Chapter 5 Molecular Orbitals
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Atomic Orbitals
Visualization of Atomic Orbitals Source: Robert R. Gotwals, Jr., Department of Chemistry, North Carolina School of Science and Mathematics, Durham, NC, 27705. Email: [email protected]. Copyright ©2007, all rights reserved, permission to use for non-commercial educational purposes is granted. Introductory Readings Where are the electrons in an atom? There are a number of Models - a description of models that look to describe the location and behavior of some physical object or electrons in atoms. It is important to know this information, as behavior in nature. Models it helps chemists to make statements and predictions about are often mathematical, describing the behavior of how atoms will react with other atoms to form molecules. The some event. model one chooses will oftentimes influence the types of statements one can make about the behavior – that is, the reactivity – of an atom or group of atoms. Bohr model - states that no One model, the Bohr model, describes electrons as small two electrons in an atom can billiard balls, rotating around the positively charged nucleus, have the same set of four much in the way that planets quantum numbers. orbit around the Sun. The placement and motion of electrons are found in fixed and quantifiable levels called orbits, Orbits- where electrons are or, in older terminology, shells. believed to be located in the There are specific numbers of Bohr model. Orbits have a electrons that can be found in fixed amount of energy, and are identified with the each orbit – 2 for the first orbit, principle quantum number 8 for the second, and so forth. -
Chemistry 2000 Slide Set 1: Introduction to the Molecular Orbital Theory
Chemistry 2000 Slide Set 1: Introduction to the molecular orbital theory Marc R. Roussel January 2, 2020 Marc R. Roussel Introduction to molecular orbitals January 2, 2020 1 / 24 Review: quantum mechanics of atoms Review: quantum mechanics of atoms Hydrogenic atoms The hydrogenic atom (one nucleus, one electron) is exactly solvable. The solutions of this problem are called atomic orbitals. The square of the orbital wavefunction gives a probability density for the electron, i.e. the probability per unit volume of finding the electron near a particular point in space. Marc R. Roussel Introduction to molecular orbitals January 2, 2020 2 / 24 Review: quantum mechanics of atoms Review: quantum mechanics of atoms Hydrogenic atoms (continued) Orbital shapes: 1s 2p 3dx2−y 2 3dz2 Marc R. Roussel Introduction to molecular orbitals January 2, 2020 3 / 24 Review: quantum mechanics of atoms Review: quantum mechanics of atoms Multielectron atoms Consider He, the simplest multielectron atom: Electron-electron repulsion makes it impossible to solve for the electronic wavefunctions exactly. A fourth quantum number, ms , which is associated with a new type of angular momentum called spin, enters into the theory. 1 1 For electrons, ms = 2 or − 2 . Pauli exclusion principle: No two electrons can have identical sets of quantum numbers. Consequence: Only two electrons can occupy an orbital. Marc R. Roussel Introduction to molecular orbitals January 2, 2020 4 / 24 The hydrogen molecular ion The quantum mechanics of molecules + H2 is the simplest possible molecule: two nuclei one electron Three-body problem: no exact solutions However, the nuclei are more than 1800 time heavier than the electron, so the electron moves much faster than the nuclei. -
No Rabbit Ears on Water. the Structure of the Water Molecule
No Rabbit Ears on Water The Structure of the Water Molecule: What Should We Tell the Students? Michael Laing University of Natal. Durban, South Africa In the vast majority of high school (I)and freshman uni- He also considers the possibility of s character in the bond- versity (2) chemistry textbooks, water is presented as a bent ing orbitals of OF2 and OH2 to improve the "strength" of the molecule whose bonding can be described bv the Gilles~ie- orbital (p 111) from 1.732 for purep to 2.00 for the ideal sp3. Nyholm approach with the oxygen atomsp3 Gyhridized. The Inclusion of s character in the hybrid will be "resisted in the lone uairs are said to he dominant causine the H-O-H anele case of atoms with an nnshared pair.. in the s orbital, to beieduced from the ideal 1091120to 104' and are regul&ly which is more stable than the p orbitals" (p 120). Estimates shown as equivalent in shape and size even being described of the H-E-H angle range from 91.2 for AsH3 to 93.5O for as "rabbit ears" (3). Chemists have even been advised to Hz0. He once again ascribes the anomalies for Hz0 to "re- wear Mickey Mouse ears when teaching the structure and uulsion of the charzes of the hvdroaeu atoms" (D 122). bonding of the H20molecule, presumably to emphasize the - In his famous hook (6)~itac~oro&kii describks the bond- shape of the molecule (and possibly the two equivalent lone ing in water and HzS (p 10). -
Theoretical Methods That Help Understanding the Structure and Reactivity of Gas Phase Ions
International Journal of Mass Spectrometry 240 (2005) 37–99 Review Theoretical methods that help understanding the structure and reactivity of gas phase ions J.M. Merceroa, J.M. Matxaina, X. Lopeza, D.M. Yorkb, A. Largoc, L.A. Erikssond,e, J.M. Ugaldea,∗ a Kimika Fakultatea, Euskal Herriko Unibertsitatea, P.K. 1072, 20080 Donostia, Euskadi, Spain b Department of Chemistry, University of Minnesota, 207 Pleasant St. SE, Minneapolis, MN 55455-0431, USA c Departamento de Qu´ımica-F´ısica, Universidad de Valladolid, Prado de la Magdalena, 47005 Valladolid, Spain d Department of Cell and Molecular Biology, Box 596, Uppsala University, 751 24 Uppsala, Sweden e Department of Natural Sciences, Orebro¨ University, 701 82 Orebro,¨ Sweden Received 27 May 2004; accepted 14 September 2004 Available online 25 November 2004 Abstract The methods of the quantum electronic structure theory are reviewed and their implementation for the gas phase chemistry emphasized. Ab initio molecular orbital theory, density functional theory, quantum Monte Carlo theory and the methods to calculate the rate of complex chemical reactions in the gas phase are considered. Relativistic effects, other than the spin–orbit coupling effects, have not been considered. Rather than write down the main equations without further comments on how they were obtained, we provide the reader with essentials of the background on which the theory has been developed and the equations derived. We committed ourselves to place equations in their own proper perspective, so that the reader can appreciate more profoundly the subtleties of the theory underlying the equations themselves. Finally, a number of examples that illustrate the application of the theory are presented and discussed. -
Structure and Bonding Electron Configurations in the Periodic Table
Structure and Bonding The study of organic chemistry must at some point extend to the molecular level, for the physical and chemical properties of a substance are ultimately explained in terms of the structure and bonding of molecules. This module introduces some basic facts and principles that are needed for a discussion of organic molecules. Electronic Configurations Electron Configurations in the Periodic Table 1A 2A 3A 4A 5A 6A 7A 8A 1 2 H He 1 2 1s 1s 3 4 5 6 7 8 9 10 Li Be B C N O F Ne 2 2 2 2 2 2 2 2 1s 1s 1s 1s 1s 1s 1s 1s 2s1 2s2 2s22p1 2s22p2 2s22p3 2s22p4 2s22p5 2s22p6 11 12 13 14 15 16 17 18 Na Mg Al Si P S Cl Ar [Ne] [Ne] [Ne] [Ne] [Ne] [Ne] [Ne] [Ne] 3s1 3s2 3s23p1 3s23p2 3s23p3 3s23p4 3s23p5 3s23p6 Four elements, hydrogen, carbon, oxygen and nitrogen, are the major components of most organic compounds. Consequently, our understanding of organic chemistry must have, as a foundation, an appreciation of the electronic structure and properties of these elements. The truncated periodic table shown above provides the orbital electronic structure for the first eighteen elements (hydrogen through argon). According to the Aufbau principle, the electrons of an atom occupy quantum levels or orbitals starting from the lowest energy level, and proceeding to the highest, with each orbital holding a maximum of two paired electrons (opposite spins). Electron shell #1 has the lowest energy and its s-orbital is the first to be filled. -
VSEPR Theory
VSEPR Theory The valence-shell electron-pair repulsion (VSEPR) model is often used in chemistry to predict the three dimensional arrangement, or the geometry, of molecules. This model predicts the shape of a molecule by taking into account the repulsion between electron pairs. This handout will discuss how to use the VSEPR model to predict electron and molecular geometry. Here are some definitions for terms that will be used throughout this handout: Electron Domain – The region in which electrons are most likely to be found (bonding and nonbonding). A lone pair, single, double, or triple bond represents one region of an electron domain. H2O has four domains: 2 single bonds and 2 nonbonding lone pairs. Electron Domain may also be referred to as the steric number. Nonbonding Pairs Bonding Pairs Electron domain geometry - The arrangement of electron domains surrounding the central atom of a molecule or ion. Molecular geometry - The arrangement of the atoms in a molecule (The nonbonding domains are not included in the description). Bond angles (BA) - The angle between two adjacent bonds in the same atom. The bond angles are affected by all electron domains, but they only describe the angle between bonding electrons. Lewis structure - A 2-dimensional drawing that shows the bonding of a molecule’s atoms as well as lone pairs of electrons that may exist in the molecule. Provided by VSEPR Theory The Academic Center for Excellence 1 April 2019 Octet Rule – Atoms will gain, lose, or share electrons to have a full outer shell consisting of 8 electrons. When drawing Lewis structures or molecules, each atom should have an octet. -
Valence Bond Theory
UMass Boston, Chem 103, Spring 2006 CHEM 103 Molecular Geometry and Valence Bond Theory Lecture Notes May 2, 2006 Prof. Sevian Announcements z The final exam is scheduled for Monday, May 15, 8:00- 11:00am It will NOT be in our regularly scheduled lecture hall (S- 1-006). The final exam location has been changed to Snowden Auditorium (W-1-088). © 2006 H. Sevian 1 UMass Boston, Chem 103, Spring 2006 More announcements Information you need for registering for the second semester of general chemistry z If you will take it in the summer: z Look for chem 104 in the summer schedule (includes lecture and lab) z If you will take it in the fall: z Look for chem 116 (lecture) and chem 118 (lab). These courses are co-requisites. z If you plan to re-take chem 103, in the summer it will be listed as chem 103 (lecture + lab). In the fall it will be listed as chem 115 (lecture) + chem 117 (lab), which are co-requisites. z Note: you are only eligible for a lab exemption if you previously passed the course. Agenda z Results of Exam 3 z Molecular geometries observed z How Lewis structure theory predicts them z Valence shell electron pair repulsion (VSEPR) theory z Valence bond theory z Bonds are formed by overlap of atomic orbitals z Before atoms bond, their atomic orbitals can hybridize to prepare for bonding z Molecular geometry arises from hybridization of atomic orbitals z σ and π bonding orbitals © 2006 H. Sevian 2 UMass Boston, Chem 103, Spring 2006 Molecular Geometries Observed Tetrahedral See-saw Square planar Square pyramid Lewis Structure Theory -
Molecular Symmetry, Super-Rotation, and Semi-Classical Motion –
Molecular symmetry, super-rotation, and semi-classical motion – New ideas for old problems Inaugural - Dissertation zur Erlangung des Doktorgrades der Mathematisch-Naturwissenschaftlichen Fakultät der Universität zu Köln vorgelegt von Hanno Schmiedt aus Köln Berichterstatter: Prof. Dr. Stephan Schlemmer Prof. Per Jensen, Ph.D. Tag der mündlichen Prüfung: 24. Januar 2017 Awesome molecules need awesome theories DR.SANDRA BRUENKEN, 2016 − Abstract Traditional molecular spectroscopy is used to characterize molecules by their structural and dynamical properties. Furthermore, modern experimental methods are capable of determining state-dependent chemical reaction rates. The understanding of both inter- and intra-molecular dynamics contributes exceptionally, for example, to the search for molecules in interstellar space, where observed spectra and reaction rates help in under- standing the various phases of stellar or planetary evolution. Customary theoretical models for molecular dynamics are based on a few fundamental assumptions like the commonly known ball-and-stick picture of molecular structure. In this work we discuss two examples of the limits of conventional molecular theory: Extremely floppy molecules where no equilibrium geometric structure is definable and molecules exhibiting highly excited rotational states, where the large angular momentum poses considerable challenges to quantum chemical calculations. In both cases, we develop new concepts based on fundamental symmetry considerations to overcome the respective limits of quantum chemistry. For extremely floppy molecules where numerous large-amplitude motions render a defini- tion of a fixed geometric structure impossible, we establish a fundamentally new zero-order description. The ‘super-rotor model’ is based on a five-dimensional rigid rotor treatment depending only on a single adjustable parameter. -
United States Patent 0 " Ice Patented May 28, 1968
3,385,666 United States Patent 0 " ice Patented May 28, 1968 1 2 of novel compositions that can be used as a source of 3,385,666 both ozone and oxygen. DIOXYGENYL FLUORIDES OF GROUP V An additional object of this invention is the preparation ELEMENTS of the nitronium ion and intermediates for preparing Archie R. Young II, Montclair, Tetsuyuki Hirata, Whar novel nitronium salts. ton, and Scott I. Morrow, Morris Plains, N.J., assign Further objects of this invention will become apparent ors to Thiokol Chemical Corporation, Bristol, Pa., a corporation of Delaware to the reader upon a further reading of this patent appli No Drawing. Filed Jan. 6, 1964, Ser. No. 336,061 cation. 11 Claims. (Cl. 23-203) The above objects among many others are achieved by 10 the direct interaction of certain ?uoride reactants with This invention relates to a novel class of ?uorinated, dioxygen di?uoride at reaction temperatures well below oxygen containing, oxidizing agents and to a process for 0° C. As indicated earlier the ?uoride reactant is selected their preparation. from the group consisting of Group V ?uorides. More particularly, this invention concerns the prepara The preferred practice is to contact the ?uoride reactant tion of certain stable ?uorides of the cationic dioxygenyl 15 with an excess of 02112 at low temperatures ranging from radical. These novel-oxidizing agents have the formula: —l60 to \—78° C. until a substantial amount of prod uct is formed. The product is isolated after evacuating off the excess 021:2, ?uorine and gaseous by-products. wherein (O2) is the dioxygenyl radical having a charge In one ‘favored process embodiment of this invention of +1, M is an element selected from the group consist 20 a ?uoride reactant chosen ‘from the preferred phosphorus, ing of phosphorus, arsenic antimony and bismuth. -
Molecular Symmetry
Molecular Symmetry Symmetry helps us understand molecular structure, some chemical properties, and characteristics of physical properties (spectroscopy) – used with group theory to predict vibrational spectra for the identification of molecular shape, and as a tool for understanding electronic structure and bonding. Symmetrical : implies the species possesses a number of indistinguishable configurations. 1 Group Theory : mathematical treatment of symmetry. symmetry operation – an operation performed on an object which leaves it in a configuration that is indistinguishable from, and superimposable on, the original configuration. symmetry elements – the points, lines, or planes to which a symmetry operation is carried out. Element Operation Symbol Identity Identity E Symmetry plane Reflection in the plane σ Inversion center Inversion of a point x,y,z to -x,-y,-z i Proper axis Rotation by (360/n)° Cn 1. Rotation by (360/n)° Improper axis S 2. Reflection in plane perpendicular to rotation axis n Proper axes of rotation (C n) Rotation with respect to a line (axis of rotation). •Cn is a rotation of (360/n)°. •C2 = 180° rotation, C 3 = 120° rotation, C 4 = 90° rotation, C 5 = 72° rotation, C 6 = 60° rotation… •Each rotation brings you to an indistinguishable state from the original. However, rotation by 90° about the same axis does not give back the identical molecule. XeF 4 is square planar. Therefore H 2O does NOT possess It has four different C 2 axes. a C 4 symmetry axis. A C 4 axis out of the page is called the principle axis because it has the largest n . By convention, the principle axis is in the z-direction 2 3 Reflection through a planes of symmetry (mirror plane) If reflection of all parts of a molecule through a plane produced an indistinguishable configuration, the symmetry element is called a mirror plane or plane of symmetry . -
Fundamental Studies of Early Transition Metal-Ligand Multiple Bonds: Structure, Electronics, and Catalysis
Fundamental Studies of Early Transition Metal-Ligand Multiple Bonds: Structure, Electronics, and Catalysis Thesis by Ian Albert Tonks In Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy CALIFORNIA INSTITUTE OF TECHNOLOGY Pasadena, California 2012 Defended December 6th 2011 ii 2012 Ian A Tonks All Rights Reserved iii ACKNOWLEDGEMENTS I am extremely fortunate to have been surrounded by enthusiastic, dedicated, and caring mentors, colleagues, and friends throughout my academic career. A Ph.D. thesis is by no means a singular achievement; I wish to extend my wholehearted thanks to everyone who has made this journey possible. First and foremost, I must thank my Ph.D. advisor, Prof. John Bercaw. I think more so than anything else, I respect John for his character, sense of fairness, and integrity. I also benefitted greatly from John’s laissez-faire approach to guiding our research group; I’ve always learned best when left alone to screw things up, although John also has an uncanny ability for sensing when I need direction or for something to work properly on the high-vac line. John also introduced me to hiking and climbing in the Eastern Sierras and Owens Valley, which remain amongst my favorite places on Earth. Thanks for always being willing to go to the Pizza Factory in Lone Pine before and after all the group hikes! While I never worked on any of the BP projects that were spearheaded by our co-PI Dr. Jay Labinger, I must also thank Jay for coming to all of my group meetings, teaching me an incredible amount while I was TAing Ch154, and for always being willing to talk chemistry and answer tough questions. -
Lewis Structure Handout
Lewis Structure Handout for Chemistry Students An electron dot diagram, also known as a Lewis Structure, is a representation of valence electrons in a single atom, and can be further utilized to depict the bonds that form based on the available electrons for covalent bonding between multiple atoms. -Each atom has a characteristic dot diagram based on its position in the periodic table and this reflects its potential for fulfillment of the octet rule. As a general rule, the noble gases have a filled octet (column VIII with eight valence electrons) and each preceding column has successively one fewer. • For example, Carbon is in column IV and has four valence electrons. It can therefore be represented as: • Each of these "lone" electrons can form a bond by sharing the orbital with another unbonded electron. Hydrogen, being in column I, has a single valence electron, and will therefore satisfy carbon's octet thusly: • When a compound has bonded electrons (as with CH4) it is most accurate to diagram it with lines representing each of the single bonds. • Using carbon again for a slightly more complicated example, it can also form double bonds. This is the case when carbon bonds to two oxygen atoms, resulting in CO2. The oxygen atoms (with six valence electrons in column VI) are each represented as: • Because carbon is the least electronegative of the atoms involved, it is placed centrally, and its valence electrons will migrate toward the more electronegative oxygens to form two double bonds and a linear structure. This can be written as: where oxygen's remaining lone pairs are still shown.