Gradient extremals and valley floor bifurcations on potential energy surfaces

Gradient extremals are curves in configuration space denned by the condition that the gradient of the potential energy is an eigenvector of the Hessian matrix. Solutions of a corresponding equation go along a valley floor or along a crest of a ridge, if the norm of the gradient is a minimum, and along a cirque or a cliff or a flank of one of the two if the gradient norm is a maximum. Properties of gradient extremals are discussed for simple 2D model surfaces including the problem of valley bifurcations.     

The lion and man problem revisited

A pursuerP, whose speed is bounded by 1, wants to get closer to an evaderE, whose speed is bounded by >1.P wants to reduce his distancePE fromE below the capture radius . Both players are confined to a circular arena. This problem is equivalent to a problem discussed by Flynn, who characterized and gave numerical bounds to the least upper boundd* on the values ofPE thatE can maintain. He used direct methods and did not use Isaacs' theory.We solve our problem relying on the theory of singular surfaces in differential games. We construct and investigate barriers of the game of kind, and we replace Flynn's bounds ond* by analytical (exact) values for various speeds .The support of the TW Department of THT, Enschede, Holland, is gratefully acknowledged.     

Atomic structure of InAs quantum dots on GaAs

In recent years, the self-assembled growth of semiconductor nanostructures, that show quantum size effects, has been of considerable interest. Laser devices operating with self-assembled InAs quantum dots (QDs) embedded in GaAs have been demonstrated. Here, we report on the InAs/GaAs system and raise the question of how the shape of the QDs changes with the orientation of the GaAs substrate. The growth of the InAs QDs is understood in terms of the Stranski–Krastanow growth mode. For modeling the growth process, the shape and atomic structure of the QDs have to be known. This is a difficult task for such embedded entities.

In our approach, InAs is grown by molecular beam epitaxy on GaAs until self-assembled QDs are formed. At this point the growth is interrupted and atomically resolved scanning tunneling microscopy (STM) images are acquired. We used preparation parameters known from the numerous publications on InAs/GaAs. In order to learn more about the self-assemblage process we studied QD formation on different GaAs(0 0 1), (1 1 3)A, and ( )B substrates. From the atomically resolved STM images we could determine the shape of the QDs. The quantum “dots” are generally rather flat entities better characterized as “lenses”. In order to achieve this flatness, the QDs are terminated by high-index bounding facets on low-index substrates and vice versa. Our results will be summarized in comparison with the existing literature.     

Role of structural flexibility in the fluorescence and photochromism of salicylideneaniline: the general scheme of the phototransformations

The mechanism of light-induced transformation in the salicylideneaniline molecule was studied by semiempirical PM3 calculations. The structures and energies of the minima and saddle points (transition states) on the S₀, S₁ and T₁ potential energy hypersurfaces (PESs) were obtained, together with the gradient lines on the PESs. The structure-energy scheme was compared with the experimental findings. According to the results obtained, the following principle processes are observed: fast S₁ excited state intramolecular proton transfer (ESIPT), followed by typical ESIPT fluorescence; the formation of two S₁ twisted intramolecular charge transfer (TICT) structures which quench the ESIPT fluorescence; the diabatic formation of two ground state metastable coloured “post-TICT” structures responsible for photochromism.     

INTROMISSION OF WATER-REPELLENT AND HYDROSCOPIC PROPERTIES SIMULTANEOUSLY TO PP BY PLASMA DISCHARGE METHOD

Plasma-induced surface graft copolymerization of acrylic acid on polypropylene non-woven fabric (PP-g-AA) and polypropylene membrane were reported. The extents of grafting were controlled by the plasma and polymerization condition. Hexadecyltrimethyl ammonium bromide was then coupled with the carboxyl group of PP-g-AA to obtain a polyion complex (PIC). At last, CF4 plasma was used to give PICs hydrophobic property. The moisture regain and water-repellency of the processed PICs was investigated. The surfaces were characterized using ATR FT-IR and XPS. The result indicates that the products have very high ability to adsorb moisture, even better than cotton fiber. At the same time, the products show excellent hydrophobic property, which can‘t be wetted by those reagents whose surface tensions were higher than 327mN/m.     

The surface and materials science of tin oxide

The study of tin oxide is motivated by its applications as a solid state gas sensor material, oxidation catalyst, and transparent conductor. This review describes the physical and chemical properties that make tin oxide a suitable material for these purposes. The emphasis is on surface science studies of single crystal surfaces, but selected studies on powder and polycrystalline films are also incorporated in order to provide connecting points between surface science studies with the broader field of materials science of tin oxide. The key for understanding many aspects of SnO₂ surface properties is the dual valency of Sn. The dual valency facilitates a reversible transformation of the surface composition from stoichiometric surfaces with Sn⁴⁺ surface cations into a reduced surface with Sn²⁺ surface cations depending on the oxygen chemical potential of the system. Reduction of the surface modifies the surface electronic structure by formation of Sn 5s derived surface states that lie deep within the band gap and also cause a lowering of the work function. The gas sensing mechanism appears, however, only to be indirectly influenced by the surface composition of SnO₂. Critical for triggering a gas response are not the lattice oxygen concentration but chemisorbed (or ionosorbed) oxygen and other molecules with a net electric charge. Band bending induced by charged molecules cause the increase or decrease in surface conductivity responsible for the gas response signal. In most applications tin oxide is modified by additives to either increase the charge carrier concentration by donor atoms, or to increase the gas sensitivity or the catalytic activity by metal additives. Some of the basic concepts by which additives modify the gas sensing and catalytic properties of SnO₂ are discussed and the few surface science studies of doped SnO₂ are reviewed. Epitaxial SnO₂ films may facilitate the surface science studies of doped films in the future. To this end film growth on titania, alumina, and Pt(1 1 1) is reviewed. Thin films on alumina also make promising test systems for probing gas sensing behavior. Molecular adsorption and reaction studies on SnO₂ surfaces have been hampered by the challenges of preparing well-characterized surfaces. Nevertheless some experimental and theoretical studies have been performed and are reviewed. Of particular interest in these studies was the influence of the surface composition on its chemical properties. Finally, the variety of recently synthesized tin oxide nanoscopic materials is summarized.     

Model studies of the chemisorption of hydrogen and oxygen on nickel surfaces

Atomic chemisorption of hydrogen and oxygen on the Ni(100) surface has been studied using an Effective Core Potential (ECP) approach described in a previous paper. Clusters of up to 50 nickel atoms have been used to model the surface. The computed chemisorption energies are 62 kcal/mol (exp. 63 kcal/mol) for hydrogen and 106 kcal/mol (exp. 115–130 kcal/mol) for oxygen. Correlating the adsorbate and the cluster-adsorbate bonds is extremely important for obtaining accceptable results, particularly for oxygen. Reasonable convergence of chemisorption energies is obtained with 40–50 cluster atoms for both hydrogen and oxygen. For hydrogen the addition of a third cluster layer stabilizes the results considerably. Both hydrogen and oxygen are adsorbed at (or close to) the four-fold hollow site. The calculated barriers for surface migration are also in good agreement with the experimental estimates. The calculated equilibrium heights above the surface are on the other hand too high compared with experiments. This disagreement is believed to be due to core-valence correlation effects, which are not incorporated in the present ECP. The cluster convergence for the height above the surface is much slower than for the chemisorption energy.     

Fourier transform infrared reflection-absorption spectroscopy of amino acids adsorbed on metal surfaces

Fourier transform infrared reflection-absorption spectroscopy (FT-IRAS) has been used to study the orientation and coordination of glycine, L-phenylalanine and L-histidine on gold and copper surfaces. It was found that glycine and L-histidine were weakly adsorbed (physisorbed) in the zwitterionic form on gold. The surface chemical bonding of L-histidine and L-phenylalanine to copper were chemical rather than physical by nature. Conclusive evidence was obtained for coordination to copper through both the amino-nitrogen and carboxylate-oxygen atoms.     

Forward and backward pericyclic photochemical reactions have intermediates in common, yet cyclobutenes break the rules.

Photochemical pericyclic reactions are believed to proceed via a so-called pericyclic minimum on the lowest excited potential surface (S(1)), which is common to both the forward and backward reactions. Such a common intermediate has never been directly detected. The photointerconversion of 1,3-butadiene and cyclobutene is the prevailing prototype for such reactions, yet only diene ring closure proceeds with the stereospecificity that the Woodward-Hoffmann rules predict. This contrast seems to exclude a common intermediate. Using ultrafast spectroscopy, we show that the excited states of two cyclobutene/diene isomeric pairs are linked by not one, but by two common minima, p* and ct*. Starting from the diene side (cyclohepta-1,3-diene and cycloocta-1,3-diene), electrocyclic ring closure passes via the pericyclic minimum p*, whereas ct* is mainly responsible for cis-trans isomerization. Starting from the corresponding cyclobutenes (bicyclo[3.2.0]heptene-6 and bicyclo[4.2.0]octene-7), the forbidden isomer is formed from ct*. The path branches at the first (S(2)/S(1)) conical intersection towards p* and ct*. The fact that the energetically unfavorable ct* path can compete is ascribed to a dynamic effect: the momentum in C=C twist direction, acquired--such as in other olefins--in the Franck-Condon region of the cyclobutenes.     

Molecular potential-energy surfaces for chemical reaction dynamics

This paper reviews the construction of molecular potential-energy surfaces by an interpolation method which has been developed over the last several years. The method uses ab initio quantum chemistry calculations of the molecular electronic energy in an automated procedure to construct global potential- energy surfaces which can be used to simulate chemical reactions with either classical or quantum dynamics. The methodology is explained and several applications are presented to illustrate the approach. Received: 22 February 2002 / Accepted: 2 May 2002 / Published online: 6 November 2002 Correspondence to: M. A. Collins e-mail: collins@rsc.anu.edu.au Acknowledgements. The methods described in this overview are the result of collaborations with former members of my group, in particular with Josef Ischtwan, Meredith Jordon, Keiran Thompson and Ryan Bettens. I am also indebted for inspiration gained from many discussions with my colleagues Leo Radom and Donghui Zhang (National University of Singapore). This work has been supported by the Supercomputer Facility of the Australian National University and the Australian Partnership for Advanced Computing.