Electronic Structure Models
|
|
- Chester Cook
- 6 years ago
- Views:
Transcription
1 Electronic Structure Models Hückel Model (1933) Basic Assumptions: (a) One orbital per atom contributes to the basis set; all orbitals "equal" (b) The relevant integrals involving the Hamiltonian are α if µ =ν (same site) Hµν = β if µ ν but µ and ν are bonded (nearest neighbors) 0 otherwise (c) The atomic orbitals are assumed normalized and orthogonal: Sµν = 1 if µ = ν 0 if µ ν α and β are parameters; their values will be adjusted to eperimental data of some sort, typically after the calculation is done (or not at all) Consider, as the easy (trivial?) eample, ethylene with the 2p(π) orbitals as the basis set. The secular determinant for two basis functions is H 11 - ES 11 H 12 - ES 12 A
2 = 0 H 21 - ES 21 H 22 - ES 22 which, in the Hückel model, becomes α - E β β α - E = 0 Multiply out the secular determinant and find the roots: (α - E)2 - β2 = 0 => (α - E)2 = β2 => α - E = ± β or E 2 = α - β α α β E 1 = α + β E 1 = α + β and E 2 = α - β We may then find the two sets of coefficients (one for φ 1, one for φ 2 ) from the secular equations B
3 α - E β c 1 0 β α - E c 2 0 (α - E) c 1 + β c 2 = 0 β c 1 + (α - E) c 2 = 0 When E = E 1 = α + β, we find by insertion (into either equation) (α - (α + β)) c 1 + β c 2 = 0 => - β c 1 + β c 2 = 0 => - β c 1 = - β c 2 => c 1 = c 2 When E = E 2 = α - β, we find (α - (α - β)) c 1 ' + β c 2 ' = 0 => β c 1 ' + β c 2 ' = 0 => β c 1 ' = - β c 2 ' => c 1 ' = -c 2 ' The coefficients must, of course, be equal in magnitude, since the two carbon atoms are symmetry equivalent. So, φ 1 = c 1 (χ 1 + χ 2 ) φ 2 = c 1 ' (χ 1 - χ 2 ) E1 = α + β E2 = α - β C
4 The MO's should be properly normalized in order to represent probability distributions. The atomic orbitals χ 1 and χ 2 are assumed to be properly normalized, and orthogonal V χ 1 χ 1 dv = V χ 2 χ 2 dv = 1 V χ 1 χ 2 dv = V χ 2 χ 1 dv = 0 So we find the actual value for c1 or c1' from the normalization condition: V φ 1 φ 1 dv = 1 => V c 1 2 (χ 1 + χ 2 )2 dv = 1 => c 1 2 V χ 1 χ 1 dv + 2c 1 2 V χ 1 χ 2 dv + c 1 2 V χ 2 χ 2 dv = 1 => c c 1 2S 12 + c 1 2 = 1 => c 1 = [2(1+ S 12 )]-1/2 Similarly: V φ 2 φ 2 dv = 1 => c 1 ' = [2(1 - S 12 )] -1/2 Within the Hückel-model, S 12 = 0 and we get c 1 = (2)-1/2 and c 1 ' = (2)-1/2. The overlap between the two pi-orbitals in ethylene is in fact near 0.25, and if there were no overlap between the orbitals, there would be no pi-bonding at all. Interatomic overlap is a prerequisite for covalent chemical bonding. Nevertheless, in most semi-empirical methods the overlap D
5 integrals are neglected in normalization considerations, as a mathematical convenience. Thus, the normalized Hückel π-mo's for ethylene are φ 1 = (2)-1/2 (χ 1 + χ 2 ) φ 2 = (2)-1/2 (χ 1 - χ 2 ) E 1 = α + β E 2 = α - β φ 2 = (2) -1/2 (χ 1 - χ 2 ) E 2 = α - β χ 1 α α χ 2 β E 1 = α + β φ 1 = (2) -1/2 (χ 1 + χ 2 ) E
6 φ 1 increases the electron density between the atoms relative to the two atoms non-interacting; φ 2 has depleted electron density between the atoms relative to the two atoms non-interacting. φ 1 is a "bonding" orbital, φ 2 is an "antibonding" orbital. Therefore, E1 is less than E2 and β must be a negative quantity. α = energy of an electron in orbital µ in the molecule (negative quantity). α depends on orbital type and nuclear charge. β = energy gained by electron "delocalization" or "resonance" between orbitals µ and ν. β depends on orbital types, nuclear charges, and degree of overlap between the orbitals. Electronic energy: E = 2E 1 = 2(α + β) E(isolated atoms) = α + α = 2α; Energy gained by bonding: 2β F
7 In fact, most useful results from Hückel calculations are epressed in terms of β. (1) Optical ecitation; Plot HOMO-LUMO energy difference vs. UVmaimum for lowest allowed absorption band for a series of polyenes or rings. E = E(LUMO) - E(HOMO) ν ma (cm -1 ) Optimal value of β = -2.7 ev (2) Ionization potential; IP = -E(HOMO) Optimal value of β = -2.9 ev (3) Electron affinities; EA = E(LUMO) Optimal value of β = -2.4 ev (4) Delocalization energy; defined as E (delocalized) - E (localized), should correlate with heats of formation data. Optimal value of β = ev (!!!) G
8 Conclusion: Different optimal parameters for different properties. The optimal parameters tend to cluster in two groups, one for "spectroscopic" properties and one for "thermodynamic" properties (dynamic vs. static). This observation and idea carries over to more elaborate electronic structure models as well --- a particular parameterization scheme works best for ground state properties whereas a (quite) different set of parameters are more appropriate for spectroscopic (ecited state) properties H
9 The pi molecular orbitals and energies for butadiene are attached. They are the results of diagonalizing a 44 determinant (χ 1,χ 2,χ 3,χ 4 ) within the Hückel model. Useful indices: charges and bond orders π-charge, i.e. number of pi-electrons per atom q µ = Σ i N i c µi 2 N = # electrons in MO i (2,1, or 0) c µi = coefficient of atom µ in MO i Sum is over all occupied MO's Ethylene: q 1 = 2[(2) -1/2 ]2 = 1.00 = q 2 Butadiene: q 1 = 2 (0.37)2 + 2 (0.60)2 = 1.00 = q 2 = q 3 = q 4 Bond order: The bond order between two (adjacent) atoms µ and ν is p µν = Σ i N i c µi c νi Ni = # electrons in MO i (2,1, or 0) c µi = coefficient on atom µ in MO i c νi = coefficient on atom ν in MO i Note: p µµ = q µ Ethylene: p 12 = 2 (2) -1/2 (2) -1/2 = 1.00 (standard) Butadiene: I
10 p 12 = 2(0.37)(0.60) + 2(0.60)(0.37) = 0.89 p 23 = 2(0.60)(0.60) + (0.37)(-0.37) = 0.45 p 34 = 2(0.37)(0.60) + 2(0.60)(0.37) = 0.89 p 12 < 1.00 and p 23 > 0.45 => delocalization of pi-electron into the central bond Pi bond-orders between adjacent atoms range from 0.0 to 1.0 (0.66 in benzene, for eample). There is ecellent correlation between pi bond orders and bond lengths. For eample, R(C 1 -C 2 ) = 1.517Å pc1-c2 Å The matri P which has as its elements the charges (diagonal) and bond-orders (off-diagonal) is called the charge - bond order matri. In fancier language, it is called the density matri; in very fancy language, it is called the "first order reduced density matri". J
11 CALCULATION FOR ETHYLENE HUCKEL MATRIX BY COLUMNS MO- 1 MO- 2 MO- 0 E/BETA C C ORBITAL OCCUPANCY MO 1--2 MO 2--0 MO HUCKEL ENERGY (UNITS OF BETA) = BOND-ORDER MATRIX BY COLUMNS CHARGE NET SPIN DENSITY CHARGE DENSITY C C SPIN DENSITY IS FOR HIGHEST MULTIPLICITY CALCULATION FOR BUTADIENE HUCKEL MATRIX BY COLUMNS K
12 MO- 1 MO- 2 MO- 3 MO- 4 MO- 0 E/BETA C C C C ORBITAL OCCUPANCY MO 1--2 MO 2--2 MO 3--0 MO 4--0 MO HUCKEL ENERGY (UNITS OF BETA) = BOND-ORDER MATRIX BY COLUMNS CHARGE NET SPIN DENSITY CHARGE DENSITY C C C C SPIN DENSITY IS FOR HIGHEST MULTIPLICITY L
PAPER:2, PHYSICAL CHEMISTRY-I QUANTUM CHEMISTRY. Module No. 34. Hückel Molecular orbital Theory Application PART IV
Subject PHYSICAL Paper No and Title TOPIC Sub-Topic (if any), PHYSICAL -II QUANTUM Hückel Molecular orbital Theory Module No. 34 TABLE OF CONTENTS 1. Learning outcomes. Hückel Molecular Orbital (HMO) Theory
More informationMolecular Orbital Theory
Molecular Orbital Theory While FMO theory allows prediction of reactions (by thermodynamics, regio or stereochemistry), all predictions seen so far have been qualitative We have predicted that HOMO or
More informationMOLECULAR STRUCTURE. Molecular Structure - B. Molecular Structure - B. Molecular Structure - B. Molecular Structure - B. Molecular Structure - B
MOLECULAR STRUCTURE Molecular Orbital all orbitals of the appropriate symmetry contribute to a molecular orbital. Bundet Boekfa Chem Div, Faculty Lib Arts & Sci Kasetsart University Kamphaeng Saen Campus
More informationσ u * 1s g - gerade u - ungerade * - antibonding σ g 1s
One of these two states is a repulsive (dissociative) state. Other excited states can be constructed using linear combinations of other orbitals. Some will be binding and others will be repulsive. Thus
More informationHückel Molecular orbital Theory Application PART III
Subject PHYSICAL Paper No and Title TOPIC Sub-Topic (if any) 2, PHYSICAL -I QUANTUM Hückel Molecular orbital Theory Module No. 33 PAPER: 2, PHYSICAL -I TABLE OF CONTENTS 1. Learning outcomes 2. Hückel
More informationIntroduction to DFTB. Marcus Elstner. July 28, 2006
Introduction to DFTB Marcus Elstner July 28, 2006 I. Non-selfconsistent solution of the KS equations DFT can treat up to 100 atoms in routine applications, sometimes even more and about several ps in MD
More informationSymmetry III: Molecular Orbital Theory. Reading: Shriver and Atkins and , 6.10
Lecture 9 Symmetry III: Molecular Orbital Theory Reading: Shriver and Atkins 2.7-2.9 and g 6.6-6.7, 6.10 The orbitals of molecules H H The electron energy in each H atom is -13.6 ev below vacuum. What
More informationGeneral Physical Chemistry II
General Physical Chemistry II Lecture 13 Aleksey Kocherzhenko October 16, 2014" Last time " The Hückel method" Ø Used to study π systems of conjugated molecules" Ø π orbitals are treated separately from
More informationModule:32,Huckel Molecular Orbital theory- Application Part-II PAPER: 2, PHYSICAL CHEMISTRY-I QUANTUM CHEMISTRY
Subject PHYSICAL Paper No and Title TOPIC Sub-Topic (if any) 2, PHYSICAL -I QUANTUM Hückel Molecular orbital Theory Application PART II Module No. 32 TABLE OF CONTENTS 1. Learning outcomes 2. Hückel Molecular
More informationMolecular Simulation I
Molecular Simulation I Quantum Chemistry Classical Mechanics E = Ψ H Ψ ΨΨ U = E bond +E angle +E torsion +E non-bond Jeffry D. Madura Department of Chemistry & Biochemistry Center for Computational Sciences
More informationSame idea for polyatomics, keep track of identical atom e.g. NH 3 consider only valence electrons F(2s,2p) H(1s)
XIII 63 Polyatomic bonding -09 -mod, Notes (13) Engel 16-17 Balance: nuclear repulsion, positive e-n attraction, neg. united atom AO ε i applies to all bonding, just more nuclei repulsion biggest at low
More information3: Many electrons. Orbital symmetries. l =2 1. m l
3: Many electrons Orbital symmetries Atomic orbitals are labelled according to the principal quantum number, n, and the orbital angular momentum quantum number, l. Electrons in a diatomic molecule experience
More informationHückel Molecular Orbital (HMO) Theory
Hückel Molecular Orbital (HMO) Theory A simple quantum mechanical concept that gives important insight into the properties of large molecules Why HMO theory The first MO theory that could be applied to
More information5.4. Electronic structure of water
5.4. Electronic structure of water Water belongs to C 2v point group, we have discussed the corresponding character table. Here it is again: C 2v E C 2 σ v (yz) σ v (xz) A 1 1 1 1 1 A 2 1 1-1 -1 B 1 1-1
More informationLast Name or Student ID
11/05/18, Chem433 Exam # 2 Last ame or Student ID 1. (2 pts) 2. (9 pts) 3. (2 pts) 4. (2 pts) 5. (2 pts) 6. (2 pts) 7. (2 pts) 8. (4 pts) 9. (14 pts) 10. (10 pts) 11. (26/31 pts) 12. (25/27 pts) Extra
More informationLUMO + 1 LUMO. Tómas Arnar Guðmundsson Report 2 Reikniefnafræði G
Q1: Display all the MOs for N2 in your report and classify each one of them as bonding, antibonding or non-bonding, and say whether the symmetry of the orbital is σ or π. Sketch a molecular orbital diagram
More informationBenzene: E. det E E 4 E 6 0.
Benzene: 2 5 3 4 We will solve Schodinger equation for this molecule by considering only porbitals of six carbons under the Huckel approximation. Huckel approximation, though quite crude, provides very
More information$ +! j. % i PERTURBATION THEORY AND SUBGROUPS (REVISED 11/15/08)
PERTURBATION THEORY AND SUBGROUPS REVISED 11/15/08) The use of groups and their subgroups is of much importance when perturbation theory is employed in understanding molecular orbital theory and spectroscopy
More informationThe Hückel Approximation Consider a conjugated molecule i.e. a molecule with alternating double and single bonds, as shown in Figure 1.
The Hückel Approximation In this exercise you will use a program called Hückel to look at the p molecular orbitals in conjugated molecules. The program calculates the energies and shapes of p (pi) molecular
More information1 r A. r B. 2m e. The potential energy of the electron is. r A and r B are the electron s distances from the nuclei A and B. This expression can be
Introduction to Molecular Structure The Born-Oppenheimer approximation The Born-Oppenheimer approximation supposes that the nuclei, being so much heavier than the electron, move relatively slow and may
More information( ) ( ) SALCs as basis functions. LCAO-MO Theory. Rewriting the Schrödinger Eqn. Matrix form of Schrödinger Eqn. Hφ j. φ 1. φ 3. φ 2. φ j. φ i.
LCAO-MO Theory In molecular orbital theory the MOs, { }, are usually expanded as combinations of atomic orbitals, {φ i }. For the µ th MO, we write this expansion as = c iµ φ i = c 1µ φ 1 + c µ φ + c 3µ
More informationPractical 1: Structure and electronic properties of organic molecules. B/ Structure, electronic and vibrational properties of the water molecule
D1CH9116 - MMCO Molecular Modelling applied to organic chemistry Practical 1: tructure and electronic properties of organic molecules B/ tructure, electronic and vibrational properties of the water molecule
More informationELEMENTARY BAND THEORY
ELEMENTARY BAND THEORY PHYSICIST Solid state band Valence band, VB Conduction band, CB Fermi energy, E F Bloch orbital, delocalized n-doping p-doping Band gap, E g Direct band gap Indirect band gap Phonon
More informationNew σ bond closes a ring. Loss of one π bond and gain of one σ bond
CHAPTER 1 Pericyclic Reactions 1.1 INTRODUCTION Pericyclic reactions are defined as the reactions that occur by a concerted cyclic shift of electrons. This definition states two key points that characterise
More informationMolecular Orbital Theory
Junior Sophister Quantum Chemistry Course 333 (Part) Molecular Orbital Theory D.A.Morton-Blake Molecular orbital theory We have seen how the atomic orbital wave function provides a complete description
More informationConjugated Systems. With conjugated double bonds resonance structures can be drawn
Conjugated Systems Double bonds in conjugation behave differently than isolated double bonds With conjugated double bonds resonance structures can be drawn With isolated double bonds cannot draw resonance
More informationBonding and Physical Properties The Molecular Orbital Theory
Bonding and Physical Properties The Molecular Orbital Theory Ø Developed by F. Hund and R. S. Mulliken in 1932 Ø Diagram of molecular energy levels Ø Magnetic and spectral properties Paramagnetic vs. Diamagnetic
More informationCovalent Bonding: Orbitals
Hybridization and the Localized Electron Model Covalent Bonding: Orbitals A. Hybridization 1. The mixing of two or more atomic orbitals of similar energies on the same atom to produce new orbitals of equal
More information- H. Predicts linear structure. Above are all σ bonds
arbon sp hybrids: : Acetylene and the Triple bond 2 2 is - - Form sp on each leaving 2p x, 2p y unused - sp sp + + sp sp - Predicts linear structure. Above are all σ bonds --- Uses up 2 valence e - for
More informationThe successful wavefunction can be written as a determinant: # 1 (2) # 2 (2) Electrons. This can be generalized to our 2N-electron wavefunction:
T2. CNDO to AM1: The Semiempirical Molecular Orbital Models The discussion in sections T2.1 T2.3 applies also to ab initio molecular orbital calculations. T2.1 Slater Determinants Consider the general
More informationValence bond theory accounts, at least qualitatively, for the stability of the covalent bond in terms of overlapping atomic orbitals.
Molecular Orbital Theory Valence bond theory accounts, at least qualitatively, for the stability of the covalent bond in terms of overlapping atomic orbitals. Using the concept of hybridization, valence
More informationLab Week 4 Experiment α 2. Delocalization: Optical and Electronic Properties of C-based Molecules
3.4 Materials Laboratory December 26 Lab Week 4 Eperiment α 2 Delocalization: Optical and Electronic Properties of C-based Molecules OBJECTIVES Instructor: Benjamin Wunsch Review the Linear Combination
More informationChemical Bonding. Lewis Theory-VSEPR Valence Bond Theory Molecular Orbital Theory
Chemical Bonding Lewis Theory-VSEPR Valence Bond Theory Molecular Orbital Theory Problems with Valence Bond Theory VB theory predicts properties better than Lewis theory bonding schemes, bond strengths,
More informationLecture 12. Symmetry Operations. NC State University
Chemistry 431 Lecture 12 Group Theory Symmetry Operations NC State University Wave functions as the basis for irreducible representations The energy of the system will not change when symmetry Operations
More informationANNOUNCEMENTS. If you have questions about your exam 2 grade, write to me or Chapter 8 homework due April. 13 th.
ANNOUNCEMENTS If you have questions about your exam 2 grade, write to me or Chem200@mail.sdsu.edu. Chapter 8 homework due April. 13 th. Chapter 9 home work due April. 20th. Exam 3 is 4/14 at 2 pm. LECTURE
More informationChapter 9. Covalent Bonding: Orbitals
Chapter 9 Covalent Bonding: Orbitals Chapter 9 Table of Contents 9.1 Hybridization and the Localized Electron Model 9.2 The Molecular Orbital Model 9.3 Bonding in Homonuclear Diatomic Molecules 9.4 Bonding
More information5. Organic Electronics and Optoelectronics
1 5. Organic Electronics and Optoelectronics Sources: W. Brütting, Physics of Organic Semiconductors, Wiley-VCH M. Schwoerer / H. C. Wolf, Organic Molecular Solids, Wiley-VCH Atkins / Friedman, Molecular
More informationQuantum mechanics can be used to calculate any property of a molecule. The energy E of a wavefunction Ψ evaluated for the Hamiltonian H is,
Chapter : Molecules Quantum mechanics can be used to calculate any property of a molecule The energy E of a wavefunction Ψ evaluated for the Hamiltonian H is, E = Ψ H Ψ Ψ Ψ 1) At first this seems like
More informationPHYSICAL CHEMISTRY I. Chemical Bonds
PHYSICAL CHEMISTRY I Chemical Bonds Review The QM description of bonds is quite good Capable of correctly calculating bond energies and reaction enthalpies However it is quite complicated and sometime
More informationChapter 9. Covalent Bonding: Orbitals
Chapter 9 Covalent Bonding: Orbitals EXERCISE! Draw the Lewis structure for methane, CH 4. What is the shape of a methane molecule? tetrahedral What are the bond angles? 109.5 o H H C H H Copyright Cengage
More informationLecture 26: Qualitative Molecular Orbital Theory: Hückel Theory
MASSACHUSETTS INSTITUTE OF TECHNOLOGY 5.6 Physical Chemistry I Fall, 07 Professor Robert W. Field Lecture 6: Qualitative Molecular Orbital Theory: Hückel Theory Models in Physical Chemistry Our job is
More informationCHAPTER 9 THEORY OF RESONANCE BY, G.DEEPA
CHAPTER 9 THEORY OF RESONANCE BY, G.DEEPA Conjugation in Alkadienes and Allylic Systems conjugation a series of overlapping p orbitals The Allyl Group allylic position is the next to a double bond 1 allyl
More information:C O: σorbitals of CO. πorbitals of CO. Assumed knowledge. Chemistry 2. Learning outcomes. Lecture 2 Particle in a box approximation. C 2p.
Chemistry 2 Lecture 2 Particle in a bo approimation Assumed knowledge Be able to predict the geometry of a hydrocarbon from its structure and account for each valence electron. Predict the hybridization
More informationMOLECULAR ORBITAL THEORY Chapter 10.8, Morrison and Boyd
MOLECULAR ORBITAL THEORY Chapter 10.8, Morrison and Boyd more understanding: why oxygen is paramagnetic, why H2 + exists; explanation of excited electronic states (e.g., visible spectra) eliminates need
More informationBe H. Delocalized Bonding. Localized Bonding. σ 2. σ 1. Two (sp-1s) Be-H σ bonds. The two σ bonding MO s in BeH 2. MO diagram for BeH 2
The Delocalized Approach to Bonding: The localized models for bonding we have examined (Lewis and VBT) assume that all electrons are restricted to specific bonds between atoms or in lone pairs. In contrast,
More informationMolecular Orbital Theory. WX AP Chemistry Chapter 9 Adapted from: Luis Bonilla Abel Perez University of Texas at El Paso
Molecular Orbital Theory WX AP Chemistry Chapter 9 Adapted from: Luis Bonilla Abel Perez University of Texas at El Paso Molecular Orbital Theory The goal of molecular orbital theory is to describe molecules
More informationChapter 9. Covalent Bonding: Orbitals. Copyright 2017 Cengage Learning. All Rights Reserved.
Chapter 9 Covalent Bonding: Orbitals Chapter 9 Table of Contents (9.1) (9.2) (9.3) (9.4) (9.5) (9.6) Hybridization and the localized electron model The molecular orbital model Bonding in homonuclear diatomic
More informationVibronic Coupling in Quantum Wires: Applications to Polydiacetylene
Vibronic Coupling in Quantum Wires: Applications to Polydiacetylene An Exhaustively Researched Report by Will Bassett and Cole Johnson Overall Goal In order to elucidate the absorbance spectra of different
More informationPericyclic Reactions: Electrocyclic Reaction
Pericyclic Reaction Pericyclic Reactions: Electrocyclic Reaction 1. Electrocyclic ring closing 2. Electrocyclic ring opening Electrocyclic ring closing reaction is characterized by a. The formation of
More informationChapter 9 - Covalent Bonding: Orbitals
Chapter 9 - Covalent Bonding: Orbitals 9.1 Hybridization and the Localized Electron Model A. Hybridization 1. The mixing of two or more atomic orbitals of similar energies on the same atom to produce new
More informationLecture B6 Molecular Orbital Theory. Sometimes it's good to be alone.
Lecture B6 Molecular Orbital Theory Sometimes it's good to be alone. Covalent Bond Theories 1. VSEPR (valence shell electron pair repulsion model). A set of empirical rules for predicting a molecular geometry
More information7: Hückel theory for polyatomic molecules
7: ückel theory for polyatomic molecules Introduction Approximate treatment of π electron systems in organic molecules: 1 Approximations 3 4 5 6 1. π and σ frameworks completely separated. Trial wavefunctions
More informationCHEM J-5 June 2014
CHEM1101 2014-J-5 June 2014 The molecular orbital energy level diagrams for H 2, H 2 +, H 2 and O 2 are shown below. Fill in the valence electrons for each species in its ground state and label the types
More information7. Arrange the molecular orbitals in order of increasing energy and add the electrons.
Molecular Orbital Theory I. Introduction. A. Ideas. 1. Start with nuclei at their equilibrium positions. 2. onstruct a set of orbitals that cover the complete nuclear framework, called molecular orbitals
More informationMolecular Structure Chapter 26: Molecular Structure Problems
Molecular Structure Chapter 26: Molecular Structure Problems 1 1. Draw the Lewis dot resonance structures for the carbonate ion, CO3 2-. Are the electrons delocalized? Give the average bond order for the
More informationANNOUNCEMENTS. If you have questions about your exam 2 grade, write to me or Chapter 7 homework due Nov, 9 th.
ANNOUNCEMENTS If you have questions about your exam 2 grade, write to me or Chem200@sdsu.edu. Chapter 7 homework due Nov, 9 th. Chapter 8 homework due Nov. 16 th. Exam 3 is 11/17 at 2 pm. LECTURE OBJECTIVES
More informationChapter 9. Molecular Geometry and Bonding Theories
Chapter 9. Molecular Geometry and Bonding Theories 9.1 Molecular Shapes Lewis structures give atomic connectivity: they tell us which atoms are physically connected to which atoms. The shape of a molecule
More informationBe H. Delocalized Bonding. Localized Bonding. σ 2. σ 1. Two (sp-1s) Be-H σ bonds. The two σ bonding MO s in BeH 2. MO diagram for BeH 2
The Delocalized Approach to Bonding: The localized models for bonding we have examined (Lewis and VBT) assume that all electrons are restricted to specific bonds between atoms or in lone pairs. In contrast,
More informationMolecular Orbital Theory This means that the coefficients in the MO will not be the same!
Diatomic molecules: Heteronuclear molecules In heteronuclear diatomic molecules, the relative contribution of atomic orbitals to each MO is not equal. Some MO s will have more contribution from AO s on
More informationhand and delocalization on the other, can be instructively exemplified and extended
Text Related to Segment 8.0 00 Claude E. Wintner The ideas developed up to this point, concerning stereochemistry on the one hand and delocalization on the other, can be instructively exemplified and extended
More informationLecture 6. Tight-binding model
Lecture 6 Tight-binding model In Lecture 3 we discussed the Krönig-Penny model and we have seen that, depending on the strength of the potential barrier inside the unit cell, the electrons can behave like
More informationConjugated 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
More informationAndrew Rosen *Note: If you can rotate a molecule to have one isomer equal to another, they are both the same
*Note: If you can rotate a molecule to have one isomer equal to another, they are both the same *Note: For hybridization, if an SP 2 is made, there is one unhybridized p orbital (because p usually has
More informationChapter 12: Chemical Bonding II: Additional Aspects
General Chemistry Principles and Modern Applications Petrucci Harwood Herring 8 th Edition Chapter 12: Chemical Bonding II: Additional Aspects Philip Dutton University of Windsor, Canada N9B 3P4 Prentice-Hall
More informationMulticonfigurational Quantum Chemistry. Björn O. Roos as told by RL Department of Theoretical Chemistry Chemical Center Lund University Sweden
Multiconfigurational Quantum Chemistry Björn O. Roos as told by RL Department of Theoretical Chemistry Chemical Center Lund University Sweden April 20, 2009 1 The Slater determinant Using the spin-orbitals,
More informationQuantum Chemistry. NC State University. Lecture 5. The electronic structure of molecules Absorption spectroscopy Fluorescence spectroscopy
Quantum Chemistry Lecture 5 The electronic structure of molecules Absorption spectroscopy Fluorescence spectroscopy NC State University 3.5 Selective absorption and emission by atmospheric gases (source:
More informationElectronegativity is a very useful concept for the explanation or understanding of chemical reactivity throughout the periodic table.
1.6. Review of Electronegativity (χ) CONCEPT: Electronegativity is a very useful concept for the explanation or understanding of chemical reactivity throughout the periodic table. There are many definitions
More informationNMRis the most valuable spectroscopic technique for organic chemists because it maps the carbon-hydrogen framework of a molecule.
Chapter 13: Nuclear magnetic resonance spectroscopy NMRis the most valuable spectroscopic technique for organic chemists because it maps the carbon-hydrogen framework of a molecule. 13.2 The nature of
More informationGeneral Chemistry. Contents. Chapter 12: Chemical Bonding II: Additional Aspects What a Bonding Theory Should Do. Potential Energy Diagram
General Chemistry Principles and Modern Applications Petrucci Harwood Herring 8 th Edition Chapter 12: Chemical Bonding II: Additional Aspects Philip Dutton University of Windsor, Canada N9B 3P4 Contents
More informationChapter 9: Molecular Geometries and Bonding Theories Learning Outcomes: Predict the three-dimensional shapes of molecules using the VSEPR model.
Chapter 9: Molecular Geometries and Bonding Theories Learning Outcomes: Predict the three-dimensional shapes of molecules using the VSEPR model. Determine whether a molecule is polar or nonpolar based
More informationBorn-Oppenheimer Approximation
Born-Oppenheimer Approximation Adiabatic Assumption: Nuclei move so much more slowly than electron that the electrons that the electrons are assumed to be obtained if the nuclear kinetic energy is ignored,
More informationCHEMISTRY. Chapter 8 ADVANCED THEORIES OF COVALENT BONDING Kevin Kolack, Ph.D. The Cooper Union HW problems: 6, 7, 12, 21, 27, 29, 41, 47, 49
CHEMISTRY Chapter 8 ADVANCED THEORIES OF COVALENT BONDING Kevin Kolack, Ph.D. The Cooper Union HW problems: 6, 7, 12, 21, 27, 29, 41, 47, 49 2 CH. 8 OUTLINE 8.1 Valence Bond Theory 8.2 Hybrid Atomic Orbitals
More informationSymmetry and Molecular Orbitals (I)
Symmetry and Molecular Orbitals (I) Simple Bonding Model http://chiuserv.ac.nctu.edu.tw/~htchiu/chemistry/fall-2005/chemical-bonds.htm Lewis Structures Octet Rule Resonance Formal Charge Oxidation Number
More informationChemistry 2000 Lecture 1: Introduction to the molecular orbital theory
Chemistry 2000 Lecture 1: Introduction to the molecular orbital theory Marc R. Roussel January 5, 2018 Marc R. Roussel Introduction to molecular orbitals January 5, 2018 1 / 24 Review: quantum mechanics
More informationChemistry 431. Lecture 14. Wave functions as a basis Diatomic molecules Polyatomic molecules Huckel theory. NC State University
Chemistry 431 Lecture 14 Wave functions as a basis Diatomic molecules Polyatomic molecules Huckel theory NC State University Wave functions as the basis for irreducible representations The energy of the
More informationTheoretical Chemistry - Level II - Practical Class Molecular Orbitals in Diatomics
Theoretical Chemistry - Level II - Practical Class Molecular Orbitals in Diatomics Problem 1 Draw molecular orbital diagrams for O 2 and O 2 +. E / ev dioxygen molecule, O 2 dioxygenyl cation, O 2 + 25
More informationPhysical Chemistry II Recommended Problems Chapter 12( 23)
Physical Chemistry II Recommended Problems Chapter 1( 3) Chapter 1(3) Problem. Overlap of two 1s orbitals recprobchap1.odt 1 Physical Chemistry II Recommended Problems, Chapter 1(3), continued Chapter
More informationChem 452 Exam III April 8, Cover Sheet Closed Book, Closed Notes
Last Name: First Name: PSU ID#: (last 4 digit) Chem 452 Exam III April 8, 2009 Cover Sheet Closed Book, Closed Notes There are 6 problems. The point value of each part of each problem is indicated. Useful
More informationReikniefnafræði - Verkefni 2 Haustmisseri 2013 Kennari - Hannes Jónsson
Háskóli Íslands, raunvísindasvið Reikniefnafræði - Verkefni 2 Haustmisseri 2013 Kennari - Hannes Jónsson Guðjón Henning 18. september 2013 1 A. Molecular orbitals of N 2 Q1: Display all the MOs for N 2
More informationPeriodic Trends in Properties of Homonuclear
Chapter 8 Periodic Trends in Properties of Homonuclear Diatomic Molecules Up to now, we have discussed various physical properties of nanostructures, namely, two-dimensional - graphene-like structures:
More informationMolecular Orbitals. Based on Inorganic Chemistry, Miessler and Tarr, 4 th edition, 2011, Pearson Prentice Hall
Molecular Orbitals Based on Inorganic Chemistry, Miessler and Tarr, 4 th edition, 2011, Pearson Prentice Hall Images from Miessler and Tarr Inorganic Chemistry 2011 obtained from Pearson Education, Inc.
More informationCHEM1901/ J-5 June 2013
CHEM1901/3 2013-J-5 June 2013 Oxygen exists in the troposphere as a diatomic molecule. 4 (a) Using arrows to indicate relative electron spin, fill the left-most valence orbital energy diagram for O 2,
More informationOn semiempirical treatment of hydrocarbons
On semiempirical treatment of hydrocarbons Debangshu Mukherjee B.Sc Physics, IInd Year Chennai Mathematical Institute 27..2009 Abstract As, we do in case of small systems like H + 2 or He atom, we write
More informationChemistry 543--Final Exam--Keiderling May 5, pm SES
Chemistry 543--Final Exam--Keiderling May 5,1992 -- 1-5pm -- 174 SES Please answer all questions in the answer book provided. Make sure your name is clearly indicated and that the answers are clearly numbered,
More informationMO theory is better for spectroscopy (Exited State Properties; Ionization)
CHEM 2060 Lecture 25: MO Theory L25-1 Molecular Orbital Theory (MO theory) VB theory treats bonds as electron pairs. o There is a real emphasis on this point (over-emphasis actually). VB theory is very
More informationSCF calculation on HeH +
SCF calculation on HeH + Markus Meuwly Department of Chemistry, University of Basel, Basel, Switzerland Abstract This document describes the main steps involved in carrying out a SCF calculation on the
More informationJournal of Chemical and Pharmaceutical Research
Available on line www.jocpr.com Journal of Chemical and Pharmaceutical Research ISSN No: 0975-7384 CODEN(USA): JCPRC5 J. Chem. Pharm. Res., 2011, 3(1):572-583 Ground state properties: Gross orbital charges,
More informationwith the larger dimerization energy also exhibits the larger structural changes.
A7. Looking at the image and table provided below, it is apparent that the monomer and dimer are structurally almost identical. Although angular and dihedral data were not included, these data are also
More informationChemistry: The Central Science. Chapter 9: Molecular Geometry and Bonding Theory
Chemistry: The Central Science Chapter 9: Molecular Geometry and Bonding Theory The shape and size of a molecule of a particular substance, together with the strength and polarity of its bonds, largely
More informationMolecular Shape and Molecular Polarity. Molecular Shape and Molecular Polarity. Molecular Shape and Molecular Polarity
Molecular Shape and Molecular Polarity When there is a difference in electronegativity between two atoms, then the bond between them is polar. It is possible for a molecule to contain polar bonds, but
More information* 1s. --- if the sign does change it is called ungerade or u
Chapter Qualitative Theory of Chemical Bondin Backround: We have briefly mentioned bondin but it now time to talk about it for real. In this chapter we will delocalied orbitals and introduce Hückel MOT.
More informationTerms used in UV / Visible Spectroscopy
Terms used in UV / Visible Spectroscopy Chromophore The part of a molecule responsible for imparting color, are called as chromospheres. OR The functional groups containing multiple bonds capable of absorbing
More informationChapter 9 Molecular Geometry and Bonding Theories
Chapter 9 Molecular Geometry and Bonding Theories 9.1 Molecular Shapes Lewis structures give atomic connectivity (which atoms are physically connected). By noting the number of bonding and nonbonding electron
More informationThe symmetry properties & relative energies of atomic orbitals determine how they react to form molecular orbitals. These molecular orbitals are then
1 The symmetry properties & relative energies of atomic orbitals determine how they react to form molecular orbitals. These molecular orbitals are then filled with the available electrons according to
More informationChapter 9. Molecular Geometries and Bonding Theories. Lecture Presentation. John D. Bookstaver St. Charles Community College Cottleville, MO
Lecture Presentation Chapter 9 Theories John D. Bookstaver St. Charles Community College Cottleville, MO Shapes The shape of a molecule plays an important role in its reactivity. By noting the number of
More informationChapter 3. Orbitals and Bonding
Chapter 3. Orbitals and Bonding What to master Assigning Electrons to Atomic Orbitals Constructing Bonding and Antibonding Molecular Orbitals with Simple MO Theory Understanding Sigma and Pi Bonds Identifying
More informationElectronic structure / bonding in d-block complexes
LN05-1 Electronic structure / bonding in d-block complexes Many, many properties of transition metal complexes (coordination number, structure, colour, magnetism, reactivity) are very sensitive to the
More informationMolecular Orbitals for Ozone
Molecular Orbitals for Ozone Purpose: In this exercise you will do semi-empirical molecular orbital calculations on ozone with the goal of understanding the molecular orbital print out provided by Spartan
More informationFlatbands in 2D boroxine-linked covalent organic frameworks
Electronic Supplementary Material (ESI) for Physical Chemistry Chemical Physics. This journal is the Owner Societies 215 Supplementary Material Flatbands in 2D boroxine-linked covalent organic frameworks
More informationChemistry 2. Lecture 1 Quantum Mechanics in Chemistry
Chemistry 2 Lecture 1 Quantum Mechanics in Chemistry Your lecturers 8am Assoc. Prof Timothy Schmidt Room 315 timothy.schmidt@sydney.edu.au 93512781 12pm Assoc. Prof. Adam J Bridgeman Room 222 adam.bridgeman@sydney.edu.au
More information