University of California Santa Barbara Applications of Computational Quantum Mechanics A dissertation submitted in partial satisfaction of the requirements for the degree of Doctor of Philosophy in Chemistry by Burçin Temel Committee in charge: Professor Horia Metiu, Chair Professor Joan-Emma Shea Professor Steven K. Buratto Professor Bernard Kirtman September 2006 UMI Number: 3233007 3233007 2006 UMI Microform Copyright All rights reserved. This microform edition is protected against unauthorized copying under Title 17, United States Code. ProQuest Information and Learning Company 300 North Zeeb Road P.O. Box 1346 Ann Arbor, MI 48106-1346 by ProQuest Information and Learning Company. The dissertation of Burçin Temel is approved. ____________________________________________ Joan-Emma Shea ____________________________________________ Steven K. Buratto ____________________________________________ Bernard Kirtman ____________________________________________ Horia Metiu, Committee Chair August 2006 iii Applications of Computational Quantum Mechanics Copyright © 2006 by Burçin Temel iv This thesis is dedicated to the two dearest people in my life: My mom Ayla and my grandma Mahmure. v ACKNOWLEDGEMENTS I would like to thank my advisor Professor Horia Metiu for his guidance and support throughout my graduate study. Being his student not only contributed to my scientific knowledge a lot but also to my personal character, work discipline, ethics and professionalism. With his enormous knowledge on everything one can imagine in chemistry and physics, Horia taught me how to stand up and defend my opinions, how to question every small detail and not to take anything for granted. His perfectionism, eventhough made me suffer time to time, at the end it allowed me to gain high scientific standards. I can say that I really enjoyed my 5 years in Santa Barbara, I do not only mean weather and beach but also the fun company with great friends. A lot of thanks: To Brandon McKenna for his ever ending tries to make me feel happy, especially during those down times of a Ph.D. student, and to Lauren Aubin, Steeve Chretien and Andrij Baumketner for their always exciting and joyful friendship. Also, I would like to express my gratuity to: Greg Mills, with whom I had great discussions on the projects we worked together. Celia Wrathall for helping me with every official document I had to fill in. Paul Weakliem for the computational support. Jane and Horia Metiu for the great two summers we spent together in Berlin, Germany, and for vi their kind invitations and support in Santa Barbara that assured my parents that I was in good hands here. Finally, thanks: to Prof. Eric McFarland for allowing a theoretician to go into his lab and start doing experiments, to Prof. Brad Chmelka for valuable conversations, and to Prof. Matthias Scheffler for his hospitality at Fritz-Haber Institute (Berlin, Germany). vii VITA OF BURÇÍN TEMEL August 2006 EDUCATION • Doctor of Philosophy, Chemistry University of California Santa Barbara, CA, August 2006 (anticipated) Thesis title: “Applications of computational quantum mechanics”. • Bachelor of Science, Chemistry Bilkent University, Ankara, Turkey, June 2001 AWARDS & SCHOLARSHIPS • Full Scholarship Award University of California, Santa Barbara, 2001-2006 • Presidential Work-Study Research Grant University of California, Santa Barbara, 2001-2004 • Full Scholarship Award Bilkent University, 1997-2001 RESEARCH EXPERIENCE THEORETICAL University of California, Santa Barbara Graduate Researcher, Chemistry and Biochemistry Department, 2001-present with Prof. Horia Metiu • Currently, using both experimental and theoretical techniques (DFT, solid state calculations) to study the heterogeneous catalysis of methanol to olefins. (Collaboration with Prof. Eric McFarland) • Studied the phenomenological kinetics and the kinetic Monte Carlo approaches for CO oxidation on RuO 2 (110) surface. Obtained the phase diagrams and found viii the most catalytically active states. (Collaboration with Prof. Matthias Scheffler, Fritz-Haber Institute, Berlin, Germany) • Used different numerical techniques (iterative and matrix methods) to solve quantum mechanics problems by time-dependent and time-independent approaches. • Applied these fast and accurate numerical techniques to calculate elastic and inelastic phase-shifts and resonances in time-independent scattering theory. • Developed a new basis set method using Chebyshev polynomials to solve non-periodic boundary value problems fast and accurately. • Studied photoexcited semiconductor-liquid interfaces to investigate the factors that affect the charge separation in the semiconductor. Proposed to utilize time-dependent Density Functional Theory to learn more about the charge dynamics at the interface. Fritz-Haber Institute, Berlin, Germany Visiting Graduate Researcher, Theory Department, July-Aug.2005 with Prof. Matthias Scheffler • Rate theory for CO oxidation on RuO 2 surface. Bilkent University, Ankara, Turkey Undergraduate Researcher, Chemistry Department, 2000-2001 with Prof. Ulrike Salzner • Designed conjugated polymer semiconductors and computed their band gaps with Density Functional Theory. Max-Planck Institute, Frankfurt, Germany Visiting Undergraduate Researcher, Theoretical Biophysics Department, July-Sept.2000 with Prof. Volkhard Helms • Studied quantum chemistry of isotopic substitution effects on vibrational IR frequencies of common organic groups. ix EXPERIMENTAL University of California, Santa Barbara Graduate Researcher, Chemistry and Biochemistry Department, January 2006-present with Prof. Horia Metiu and Prof. Eric McFarland • Currently, using both experimental (material synthesis, characterization, heterogeneous catalytic reactions, MS, GC, IR) and theoretical techniques (DFT, solid state calculations) to study the heterogeneous catalysis of methanol to olefins. Bilkent University, Ankara, Turkey Undergraduate Researcher, Chemistry Department, June-July 1999 with Prof. Omer Dag • Characterized inorganic metal complexes with UV and IR spectroscopy techniques. Ministry of Environment, Ankara, Turkey Summer Intern, Golbasi Research Lab., August 1999 • Used analytical methods such as HPLC, GC, MS, Ion Chromatography, separation, purification to characterize molecules. PUBLICATIONS & PRESENTATIONS 1. Temel, B.; Mills, G.; Metiu, H. “Time-independent potential scattering with variational methods.” (submitted to Journal of Physical Chemistry A). 2. Temel, B.; Mills, G.; Metiu, H. “Inelastic scattering with Chebyshev polynomials.” (to be submitted). 3. Temel, B.; Reuter, K.; Metiu, H.; Scheffler, M. “First-principles kinetic Monte Carlo simulations for heterogeneous catalysis versus meanfield rate theory.” (to be submitted). 4. Mills, G.; Wang, B.; Temel, B.; Metiu, H. “Chebyshev polynomials for quantum mechanical problems (bound states).” (to be submitted) [...]... structural properties of these particles Discovery of the quarks by inelastic electron-nucleon scattering experiments has been one of the most exciting structural investigations of the last century Scattering is a dynamic event: it provides details on the (1) types of forces between the particles hence structures, (2) chemical 2 dynamics information in the case of reactive scattering of the molecules,... to laser systems Figure 1: Schematic drawing of a scattering process The result of a scattering experiment (see Figure 1) is usually expressed in terms of cross sections Cross sections are defined as: number of events per unit time and per unit scatterer divided by the relative flux of the incident particles.1,2 Therefore, it is equal to the outgoing flux of particles scattered through the spherical... look for the solutions of δ J = 0 that depend on a number of variational parameters {c1 , c2 , , cn } Then, the functional J becomes a function of these variational parameters J ( c1 , c2 , , cn ) The stationary property of the functional yields a system of equations ∂J = 0 to ∂ci o o determine the optimum variational parameters: {c1o , c2 , , cn } to give the true minimum of the functional J The... nearest neighbors) not with the product of their coverages Using the product assumes a perfect and rapid mixing of the reactants, and the lack of spatial inhomogeneity in the distribution of reactants on the surface In most catalytic reactions this may not be the case The interaction between the adsorbed molecules can lead to segregation into domains of mostly one kind of molecules Even if this does not... provides the evolution of the system out of equilibrium, in real time (not in number of Monte Carlo moves) Different methods of implementation differ mainly in their efficiency and in the complexity of the events taken into account The KMC method solves exactly the rate equations for the events included in the model When performed properly, kinetic Monte Carlo simulations do not have any of the shortcomings... small number of molecules Practical catalytic research and much of surface science uses phenomenological rate equations, in which the reaction rate is proportional to the concentration of the reactants One proposes a mechanism, writes the corresponding rate equations and varies the rate constants to fit the data Very often the fitting is rather good and this is taken as a confirmation of the proposed... Advance Quantum Chemistry, Molecular Spectroscopy, Density Functional Theory, Non-linear Statistical Mechanics (stochastic phenomena) EXPERIMENTAL • Materials synthesis (sol-gel), characterization; X-ray diffraction (XRD), surface area and pore size analysis (BET), heterogeneous catalytic reactions, mass spectrometry (MS), gas chromatography (GC), infrared spectroscopy (IR) xi ABSTRACT Applications of Computational. .. the spherical Bessel functions: yl ( r ) = k r jl ( k r ) (14) The asymptotic form of yl ( r ) is given as lπ ⎞ ⎛ k r jl ( k r ) ⎯⎯⎯ Sin ⎜ k r − ⎟ → r →∞ 2 ⎠ ⎝ (15) Therefore, this demonstrates that the effect of U ( r ) in the radial equation is to introduce a shift in the phase of the l th scattered wave in the amount of nl (assuming A = 1 ) Then the scattering amplitude becomes: f (Ω) = 1 ∞ ∑ ( 2l... for a new class of catalysts: doped metal oxides Bibliography: (1) Joachain, C J Quantum Collision Theory, 3rd ed.; Elsevier Science Publishers: Amsterdam, 1983 (2) Mott, N F.; Massey, H S The Theory of Atomic Collisons, Third ed.; Clarendon Press: Oxford, 1965 (3) Burke, P Potential Scattering in Atomic Physics; Plenum: New York, 1977 (4) Demkov, Y N Variational Principles in the Theory of Collisions;... thereof; Patent, U S., Ed.; Haldor Topsoe A/S (DK), 1988 (17) Jorgen, T.-J Process for the preparation of catalysts for use in ether synthesis; Patent, U S., Ed.; Haldor Topsoe A/S (DK), 1985 (18) Bjorgen, M.; Olsbye, U.; Kolboe, S Journal Of Catalysis 2003, 215, 30 (19) Chen, D.; Moljord, K.; Fuglerud, T.; Holmen, A Microporous And Mesoporous Materials 1999, 29, 191 (20) Dahl, I M.; Kolboe, S Journal Of . University of California Santa Barbara Applications of Computational Quantum Mechanics A dissertation submitted in partial satisfaction of the requirements for the degree of Doctor of Philosophy. vii VITA OF BURÇÍN TEMEL August 2006 EDUCATION • Doctor of Philosophy, Chemistry University of California Santa Barbara, CA, August 2006 (anticipated) Thesis title: Applications of computational. spectroscopy (IR). xii ABSTRACT Applications of Computational Quantum Mechanics by Burçin Temel This original research dissertation is composed of a new numerical technique based