DOCSLIB.ORG

HETEROLEPTIC PADDLEWHEEL COMPLEXES and MOLECULAR ASSEMBLIES of DIMOLYBDENUM and DITUNGSTEN: a Study of Electronic and Structural Control

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
HETEROLEPTIC PADDLEWHEEL COMPLEXES and MOLECULAR ASSEMBLIES of DIMOLYBDENUM and DITUNGSTEN: a Study of Electronic and Structural Control HETEROLEPTIC PADDLEWHEEL COMPLEXES AND MOLECULAR ASSEMBLIES OF DIMOLYBDENUM AND DITUNGSTEN: A Study of Electronic and Structural Control DISSERTATION Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University By DOUGLAS J. BROWN, B.S., M.S. ***** The Ohio State University 2006 Dissertation Committee: Approved by Professor MALCOLM H. CHISHOLM, Advisor Professor CLAUDIA TURRO _________________________________ Professor CHRISTOPHER M. HADAD Advisor Graduate Program in Chemistry ABSTRACT Molybdenum and tungsten have a rich chemistry in quadruply-bonded paddlewheel complexes that are very similar in many ways, yet significantly different in other ways. Details and findings from Density Functional Theory studies of homoleptic and heteroleptic ligand complexes as well as simple pairs of dimers linked by a bifunctional oxalate bridge are discussed. Special interest is given to metal-to-ligand interactions in paddlewheel complexes and metal-to-bridge interactions in simple pairs of dimers. Computational studies provide great insight, reliable explanations, and qualitative predictions of physicochemical properties. A new series of dimolybdenum and ditungsten paddlewheel complexes with i i mixed amidinate-carboxylate ligands of the form trans-M2(O2CCH3)2( PrNC(R)N Pr)2 where M = Mo, W and R = Me, C≡CtBu, C≡CPh, or C≡CFc have been synthesized and characterized with the exception of the tungsten complex where R = Me. The synthesis of a series of complexes with each metal allowed for the analysis and comparison of molecular structural features, spectroscopic properties, and electrochemical behavior. The dinuclear centers exhibit redox chemistry which is dependent upon the nature of the ancillary ligand, and the electrochemical properties can be tuned through ligand ii modifications. DFT calculations on model complexes are used to help assign observable UV-vis absorptions and electrochemical redox behavior. The use of amidate complexes of the form M2(mhp)4, where M = Mo, W and mhp is the anion of 2-hydroxy-6-methylpyridine, as building blocks in simple molecular assemblies including simple pairs of dimers and molecular squares is also explored. Metathesis reactions employing solvento derivatives of Mo2(mhp)4 and attempts to prepare solvento derivatives of W2(mhp)4 are discussed. For simple pairs of dimers, the cooperative effect of linkers to electronically couple dimetal units is observed through electrochemistry. Finally, the preliminary findings of using the unique trans-geometry of mixed amidinate-carboxylate complexes to construct metallated conjugated oligomers or polymers when linked by a bifunctional bridge is explored. MALDI-TOF mass spectrometry was useful in resolving both the type and the number of species present. Based on solubility, only higher order assemblies are formed rather than true metallated conjugated polymers. iii Dedicated to my family iv ACKNOWLEDGMENTS I would like to first thank The Ohio State University for affording me a great education. The faculty and staff in the chemistry department were always professional and helpful. There are four individuals I would like to specifically acknowledge. Professor Bruce Bursten encouraged and paved the way for me to pursue a Ph.D. in Columbus. My advisor, Professor Malcolm Chisholm, has given me a firm foundation in chemistry. His expertise is well recognized and I am grateful for all that he has passed on to me. Professor Christopher Hadad and Dr. Judith Gallucci have given me priceless advice and assistance in computational chemistry and crystallography, respectively. In the Chisholm group, I have had the privilege to work with many talented chemists over the past four years. I have learned a great deal from Dr. Matthew Byrnes, Dr. Nathan Patmore, Dr. Florian Feil and Dr. Ramkrishna Ramnauth. They have helped me hone my synthetic skills, and I am forever grateful. I would like to thank all of the remaining Chisholm group members, past and present. Those before me have laid a strong foundation that helped focus my efforts. For those that I have worked with, I have enjoyed our time together and have truly learned something from everyone. As each of you start out your chemistry careers, I wish you the best and much success. v Thanks to Professor Thomas Bitterwolf for encouraging me to become a chemist over 20 years ago and Professor Joyce Shade, my first research advisor, who has been a true mentor and friend since the beginning. Her belief in me has been invaluable. I would also like to recognize the United States Naval Academy who afforded me many career and educational opportunities including this one. Finally, I would like to acknowledge the people closest to me. I thank my parents in general for their help and encouragement. I would like to thank my beautiful wife Suzanne and our children Rachael and Matthew for making all my dreams possible and worthwhile. vi VITA July 26, 1961. Born – Orlando, Florida 1984. B.S. in Chemistry United States Naval Academy 1991. M.S. in Business Rennselear Polytehnical Institute 2002 – Present . Graduate Research Asst. The Ohio State University PUBLICATIONS Research Publications 1. Berry, A. D., Brown, D. J., Kaplan, R., Cukauskas, E. J. “Ru and Os film deposition from metal carbonyls”, J. Vac. Sci. Technol. A 1986, 4, 215. FIELDS OF STUDY Major Field: Chemistry Division: Inorganic vii TABLE OF CONTENTS P a g e Abstract . ii Dedication . iv Acknowledgments . v Vita . vii List of Schemes . xiii List of Tables . xiv List of Figures . xiv List of Abbreviations . xxi Chapters: 1. Introduction . 1 1.1 The discovery of the metal-metal multiple bonds . 1 1.2 Structural motifs . 1 1.3 Dimolybdenum and ditungsten tetracarboxylate compounds . 2 1.3.1 The quadruple bond . 3 1.3.2 M2 manifold . 4 1.3.3 Tungsten vs molybdenum . 5 1.3.4 General synthesis . 7 1.3.5 Substitutional chemistry . 8 1.3.6 Electronic absorptions . 9 1.3.7 Physical properties . 10 1.3.8 Other ancillary ligands . 12 1.3.9 Mixed ligands . 15 viii 1.4 Simple pairs of dimers . 15 1.4.1 General synthesis . 16 1.4.2 Metal-bridge interaction . 17 1.4.3 Electronic coupling . 18 1.4.4 Typical bridges . 19 1.5 Mixed valence species . 20 1.5.1 Robin-Day Classification . 21 1.5.2 Electrochemistry . 22 1.5.3 UV-vis spectroscopy . 24 1.5.3.1 OTTLE cell . 29 1.5.4 EPR spectroscopy . 31 1.5.5 Superexchange . 34 1.6 Molecular wires . 35 1.7 Molecular assemblies . 36 1.8 Statement of purpose . 38 1.9 References . 40 2. Density Functional Theory (DFT) Study of Paddlewheel Complexes and Bridged Dimers . 43 2.1 Introduction . 43 2.2 Computational methodology . 44 2.3 Benchmarking . 45 2.4 Homoleptic paddlewheel complexes . 47 2.4.1 M2 manifold . 47 2.4.2 µ-bridging ligands . 49 2.4.3 Ligand π system . 49 2.4.4 Symmetry-allowed linear combinations . 50 2.4.5 Metal-ligand interaction . 52 2.4.6 Ligand effects . 54 2.5 Predicting heteroleptic paddlewheel properties . 57 2.5.1 Optimized geometry . 60 2.5.2 Molecular orbitals . 61 2.5.3 Ionization potentials . 63 2.5.4 UV-vis calculations . 64 2.5.5 Additional calculations . 65 2.6 Bridged Dimers . .66 2.6.1 [M2]2 manifold . 66 2.6.2 Oxalate π system . 66 2.6.3 Metal-bridge interaction . ..
Load more

Recommended publications
  • Evaluation of Gaussian Molecular Integrals I
    The Mathematica® Journal Evaluation of Gaussian Molecular Integrals I. Overlap Integrals Minhhuy Hô Julio Manuel Hernández-Pérez This article discusses the evaluation of molecular overlap integrals for Gaussian-type functions with arbitrary angular dependence. As an example, we calculate the overlap matrix for the water molecule in the STO-3G basis set. ‡ Introduction Computational quantum chemistry makes extensive use of various integrals (and their derivatives) of the general form [1, 2, 3] ¶ ‡ caHrL O cbHrL dr, (1) -¶ where caHrL is an unnormalized Cartesian Gaussian function centered at A = 9Ax, Ay, Az=: 2 ax ay az -a r-A caHr; a, A, aL = Hx - AxL Iy - AyM Hz - AzL e , (2) where A is normally taken at the nucleus, a is the orbital exponent, and the polynomial rep- resents the angular part, in that the sum of the Cartesian angular momenta ax + ay + az = 0, 1, 2, … corresponds to functions of type s, p, d, f, …. When the operator O is 1, one simply has the overlap/density integral; otherwise it can be the energy operator for kinetic energy - 1 2, electron-nuclear attraction r - R -1, or electron-electron 2 ! -1 repulsion ri - rj (which would involve double integrals). Other molecular properties involving external fields (response functions) or transition moments can also be computed from integrals of this form. The Mathematica Journal 14 © 2012 Wolfram Media, Inc. 2 Minhhuy Hô and Julio Manuel Hernández-Pérez · Gaussian-Type Functions Gaussian-type functions are not the most natural choice for expanding the wavefunction. Slater-type functions, where the exponent is -a r - A instead, can describe atomic systems more realistically.
    [Show full text]
  • Orbital Exchange Calculations: an Alternative View of the Chemical Bond Paul B
    Orbital Exchange Calculations: An Alternative View of the Chemical Bond Paul B. Merrithewa PO Box 120, Amherst, New Hampshire 03031-0120 USA Abstract The purpose of this paper is to explore a model of the chemical bond which does not assume that the electrons of the chemical bonding electron pair can be unambiguously identified with either the left hand or right hand of the bonding atoms when their orbitals overlap to bond. In order to provide maximum flexibility in the selection of the electron’s orbitals, the orbitals have been represented as spatial arrays and the calculations performed numerically. This model of the chemical bond assumes that the identifiability of the bonding electrons is a function of 1-(overlap/(1+overlap)) where the overlap of the two bonding electron’s orbitals is calculated in the usual manner. The kinetic energy of the bonding electron pair and the energy required to meet the orthogonality requirements, mandated by the Pauli principle, are a function of overlap/(1+overlap). The model assumes that the bonding orbitals are straight-forward atomic orbitals or hybrids of these atomic orbitals. The results obtained by applying this simple approach to eleven di-atomics and seven common poly-atomics are quite good. The calculated bond lengths are generally within 0.005Å of the measured values and bond energies to within a few percent. Bond lengths for bonds to H are about 0.02 Å high. Except for H2, bond lengths are determined, independent of bond energy, at that point where overlap/(1+overlap) equals 0.5. I. INTRODUCTION The purpose of the work described here is to test a model for the chemical bond that assumes that the two electrons of the bonding pair are not completely identifiable, with respect to their source atom, when their orbitals overlap.
    [Show full text]
  • Chapter 1: Electronic Structure and Bonding a Brief Review of General Chemistry
    Chapter 1: Electronic Structure and Bonding Or A Brief Review of General Chemistry Part 2: Quantum Mechanics and Molecular Orbital Theory Review ideas from general chemistry: atoms, bonds, molecular geometry Hybrid Orbitals of Ethene, C2H4 Bonding in Ethene (Ethylene): A Double Bond The sigma bond is unaffected by rotation of one of the CH2 groups. The overlap of the p orbitals is disrupted by rotation of one of the CH2 groups. This would cause the double bond to break. Hybrid Orbitals of Ethene, C2H4 An sp2-Hybridized Carbon - The bond angle in the sp2 carbon is 120°. The sp2 carbon is the trigonal planar carbon. Molecular Orbital Theory So let’s look at Ethyne (Acetylene) . Draw a Lewis Dot Structure for Ethyne Hybrid Orbitals of Ethyne, C2H2 Bonding in Ethyne (Acetylene) : A Triple Bond A triple bond consists of one s bond and two p bonds. Bond angle of the sp carbon: 180°. Molecular Orbital Theory + - + Molecular Orbital Theory Summary The sharing of one pair of electrons is a single bond. The sharing of two pairs gives a double bond. The sharing of three pairs gives a triple bond. The greater the electron density in the region of orbital overlap, the stronger the bond. The more s character, the shorter and stronger is the bond. The more s character, the larger is the bond angle. A bond is weaker than a bond. Hybridization of Nitrogen and Oxygen Elements other than C can have hybridized orbitals H–N–H bond angle in ammonia (NH3) 107.3° C-N-H bond angle is 110.3 ° N’s orbitals (sppp) hybridize to form four sp3 orbitals One sp3 orbital is occupied by two nonbonding electrons, and three sp3 orbitals have one electron each, forming bonds to H and CH3.
    [Show full text]
  • Electronic Structure of Epitaxial Interfaces
    Pramana - J. Phys., Vol. 38, No. 6, June 1992, pp. 545-639. © Printed in India. Electronic structure of epitaxial interfaces G P DAS Solid State Physics Division, Bhabha Atomic Research Centre, Bombay 400085, India MS received I0 October 1991; revised 2 April 1992 Abstract. Metal-semiconductor (Schottky barrier) and semiconductor-semiconductor (hetero- junction) interfaces show rectifying barrier heights and band offsets, which are two key quantities required to optimize the performance of a device. A large number of models and empirical theories have been put forward by various workers in the field during the last 50 years. But a proper understanding of the microscopic origin of these quantities is still missing. In this article, our focus is mainly to present a unified framework for first principles investigation of the electronic structure of epitaxial interfaces, in which one of the constituents is a semiconductor. LMTO method is now a well established tool for self-consistent electronic structure calculations of solids within LDA. Such calculations, when performed on supercell geometries, are quite successful in predicting a wide range of interface specific electronic properties accurately and elBciently. We describe here the basic formalism of this LMTO- supercell approach in its various levels of sophistication and apply it to investigate the electronic structure of A- and B-type NiSi2/Si(lll) interface as a prototype metal- semiconductor system, and CaF2/Si(I I 1) interface as a prototype insulator-semiconductor system. These are a few of the most ideal lattice matched epitaxial interfaces whose atomic and electronic structures have been extensively studied using a wide range of experimental probes.
    [Show full text]
  • Chemical Bond Analysis in the Ten-Electron Series
    Department of Physics, Chemistry and Biology Bachelor’s Thesis Chemical bond analysis in the ten-electron series Thomas Fransson LITH-IFM-G-EX–09/2112–SE Department of Physics, Chemistry and Biology Link¨opings universitet, SE-581 83 Link¨oping, Sweden Bachelor’s Thesis LITH-IFM-G-EX–09/2112–SE Chemical bond analysis in the ten-electron series Thomas Fransson Adviser: Patrick Norman IFM Examiner: Patrick Norman IFM Link¨oping, 4 June, 2009 Avdelning, Institution Datum Division, Department Date Computational Physics 2009-06-04 Department of Physics, Chemistry and Biology Link¨opings universitet, SE-581 83 Link¨oping, Sweden Spr˚ak Rapporttyp ISBN Language Report category — Svenska/Swedish Licentiatavhandling ISRN ⊠ ⊠ Engelska/English Examensarbete LITH-IFM-G-EX–09/2112–SE C-uppsats Serietitel och serienummer ISSN D-uppsats Title of series, numbering Ovrig¨ rapport — URL f¨or elektronisk version Titel Title Chemical bond analysis in the ten-electron series F¨orfattare Thomas Fransson Author Sammanfattning Abstract This thesis presents briefly the application of quantum mechanics on systems of chemical interest, i.e., the field of quantum chemistry and computational chem- istry. The molecules of the ten-electron series, hydrogen fluoride, water, ammonia, methane and neon, are taken as computational examples. Some applications of quantum chemistry are then shown on these systems, with emphasis on the na- ture of the molecular bonds. Conceptual methods of chemistry and theoretical chemistry for these systems are shown to be valid with some restrictions, as these interpretations does not represent physically measurable entities. The orbitals and orbital energies of neon is studied, the binding van der Waals- interaction resulting in a Ne2 molecule is studied with a theoretical bond length of 3.23 A˚ and dissociation energy of 81.75 µEh.
    [Show full text]
  • Indian Institute of Science Education and Research
    INDIAN INSTITUTE OF SCIENCE EDUCATION AND RESEARCH THIRUVANANTHAPURAM An autonomous institution under the Ministry of Human Resource Development, Government of India CURRICULUM AND SYLLABUS FOR THE INTEGRATED Ph. D. PROGRAMME Contents Structure .................................................1 School of Biology Curriculum...........................1 School of Chemistry Curriculum.........................2 School of Mathematics Curriculum.......................3 School of Physics Curriculum............................4 Biology Syllabus...........................................5 Theory Courses........................................6 Laboratory Courses..................................... 17 Chemistry Syllabus ........................................ 21 Theory Courses........................................ 22 Laboratory Courses..................................... 40 Mathematics Syllabus ...................................... 47 Physics Syllabus ........................................... 61 Theory Courses........................................ 61 Laboratory Courses..................................... 73 v Structure School of Biology Curriculum SCHOOL OF BIOLOGY CURRICULUM Semester –I Semester -II Course Course Name L T P C Course Course Name L T P C BIO 311 Microbiology 3 0 0 3 BIO 321 Structural Biology 3 0 0 3 BIO 312 Advanced Genetics 3 0 0 3 BIO 322 Immunology 3 0 0 3 and Genomics BIO 313 Physiology 3 0 0 3 BIO 323 Cell Biology 3 0 0 3 BIO 314 Biochemistry 3 0 0 3 BIO 324 Molecular Biology 3 0 0 3 BIO 315 Advanced Biology 0 0
    [Show full text]
  • Chapter 5 Molecular Orbitals
    Chapter 5 Molecular Orbitals Molecular orbital theory uses group theory to describe the bonding in molecules ; it comple- ments and extends the introductory bonding models in Chapter 3 . In molecular orbital theory the symmetry properties and relative energies of atomic orbitals determine how these orbitals interact to form molecular orbitals. The molecular orbitals are then occupied by the available electrons according to the same rules used for atomic orbitals as described in Sections 2.2.3 and 2.2.4 . The total energy of the electrons in the molecular orbitals is compared with the initial total energy of electrons in the atomic orbitals. If the total energy of the electrons in the molecular orbitals is less than in the atomic orbitals, the molecule is stable relative to the separate atoms; if not, the molecule is unstable and predicted not to form. We will first describe the bonding, or lack of it, in the first 10 homonuclear diatomic molecules ( H2 through Ne2 ) and then expand the discussion to heteronuclear diatomic molecules and molecules having more than two atoms. A less rigorous pictorial approach is adequate to describe bonding in many small mole- cules and can provide clues to more complete descriptions of bonding in larger ones. A more elaborate approach, based on symmetry and employing group theory, is essential to under- stand orbital interactions in more complex molecular structures. In this chapter, we describe the pictorial approach and develop the symmetry methodology required for complex cases. 5.1 Formation of Molecular Orbitals from Atomic Orbitals As with atomic orbitals, Schrödinger equations can be written for electrons in molecules.
    [Show full text]
  • 5.61 F17 Lecture 26: Qualitative Molecular Orbital Theory
    MASSACHUSETTS INSTITUTE OF TECHNOLOGY 5.61 Physical Chemistry I Fall, 2017 Professor Robert W. Field Lecture 26: Qualitative Molecular Orbital Theory: Huc¨ kel Theory Models in Physical Chemistry Our job is to make models that are intentionally as simple as possible. We do this to develop intuition. Often the models are obviously too crude to be quantitatively correct. But our goal is to find a model that is qualitatively in agreement with a large body of experimental and theoretical results. And then we try to find examples that break the model! This is where new insights are generated. + LCAO{MO Theory applied to H2 , H2, AH, A2, AB diatomic molecules in 5.61 has been entirely qualitative. We attempt to use insights about atomic properties as embodied in the Periodic Table to explain molecular properties. A key property is orbital size, based on hydrogen atom properties. hc< I = n n?2 ?2 hc< rn∗ = a0n = a0 In Atomic Orbital sizes, orbital energies, and non{degenerate perturbation theory generate enormous insights into the electronic properties of the valence states of diatomic molecules. From diatomic molecules we have confidence to move to larger molecules, based on the di- atomic molecule{like properties of \chromophores". A chromophore is a small group of atoms in a molecule identified by LCAO-MO Theory as having a dominant role in determining a particular molecular property. The next step is to develop a semi-quantitative model that starts with planar conjugated polyatomic molecules. This model exploits the variational method to generate molecular energy levels and wavefunctions. But the model, H¨uckel Theory, is based on shocking sim- plifications.
    [Show full text]
  • Orbital Overlap As a Tool in Computational Design of Molecules
    ORBITAL OVERLAP AS A TOOL IN COMPUTATIONAL DESIGN OF MOLECULES by STEPHANIE ING JONES Bachelors of Science, 2014 California State University, Los Angeles Los Angeles, California Submitted to the graduate faculty of the College of Science and Engineering Texas Christian University in partial fulfillment of the requirements for the degree of Doctor of Philosophy May, 2019 Acknowledgement I’m extremely grateful to Dr. Benjamin Janesko. The completion of my work here would not have been possible without his support. His unwavering guidance, insightful suggestions, constructive criticism, and extensive knowledge helped me grow in my abilities as a chemist and I could never thank him enough for his efforts. I would like to express my deepest appreciation to my committee- Drs. Eric Simanek, Onofrio Annunziata, and Thomas Cundari. Their invaluable advice on my research has challenged me to think beyond the scope of my knowledge. I’m deeply indebted to my colleague, Arshad Mehmood, who I have done collaborative research with. His work ethic and ever-patient character eased the difficulty of tackling the exhaustive tools/theories used in computational chemistry. He helped me grow as an individual and has taught me a lot. I’d also like to extend my gratitude to the other members of the Janesko Group- Drs. Mark Bridle, Emil Proynov and Andrew Mahler, for helping in my understanding of quantum chemistry. I’m extremely grateful for my family, who supported me throughout this journey. My parents, who encouraged me to pursue a PhD and my father in law, Dr. Jack Yu, who helped me grow in my knowledge in biochemistry.
    [Show full text]
  • Electron Correlation in Diatomic Molecules: Exchange Integrals And
    Iowa State University Capstones, Theses and Retrospective Theses and Dissertations Dissertations 1968 Electron correlation in diatomic molecules: exchange integrals and separated pair calculations on lithium hydride and boron hydride Ernest Louis Mehler Iowa State University Follow this and additional works at: https://lib.dr.iastate.edu/rtd Part of the Physical Chemistry Commons Recommended Citation Mehler, Ernest Louis, "Electron correlation in diatomic molecules: exchange integrals and separated pair calculations on lithium hydride and boron hydride " (1968). Retrospective Theses and Dissertations. 3495. https://lib.dr.iastate.edu/rtd/3495 This Dissertation is brought to you for free and open access by the Iowa State University Capstones, Theses and Dissertations at Iowa State University Digital Repository. It has been accepted for inclusion in Retrospective Theses and Dissertations by an authorized administrator of Iowa State University Digital Repository. For more information, please contact [email protected]. This dissertation has been miciofilnied exactly as received 69-4262 MEHLER, Ernest Louis, 1938- ELECTRON CORRELATION IN DIATOMIC MOLECULES: EXCHANGE INTEGRALS AND SEPARATED PAIR CALCULATIONS ON LITHIUM HYDRIDE AND BORON HYDRIDE. Iowa State University, Ph.D., 1968 Chemistry, physical University Microfilms, Inc., Ann Arbor, Michigan ELECTRON CORRELATION IN DIATOMIC MOLECULES: EXCHANGE INTEGRALS AND SEPARATED PAIR CALCULATIONS ON LITHIUM HYDRIDE AND BORON HYDRIDE by Ernest Louis Mehler A Dissertation Submitted to the Graduate Faculty In Partial Fulfillment of The Requirements for the Degree of DOCTOR OF PHILOSOPHY Major Subject: Physical Chemistry Approved: Signature was redacted for privacy. In Charge of Major Work Signature was redacted for privacy. Heéa r Major Depar tmen t Signature was redacted for privacy.
    [Show full text]
  • Physics/0610288
    An approximate method for calculating transfer integrals based on the ZINDO Hamiltonian James Kirkpatrick∗ Centre for Electronic Materials and Devices, Department of Physics, Imperial College London, Prince Consort Road, London SW7 2BW, U.K. (Dated: February 2, 2008) In this paper we discuss a method for calculating transfer integrals based on the ZINDO Hamil- tonian which requires only a single self consistent field on an isolated molecule to be performed in order to determine the transfer integral for a pair of molecules. This method is compared to results obtained by projection of the pair of molecules’ molecular orbitals onto the vector space defined by the molecular orbitals of each isolated molecule. The two methods are found to be in good agreement using three compounds as model systems: pentacene, ethylene and hexabenzocoronene. I. INTRODUCTION In a disordered material - such as a glass of small molecules or a conjugated polymer film- charge transport can be modeled as a series of discrete hops on an idealized lattice; rates are controlled by parameters distributed according to some empirical distribution chosen to fit the experimentally measured field and temperature dependence of mobility[1, 2, 3] . The fundamental mechanism underpinning charge transport in many disordered organic solids is thought to be small polaron hopping, which - in the high temperature limit - can be described by the Marcus Equation [4]: |J|2 π (∆E − λ)2 exp(− ) (1) ~ rλkT 4λkT where J represents the transfer integral, ∆E represents the difference in site energies,
    [Show full text]
  • Molecular Orbital and Valence Bond Theory
    MOLECULAR ORBITAL AND VALENCE BOND THEORY Quantum Mechanics is a very difficult topic, with a great deal of detail that is extremely complex, yet interesting. However, in this Chemistry Class we only need to understand certain key aspects of Quantum Mechanics as applied to electronic theory. What follows is an outline of many of the important concepts, color coded to help you. The statements in red are items you need to know. Items in black are for your information, but it is not essential that you know them. Items in purple describe what you need to be able to do, namely describe organic molecules in terms of overlap of hybridized orbitals. Keep this in mind as you go through the following. QUANTUM OR WAVE MECHANICS Electrons have certain properties of particles and certain properties of waves. Electrons have mass and charge like particles. Because they are so small and are moving so fast, electrons have no defined position. Their location is best described by wave mechanics (i.e. a three-dimensional wave) and a wave equation called the Schrödinger equation. Solutions of the Schrödinger equation are called wave functions and are represented by the Greek letter psi. Each wave function describes a different orbital. The sign of the wave function can change from positive (+) to negative (-) in different parts of the same orbital. This is analogous to the way that waves can have positive or negative amplitudes. The sign of the wave function does not indicate anything about charge. [This can be confusing. Make sure that you understand it before you go on.] The value of the square of the wave function is proportional to the probability of finding electron density at a given point in an orbital.
    [Show full text]