3 resultados para Distance-balanced graph
em CaltechTHESIS
Resumo:
The rate of electron transport between distant sites was studied. The rate depends crucially on the chemical details of the donor, acceptor, and surrounding medium. These reactions involve electron tunneling through the intervening medium and are, therefore, profoundly influenced by the geometry and energetics of the intervening molecules. The dependence of rate on distance was considered for several rigid donor-acceptor "linkers" of experimental importance. Interpretation of existing experiments and predictions for new experiments were made.
The electronic and nuclear motion in molecules is correlated. A Born-Oppenheimer separation is usually employed in quantum chemistry to separate this motion. Long distance electron transfer rate calculations require the total donor wave function when the electron is very far from its binding nuclei. The Born-Oppenheimer wave functions at large electronic distance are shown to be qualitatively wrong. A model which correctly treats the coupling was proposed. The distance and energy dependence of the electron transfer rate was determined for such a model.
Resumo:
A series of meso-phenyloctamethylporphyrins covalently bonded at the 4'phenyl position to quinones via rigid bicyclo[2.2.2]octane spacers were synthesized for the study of the dependence of electron transfer reaction rate on solvent, distance, temperature, and energy gap. A general and convergent synthesis was developed based on the condensation of ac-biladienes with masked quinonespacer-benzaldehydes. From picosecond fluorescence spectroscopy emission lifetimes were measured in seven solvents of varying polarity. Rate constants were determined to vary from 5.0x109sec-1 in N,N-dimethylformamide to 1.15x1010 Sec-1 in benzene, and were observed to rise at most by about a factor of three with decreasing solvent polarity. Experiments at low temperature in 2-MTHF glass (77K) revealed fast, nearly temperature-independent electron transfer characterized by non-exponential fluorescence decays, in contrast to monophasic behavior in fluid solution at 298K. This example evidently represents the first photosynthetic model system not based on proteins to display nearly temperature-independent electron transfer at high temperatures (nuclear tunneling). Low temperatures appear to freeze out the rotational motion of the chromophores, and the observed nonexponential fluorescence decays may be explained as a result of electron transfer from an ensemble of rotational conformations. The nonexponentiality demonstrates the sensitivity of the electron transfer rate to the precise magnitude of the electronic matrix element, which supports the expectation that electron transfer is nonadiabatic in this system. The addition of a second bicyclooctane moiety (15 Å vs. 18 Å edge-to-edge between porphyrin and quinone) reduces the transfer rate by at least a factor of 500-1500. Porphyrinquinones with variously substituted quinones allowed an examination of the dependence of the electron transfer rate constant κET on reaction driving force. The classical trend of increasing rate versus increasing exothermicity occurs from 0.7 eV≤ |ΔG0'(R)| ≤ 1.0 eV until a maximum is reached (κET = 3 x 108 sec-1 rising to 1.15 x 1010 sec-1 in acetonitrile). The rate remains insensitive to ΔG0 for ~ 300 mV from 1.0 eV≤ |ΔG0’(R)| ≤ 1.3 eV, and then slightly decreases in the most exothermic case studied (cyanoquinone, κET = 5 x 109 sec-1).
Resumo:
Multi-finger caging offers a rigorous and robust approach to robot grasping. This thesis provides several novel algorithms for caging polygons and polyhedra in two and three dimensions. Caging refers to a robotic grasp that does not necessarily immobilize an object, but prevents it from escaping to infinity. The first algorithm considers caging a polygon in two dimensions using two point fingers. The second algorithm extends the first to three dimensions. The third algorithm considers caging a convex polygon in two dimensions using three point fingers, and considers robustness of this cage to variations in the relative positions of the fingers.
This thesis describes an algorithm for finding all two-finger cage formations of planar polygonal objects based on a contact-space formulation. It shows that two-finger cages have several useful properties in contact space. First, the critical points of the cage representation in the hand’s configuration space appear as critical points of the inter-finger distance function in contact space. Second, these critical points can be graphically characterized directly on the object’s boundary. Third, contact space admits a natural rectangular decomposition such that all critical points lie on the rectangle boundaries, and the sublevel sets of contact space and free space are topologically equivalent. These properties lead to a caging graph that can be readily constructed in contact space. Starting from a desired immobilizing grasp of a polygonal object, the caging graph is searched for the minimal, intermediate, and maximal caging regions surrounding the immobilizing grasp. An example constructed from real-world data illustrates and validates the method.
A second algorithm is developed for finding caging formations of a 3D polyhedron for two point fingers using a lower dimensional contact-space formulation. Results from the two-dimensional algorithm are extended to three dimension. Critical points of the inter-finger distance function are shown to be identical to the critical points of the cage. A decomposition of contact space into 4D regions having useful properties is demonstrated. A geometric analysis of the critical points of the inter-finger distance function results in a catalog of grasps in which the cages change topology, leading to a simple test to classify critical points. With these properties established, the search algorithm from the two-dimensional case may be applied to the three-dimensional problem. An implemented example demonstrates the method.
This thesis also presents a study of cages of convex polygonal objects using three point fingers. It considers a three-parameter model of the relative position of the fingers, which gives complete generality for three point fingers in the plane. It analyzes robustness of caging grasps to variations in the relative position of the fingers without breaking the cage. Using a simple decomposition of free space around the polygon, we present an algorithm which gives all caging placements of the fingers and a characterization of the robustness of these cages.