composed of platelets of various shapes using grand canonical simulations. This is of relevance for recently synthesized hard platelet systems, since the platelets in such systems are found to be not circular but irregular hexagons, and so cannot be described by the simulation data currently available. We show that the coexistence densities scale with an effective volume related to the isotropic orientation-averaged excluded volume of a pair of platelets. This excluded volume can be obtained from the perimeter of the face of the particles and so can be easily calculated for both regular and irregular particle shapes. © 1999 American Institute of Physics.

Notes: The microphase separation of symmetric cyclic diblock copolymer with decreasing temperature is simulated using the Monte Carlo method. In order to investigate the effect of the ring-shape chain architecture on order–disorder transition (ODT), the microphase separation of the cyclic diblock copolymer is compared with that of a symmetric linear diblock copolymer with the same chain length. For both systems, the ODT is observed as a first-order transition, and the ordered structure formed through the ODT is lamellar. The ratio of the domain spacing in the cyclic diblock copolymer to that in the linear one is 0.7 at the ODT, and the scattering intensity of the former is weaker than that of the latter. The ring-shape chain architecture suppresses the random thermal force, so that the cyclic diblock copolymer still shows a mean-field behavior at the temperature at which the linear diblock copolymer does not obey the mean-field prediction. The value of (χeffN)ODT of the linear diblock copolymer is calculated to be in the range of 25.36〈(χeffN)〈26.04, which is in good agreement with the theoretical prediction, (χeffN)ODT=25.61, indicating that this simulation properly describes the ODT of the diblock copolymer. The value of (χeffN)ODT of the cyclic diblock copolymer is predicted to be in the range of 40.83〈(χeffN)〈43.02. © 1999 American Institute of Physics.

Notes: The role played by the ion beam in the depolymerization of poly(methyl methacrylate) (PMMA) is the creation of initiators for the unzipping reaction at relatively low temperatures [lower than the ceiling temperature of PMMA (TC=220 °C)]. Monomer (MMA) evolution out of the polymeric film is thus governed by the kinetics of the chemical reaction and also by the diffusion of monomer inside the polymeric film. In this work this phenomenon has been described by using simple models in which both one- and two-dimension monomer diffusion is considered. Exact analytical solutions of the models are provided. The theory fit well the experimental data and allows for the determination of important parameters such as the kinetics constant of the depolymerization and the monomer diffusion coefficient, D, inside the polymer film. Thus, the pulsed ion beam technique, here modeled, is useful not only for extracting D values of slow diffusants in polymers, but even for measuring kinetics constants of depolymerization at a temperature well below that needed for the formation of suitable thermal initiators. © 1999 American Institute of Physics.

Notes: A simple theoretical scheme based on a perturbative density functional approach using an approximate three-particle correlation function in conjunction with a sum rule relating the bulk pressure with the free energy functional of an inhomogeneous system has been proposed to study the structure of a model colloidal suspension (with screened Coulomb interaction) confined in a charged cylindrical pore. The calculated density profiles for the confined colloidal suspension for different values of the wall charges are shown to compare well with the available computer simulation results. The importance of the third order term has been demonstrated through the significantly better agreement of the present results as compared to those based on second order perturbative approach. The relative contribution of the third order term, however, is shown to depend on the screening parameter and hence the salt concentration in the suspension. The effect of the diameters of the cylindrical pores on the density profiles is also investigated. © 1999 American Institute of Physics.

Notes: We report on the structure and dynamics of model mono-, di-, and tri-ω-functionalized three-arm star polybutadiene melts. By using x-ray scattering and dynamic rheological measurements, we find that functionalization of the arm ends can lead to distinctly different supramolecular structures and material behavior. The monofunctionalized samples behave like multiarm nonionic star-like dendrimers, whereas the difunctional stars resemble a transient network consisting of highly branched structures with a very broad relaxation spectrum. On the other hand, the trifunctional stars seem to develop an unusually regular structure of dominant intramolecularly aggregated functional groups leading to collapsed star conformations, resembling soft spheres, and a well-defined terminal relaxation. These results suggest that by tailoring the telechelic functionalization of regular star polymers, a route to design and obtain a wealth of controlled supramolecular structures exhibiting a rich and variable dynamics could open. © 1999 American Institute of Physics.

Notes: We compare the linear viscoelastic spectra of star polymer melts, with varying functionality (4-128) and chemistry (isoprenes, butadienes), with a recent parameter-free theory of arm relaxation [S. T. Milner and T. C. B. McLeish, Macromolecules 30, 2159 (1997)]. The theory, which considers this activated process within the framework of dynamic dilution and with appropriate account of the entanglement length scaling and the higher Rouse modes, is universal as it works remarkably well for a very wide range of star functionalities and arm molecular weights. However, for hyperstars consisting of 64 or 128 arms, the viscoelastic response is characterized by the presence of a slow relaxation process in addition to the faster arm relaxation. This additional process is due to the soft ordering of these systems because of their nonuniform monomer density distribution, and exhibits a very strong functionality and molecular weight dependence. It is accounted for by a mean field approach which considers the structural relaxation of the ordered stars as an activated process involving partial disentanglement of the interpenetrating arms and a jump of the star over a distance of its size, in good qualitative agreement with the experimental findings. © 1999 American Institute of Physics.

Notes: The self-diffusion of fluorescently tagged poly(γ-benzyl-α,L-glutamate), a helical, semiflexible synthetic homopolypeptide, has been measured in isotropic and cholesteric liquid-crystalline solutions by pattern fluorescence photobleaching recovery. On the isotropic side of the sharp isotropic–liquid-crystalline (ISO–LC) phase boundary, the rodlike polymers assume all possible orientations in a three-dimensional space, becoming enmeshed. In liquid-crystalline solutions, as first shown by Robinson [Trans. Faraday Soc. 52, 571 (1956)], spontaneous alignment of the cholesteric screw axis parallel to the optical (z) axis of the instrument produces small monodomains in which parallel rodlike polymers are organized into planes. Each horizontal plane is twisted slightly compared to its neighbors. Over the thickness of the sample, the rodlike polymers assume all possible orientations in this two-dimensional space. Despite the small size of the monodomains, it was possible to determine the self-diffusion coefficient of the semiflexible rods, orientationally averaged in two dimensions. Crossing the sharp ISO–LC phase boundary corresponds to the sudden release of any putative topological constraints active in the isotropic phase, and produced a modest but significant increase in diffusion. A relationship developed by Hess, Frenkel, and Allen [Mol. Phys. 74, 765 (1991)] is used to show that diffusion perpendicular to the rod axis is about ten times slower than diffusion parallel to the rod axis in the liquid-crystalline phase. In dilute solution, the comparable number would be 2. The perpendicular diffusion had decreased to about 8% of its initial value in dilute, isotropic solution. The parallel diffusion decreased to about 40% of its initial value. These results were obtained by neglecting the uncertain effects of semiflexibility. Likewise, the effects of modest polydispersity have not been treated explicitly. © 1999 American Institute of Physics.

Notes: Hermite polynomial expansions of the error function and the related F0(w) integral is presented. Expansion in even Hermite polynomials is convergent in the whole argument space of interest, with a smaller number of terms necessary to achieve the desired accuracy than in usual calculation methods of F0(w). Hermite polynomial asymptotic expansion is presented too. It is compared with the standard asymptotic expansion as well as with the interpolation method of P. M. Gill. © 1999 American Institute of Physics.

Notes: Using Langevin dynamics simulations, we model the dynamics of a polymer in a fixed network of random obstacles containing a spherical cavity. We define the partition coefficient K as the time-averaged ratio of the number of monomers inside/outside the cavity and calculate this quantity as a function of polymer length N. Our results show that ln K(N) increases with N until the polymer's radius of gyration is approximately equal to the size of the cavity Lh. Further increase of N leads to a decrease in ln K. The linear regime of this curve can be understood by comparing the free energy of a polymer confined through the spherical cavity to the corresponding free energy of the polymer in the mesh of the random network (this is the origin of the phenomenon of entropic trapping). The decrease in ln K when N is large results from imperfect confinement of the polymer inside the cavity. The number of monomers confined inside the cavity is limited by the size of the cavity and thus ln K decreases with N, roughly logarithmically, when N is very large. © 1999 American Institute of Physics.

Notes: The relative mixing coefficients of the zero-order 1B1(n,0,0) vibrational levels present in the hybrid 1A2–1B1 wave functions are estimated according to the observed Franck–Condon patterns in dispersed fluorescence spectra. Non-Condon effects and spin–orbit coupling have been ignored in the treatment. The data cover nearly 50 cold vibronic bands in the 32 895–34 040 cm−1 region in addition to 9 vibronic bands in the 32 185–32 559 cm−1 region. © 1999 American Institute of Physics.

Notes: A simple model is proposed for the moments of the inhomogeneous direct correlation function entering the theory of surface tension and liquid–vapor interfacial profile for a classical fluid. © 1999 American Institute of Physics.

Notes: We describe a time-of-flight apparatus that uses core extraction to determine nascent product laboratory velocity distributions from which differential cross sections may be deduced. We emphasize the characterization of the instrument, the reaction conditions, and the calibration procedure. For this purpose, we have measured H-atom velocity distributions from HBr photolysis, as well as the H2(v′=4,J′=1) velocity distribution arising from the H+HBr reaction under quasi-monoenergetic collision conditions at 1.9 eV. Collisional energy spread and reagent internal state distributions were determined from the rotational and translational temperatures of the HBr photolytic precursor and the D2 diatomic reagent. The differential cross section for H+D2→HD(v′=2,J′=3)+D at 1.55±0.05 eV is presented and found to peak near 145°±10° with an approximate full width at half maximum (FWHM) of 40°. © 1999 American Institute of Physics.

Notes: We propose a first-principle computation of the equilibrium thermodynamics of simple fragile glasses starting from the two-body interatomic potential. A replica formulation translates this problem into that of a gas of interacting molecules, each molecule being built of m atoms, and having a gyration radius (related to the cage size) which vanishes at zero temperature. We use a small cage expansion, valid at low temperatures, which allows to compute the cage size, the specific heat (which follows the Dulong and Petit law), and the configurational entropy. © 1999 American Institute of Physics.

Notes: We present a new approach to molecular simulation of bubble nucleation. Our approach does not involve any ad hoc criteria to define a bubble for a given instantaneous configuration of molecules. Instead, we explore the stochastic evolution of a system chosen as a small part of the liquid phase by means of an isothermal–isobaric Monte Carlo simulation aided by the umbrella sampling technique. The physical clusters relevant to nucleation, bubbles in the present case, emerge naturally as we attain a coarse-grained description of this stochastic process by introducing proper order parameters, i.e., the volume and the interaction potential of the system. Thus, the concept of cluster commonly employed to describe vapor to liquid nucleation is generalized naturally for the case of bubble nucleation. The method is applied to Lennard-Jones fluids to evaluate the free energy of bubble formation under a moderate negative pressure. The interaction potential plays a similar role to that in vapor to liquid nucleation in that it characterizes the spatial extent of the bubble. There is thus a unity in free energetics of vapor to liquid nucleation and of bubble nucleation. © 1999 American Institute of Physics.

Notes: The structure of liquid ammonia at T=273 K has been studied using classical ab initio molecular dynamics, classical molecular dynamics, and the path-integral molecular dynamics methods. The three different types of calculation are employed to generate new insights into the ability of theoretical methods to model liquid ammonia effectively. Thus, the limitations of using classical nuclei, simple point charge models, small systems, and gradient corrected density functional theory are assessed through a comparison of the results of the different types of calculations to each other and recent experiments in a consistent manner. Briefly, the experimental intermolecular quantum structure is very well reproduced by the classical approximation while the intramolecular classical and quantum structures exhibit large deviations. The intermolecular ab initio partial radial structure factors of liquid ammonia and the associated radial distribution functions are in better agreement with experiment than the empirical models. However, the empirical models also perform reasonably well. © 1999 American Institute of Physics.

Notes: A method is developed for the theoretical investigation of the structure of fluids comprised of hard nonspherical molecules carrying electric charge. The development is based upon the mean spherical approximation for the direct correlation function of such fluids. Since the equations based upon this approximation cannot in general be solved analytically an approximate ansatz for the direct correlation function containing a small number of free parameters is introduced. The free parameters are then determined from a standard variational principle. The ansatz itself is chosen to produce the known results in the strong coupling (large charge) limit and in the special case of hard spheres. In order to ensure that the solution in the limit of strong coupling has a tractable analytic form a new model is proposed for the charge distribution on an individual molecule. The method is applied in detail to a model of charged hard ellipsoids which is a generalization of the primitive model for ionic fluids and is found to be practical; it reduces to the primitive model in the special case of charged hard spheres. It is shown that the approximation preserves the conservation of charge. Properties investigated include the direct correlation function itself, the electrostatic energy of the fluid, the pair distribution function and the electrical potential surrounding an individual molecule. Results for these quantities are obtained for a range of densities and charge covering four orders of magnitude and for molecules with elongations (ratios of lengths of axes) from 0.5 (oblate) to 10 (prolate). The direct correlation function itself is given in an analytic form which can be used together with an appropriate density functional to investigate the structure of the electrical double layer formed by the fluid at a solid boundary. © 1999 American Institute of Physics.

Notes: We report the first molecular dynamics simulation of an amide in water in which the solute is fully described through quantum mechanics methods (density functional theory in our case). All solute's degrees of freedom are allowed to vary. The solvent is described through a classical potential. We have chosen for our study the simple formamide molecule since it allows hybrid simulations to be carried out at a sophisticated quantum level. More precisely, we have considered two computational schemes: in the first one, we use a small double-ζ basis set and a local approximation of the exchange-correlation functional whereas, in the second, an extended triple-ζ+polarization basis set, as well as a gradient-corrected functional, has been employed. The analysis of the results is focused on both structural and energetic aspects. Particular attention is paid to the time variation of dihedral angles in formamide connected to nitrogen pyramidalization and NH2 subunit rotation. The agreement with available experimental and theoretical data is satisfactory. Nevertheless, the limits of the method are pointed out, in particular the need to improve the description of the nonelectrostatic term of the solute-solvent interaction potential. One of the main advantages of the hybrid approach is that polarization effects are included in a rigorous manner. This renders possible a detailed discussion on the role of hydration effects on amides structure, a point of considerable relevance due to the biochemical importance of the peptidic bond. © 1999 American Institute of Physics.

Notes: We generalize the frequently used model of isotropic reorientational Brownian motion via small but finite angular steps to the case in which molecular reorientations by different angles take place around arbitrary axes. A simple approximation allows to give analytical expressions for experimentally relevant correlation functions, including spin lattice relaxation rates. We compare the results of our model to earlier treatments of rotational Brownian motion. © 1999 American Institute of Physics.

Notes: The dynamical effects on the quantum yield for the electronic state, D+MA− (the final state) representing the efficiency of the system as an energy conversion system in a model triad system made out of an electron donor, D, an acceptor, A and a medium, M are investigated. The effective quantum yield for the final state is introduced, which is calculated only from the rates in a long time limit, and is applicable even when a memory effect from nuclear dynamics on the rates is considerable. Applying the effective quantum yield formalism, and taking into account multidimensional solvation dynamics by the theory previously developed by the authors, the yield for the final state, is calculated. Considerable dynamical effects are found in some specific situations. For example, the larger yield for the final state is obtained for the larger solvation time scale when the transfer from the initial state, D*MA to the final state occurs through the intermediate state, D+M−A prior to nuclear thermalization in the intermediate state; whereas the similar transfer but with nuclear thermalization in the intermediate state is almost impossible. © 1999 American Institute of Physics.

Notes: The adsorption of fluoroform CHF3 on an ice Ih(0001) surface grown on Pt(111) under UHV conditions was studied using high resolution elastic and inelastic helium atom scattering. The results indicate that the CHF3 molecules are aligned with their H-atoms pointing downwards and form an ordered p(1×1) overlayer at temperatures less than Ts=75 K. The Debye temperature decreases from aitch-thetaiceD=132 K for the clean ice surface to aitch-thetaCHF3D=53 K on adsorption of one monolayer. From time-of-flight measurements the reduction in aitch-thetaD appears to be due to a substantial increase in multiphonon processes and the creation of a new, broad, dispersionless, low frequency vibrational mode at (h-dash-bar)ω=2.1 meV. © 1999 American Institute of Physics.

Notes: We study, from first principles, structural, electronic, and bonding properties of liquid water. Our system is twice as large as that used in previous ab initio simulations and our computed structural properties are in good agreement with the most recent neutron scattering experiments. Moreover, the use of a novel technique, based on the generation of maximally localized Wannier functions, allowed us to describe the molecular charge distribution and the polarization effects in liquid water with a degree of accuracy not previously possible. We find that, in the liquid phase, the water molecule dipole moment has a broad distribution around an average value of about 3.0 D. This value is 60% higher than that of the gas phase and significantly larger than most previous estimates. A considerable increase is also observed in the magnitude of the average eigenvalues of the quadrupole moment tensor. We also find that the anisotropy of the electronic charge distribution of the water molecule is reduced in the liquid. The relevance of these results for current modeling of liquid water is discussed. © 1999 American Institute of Physics.

Notes: We study theoretically the generation of coherent, anharmonic phonon-polariton responses through impulsive stimulated Raman scattering with intense, crossed ultrafast excitation pulses. We find that the refractive index appears modulated at the stimulated scattering wave vector and the corresponding phonon-polariton frequency, and, due to anharmonicity, at stimulated scattering wave vector overtones and their corresponding frequencies. A realistic model of the soft lattice vibrational mode of the ferroelectric crystal lithium tantalate is considered in detail. Specific predictions for the magnitudes of different wave vector overtone contributions to the lattice displacement are made compared to experimental observations of anharmonic lattice responses. © 1999 American Institute of Physics.

Notes: Umbrella sampling Monte Carlo simulations are used to calculate free energy barriers to homogeneous liquid–vapor nucleation in the superheated Lennard-Jones fluid. The calculated free energy barriers decrease with increased superheating and vanish at the spinodal curve. A statistical geometric analysis reveals the existence of two types of voids: Small interstitial cavities, which are present even in the equilibrium liquid, and much larger cavities that develop as the system climbs the nucleation free energy barrier. The geometric analysis also shows that the average cavity size within the superheated liquid is a function of density but not of temperature. The critical nucleus for the liquid–vapor transition is found to be a large system-spanning cavity that grows as the free energy barrier is traversed. The weblike cavity is nonspherical at all superheatings studied here, suggesting a phenomenological picture quite different from that of classical nucleation theory. © 1999 American Institute of Physics.

Notes: High-resolution Stark effect measurements on the S1←S0(ππ*) origin of cis-free base isobacteriochlorin in single crystals of n-octane at 5 K are reported. The spectral splittings of the band at 15 822 cm−1 are linearly dependent on the applied electric field. The change in dipole moment (Δμ) was found to be 1.32 D and is parallel to the crystal's b-axis. This band blueshifted as the polarity of the solvents at room temperature was increased, which implies that Δμ is negative. To rationalize the large magnitudes and opposite signs of the cis and trans tautomers' Δμ values, we propose a simple valence-bond model based on ionic resonance structures. © 1999 American Institute of Physics.

Notes: The peculiar thermal behavior of the thallium(I) n-alkanoates series (consisting in several transitions between polymorphic and mesomorphic phases) in comparison with other metallic n-alkanoates series is stated. The allowance of highly accurate adiabatic heat capacity data permits a study of the CH2 contributions to the lattice heat capacity curve at low temperature. Moreover, in this series an anomalous gradual enhancement of the lattice heat capacity has been interpreted from vibrational spectroscopy results as a noncooperative effect due to the internal hindered rotation of the alkyl chain (formation of gauche defects, even in the solid state). The thermodynamics of the "stepwise melting process" from the totally ordered solid at low temperature to the isotropic liquid is based on a revised lattice heat-capacity curve. This was used to evaluate the energy and entropy not only of the clear first order transitions present in the series but also of the described noncooperative effect. The CH2 enthalpy and entropy contribution for this series is estimated and a comparison with the published values for other series is carried out. Moreover, the texture of the mesophases is revealed by polarized light microscopy. © 1999 American Institute of Physics.

Notes: We present classical molecular dynamics simulations of the solvation dynamics of a strongly polar dye molecule in a weakly polar solvent. Solvation times and amplitudes are compatible with recent measurements. Several differences in the solvation dynamics relative to the widely studied case of strong polar solvents are exhibited: lesser importance of the inertial component of the Stokes shift, relaxation times close to individual solvent reorientational times, instead of the longitudinal relaxation time of the solvent, large amplitudes of translational and orientational relaxation over about 10 ps and the presence of a long-lived solvation shell in the excited state. © 1999 American Institute of Physics.

Notes: Monochromatically excited total emission spectra have been measured for the S1→S0 transition of azulene in polyethylene, polystyrene, and poly(methylmethacrylate) matrices over a temperature range from 1.4 to 100 K. The spectra in all three polymers exhibit strong zero-phonon lines (excitation of azulene vibrations only) accompanied by well-defined Stokes-shifted phonon sidebands at the lowest temperatures. As the temperature is raised the phonon bands broaden and gain relative intensity at the expense of the zero-phonon lines, and the spectra become qualitatively similar to the room-temperature liquid-phase spectra with sharp Raman lines on a broad fluorescence background. The near-origin-excited data are simulated by calculating the complete emission spectrum as a χ(3) process that assumes no artificial partitioning between "Raman" and "fluorescence." The internal vibrations of azulene are modeled as simple undamped displaced harmonic oscillators while the intermolecular or matrix phonons are either modeled as a Brownian oscillator or treated as effective spectral densities extracted from published neutron scattering and/or low-frequency nonresonant Raman data in the same polymers. While the qualitative features of the spectra and their temperature dependence are reproduced, none of the spectral densities employed give a fully satisfactory fit to the experimental spectra. The results demonstrate the sensitivity of total emission spectra to the chromophore–matrix interactions, and suggest that the spectral densities describing these interactions are functions not only of the matrix but also of the chromophore involved. © 1999 American Institute of Physics.

Notes: A modified form of Shepard interpolation of ab initio molecular potential energy surfaces is presented. This approach yields significant improvement in accuracy over previous related schemes. Here each Taylor expansion used in the interpolation formula is assigned a confidence volume which controls the relative weight assigned to that expansion. The parameters determining this confidence volume are derived automatically from a simple Bayesian analysis of the interpolation data. As the iterative scheme expands the data set, the confidence volumes are also iteratively refined. The potential energy surfaces for nine reactions are used to illustrate the accuracy obtained. © 1999 American Institute of Physics.

Notes: A methodology is developed for finding a formal solution to the entire stationary Bogoliubov, Born, Green, Kirkwood, Yvon (BBGKY) hierarchy for a classical inhomogeneous fluid in thermal equilibrium. The method is unique in that neither a closure relationship nor a restriction on the density or the temperature of the fluid is required. The decisive step in the analysis is the creation of a more general system of coupled integrodifferential equations through the introduction of a coupling parameter. Recognizing that the coupling parameter can also act as an expansion parameter, series solutions to the generalized hierarchy can be obtained through the application of regular perturbation theory. At the end of the calculation, a formal solution to the original BBGKY hierarchy can be recovered by setting the coupling parameter to unity. © 1999 American Institute of Physics.

Notes: A series of molecules related to malonaldehyde, containing an intramolecular H-bond, are used as the testbed for a variety of levels of ab initio calculation. Of particular interest are the excitation energies of the first set of valence excited states, nπ* and ππ*, both singlet and triplet, as well as the energetics of proton transfer in each state. Taking coupled cluster results as a point of reference, configuration interaction-singles–second-order Møller–Plesset (CIS–MP2) excitation energies are too large, as are CIS to a lesser extent, although these approaches successfully reproduce the order of the various states. The same may be said of complete active space self-consistent-field (CASSCF), which is surprisingly sensitive to the particular choice of orbitals included in the active space. Complete active space–second-order perturbation theory (CASPT2) excitation energies are rather close to coupled cluster singles and doubles (CCSD), as are density functional theory (DFT) values. CASSCF proton transfer barriers are large overestimates; the same is true of CIS to a lesser extent. MP2, CASPT2, and DFT barriers are closer to coupled cluster results, although yielding slight underestimates. © 1999 American Institute of Physics.

Notes: In the finite field (FF) treatment of vibrational polarizabilities and hyperpolarizabilities, the field-free Eckart conditions must be enforced in order to prevent molecular reorientation during geometry optimization. These conditions are implemented for the first time. Our procedure facilities identification of field-induced internal coordinates that make the major contribution to the vibrational properties. Using only two of these coordinates, quantitative accuracy for nuclear relaxation polarizabilities and hyperpolarizabilities is achieved in π-conjugated systems. From these two coordinates a single most efficient natural conjugation coordinate (NCC) can be extracted. The limitations of this one coordinate approach are discussed. It is shown that the Eckart conditions can lead to an isotope effect that is comparable to the isotope effect on zero-point vibrational averaging, but with a different mass-dependence. © 1999 American Institute of Physics.

Notes: Two nonempirical kinetic energy density dependent approximations are introduced. First, the local τ approximation (LTA) is proposed in which the exchange energy Ex depends only on a kinetic energy density τ. This LTA scheme appears to be complementary to the local spin density (LSD) approximation in the sense that its exchange contribution to the atomization energy ΔEx=Exatoms−Exmolecule is fairly accurate for systems where LSD fails. On the other hand, in cases where LSD works well LTA results for ΔEx are worse. Secondly, the τPBE approximation to Ex is developed which combines some of the advantages of LTA and of the Perdew–Burke–Ernzerhof (PBE) exchange functional. Like the PBE exchange functional, τPBE is free of empirical parameters. Furthermore, it yields improved atomization energies compared to the PBE approximation. © 1999 American Institute of Physics.

Notes: A scheme for total electronic energy partitioning within the framework of a one-electron theory of the extended Hückel-type is presented, with a view to extending and augmenting the capabilities of existing theoretical electronic structure analysis tools, specifically overlap population analysis. A total electronic energy partitioning is developed first for molecular and subsequently extended materials. In constructing the partitioning, we define molecular orbital Hamilton populations (MOHP's) for discrete systems, and Crystal Orbital Hamilton Populations (COHP's) for extended systems. The various energy partitionings and overlap population analyses are exemplified and contrasted for HX (X=F,Cl,Br), ethane, and a [PtH4]2− polymer. The utility of energy partitioning is demonstrated by effecting a COHP partitioning of the surface–CO interaction for the c(2×2)-CO/Ni(100) chemisorption system. Aspects of the surface–CO interaction less amenable to overlap population analysis are addressed, specifically the role of energetically low-lying filled CO orbitals and the relative contributions of surface s, p, and d bands to surface–CO interaction. Hamilton population analysis leads to a CO (4σ, 5σ)–metal forward donation, metal–CO(2π*) backdonation model for the surface–CO interaction. The metal σ contribution to surface–CO bonding is described as sp dominated metal spd hybrid–CO bonding, modifying slightly the metal d–CO σ bonding model proposed by Blyholder. The metal d-2π* backdonation of the Blyholder model remains. The role of the CO(1π) orbitals is also discussed in the context of CO orbital mixing on binding CO to the Ni(100) surface. © 1999 American Institute of Physics.

Notes: The dissociation energy of the InI ground state (X 1Σ+(O+)) and the relative yield of In(6s 2S1/2) from the photodissociation of InI by sequential two-photon absorption have been measured by laser-induced fluorescence and excitation spectroscopy in the 390–431 nm region. Laser excitation spectroscopy and photoionization experiments demonstrate that the XO+ dissociation energy is 25 340±90 cm−1, which agrees with the value suggested by Vempati and Jones [J. Mol. Spectrosc. 127, 232 (1988)] if the InI ground state is covalent. Seven previously unreported vibrational bands of the InI(B←X) transition have been observed and the molecular emission spectra indicate that the B 3Π1(1) state is predissociated above v=6. Splitting between the fine structure levels of the In np 2P1/2,3/2 (15≤n≤17) states has also been measured by fluorescence suppression spectroscopy, following the three photon excitation of InI in the 450–470 nm interval. © 1999 American Institute of Physics.

Notes: The kinetic energies of fast neutrals ejected from photoexcited rare gas cluster ions have been measured for the following systems: Arn+, Krn+, Xen+ at two photon wavelengths: 355 and 532 nm, and for n in the range 2–19. New data are presented for xenon at both wavelengths, and for argon and krypton cluster ions at 355 nm. For argon and krypton cluster ions at 532 nm, new data have been recorded which are more accurate than those presented previously. A Monte Carlo model of the experiment has been used to simulate the kinetic energy releases and also to investigate variations in the scattering anisotropy parameter (β) as a function of photon energy and cluster composition and size. Significant fluctuations in β are observed, and these are attributed to a combination of structural variation and changes to the nature of the central chromophore. For small cluster ions the kinetic energy release data show evidence of being influenced by the final spin-orbit state of the atomic ion. Overall, there is a gradual decline in kinetic energy release as a function of increasing cluster size; however, there are marked variations within this trend. For all three rare gas systems the results show that the primary response to photoexcitation is the ejection of a single atom with a high kinetic energy on a time scale that is short compared with the rotational period of a cluster. © 1999 American Institute of Physics.

Notes: Equilibria involving the isomers AlNC and AlCN above a mixture of aluminum nitride, graphite, and gold contained in a graphite Knudsen cell were investigated with a mass spectrometer. The enthalpies of formation, ΔfH0o, and of atomization, ΔaH0o, in kJ mol−1, for AlNC and AlCN, were derived as 281.3±14 and 303.8±14, and as 1228.1±15 and 1205.6±15, respectively. © 1999 American Institute of Physics.

Notes: We reconsider the potential energy surface of the He–LiH system recently examined by Gianturco and co-workers [F. A. Gianturco et al., Chem. Phys. 215, 227 (1997)]. We compute the He–LiH interaction energy at the CCSD(T) level using large correlation consistent atomic basis sets supplemented with bond functions. To capture the severe anisotropy of the He–LiH potential, we interpolate our ab initio points in the angular direction with cubic splines, then expand the splines in terms of Legendre polynomials. The resulting smooth potential surface differs substantially from that of Gianturco et al.; in particular, our attractive He–LiH well is more than twice as deep as that of Gianturco et al., with a He–LiH binding energy of De=176.7 cm−1. © 1999 American Institute of Physics.

Notes: High quality ab initio calculations for the interaction of He with the B 3Π0u+ state of Cl2 for three r(Cl–Cl) distances, and for the He(1S)+Cl(2P) interaction are used to obtain a three-dimensional potential energy surface for the system. The surface was used to calculate HeCl2 excitation spectra, predissociation lifetimes, and product state distributions for comparison with experimental data, and yields a remarkably good agreement. The largest discrepancy is in the dependence of the lifetime on the excited state vibrational level. The calculated lifetimes are too short for the lowest measured vibrational levels. To investigate how the surface could be modified to obtain even better agreement, a microgenetic algorithm was used to adjust the potential parameters to improve the fit. The adjusted surface has a softer repulsive wall for small Cl–Cl separations which helps to lengthen the excited state lifetimes and yields better agreement with the data. Also, the shape of the well region is adjusted somewhat in the fitting process, which yields a stronger dependence of lifetime on vibrational level. © 1999 American Institute of Physics.

Notes: The study of the phenol–(NH3)3 cluster with two-color two-photon ionization shows that the main ion observed with delays between the lasers up to a few hundred nanoseconds is the (NH4)+(NH3)2 fragment, resulting from direct ionization of the (NH4)(NH3)2 product coming from the reaction: PhOH(S1)–(NH3)3→PhO•+(NH4)(NH3)2. © 1999 American Institute of Physics.

Notes: The infrared (IR) absorption spectra of the jet-cooled C6H6 and C6D6 cations, complexed with Ar, are measured throughout the 450–1500 cm−1 region via IR-laser-induced vibrational dissociation spectroscopy. The IR spectrum of the C6H6–Ar cation is dominated by a Fermi resonance between the IR active ν11 mode and two components of the combination mode of the lowest frequency modes ν6 and ν16. A stringent upper limit of 316 cm−1 is found for the value of the dissociation limit D0 of the neutral C6D6–Ar complex. © 1999 American Institute of Physics.

Notes: The empirical force fields used for protein simulations contain short-ranged terms (chemical bond structure, steric effects, van der Waals interactions) and long-ranged electrostatic contributions. It is well known that both components are important for determining the structure of a protein. We show that the dynamics around a stable equilibrium state can be described by a much simpler midrange force field made up of the chemical bond structure terms plus unspecific harmonic terms with a distance-dependent force constant. A normal mode analysis of such a model can reproduce the experimental density of states as well as a conventional molecular dynamics simulation using a standard force field with long-range electrostatic terms. This finding is consistent with a recent observation that effective Coulomb interactions are short ranged for systems with a sufficiently homogeneous charge distribution. © 1999 American Institute of Physics.

Notes: It is shown how the forward–backward (FB) approximation to the semiclassical initial value representation (IVR) can be used to calculate the probability (or cross section) for molecular energy transfer. Specifically, the probability P(ΔEA) for a molecule A to gain (or lose) an amount of internal energy ΔEA by collision with a bath molecule B is given by the Fourier transform of a time correlation function C(t), which is in turn given by a single phase space average over the initial conditions of classical trajectories of the A+B collision system. Application to energy transfer of H2 by collision with He is carried out to demonstrate that the FB-IVR provides a good description of quantum effects in P(ΔEA). © 1999 American Institute of Physics.

Notes: Geometry optimization has become an essential part of quantum-chemical computations, largely because of the availability of analytic first derivatives. Quasi-Newton algorithms use the gradient to update the second derivative matrix (Hessian) and frequently employ corrections to the quadratic approximation such as rational function optimization (RFO) or the trust radius model (TRM). These corrections are typically carried out via diagonalization of the Hessian, which requires O(N3) operations for N variables. Thus, they can be substantial bottlenecks in the optimization of large molecules with semiempirical, mixed quantum mechanical/molecular mechanical (QM/MM) or linearly scaling electronic structure methods. Our O(N2) approach for solving the equations for coordinate transformations in optimizations has been extended to evaluate the RFO and TRM steps efficiently in redundant internal coordinates. The regular RFO model has also been modified so that it has the correct size dependence as the molecular systems become larger. Finally, an improved Hessian update for minimizations has been constructed by combining the Broyden–Fletcher–Goldfarb–Shanno (BFGS) and (symmetric rank one) SR1 updates. Together these modifications and new methods form an optimization algorithm for large molecules that scales as O(N2) and performs similar to or better than the traditional optimization strategies used in quantum chemistry. © 1999 American Institute of Physics.

Notes: We present an investigation of Hermite polynomials as a basic paradigm for quantum dynamics, and make a thorough comparison with the well-known Chebyshev method. The motivation of the present study is to develop a compact and numerically efficient formulation of the spectral filter problem. In particular, we expand the time evolution operator in a Hermite series and obtain thereby an exponentially convergent propagation scheme. The basic features of the present formulation vìs a vìs Chebyshev scheme are as follows: (i) Contrary to the Chebyshev scheme Hamiltonian renormalization is not needed. However, an arbitrary time scaling may be necessary in order to avoid numerical hazards, and this time scaling also provides a leverage to accelerate the convergence of the Hermite series. We emphasize the final result is independent of the arbitrary scaling. (ii) As with the Chebyshev scheme the method is of high accuracy but not unitary by definition, and thus any deviation from unitarity may be used as a guideline for accuracy. The calculation of expansion coefficients in the present scheme is extremely simple. To contrast the convergence property of present method with that of the Chebyshev one for finite time propagation, we have introduced a time–energy scaling concept, and this has given rise to a unified picture of the overall convergence behavior. To test the efficacy of the present method, we have computed the transmission probability for a one-dimensional symmetric Eckart barrier, as a function of energy, and shown that the present method, by suitable time–energy scaling, can be very efficient for numerical simulation. Time–energy scaling analysis also suggests that it may be possible to achieve a faster convergence with the Hermite based method for finite time propagation, by a proper choice of scaling parameter. We have further extended the present formulation directed toward the spectral filter problem. In particular, we have utilized the Gaussian damping function for the purpose. The Hermite propagation scheme has allowed all the time integrals to be done fully analytically, a feature not completely shared by the Chebyshev based scheme. As a result, we have obtained a very compact and numerically efficient scheme for the spectral filters to compute the interior eigenspectra of a large rank eigensystem. The present formulation also allows us to obtain a closed form expression to estimate the error of the energies and spectral intensities. As a test, we have utilized the present spectral filter method to compute the highly excited vibrational states for the two-dimensional LiCN (J=0) system and compared with the exact diagonalization result. © 1999 American Institute of Physics.