Cold chemistry with electronically excited Ca+ Coulomb crystals

Rate constants for chemical reactions of laser-cooled Ca(+) ions and neutral polar molecules (CH(3)F, CH(2)F(2), or CH(3)Cl) have been measured at low collision energies (/k(B)=5-243 K). Low kinetic energy ensembles of (40)Ca(+) ions are prepared through Doppler laser cooling to form "Coulomb crystals" in which the ions form a latticelike arrangement in the trapping potential. The trapped ions react with translationally cold beams of polar molecules produced by a quadrupole guide velocity selector or with room-temperature gas admitted into the vacuum chamber. Imaging of the Ca(+) ion fluorescence allows the progress of the reaction to be monitored. Product ions are sympathetically cooled into the crystal structure and are unambiguously identified through resonance-excitation mass spectrometry using just two trapped ions. Variations of the laser-cooling parameters are shown to result in different steady-state populations of the electronic states of (40)Ca(+) involved in the laser-cooling cycle, and these are modeled by solving the optical Bloch equations for the eight-level system. Systematic variation of the steady-state populations over a series of reaction experiments allows the extraction of bimolecular rate constants for reactions of the ground state ((2)S(1/2)) and the combined excited states ((2)D(3/2) and (2)P(1/2)) of (40)Ca(+). These results are analyzed in the context of capture theories and ab initio electronic structure calculations of the reaction profiles. In each case, suppression of the ground state rate constant is explained by the presence of a submerged or real barrier on the ground state potential surface. Rate constants for the excited states are generally found to be in line with capture theories.     

Low temperature phases of the Andelman-de Gennes model of chiral discrimination: rigorous results

We determine the ordered low temperature phases of the Andelman-de Gennes model of chiral discrimination, using rigorous statistical mechanical methods. The system is considered in the close-packed regime, equivalent to placing the molecules at every site of a honeycomb lattice. If the system contains an equimolar mixture of each of a pair of enantiomers, we prove in general that a heterochiral phase (disfavoring enantiomeric segregation) as well as a homochiral phase (favoring the segregation) is possible, depending on the types of intermolecular interactions. We apply our general results to the specific examples of the interactions considered by Andelman and de Gennes and provide a comparison with their conjectures that were based on two-molecule partition functions.     

Shell models of two-dimensional Coulomb crystals: assessment and comparison with the three-dimensional case

Three shell models, differing in accuracy and computational cost, are formulated for two-dimensional Coulomb crystals. Offering a new means of predicting and analyzing properties of these species, the new models also provide new insights into their previously derived three-dimensional counterparts. In particular, analysis of the individual components of the energy error points out to the neglect of the positional relaxation as the main source of the differences between the approximate and exact energies. Within the realm of shell models, the two-dimensional case turns out to be somewhat more challenging than the three-dimensional one. Due to the lack of exact closed-form expressions for the optimal shell radii, it is computationally more expensive and the energy predictions at the same level of approximation are less accurate (as indicated by the maximum relative energy error of 0.15% vs. that of 0.03% found for spherical Coulomb crystals).     

LGS and GaPO4 piezoelectric crystals: New results

Theoretical and experimental results of two interesting piezoelectric crystals for vibrating sensors, the La₅Ga₃SiO₁₄ (also written LGS) and the GaPO₄, are presented. First a comparison of different piezoelectric crystals in terms of quality factor and temperature stability is given and shows the theoretical interest of the GaPO₄ and the LGS isomorphs (LGX). Then an experimental validation has been undertaken: a dedicated decoupling structure allowing high insulation of two flexural modes is described, as well as its micromachining by ultrasonic machining (USM). The experimental measurements of the LGS resonator gave disappointing results with very low measured quality factors of about 10,000 (under vacuum) for a beam working at 10 kHz. On the other hand, the GaPO₄ resonator behaves very well: a quality factor higher than 700,000 (beam frequency 9 kHz) at room temperature and under vacuum has been obtained, as well as a low temperature frequency dependence of ?12 ppm/K, in accordance with the theoretical predictions. The impact of the Au excitation/detection electrodes on the quality factor has also been studied in detail and it clearly explains why the measured quality factors are lower than the thermoelastic limit.     

Coulomb crystals of few particles: Closed-form expressions for equilibrium energies and geometries, and vibrational force constants

Analytical expressions for equilibrium energies and geometries, and the corresponding vibrational force constants are derived for clusters of between three and eight particles interacting through a pairwise potential of the form (r)=(1/3)(r²+2r^-1). In the case of five-, seven-, and eight-particle clusters, these expressions are functions of single parameters that are the larger real roots of respective twelfth-degree polynomials.     

Universal solution of the problem of the thermodynamic limit in crystals with Coulomb and multipole interactions

A solution of the problem of conditional convergence is obtained in the calculation of Coulomb and multipole energy contributions within direct summation over the crystal lattice. The values correcting the results of the direct summation are shown to have the universal character described by the Lorentz tensor whose components are determined only by crystal symmetry and the direct summation method.     

Properties of methylammonium lead iodide perovskite single crystals

The technique for growing CH₃NH₃PbI₃ single crystals from saturated solutions in concentrated hydroiodic acid is improved by introducing a reducing agent (hypophosphorous acid). The structure of perovskite is confirmed by single crystal XRD. By energy dispersive spectroscopy and X-ray photoelectron spectroscopy it is established that the stoichiometry of the grown crystals corresponds to the CH₃NH₃PbI₃ compound. Changes in the photoluminescence intensity during in-air measurements show that the crystals synthesized using the reducing agent are more stable in the external environment with laser exposure than without it.     

On the theory of radical depolymerization: A rigorous solution

A rigorous solution to a model of radical depolymerization is presented. The model includes random chain scission, depropagation, radical transfer, and first‐order radical termination. The evolution of the molecular weight distribution in the course of depolymerization has been determined under the condition that the initial polymer is characterized by Flory's distribution. The kinetic equations consider the presence of chains with two radicalized ends, which are usually neglected. The commonly used simplifying assumption of the steady‐state radical concentration is not employed, and this makes the obtained results valid at any ratios between the rate constants. The predictions of the steady‐state approximation are compared to those of the rigorous approach in the case of depolymerization accompanied by volatilization of monomeric species. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 965–982, 2003     

Modeling of the hysteresis phenomena in finite-sized slitlike nanopores. Revision of the recent results by rigorous numerical analysis

The systematic investigation of the hysteresis phenomena in finite-sized slitlike nanopores via the Aranovich-Donohue (AD) lattice density functional theory (LDFT) is presented. The new reliable quantitative modeling of the adsorption and desorption branch of the hysteresis loop, through the formation and movement of the curved meniscus, is formulated. As a result, we find that our proposal, which closely mimics the experimental findings, can reproduce a rounded shape of the desorption branch of the hysteresis loop. On the basis of the exhausted commutations, we proved that the hysteresis loop obtained in the considered finite-sized slitlike geometry is of the H1 type of the IUPAC classification. This fundamental result and the other most important results do not confirm the results of the recent studies of Sangwichien et al., whereas they fully agree with the recent lattice studies due to Monson et al. We recognize that the nature of the hysteresis loops (i.e. position, width, shape, and the multiple steps) mainly depends on the value of the energy of both the adsorbate-adsorbate and adsorbate-adsorbent interactions; however, the first one is critical for the appearance of hysteresis. Thus, for relatively small adsorbate-adsorbate interactions, the adsorption-desorption process is fully reversible in the whole region of the bulk density. We show that the strong adsorbate-adsorbent interactions produce (also observed experimentally) multiple steps within hysteresis loops. Contrary to the other studies of the hysteresis phenomena in confined geometry via the LDFT formalism, we constructed both ascending and descending scanning curves, which are known from the experimental observations. Additionally, we consider the problem of the stability of both the obtained adsorption and desorption branches of the computed hysteresis loop in finite-sized slitlike nanopores.     

Properties of the low-lying electronic states of phenanthrene: Exact PPP results

We report properties of the exact low-lying states of phenanthrene, its anion and dianion within the Pariser-Parr-Pople (PPP ) model. The experimentally known singlet states of the neutral molecule are well reproduced by the model. The intensities for one and two photon absorption to various singlet states are also in good agreement with experiment. From the bond orders of these states, we predict the equilibrium geometries. The relaxation energies of these states, computed from charge-charge correlations and bond orders, are presented. We also present results of ring current calculations in the singlet ground state of phenanthrene. We have also reported energies, spin densities, bond orders, and relaxation energies of several triplet states and compared them with experiments as well as with other calculations, where available. The fine structure constants D and E, computed in the lowest triplet state, compare well with those obtained from experiments. These properties are also presented for the anions and the dianions. The PPP model in these cases predicts a low-energy (<1 eV) dipole excitation. © 1996 John Wiley & Sons, Inc.     

Stringent test of the statistical quasiclassical trajectory model for the H+3 exchange reaction: a comparison with rigorous statistical quantum mechanical results

A complete formulation of a statistical quasiclassical trajectory (SQCT) model is presented in this work along with a detailed comparison with results obtained with the statistical quantum mechanical (SQM) model for the H+ +D2 and H+ +H2 reactions. The basic difference between the SQCT and the SQM models lies in the fact that trajectories instead of wave functions are propagated in the entrance and exit channels. Other than this the two formulations are entirely similar and both comply with the principle of detailed balance and conservation of parity. Reaction probabilities, and integral and differential cross sections (DCS's) for these reactions at different levels of product's state resolution and from various initial states are shown and discussed. The agreement is in most cases excellent and indicates that the effect of tunneling through the centrifugal barrier is negligible. Some differences are found, however, between state resolved observables calculated by the SQCT and the SQM methods which makes use of the centrifugal sudden (coupled states) approximation (SQM-CS). When this approximation is removed and the full close coupling treatment is used in the SQM model (SQM-CC), an almost perfect agreement is achieved. This shows that the SQCT is sensitive enough to show the relatively small inaccuracies resulting from the decoupling inherent to the CS approximation. In addition, the effect of ignoring the parity conservation is thoroughly examined. This effect is in general minor except in particular cases such as the DCS from initial rotational state j=0. It is shown, however, that in order to reproduce the sharp forward and backward peaks the conservation of parity has to be taken into account.     

Preliminary communication Properties of nonlinear supramolecular liquid crystals containing thiophenedicarboxylic acids

Novel mesogenic supramolecules have been constructed from the 2 :1 molar ratio of trans 4-alkoxy-4-stilbazoles CnPS (1) complexed with 2,5-thiophenedicarboxylic acid THDA (4) to form the kinked hydrogen-bonded (H-bonded) complexes (CnPS)-THDA. The analogous H-bonded complexes (CnPP)2-THDA consisting of the 2:1 molar ratio of 4-alkoxypyridines CnPP (2) and THDA (4) are also compared. In contrast to linear complexes (CnPS)2-TA prepared from the 2 :1 molar ratio of CnPS (1) and terephthalic acid TA (5), supramolecular liquid crystals with kinked molecular structures (CnPS)2-THDA are generated by introducing the thiophene unit into the H-bonded complexes. In addition, the chiral complex (C5*PS)2-THDA composed of an optically active proton acceptor (S)-(-)-4-(2-methylbutoxy)-4-stilbazole C5*PS ( 3 ) and THDA ( 4 ) (2 :1 molar ratio) is reported. Significantly, the first thiophene based supramolecular liquid crystals have been constructed in this study, and the mesogenic properties of the supramolecules can be easily adjusted not only by the nonlinear shape of the thiophene unit but also by the dipole moment derived from the lone-pair electrons of the sulphur hetero-atom.     

A rigorous theory of ring tensiometry: Addendum on the wall effect

Summary As a supplement to our theoretical calculations for the ring method of measuring surface and interfacial tensions of liquids, the effect of the finite size of the liquid container on the measurement has been studied employing (i) an exact analysis for the case of an infinite straight cylinder midway between two parallel walls and (ii) an approximate analysis for a ring in a circular container. The parameters which can cause errors are identified, and their magnitude is estimated and compared with the experimental results for surface tension of water in air. It is shown that conditions can be readily adjusted to produce negligrors.Nomenclature a radius of cylinder or ring wire; - C ₂₃ (₂ –₃)g/ ₂₃ D=semi-gap width between parallel walls, or radius of liquid container; - f Harkins-Jordan (1) factor - F, E elliptic integrals of the first and second kind (k = modulus) - F equilibrium capillary force on ring or per unit length of a straight cylinder; - F _D,F maximumF for finiteD andD = - g gravity - r _i,z _i r- andz-coordinates of the inner (i =1) and outer (i = 2) contact line circles on ring; - z _c vertical coordinate of the contact line on cylinder; - Y23, YD interfacial tension (D= ; uncorrected interfacial tension measured in container of radiusD - _i density of thei phase - _i slope angle of the inner (i = 1) and outer (i = 2) menisci on ring - 180° - _c slope angle of cylindrical meniscus at the contact line - ₂ 180° – ₂ - Oo contact angle at container wall - (F _D -F )/F for cylinder; (YD - ₂₃)/Y23 for ring     

Gaussian and finite-element Coulomb method for the fast evaluation of Coulomb integrals

The authors propose a new linear-scaling method for the fast evaluation of Coulomb integrals with Gaussian basis functions called the Gaussian and finite-element Coulomb (GFC) method. In this method, the Coulomb potential is expanded in a basis of mixed Gaussian and finite-element auxiliary functions that express the core and smooth Coulomb potentials, respectively. Coulomb integrals can be evaluated by three-center one-electron overlap integrals among two Gaussian basis functions and one mixed auxiliary function. Thus, the computational cost and scaling for large molecules are drastically reduced. Several applications to molecular systems show that the GFC method is more efficient than the analytical integration approach that requires four-center two-electron repulsion integrals. The GFC method realizes a near linear scaling for both one-dimensional alanine alpha-helix chains and three-dimensional diamond pieces.     

The rigorous computation of the molecular electric potential

A method is presented for the rigorous computation of the electric potential of molecules of arbitrary shape, under the assumption of continuous linear dielectric media. The computational technique involves finding the distribution of induced polarization charge on the molecular surface, and proceeds by an application of the method of boundary elements. The surface, which separates the molecular interior (of low dielectric constant) from the highly polar solvent, is given a piece-wise analytic representation as a collection of curvilinear elements. Given a set of internal fixed charges, the distribution of polarization-charge is found as a continuous function over the surface elements, and the electric potential (including all polarization effects) is then easily computed at any point. The method is applied to a spherical interface, and to several small molecules of biological interest, including a hexapeptide. The resulting potentials show good convergence in all cases. The future application of the method to macromolecules is discussed.     

Resolutions of the Coulomb operator

We discuss a generalization of the resolution of the identity by considering one-body resolutions of two-body operators, with particular emphasis on the Coulomb operator. We introduce a set of functions that are orthonormal with respect to 1r(12) and propose that the resulting "resolution of the Coulomb operator," r(12) (-1)=mid R:phi(i)phi(i)mid R:, may be useful for the treatment of large systems due to the separation of two-body interactions. We validate our approach by using it to compute the Coulomb energy of large systems of point charges.     

A systematic and rigorous statistical approach for establishing the accuracy of analytical results and its application to a comparison of alternative d

Previously established optimum operating conditions for simultaneous multi-element trace analysis of geological materials using a d.c. arc were applied