DOCSLIB.ORG

Frontier Molecular Orbital Theory

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Frontier Molecular Orbital Theory Frontier Molecular Orbital Theory CHEM 430 Great Books on Frontier Orbital Theory Basics of Frontier Molecular Orbital Theory Since the majority of energy gain in a reaction between two molecules is a result of the HOMO of one molecule reacting with the LUMO of a second molecule this interaction is called a Frontier Molecular Orbital (FMO) interaction A reaction is thus favored when the HOMO (nucleophile) is unusually high in energy and the LUMO (electrophile) is unusually low in energy What does unusually high HOMO or unusually low LUMO mean? Must be compared relative to something -usually compare energy levels with a known unreactive C-H (or C-C) single bond If the HOMO of a new compound is higher in energy than the HOMO of the C-H bond, then it will be more reactive as a nucleophile If the LUMO of a new compound is lower in energy than the LUMO of the C-H bond, then it will be more reactive as an electrophile How much higher or lower in energy will determine the relative rates of reactions Basics of Frontier Molecular Orbital Theory Frontier Molecular Orbitals – HOMO and LUMO It makes sense that the HOMO and LUMO are the orbitals most likely to be involved in chemical reactivity. • Chemical reactions involve the redistribution of electrons (creation and destruction of bonds, oxidation, reduction, …) • The HOMO is the orbital of highest energy that is still occupied, so energetically it is the easiest to remove electrons from this orbital. This could be simply donating electron density to form a bond (act as a Lewis base) or it could be oxidation. • The LUMO is the lowest lying orbital that is empty, so energetically it is the easiest to add more electrons into this orbital…Lewis acid; reduction. • It isn’t always the HOMO and/or LUMO involved in chemical reactivity. Symmetry plays a role, too. If the HOMO or LUMO isn’t of the correct symmetry, it might be the HOMO-1 or the LUMO+1 that is involved in the reaction. Basics of Frontier Molecular Orbital Theory We can compare the placement of HOMO and LUMO levels relative to placement of C-H bonds Very high LUMO, therefore poor electrophile Lone pair of electrons placed in * C-H atomic orbital No electrons in atomic orbital, therefore very electrophilic Because nitrogen is more electronegative than carbon, orbital is lower in energy sp3 1s C H H+ (likewise oxygen is lower than nitrogen) :NH3 Both are very nucleophilic, :OH2 ammonia more than water C-H Very low HOMO, Factors that can adjust MO energy levels: therefore poor nucleophile 1) Unmixed valence shell atomic orbitals A sp3 hybridized carbon atom and a 1s orbital of hydrogen have similar energy levels and strong overlap, therefore high mixing Basics of Frontier Molecular Orbital Theory We can compare the placement of HOMO and LUMO levels relative to placement of C-H bonds Very high LUMO, therefore poor electrophile *C-H Negative charge will raise the energy of orbital, therefore make compound more nucleophilic CH3 3 sp C 1s H H+ OH :NH3 :OH2 C-H Very low HOMO, Factors that can adjust MO energy levels: therefore poor nucleophile 1) Unmixed valence shell atomic orbitals A sp3 hybridized carbon atom and a 1s orbital of hydrogen have similar 2) Electric charge energy levels and strong overlap, therefore high mixing Basics of Frontier Molecular Orbital Theory We can compare the placement of HOMO and LUMO levels relative to placement of C-H bonds Very high LUMO, therefore poor electrophile The degree of mixing of two orbitals is related to the amount *C-H of overlap between the orbitals *C-C This makes HOMO into a good nucleophile 3 2p C 2p C sp C 1s H C-C When two p orbitals overlap to form a bond, the orbitals begin higher in energy than a C-H hybridized orbital and the amount of overlap is less Very low HOMO, Factors that can adjust MO energy levels: therefore poor nucleophile 1) Unmixed valence shell atomic orbitals A sp3 hybridized carbon atom and a 1s orbital of hydrogen have similar 2) Electric charge energy levels and strong overlap, 3) Poor overlap of atomic orbitals therefore high mixing Basics of Frontier Molecular Orbital Theory We can compare the placement of HOMO and LUMO levels relative to placement of C-H bonds Very high LUMO, therefore poor electrophile Since the oxygen 2p orbital is * C-H much lower in energy, the This makes LUMO energy match with carbon 2p is into a good worse and therefore less mixing electrophile 2p C *C-O 3 sp C 1s H 2p O C-O C-H Very low HOMO, Factors that can adjust MO energy levels: therefore poor nucleophile 1) Unmixed valence shell atomic orbitals A sp3 hybridized carbon atom and a 1s orbital of hydrogen have similar 2) Electric charge energy levels and strong overlap, 3) Poor overlap of atomic orbitals therefore high mixing 4) Poor energy match of orbitals Basics of Frontier Molecular Orbital Theory We can compare the placement of HOMO and LUMO levels relative to placement of C-H bonds Very high LUMO, Can also use orbital energy levels to understand therefore poor electrophile differences in reactivity for C-X bonds *C-H A C-Cl bond is good *C-Mg electrophile spMg *C-Cl 3 3 3 sp C 1s H sp C sp C C-Mg A C-Mg bond is sp3 Cl good nucleophile C-Cl C-H Very low HOMO, Factors that can adjust MO energy levels: therefore poor nucleophile 1) Unmixed valence shell atomic orbitals A sp3 hybridized carbon atom and a 1s orbital of hydrogen have similar 2) Electric charge energy levels and strong overlap, 3) Poor overlap of atomic orbitals therefore high mixing 4) Poor energy match of orbitals Basics of Frontier Molecular Orbital Theory Frontier molecular orbital (FMO) theory allows a chemist to make predictions about a reaction by knowing the placement of the HOMO and LUMO energy levels A high HOMO level represents a compound that is a good nucleophile Anything that will raise CH3 > NH2 > OH energy level of HOMO will increase nucleophilicity A low LUMO level represents a compound that is a good electrophile R Anything that will lower CO H3C Cl energy level of LUMO will R increase electrophilicity The energy level of the HOMO and LUMO can be predicted by knowing that when two atomic orbitals mix they form two new molecular orbitals, one lower in energy and one higher in energy The amount of mixing is dependent upon: 1) The amount of overlap between the mixing orbitals (e.g., the overlap for a bond is greater than the overlap for a bond) 2) The closer in energy are two orbitals, the greater the amount of mixing that occurs Basics of Frontier Molecular Orbital Theory FMO will also allow prediction about where a reaction will occur (regiochemistry) and direction of approach (stereochemistry) Consider a reaction with a carbonyl compound FMO predicts that a carbonyl should react as an electrophile due to the low energy LUMO The regio- and stereochemistry can also be predicted by considering the interacting frontier orbital (the LUMO) The coefficient on carbon is rotate larger than the coefficient on oxygen, therefore nucleophile reacts at carbon LUMO of formaldehyde Basics of Frontier Molecular Orbital Theory What direction should a nucleophile approach the carbonyl? NUC NUC Direction appears better, Optimal interaction but still not optimal interaction (best overlap of interacting orbitals) NUC Expect this direction to be highly disfavored due to orthogonal interaction with orbitals Could there possibly be a method to test the angle of approach of nucleophile to carbonyl? X-ray structures come to the solution once again! Basics of Frontier Molecular Orbital Theory What direction should a nucleophile approach the carbonyl? Studied a variety of X-ray NUC structures where a N Optimal interaction reacts with a carbonyl (best overlap of intramolecularly interacting orbitals) As the N came closer to carbonyl, the C-O bond lengthened and the carbonyl carbon becomes pyramidalized Called the “Bürgi-Dunitz” angle The angle of <N-C-O averaged 107˚ ( ) Could there possibly be a method to test the angle of approach of nucleophile to carbonyl? X-ray structures come to the solution once again! Bürgi, H.B., Dunitz, J.D., Shefter,E., J. Am. Chem. Soc. (1973), 95, 5065-5067 Basics of Frontier Molecular Orbital Theory What about the stereochemistry for a reaction with an alkyl halide? Since alkyl halide is reacting as the electrophile, need to look at the LUMO Largest coefficient is on the backside of the carbon Nucleophile thus reacts with a NUC methyl halide in a SN2 reaction with backside attack So called “inversion of configuration” LUMO of methyl halide Bonds that break base Base thus reacts by abstracting hydrogen anticoplanar to The base will abstract the leaving group and form new hydrogen that is anticoplanar bond in E2 reaction to leaving group New bond LUMO of 2˚ alkyl halide Steric, Inductive & Stereoelectronic Effects General Reviews Stereoelectronic Effects Fleming, I. Frontier Orbitals and Organic Chemical Reactions Geometrical constraints placed upon ground and transition states by orbital overlap considerations. Fukui, Acc. Chem. Res. 1971, 4, 57. Kirby, A. J. Stereoelectronic Effects. Fukui Postulate for reactions: During the course of chemical reactions, the interaction of Universal Effects Governing all Chemical Reactions the highest filled (HOMO) and lowest unfilled (antibonding) molecular orbital (LUMO) in reacting species is very important Steric Effects to the stabilization of the transition structure. Nonbonding interactions (van der Waals repulsion) between substituents within a molecule or between reacting molecules General Reaction Types Me Me SN2 – Nu: CBr Nu C R Br: R Radical Reactions
Load more

Recommended publications
  • 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.
    [Show full text]
  • 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.
    [Show full text]
  • Introduction to Molecular Orbital Theory
    Chapter 2: Molecular Structure and Bonding Bonding Theories 1. VSEPR Theory 2. Valence Bond theory (with hybridization) 3. Molecular Orbital Theory ( with molecualr orbitals) To date, we have looked at three different theories of molecular boning. They are the VSEPR Theory (with Lewis Dot Structures), the Valence Bond theory (with hybridization) and Molecular Orbital Theory. A good theory should predict physical and chemical properties of the molecule such as shape, bond energy, bond length, and bond angles.Because arguments based on atomic orbitals focus on the bonds formed between valence electrons on an atom, they are often said to involve a valence-bond theory. The valence-bond model can't adequately explain the fact that some molecules contains two equivalent bonds with a bond order between that of a single bond and a double bond. The best it can do is suggest that these molecules are mixtures, or hybrids, of the two Lewis structures that can be written for these molecules. This problem, and many others, can be overcome by using a more sophisticated model of bonding based on molecular orbitals. Molecular orbital theory is more powerful than valence-bond theory because the orbitals reflect the geometry of the molecule to which they are applied. But this power carries a significant cost in terms of the ease with which the model can be visualized. One model does not describe all the properties of molecular bonds. Each model desribes a set of properties better than the others. The final test for any theory is experimental data. Introduction to Molecular Orbital Theory The Molecular Orbital Theory does a good job of predicting elctronic spectra and paramagnetism, when VSEPR and the V-B Theories don't.
    [Show full text]
  • 3-MO Theory(U).Pptx
    Molecular Orbital Theory Valence Bond Theory: Electrons are located in discrete pairs between specific atoms Molecular Orbital Theory: Electrons are located in the molecule, not held in discrete regions between two bonded atoms Thus the main difference between these theories is where the electrons are located, in valence bond theory we predict the electrons are always held between two bonded atoms and in molecular orbital theory the electrons are merely held “somewhere” in molecule Mathematically can represent molecule by a linear combination of atomic orbitals (LCAO) ΨMOL = c1 φ1 + c2 φ2 + c3 φ3 + cn φn Where Ψ2 = spatial distribution of electrons If the ΨMOL can be determined, then where the electrons are located can also be determined 66 Building Molecular Orbitals from Atomic Orbitals Similar to a wave function that can describe the regions of space where electrons reside on time average for an atom, when two (or more) atoms react to form new bonds, the region where the electrons reside in the new molecule are described by a new wave function This new wave function describes molecular orbitals instead of atomic orbitals Mathematically, these new molecular orbitals are simply a combination of the atomic wave functions (e.g LCAO) Hydrogen 1s H-H bonding atomic orbital molecular orbital 67 Building Molecular Orbitals from Atomic Orbitals An important consideration, however, is that the number of wave functions (molecular orbitals) resulting from the mixing process must equal the number of wave functions (atomic orbitals) used in the mixing
    [Show full text]
  • Simple Molecular Orbital Theory Chapter 5
    Simple Molecular Orbital Theory Chapter 5 Wednesday, October 7, 2015 Using Symmetry: Molecular Orbitals One approach to understanding the electronic structure of molecules is called Molecular Orbital Theory. • MO theory assumes that the valence electrons of the atoms within a molecule become the valence electrons of the entire molecule. • Molecular orbitals are constructed by taking linear combinations of the valence orbitals of atoms within the molecule. For example, consider H2: 1s + 1s + • Symmetry will allow us to treat more complex molecules by helping us to determine which AOs combine to make MOs LCAO MO Theory MO Math for Diatomic Molecules 1 2 A ------ B Each MO may be written as an LCAO: cc11 2 2 Since the probability density is given by the square of the wavefunction: probability of finding the ditto atom B overlap term, important electron close to atom A between the atoms MO Math for Diatomic Molecules 1 1 S The individual AOs are normalized: 100% probability of finding electron somewhere for each free atom MO Math for Homonuclear Diatomic Molecules For two identical AOs on identical atoms, the electrons are equally shared, so: 22 cc11 2 2 cc12 In other words: cc12 So we have two MOs from the two AOs: c ,1() 1 2 c ,1() 1 2 2 2 After normalization (setting d 1 and _ d 1 ): 1 1 () () [2(1 S )]1/2 12 [2(1 S )]1/2 12 where S is the overlap integral: 01 S LCAO MO Energy Diagram for H2 H2 molecule: two 1s atomic orbitals combine to make one bonding and one antibonding molecular orbital.
    [Show full text]
  • Conjugated Systems, Orbital Symmetry and UV Spectroscopy
    Conjugated Systems, Orbital Symmetry and UV Spectroscopy Introduction There are several possible arrangements for a molecule which contains two double bonds (diene): Isolated: (two or more single bonds between them) Conjugated: (one single bond between them) Cumulated: (zero single bonds between them: allenes) Conjugated double bonds are found to be the most stable. Ch15 Conjugated Systems (landscape).docx Page 1 Stabilities Recall that heat of hydrogenation data showed us that di-substituted double bonds are more stable than mono- substituted double bonds. H2, Pt Ho= -30.0kcal H2, Pt Ho= -27.4kcal When a molecule has two isolated double bonds, the heat of hydrogenation is essentially equal to the sum of the values for the individual double bonds. H2, Pt Ho= -60.2kcal For conjugated dienes, the heat of hydrogenation is less than the sum of the individual double bonds. H2, Pt Ho= -53.7kcal The conjugated diene is more stable by about 3.7kcal/mol. (Predicted –30 + (–27.4) = –57.4kcal, observed –53.7kcal). Ch15 Conjugated Systems (landscape).docx Page 2 Allenes, which have cumulated double bonds are less stable than isolated double bonds. H H H2, Pt C C C Ho= -69.8kcal H CH2CH3 Increasing Stability Order (least to most stable): Cumulated diene -69.8kcal Terminal alkyne -69.5kcal Internal alkyne -65.8kcal Isolated diene -57.4kcal Conjugated diene -53.7kcal Ch15 Conjugated Systems (landscape).docx Page 3 Molecular Orbital (M.O.) Picture The extra stability of conjugated double bonds versus the analogous isolated double bond compound is termed the resonance energy. Consider buta-1,3-diene: H2, Pt Ho= -30.1kcal H2, Pt Ho= -56.6kcal (2 x –30.1 = –60.2kcal).
    [Show full text]
  • An Introduction to Molecular Orbital Theory
    Objectives of the course • Wave mechanics / Atomic orbitals (AOs) – The basis for rejjgecting classical mechanics ( the Bohr Model) in treating An introduction to electrons – Wave mechanics and the Schrödinger equation Molecular Orbital Theory – Representatifion of atom ibilic orbitals as wave fifunctions – Electron densities and radial distribution functions – Understanding the effects of shielding and penetration on AO energies 6 Lecture Course • Bonding – Review VSEPR and Hybridisation Prof G. W. Watson – Linear combination of molecular orbitals (LCAO), bonding / antibonding Lloyd d Ins titut e 2 .36 – La be lling o f mo lecu lar or bital s (MO s) ( σ, π and)d g, u) [email protected] – Homonuclear diatomic MO diagrams – mixing of different AO’s – More complex molecules (CO , H 2O)O ….) – MO diagrams for Inorganic complexes 2 Lecture schedule Literature Lecture 1 Revision of Bohr model of atoms • Book Sources: all titles listed here are available in the Hamilton Library Lecture 2 Schrödinger equation, atomic wavefunctions and radial – 1. Chemical Bonding, M. J. Winter (Oxford Chemistry primer 15) distribution functions of s orbitals Oxford Science Publications ISBN 0 198556942 – condensed text, excellent diagrams Lecture 3 More complex wavefunctions and radial distribution functions and electron shielding – 2. Basic Inorggy(y),,anic Chemistry (Wiley) F.A.Cotton, G. Wilkinson, P. L. Gaus – comprehensive text, very detailed on aufbau principle Lecture 4 Lewis bonding, Hybridisation, and molecular orbitals – 3. Inorgan ic Chemi stry (P renti
    [Show full text]
  • Molecular Orbital Theory
    Prof. Manik Shit, SACT, Department of Chemistry, Narajole Raj College, Narajole. Molecular Orbital Theory Introduction to Molecular Orbital Theory Valence Bond Theory fails to answer certain questions like Why He2 molecule does not exist and why O2 is paramagnetic? Therefore in 1932 F. Hood and RS. Mulliken came up with theory known as Molecular Orbital Theory to explain questions like above. According to Molecular Orbital Theory individual atoms combine to form molecular orbitals, as the electrons of an atom are present in various atomic orbitals and are associated with several nuclei. Fig. No. 1 Molecular Orbital Theory Electrons may be considered either of particle or of wave nature. Therefore, an electron in an atom may be described as occupying an atomic orbital, or by a wave function Ψ, which are solution to the Schrodinger wave equation. Electrons in a molecule are said to occupy molecular orbitals. The wave function of a molecular orbital may be obtained by one of two method: 1. Linear Combination of Atomic Orbitals (LCAO). 2. United Atom Method. PAPER: C6T (Inorganic Chemistry - II) TOPIC : Chemical Bonding (Part -1) Prof. Manik Shit, SACT, Department of Chemistry, Narajole Raj College, Narajole. Linear Combination of Atomic Orbitals (LCAO) As per this method the formation of orbitals is because of Linear Combination (addition or subtraction) of atomic orbitals which combine to form molecule. Consider two atoms A and B which have atomic orbitals described by the wave functions ΨA and ΨB .If electron cloud of these two atoms overlap, then the wave function for the molecule can be obtained by a linear combination of the atomic orbitals ΨA and ΨB i.e.
    [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]
  • Molecular Orbital Theory Reading: Dekock and Gray, Chap 4 (But Not
    Chem 104A, UC, Berkeley Molecular Orbital Theory Reading: DeKock and Gray, Chap 4 (but not 4-8) Chap 5 (through 5-8) Miessler and Tarr, Chap 5 Chem 104A, UC, Berkeley 1 Chem 104A, UC, Berkeley Linear Combination of Atomic Orbitals (LCAO) k c11 c22 .... cnn 1. n atomic orbitals n molecular orbitals. 2. Like atomic orbitals, MOs are ortho-normal dv 1...(i j) i j dv 0...(i j) i j Chem 104A, UC, Berkeley 2 Chem 104A, UC, Berkeley * * ( u ) N (1sA 1sB ) b b ( g ) N (1sA 1sB ) [ ( b )]2dv [N b (1s 1s )]2 dv 1 g A B (N b )2[ (1s )2 dv 2 (1s )(1s )dv (1s )2 dv] 1 A A B B 1 SAB 1 1 N b 2 2S AB Overlap integral * 1 Degree of spatial overlap between any two AOs N From different atoms in a molecule. 2 2S AB Chem 104A, UC, Berkeley Gerade and Ungerade MO symmetry 1s 1s 1s 1s a b b a 2(1 Sab ) 2(1 Sab ) a, b, exchange position, MO does not change, inversion Even parity, Gerade: German word for “even”. 1s 1s 1s 1s a b b a 2(1 Sab ) 2(1 Sab ) a, b, exchange position, MO does change, no inversion odd parity, ungerade: German word for “odd”. 3 Chem 104A, UC, Berkeley The energy of these two orbitals are obtained by applying Schrodinger Equation Orbital Interaction Diagram 1. Always draw axis 2. Fill in electron using Aufbau principle Chem 104A, UC, Berkeley * N*=1.4 * u -13.6 eV b Nb=0.53 * b > b g 4 Chem 104A, UC, Berkeley •Bond order = ½ (#bonding e-s - #antibonding e-s) •Bond order = 0 indicates the species will not exist.
    [Show full text]
  • Local Density Functional Theory of Atoms and Molecules (Statistical Theory/Thomas-Fermi Method) ROBERT G
    Proc. NatI. Acad. Sci. USA Vol. 76, No. 6, pp. 2522-2526, June 1979 Physics Local density functional theory of atoms and molecules (statistical theory/Thomas-Fermi method) ROBERT G. PARR, SHRIDHAR R. GADRE, AND LIBERO J. BARTOLOTTI Department of Chemistry, University of North Carolina, Chapel Hill, North Carolina 27514 Contributed by Robert G. Parr, February 26, 1979 ABSTRACT A local density functional theory of the ground LOCAL DENSITY FUNCTIONAL THEORY electronic states of atoms and molecules is generated from three assumptions: (i) The energy functional is local. (ii) The chemical By a local density functional is meant a functional whose potential of a neutral atom is zero. (iii)The energy of a neutral functional derivative with respect to the density, at a point, is atom of atomic number Z is -0.6127 Z7/3. The energy func- a function only of the density at that point (and not its deriva- tional is shown to have the form tives or integrals). A local approximation for T[p] is an integral ft(p)dr; a local approximation for V,[p] is an integral E[p] = Aofp5/3dT + - BoN2/3fp4/3dr + Svpdr fwVee(p)dr. That these are portions of kinetic and potential energies, respectively, in fact uniquely fixes the forms of t(p) where AO = 6.4563 and Bo = 1.0058. The first term represents the electronic kinetic energy, the second term represents the and v,(p) (3); up to multiplicative constants they must be, re- electron-electron repulsion energy for Nelectrons, and the third spectively, p5/3 and p4/3.
    [Show full text]
  • Molecular Orbital and Valence Bond Theory Explained (Hopefully)
    MOLECULAR ORBITAL AND VALENCE BOND THEORY EXPLAINED (HOPEFULLY) Quantum Mechanics is a very difficult topic, with a great deal of detail that is extremely complex, yet interesting. However, in this Organic 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. There are many solutions to the Schrödinger equation for a given atom. 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.
    [Show full text]