On the decay of highly excited oscillator in a crystal

The diagonal density matrix elements are found for a dynamical subsystem which is either anharmonic or harmonic highly excited oscillator interacting with the crystal vibrations. For the extreme case of the infinitely highly excited oscillator the result is exact. Different limiting cases are considered. In particular for the harmonic oscillator the validity criterion for the balance equation is found.     

Modeling flexible pharmacophores with distance geometry, scoring, and bound stretching

The study of pharmacophores, i.e., of common features between different ligands, is important for the quantitative identification of "compatible" enzymes and binding species. A pharmacophore-based technique is developed that combines multiple conformations with a distance geometry method to create flexible pharmacophore representations. It uses a set of low-energy conformations combined with a new process we call bound stretching to create sets of distance bounds, which contain all or most of the low-energy conformations. The bounds can be obtained using the exact distances between pairs of atoms from the different low-energy conformations. To avoid missing conformations, we can take advantage of the triangle distance inequality between sets of three points to logically expand a set of upper and lower distance bounds (bound stretching). The flexible pharmacophore can be found using a 3-D maximal common subgraph method, which uses the overlap of distance bounds to determine the overlapping structure. A scoring routine is implemented to select the substructures with the largest overlap because there will typically be many overlaps with the maximum number of overlapping bounds. A case study is presented in which 3-D flexible pharmacophores are generated and used to eliminate potential binding species identified by a 2-D pharmacophore method. A second case study creates flexible pharmacophores from a set of thrombin ligands. These are used to compare the new method with existing pharmacophore identification software.     

Effects of contact geometry on pull-off force measurements with a colloidal probe

This paper examines the effects of contact geometry on the pull-off (adhesion) force between a glass sphere (colloidal probe) and a silicon wafer in an environment with controlled relative humidity. An atomic force microscope is used to measure the pull-off force between the colloidal probe and the sample mounted at different tilt angles. The results show that the measured pull-off force is very sensitive to the tilt angle. Through the use of a newly developed direct scanning method, the exact contact geometry is determined for the zero-tilt angle case. The obtained digital image is then rotated to determine the contact geometry for the cases with other tilt angles. A detailed examination of the contact geometry, along with a magnitude analysis of the capillary force, suggests that the adhesion is most likely dominated by the capillary force from the meniscus formed between the probe and the sample. The strong dependence of the adhesion on the tilt angle may result from the change of meniscus dimensions associated with the probe-sample separation, which in turn is controlled by the highest peak on the probe sphere. Our observation emphasizes the combined role of microsurface shape near the contact and nanoroughness within the contact in determining the colloidal probe pull-off force and also microadhesion force in general.     

Utility of peak shape analyses in determining unresolved interferences in exact mass measurements at low resolution

Low resolution methods can provide exact mass data comparable to that obtained with high resolution instrumentation and offer potential advantages in throughput and robustness. However, low resolution exact mass techniques have realized limited use largely because of the possibility of errors caused by unresolved interferences. Here the utility of statistical peak shape analysis for determining unresolved interferences at low resolution is considered. Equations describing the effect of unresolved interferences on statistical peak shape parameters are developed and used to investigate the extent to which evaluations of peak shape can be used to reduce the likelihood of mass measurement errors. Peak shape analysis is shown to be a highly effective and sensitive method of determining unresolved interferences. Mass measurement errors resulting from undetermined interferences are found to increase with increasing relative abundance of the interfering peak, to increase with decreasing resolution, and to increase with decreasing precision in the intensity measurement. At low resolution, undetermined interferences as small as a few percent relative abundance can produce mass measurement errors in excess of 5 ppm. Peak shape analyses alone do not appear adequate to eliminate the risk of significant mass measurement errors resulting from unresolved interferences at low resolution.     

1H NMR chemical shift calculations as a probe of supramolecular host-guest geometry

The self-assembled supramolecular host [Ga(4)L(6)](12-) (1; L = 1,5-bis[2,3-dihydroxybenzamido]naphthalene) can encapsulate cationic guest molecules within its hydrophobic cavity and catalyze the chemical transformations of bound guests. The cavity of host 1 is lined with aromatic naphthalene groups, which create a magnetically shielded interior environment, resulting in upfield shifted (1-3 ppm) NMR resonances for encapsulated guest molecules. Using gauge independent atomic orbital (GIAO) DFT computations, we show that (1)H NMR chemical shifts for guests encapsulated in 1 can be efficiently and accurately calculated and that valuable structural information is obtained by comparing calculated and experimental chemical shifts. The (1)H NMR chemical shift calculations are used to map the magnetic environment of the interior of 1, discriminate between different host-guest geometries, and explain the unexpected downfield chemical shift observed for a particular guest molecule interacting with host 1.     

Sterically induced shape and crystalline phase control of GaP nanocrystals

We demonstrate a novel synthetic scheme that can be used to control the crystalline phase and shape of GaP semiconductor nanocrystals. Our study shows that steric effects of surfactant ligands can modulate the crystalline phases and control the shapes of nanocrystals. The shape of the nanocrystals obtained varies from zero-dimensional spheres to one-dimensional rods via controlling the ratio between primary and tertiary alkylamines. III-V semiconductors (in our case: GaP) under 10 nm in width are first reported, and unique optical properties due to shape anisotropy are also observed.     

On the optimisation of the bed porosity and the particle shape of ordered chromatographic separation media

We report on a theoretical study wherein we considered a large number of ordered two-dimensional porous pillar arrays with different pillar shapes and widely varying external porosity and calculated the flow resistance and the band broadening (under retentive conditions) over the complete range of practical velocities using a commercial computational fluid dynamics software package. It is found that the performance of the small porosity systems is very sensitive to the exact pillar shape, whereas this difference gradually disappears with increasing porosity. The obtained separation impedances are very small in comparison to packed bed and monolithic columns and decrease with increasing porosity. If accounting for the current micromachining limitations, a proper selection of the exact shape and porosity even becomes more critical, and different design rules are obtained depending on whether porous or non-porous pillars are considered.     

Periodic ab initio estimates of the dispersive interaction between molecular nitrogen and a monolayer of hexagonal BN

The ab initio determination of the leading long-range term of pairwise additive dispersive interactions, based on the independent analysis of the response properties of the interacting objects, is here considered in the case where these are part of a periodic system. The interaction of a nitrogen molecule with a thin film of hexagonal BN has been chosen as a case study for identifying some of the problems involved, and for proposing techniques for their solution. In order to validate the results so obtained, the interaction energy between N(2) and a BN monolayer at different distances has been estimated following a totally different approach, namely by performing post-Hartree-Fock (MP2) supercell calculations using the Crystal+Cryscor suite of programs. The results obtained with the two approaches closely agree over a long range, while the limit of validity of the purely dispersive regime can be clearly assessed.     

Mechanism and Kinetics of Hexamethyldisilazane Reaction with a Fumed Silica Surface

An analytical study is presented on the thermocapillary migration of a fluid sphere within a constant applied temperature gradient in an arbitrary direction with respect to a plane surface. The Peclet and Reynolds numbers are assumed to be small so that the Laplace and Stokes equations, respectively, govern the temperature distributions and fluid velocities inside and outside the droplet. The asymptotic formulas for the temperature and the velocity fields in the quasi-steady situation are obtained by using a method of reflections. The plane surface can be a no-slip solid wall and/or a perfect-slip free surface. The boundary effect on the thermocapillary migration is found to be weaker than that on the motion driven by a body force. Even so, the interaction between the plane and the droplet can be very significant when the gap thickness approaches zero. For the motion of a droplet normal to a solid wall, the effect of the plane surface reduces the translational velocity of the droplet; however, this solid wall can be an enhancement factor on the particle migration as it is translating parallel to the wall. On the other hand, in case of a droplet migrating close to a free surface due to thermocapillarity, the droplet velocity can be either greater or smaller than that which would exist in the absence of the plane surface, depending on the relative thermal conductivity and the surface properties of the particle and its relative distance from the plane. Furthermore, the interacting thickness of the affected region by the presence of the plane is discussed by considering the droplet mobility. Generally speaking, a free surface exerts less influence on the particle movement than does a solid surface. Copyright 2000 Academic Press.     

Electrostatic Interaction between Two Dissimilar Spheres with Constant Surface Charge Density

Explicit exact analytic expressions are obtained in the form of infinite series for the potential energy of the electrostatic interaction for the system of two dissimilar hard spheres with constant surface charge density in an electrolyte solution on the basis of the linearized Poisson-Boltzmann equation. The effects of the particle polarization, that is, the internal fields induced within tim interacting spheres, which are found to be of the order of instead of 1/κa (where κ is the Debye-Hückel parameter and a is the sphere radius), are taken into account. As in the case of the interaction at constant surface potential, the zeroth-order approximation to the interaction energy corresponds to the interaction energy that would be obtained if both spheres were ion-penetrable spheres ("soft" spheres) and to that obtained by the linear superposition approximation. The first-order approximation corresponds to the interaction energy that would be obtained if either sphere were a soft sphere, with the other being a hard sphere with constant surface charge density. The first-order correction term can be interpreted as the image interaction between the soft sphere and its image with respect to the hard sphere.     

Discontinuous molecular dynamics for semiflexible and rigid bodies

A general framework for performing event-driven simulations of systems with semiflexible or rigid bodies interacting under impulsive forces is outlined. The method consists of specifying a means of computing the free evolution of constrained motion, evaluating the times at which interactions occur, and determining the consequences of interactions on subsequent motion. Algorithms for computing the times of interaction events and carrying out efficient event-driven simulations are discussed. The semiflexible case and the rigid case differ qualitatively in that the free motion of a rigid body can be computed analytically and need not be integrated numerically.     

An Exact Solution to the Electrostatic Interaction between an Ion-Penetrable Sphere and an Ion-Penetrable Rod

No exact solution for the free energy of electrostatic interaction for a charged sphere and rod geometry in an electrolyte solution has yet been proposed. This geometry is interesting because it can be applied to describe macromolecules interacting with a random fiber-matrix for modeling of hindered transport in diffusional systems. Here we present an analytical approach that yields an exact solution to the problem for ion-penetrable-also called "soft"-sphere and infinitely long rod. This solution is compared to a published finite-element analysis of the same system with nonpenetrable-also called "hard"-sphere and infinitely long rod maintaining a constant surface charge density restriction. For any ionic strength or ratio of rod radius to sphere radius the ion-penetrable method yields an electrostatic free energy of interaction which is lower than that given by the analysis for hard bodies. This free energy is significantly lower for most parameter value combinations and therefore suggests that one should carefully examine the system being modeled to determine if it is approximated better by a hard body or ion-penetrable body approach. Copyright 2000 Academic Press.     

Does really Born–Oppenheimer approximation break down in charge transfer processes? An exactly solvable model

Effects of deviation from the Born–Oppenheimer approximation (BOA) on the non-adiabatic transition probability for the transfer of a quantum particle in condensed media are studied within an exactly solvable model. The particle and the medium are modeled by a set of harmonic oscillators. The dynamic interaction of the particle with a single local mode is treated explicitly without the use of BOA. Two particular situations (symmetric and non-symmetric systems) are considered. It is shown that the difference between the exact solution and the true BOA is negligibly small at realistic parameters of the model. However, the exact results differ considerably from those of the crude Condon approximation (CCA) which is usually considered in the literature as a reference point for BOA (Marcus–Hush–Dogonadze formula). It is shown that the exact rate constant can be smaller (symmetric system) or larger (non-symmetric one) than that obtained in CCA. The non-Condon effects are also studied.     

Heavy (or large) ions in a fluid in an electric field: The diffusion equation exactly following from the Fokker-Planck equation

The problem of the derivation of the diffusion equation exactly following from the Fokker-Planck (or Klein-Kramers) equation for heavy (or large) particles in a fluid in an external force field is solved in the case in which the particles are ions subject to a uniform (but in general time-varying) electric field. It is found that such a diffusion equation maintains memory of the initial ion velocity distribution, unless sufficiently large values of time are considered. In such temporal asymptotic limit, the diffusion equation exactly becomes (i) the Smoluchowski equation when the electric field is constant in time, and (ii) a new equation generalizing the Smoluchowski equation, when the electric field is arbitrarily time varying. Finally, it is shown that the obtained exact (or asymptotic) results make questionable the procedures and the results of approximate theories developed in the past to get a "corrected" Smoluchowski equation when the external force can also be, in general, position dependent.     

Grassmann coherent states representation of the path integral: Evaluation of the generating function for spin systems

An interacting spin system is investigated within the scenario of the Feynman path integral representation of quantum mechanics. Short‐time propagator algorithms and a discrete time formalism are used in combination with a basis set involving Grassmann variables coherent states to get a many‐body analytic propagator. The generating function thus obtained leads, after an adequate tracing over Grassmann variables in the imaginary time domain, to the partition function. A spin 1/2 Hamiltonian involving the whole set of interactions is considered. Fermion operators satisfying the standard anticommutation relations are constructed from the raising and lowering spin operators via the Jordan–Wigner transformation. The partition function obtained is more general than the partition function of the traditional Ising model involving only first‐neighbor interactions. Computations were performed assuming that the coupling as a function of the distance can be reasonably well represented by an Airy function. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002     

Surface tension of a Lennard-Jones liquid under supersaturation

A formally exact Kirkwood-Buff virial formula for the surface tension of a supersaturated interface is derived. A modified Gibbs ensemble method is given that allows the creation of interacting supersaturated phases of equal chemical potential, and which enables the Kirkwood-Buff formula to be applied. The methods are tested by Monte Carlo simulation of a supersaturated Lennard-Jones fluid with a planar liquid-vapor interface. The Kirkwood-Buff results for the supersaturated surface tension are found to be in reasonable agreement with new results obtained here using the recently developed, formally exact, ghost interface method, [M. P. Moody and P. Attard, J. Chem. Phys., 2002, 117, 6705]. The surface tension is obtained as a function of supersaturation at four temperatures, and it is found to decrease with increasing supersaturation, and to vanish at the vapor spinodal. The relevance of the present results to the nucleation of droplets in a supersaturated vapor is discussed.     

Experimental and theoretical (e,2e) ionization cross sections for a hydrogen target at 75.3 eV incident energy in a coplanar asymmetric geometry

Very recently it was shown that the molecular three-body distorted wave (M3DW) approach gives good agreement with the shape of the experimental data for electron-impact ionization of H(2) in a coplanar symmetric geometry, providing the incident electrons have an energy of 35 eV or greater. One of the weaknesses of these studies was that only the shape of the cross section could be compared to experiment, since there was no absolute or relative normalization of the data. Here we report a joint experimental/theoretical study of electron-impact ionization of H(2) in a coplanar asymmetric geometry where the energy of the incident electron was fixed, and different pairs of final state electron energies were used. In this case, the experimental data can be normalized such that only one renormalization factor is required. It is shown that the M3DW is pretty good in agreement with experiment. However, a better treatment of polarization and exchange between the continuum and bound state electrons is required before quantitative agreement between experiment and theory is achieved.     

Frequency distribution of radiation emitted from excited atomic systems

General expressions for the time-dependent probability amplitudes of the quantum states of two arbitrary, interacting atoms are calculated when one atom is initially in an excited p state and the other atom is in an s ground state. The lifetimes of the excited states and the line shape of the emitted radiation are obtained as functions of both the atomic separation and the energy difference between the excited states of the two atoms. The emission line shape is shown to be doubly peaked and to agree with the line shape of the radiation scattered by a system of two interacting atoms. The expressions for the lifetimes of the excited states are found to be identical to those obtained for the radiation scattering situation.     

Remarks on the geometry of micelles, bilayers and cell membranes

Starting from simple geometric properties of parallel surfaces, it is suggested that bilayers, and also monolayers, present two spontaneous principal curvatures gamma and gamma , so that a narrow disc of freely deformable bilayer might adopt either a 'saddle' shape, or a 'hat' shape, or a cylindrical shape. Besides the usually considered spontaneous splay c0 = gamma + gamma , there is also a spontaneous gaussian curvature g0= gammagamma , with noticeable effects in strongly curved bilayers. An excess of area of the median hydrophobic level with respect to the mean area occupied by the two hydrophilic layers creates a saddle shape, whereas a deficit leads to a hat shape, the equality corresponding to a cylindrical shape. The usual two layers theory of the spontaneous curvature seems to be improved by considering the role of a median layer. We have tried to illustrate this new point of view by many examples. Due to their asymmetry, monolayers and cell membranes give rise to micelles and vesicles of comparable geometries, but of very different sizes. At the considered scales, a term of order higher than quadratic, such as kt(cc- gammagamma )2, seems to be necessary in the expression of the elastic energy.