Outline of Crystal Field Theory Bums, R
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CHEM 250 (4 Credits): Reactions of Nucleophiles and Electrophiles (Reactivity 1)
CHEM 250 (4 credits): Reactions of Nucleophiles and Electrophiles (Reactivity 1): Description: This course investigates fundamental carbonyl reactivity (addition and substitution) in understanding organic, inorganic and biochemical processes. Some emphasis is placed on enthalpy, entropy and free energy as a basis of understanding reactivity. An understanding of chemical reactivity is based on principles of Lewis acidity and basicity. The formation, stability and reactivity of coordination complexes are included. Together, these topics lead to an understanding of biochemical pathways such as glycolysis. Enzyme regulation and inhibition is discussed in the context of thermodynamics and mechanisms. Various applications of modern multi-disciplinary research will be explored. Prerequisite: CHEM 125. Course Goals and Objectives: 1. Students will gain a qualitative understanding of thermodynamics. A. Students will develop a qualitative understanding of enthalpy and entropy. B. Students will predict the sign of an entropy change for chemical or physical processes. C. Students will understand entropy effects such as the chelate effect on chemical reactions. D. Students will use bond enthalpies or pKas to determine the enthalpy change for a reaction. E. Students will draw or interpret a reaction progress diagram. F. Students will apply the Principle of Microscopic Reversibility to understand reaction mechanisms. G. Students will use Gibbs free energy to relate enthalpy and entropy changes. H. Students will develop a qualitative understanding of progress toward equilibrium under physiological conditions (the difference between G and Go.) I. Students will understand coupled reactions and how this can be used to drive a non- spontaneous reaction toward products. J. Students will apply LeChatelier’s Principle to affect the position of anequilibrium by adding or removing reactants or products. -
Symmetry of Fulleroids Stanislav Jendrol’, František Kardoš
Symmetry of Fulleroids Stanislav Jendrol’, František Kardoš To cite this version: Stanislav Jendrol’, František Kardoš. Symmetry of Fulleroids. Klaus D. Sattler. Handbook of Nanophysics: Clusters and Fullerenes, CRC Press, pp.28-1 - 28-13, 2010, 9781420075557. hal- 00966781 HAL Id: hal-00966781 https://hal.archives-ouvertes.fr/hal-00966781 Submitted on 27 Mar 2014 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Symmetry of Fulleroids Stanislav Jendrol’ and Frantiˇsek Kardoˇs Institute of Mathematics, Faculty of Science, P. J. Saf´arikˇ University, Koˇsice Jesenn´a5, 041 54 Koˇsice, Slovakia +421 908 175 621; +421 904 321 185 [email protected]; [email protected] Contents 1 Symmetry of Fulleroids 2 1.1 Convexpolyhedraandplanargraphs . .... 3 1.2 Polyhedral symmetries and graph automorphisms . ........ 4 1.3 Pointsymmetrygroups. 5 1.4 Localrestrictions ............................... .. 10 1.5 Symmetryoffullerenes . .. 11 1.6 Icosahedralfulleroids . .... 12 1.7 Subgroups of Ih ................................. 15 1.8 Fulleroids with multi-pentagonal faces . ......... 16 1.9 Fulleroids with octahedral, prismatic, or pyramidal symmetry ........ 19 1.10 (5, 7)-fulleroids .................................. 20 1 Chapter 1 Symmetry of Fulleroids One of the important features of the structure of molecules is the presence of symmetry elements. -
An Earlier Collection of These Notes in One PDF File
UNIVERSITY OF THE WEST INDIES MONA, JAMAICA Chemistry of the First Row Transition Metal Complexes C21J Inorganic Chemistry http://wwwchem.uwimona.edu.jm/courses/index.html Prof. R. J. Lancashire September 2005 Chemistry of the First Row Transition Metal Complexes. C21J Inorganic Chemistry 24 Lectures 2005/2006 1. Review of Crystal Field Theory. Crystal Field Stabilisation Energies: origin and effects on structures and thermodynamic properties. Introduction to Absorption Spectroscopy and Magnetism. The d1 case. Ligand Field Theory and evidence for the interaction of ligand orbitals with metal orbitals. 2. Spectroscopic properties of first row transition metal complexes. a) Electronic states of partly filled quantum levels. l, ml and s quantum numbers. Selection rules for electronic transitions. b) Splitting of the free ion energy levels in Octahedral and Tetrahedral complexes. Orgel and Tanabe-Sugano diagrams. c) Spectra of aquated metal ions. Factors affecting positions, intensities and shapes of absorption bands. 3. Magnetic Susceptibilities of first row transition metal complexes. a) Effect of orbital contributions arising from ground and excited states. b) Deviation from the spin-only approximation. c) Experimental determination of magnetic moments. Interpretation of data. 4. General properties (physical and chemical) of the 3d transition metals as a consequence of their electronic configuration. Periodic trends in stabilities of common oxidation states. Contrast between first-row elements and their heavier congeners. 5. A survey of the chemistry of some of the elements Ti....Cu, which will include the following topics: a) Occurrence, extraction, biological significance, reactions and uses b) Redox reactions, effects of pH on the simple aqua ions c) Simple oxides, halides and other simple binary compounds. -
Crystal Field Theory (CFT)
Crystal Field Theory (CFT) The bonding of transition metal complexes can be explained by two approaches: crystal field theory and molecular orbital theory. Molecular orbital theory takes a covalent approach, and considers the overlap of d-orbitals with orbitals on the ligands to form molecular orbitals; this is not covered on this site. Crystal field theory takes the ionic approach and considers the ligands as point charges around a central metal positive ion, ignoring any covalent interactions. The negative charge on the ligands is repelled by electrons in the d-orbitals of the metal. The orientation of the d orbitals with respect to the ligands around the central metal ion is important, and can be used to explain why the five d-orbitals are not degenerate (= at the same energy). Whether the d orbitals point along or in between the cartesian axes determines how the orbitals are split into groups of different energies. Why is it required? The valence bond approach could not explain the Electronic spectra, Magnetic moments, Reaction mechanisms of the complexes. Assumptions of CFT: 1. The central Metal cation is surrounded by ligand which contain one or more lone pair of electrons. 2. The ionic ligand (F-, Cl- etc.) are regarded as point charges and neutral molecules (H2O, NH3 etc.) as point dipoles. 3. The electrons of ligand does not enter metal orbital. Thus there is no orbital overlap takes place. 4. The bonding between metal and ligand is purely electrostatic i.e. only ionic interaction. The approach taken uses classical potential energy equations that take into account the attractive and repulsive interactions between charged particles (that is, Coulomb's Law interactions). -
Nobel Lecture, 8 December 1981 by ROALD HOFFMANN Department of Chemistry, Cornell University, Ithaca, N.Y
BUILDING BRIDGES BETWEEN INORGANIC AND ORGANIC CHEMISTRY Nobel lecture, 8 December 1981 by ROALD HOFFMANN Department of Chemistry, Cornell University, Ithaca, N.Y. 14853 R. B. Woodward, a supreme patterner of chaos, was one of my teachers. I dedicate this lecture to him, for it is our collaboration on orbital symmetry conservation, the electronic factors which govern the course of chemical reac- tions, which is recognized by half of the 1981 Nobel Prize in Chemistry. From Woodward I learned much: the significance of the experimental stimulus to theory, the craft of constructing explanations, the importance of aesthetics in science. I will try to show you how these characteristics of chemical theory may be applied to the construction of conceptual bridges between inorganic and organic chemistry. FRAGMENTS Chains, rings, substituents - those are the building blocks of the marvelous edifice of modern organic chemistry. Any hydrocarbon may be constructed on paper from methyl groups, CH 3, methylenes, CH 2, methynes, CH, and carbon atoms, C. By substitution and the introduction of heteroatoms all of the skeletons and functional groupings imaginable, from ethane to tetrodotoxin, may be obtained. The last thirty years have witnessed a remarkable renaissance of inorganic chemistry, and the particular flowering of the field of transition metal organo- metallic chemistry. Scheme 1 shows a selection of some of the simpler creations of the laboratory in this rich and ever-growing field. Structures l-3 illustrate at a glance one remarkable feature of transition metal fragments. Here are three iron tricarbonyl complexes of organic moie- ties - cyclobutadiene, trimethylenemethane, an enol, hydroxybutadiene - which on their own would have little kinetic or thermodynamic stability. -
Origin of Icosahedral Symmetry in Viruses
Origin of icosahedral symmetry in viruses Roya Zandi†‡, David Reguera†, Robijn F. Bruinsma§, William M. Gelbart†, and Joseph Rudnick§ Departments of †Chemistry and Biochemistry and §Physics and Astronomy, University of California, Los Angeles, CA 90095-1569 Communicated by Howard Reiss, University of California, Los Angeles, CA, August 11, 2004 (received for review February 2, 2004) With few exceptions, the shells (capsids) of sphere-like viruses (11). This problem is in turn related to one posed much earlier have the symmetry of an icosahedron and are composed of coat by Thomson (12), involving the optimal distribution of N proteins (subunits) assembled in special motifs, the T-number mutually repelling points on the surface of a sphere, and to the structures. Although the synthesis of artificial protein cages is a subsequently posed ‘‘covering’’ problem, where one deter- rapidly developing area of materials science, the design criteria for mines the arrangement of N overlapping disks of minimum self-assembled shells that can reproduce the remarkable properties diameter that allow complete coverage of the sphere surface of viral capsids are only beginning to be understood. We present (13). In a similar spirit, a self-assembly phase diagram has been here a minimal model for equilibrium capsid structure, introducing formulated for adhering hard disks (14). These models, which an explicit interaction between protein multimers (capsomers). all deal with identical capsomers, regularly produced capsid Using Monte Carlo simulation we show that the model reproduces symmetries lower than icosahedral. On the other hand, theo- the main structures of viruses in vivo (T-number icosahedra) and retical studies of viral assembly that assume icosahedral sym- important nonicosahedral structures (with octahedral and cubic metry are able to reproduce the CK motifs (15), and, most symmetry) observed in vitro. -
Copyrighted Material
1 INTRODUCTION 1.1 WHY STUDY ORGANOMETALLIC CHEMISTRY? Organometallic chemists try to understand how organic molecules or groups interact with compounds of the inorganic elements, chiefl y metals. These elements can be divided into the main group, consisting of the s and p blocks of the periodic table, and the transition elements of the d and f blocks. Main-group organometallics, such as n -BuLi and PhB(OH)2 , have proved so useful for organic synthesis that their leading characteristics are usually extensively covered in organic chemistry courses. Here, we look instead at the transition metals because their chemistry involves the intervention of d and f orbitals that bring into play reaction pathways not readily accessible elsewhere in the periodic table. While main-group organometallics are typically stoichiometric reagents, many of their transition metal analogs are most effective when they act as catalysts. Indeed, the expanding range of applications of catalysis is a COPYRIGHTEDmajor reason for the continued MATERIAL rising interest in organo- metallics. As late as 1975, the majority of organic syntheses had no recourse to transition metals at any stage; in contrast, they now very often appear, almost always as catalysts. Catalysis is also a central prin- ciple of Green Chemistry 1 because it helps avoid the waste formation, The Organometallic Chemistry of the Transition Metals, Sixth Edition. Robert H. Crabtree. © 2014 John Wiley & Sons, Inc. Published 2014 by John Wiley & Sons, Inc. 1 2 INTRODUCTION for example, of Mg salts from Grignard reactions, that tends to accom- pany the use of stoichiometric reagents. The fi eld thus occupies the borderland between organic and inorganic chemistry. -
The Cubic Groups
The Cubic Groups Baccalaureate Thesis in Electrical Engineering Author: Supervisor: Sana Zunic Dr. Wolfgang Herfort 0627758 Vienna University of Technology May 13, 2010 Contents 1 Concepts from Algebra 4 1.1 Groups . 4 1.2 Subgroups . 4 1.3 Actions . 5 2 Concepts from Crystallography 6 2.1 Space Groups and their Classification . 6 2.2 Motions in R3 ............................. 8 2.3 Cubic Lattices . 9 2.4 Space Groups with a Cubic Lattice . 10 3 The Octahedral Symmetry Groups 11 3.1 The Elements of O and Oh ..................... 11 3.2 A Presentation of Oh ......................... 14 3.3 The Subgroups of Oh ......................... 14 2 Abstract After introducing basics from (mathematical) crystallography we turn to the description of the octahedral symmetry groups { the symmetry group(s) of a cube. Preface The intention of this account is to provide a description of the octahedral sym- metry groups { symmetry group(s) of the cube. We first give the basic idea (without proofs) of mathematical crystallography, namely that the 219 space groups correspond to the 7 crystal systems. After this we come to describing cubic lattices { such ones that are built from \cubic cells". Finally, among the cubic lattices, we discuss briefly the ones on which O and Oh act. After this we provide lists of the elements and the subgroups of Oh. A presentation of Oh in terms of generators and relations { using the Dynkin diagram B3 is also given. It is our hope that this account is accessible to both { the mathematician and the engineer. The picture on the title page reflects Ha¨uy'sidea of crystal structure [4]. -
Werner-Type Complexes of Uranium(III) and (IV) Judith Riedhammer, J
pubs.acs.org/IC Article Werner-Type Complexes of Uranium(III) and (IV) Judith Riedhammer, J. Rolando Aguilar-Calderon,́ Matthias Miehlich, Dominik P. Halter, Dominik Munz, Frank W. Heinemann, Skye Fortier, Karsten Meyer,* and Daniel J. Mindiola* Cite This: Inorg. Chem. 2020, 59, 2443−2449 Read Online ACCESS Metrics & More Article Recommendations *sı Supporting Information ABSTRACT: Transmetalation of the β-diketiminate salt [M]- Me Ph + Me Ph− − [ nacnac ](M =NaorK; nacnac = {PhNC(CH3)}2CH ) with UI3(THF)4 resulted in the formation of the homoleptic, Me Ph octahedral complex [U( nacnac )3](1). Green colored 1 was fully characterized by a solid-state X-ray diffraction analysis and a combination of UV/vis/NIR, NMR, and EPR spectroscopic studies as well as solid-state SQUID magnetization studies and density functional theory calculations. Electrochemical studies of 1 revealed this species to possess two anodic waves for the U(III/IV) and U(IV/V) redox couples, with the former being chemically accessible. Using mild oxidants, such as [CoCp2][PF6]or [FeCp ][Al{OC(CF ) } ], yields the discrete salts [1][A] (A = − 2 3 −3 4 PF6 , Al{OC(CF3)3}4 ), whereas the anion exchange of [1][PF6] with NaBPh4 yields [1][BPh4]. Me Dipp μ 12 ■ INTRODUCTION UCl3(THF)] and [{( nacnac )UCl}2( 2-Cl)3]Cl. In Me Dipp− ’ some cases, disubstitution of nacnac generates the Alfred Werner s disapproval of the complex ion-chain theory Me Dipp η3 Me Dipp 13 proposed by Jørgensen and Blomstrand,1 via the introduction rearranged species [( nacnac )( - nacnac )UI], of coordination complexes and the concept of Nebenvalenz,1,2 where one ligand has changed hapticity, most likely due to fi steric constraints. -
Design of Large Space Structures Derived from Line Geometry Principles
DESIGN OF LARGE SPACE STRUCTURES DERIVED FROM LINE GEOMETRY PRINCIPLES By PATRICK J. MCGINLEY A THESIS PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE UNIVERSITY OF FLORIDA 2002 Copyright 2002 by Patrick J. McGinley I would like to dedicate this work to Dr. Joseph Duffy - mentor, friend, and inspiration. My thanks also go out to my parents, Thomas and Lorraine, for everything they have taught me, and my friends, especially Byron, Connie, and Richard, for all their support. ACKNOWLEDGMENTS I would like to thank my advisor, Dr. Carl D. Crane, III, the members of my advisory committee, Dr. John Schueller and Dr. John Ziegert, as well as Dr. Joseph Rooney, for their help and guidance during my time at UF, and especially their understanding during a difficult last semester. iv TABLE OF CONTENTS page ACKNOWLEDGMENTS ................................................................................................. iv LIST OF TABLES............................................................................................................ vii LIST OF FIGURES ......................................................................................................... viii ABSTRACT...................................................................................................................... xii CHAPTER 1 INTRODUCTION ............................................................................................................1 2 BACKGROUND ..............................................................................................................5 -
Systematics of Atomic Orbital Hybridization of Coordination Polyhedra: Role of F Orbitals
molecules Article Systematics of Atomic Orbital Hybridization of Coordination Polyhedra: Role of f Orbitals R. Bruce King Department of Chemistry, University of Georgia, Athens, GA 30602, USA; [email protected] Academic Editor: Vito Lippolis Received: 4 June 2020; Accepted: 29 June 2020; Published: 8 July 2020 Abstract: The combination of atomic orbitals to form hybrid orbitals of special symmetries can be related to the individual orbital polynomials. Using this approach, 8-orbital cubic hybridization can be shown to be sp3d3f requiring an f orbital, and 12-orbital hexagonal prismatic hybridization can be shown to be sp3d5f2g requiring a g orbital. The twists to convert a cube to a square antiprism and a hexagonal prism to a hexagonal antiprism eliminate the need for the highest nodality orbitals in the resulting hybrids. A trigonal twist of an Oh octahedron into a D3h trigonal prism can involve a gradual change of the pair of d orbitals in the corresponding sp3d2 hybrids. A similar trigonal twist of an Oh cuboctahedron into a D3h anticuboctahedron can likewise involve a gradual change in the three f orbitals in the corresponding sp3d5f3 hybrids. Keywords: coordination polyhedra; hybridization; atomic orbitals; f-block elements 1. Introduction In a series of papers in the 1990s, the author focused on the most favorable coordination polyhedra for sp3dn hybrids, such as those found in transition metal complexes. Such studies included an investigation of distortions from ideal symmetries in relatively symmetrical systems with molecular orbital degeneracies [1] In the ensuing quarter century, interest in actinide chemistry has generated an increasing interest in the involvement of f orbitals in coordination chemistry [2–7]. -
An,4B Tnitt{:} Mûleculaã.Orbital .A-Pproact{
T}IE STEREÛC}{E}4ISTRY ÛF CUg- ÛXYSALT MNNERALS AN,4B TNITT{:} MÛLECULAÃ.ORBITAL .A-PPROACT{ Þ\¡ PETER C. EL-RNS A Thesis Subrnitted to the Faculty of Graduate Studies in Pa-rtial Fulfilment, of the Requireraents for the Ðegree of ÐOCT'OR OF THiLOSOPHY Ðepartment of Geological Sciences University of Manitoba Winnipeg, Manitoba @ Copyright by Peter Carman Bu¡¡rs, 1994 WWW National Library B¡bliothèqLre naiioftale W'r @ of Canada du Canâda Acquisitions and Direction des acquisitions et B¡bf iographic Seruices Branch des servìces bibl¡ographiques 395 Wellington Slreet 395, rue WeJlingron Otlawa, Onta¡io Onawa (Oniar¡o) K1A ON4 K1A ON4 aùtLle Na¡e èlùerce T'he at¡th@ü' has graü-lted aãx Ë*'au¡tec¡r a aaaondé s"!ne licemce írrevoeabIe nÕrÌ-ex6t¿.Esive ¡¡eemcc inr¡ávoaab[e et ntm exc[usíve allowing t['re F,Iationat Lihrany of penmrettant à $a Eihliothèque Camada tÕ reprtdL¡ce, åoana, natiomale du Canada de distribute Õr sell copíes of reprods.rãre, prêter, distribuer ou his/hen thesís by any sneams arsd vendre des aopies de sa thèse in any fonm or fonnlat, rnaking de quelque rna¡rière et sous tÍ'lis tl'lesis available to E¡'¡terested qt¡elque forrne que ce soit poun persons. rnettre des exenarplaires de cette thèse à [a disposition des personnes intéressées. T'[re a¡.¡t['ror retains ownershíp of E-'a¡.¡teun conserve la propriété du the eopyrig[et im hrislher tÍresis" droit d'auteun quri protège sa Ê.deít[rer ttre thesís sror substantåa[ t['rèse. hdå 8a thèse ni des extnaits extnacts fnonn it may be pnin-lted or substantiels de celle-ci ne otlrerwíse neproduced wãtå'¡or¡t doívent être ãrrrpria'nés oL¡ [rüs/her pernnlssiom.