LUMO + 1 LUMO. Tómas Arnar Guðmundsson Report 2 Reikniefnafræði G
|
|
|
- Robyn Bishop
- 5 years ago
- Views:
Transcription
1 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 using the values of the energy of the MOs from the output file and compare your diagram with the one in your physical chemistry or freshman chemistry textbook. LUMO + 1 Antibonding π orbitals E8 = Hartree = ev LUMO Antibonding π orbitals E7 = Hartree = ev 1
2 HOMO Bonding π orbitals E6 = Hartree = ev HOMO-1 Bonding π orbitals E5 = Hartree = ev 2
3 HOMO-2 E4 = Hartree = ev HOMO-3 Antibonding σ orbitals E3 = Hartree = ev HOMO-4 E2 = Hartree = ev 3
4 HOMO-5 Antibonding σ orbitals E1 = Hartree = ev HOMO-6 E0 = Hartree = ev MO diagram: LUMO+1: ev π* LUMO: ev π* HOMO: ev π HOMO-2: ev σ HOMO-1: ev π HOMO-3: ev σ* HOMO-4: ev σ HOMO-5: ev σ* HOMO-6: ev σ 4
5 Q2: Which spin state is lower in energy for the O2 molecule? Explain by referring to the energy of the MOs (recall Hund s rule). Note, that when you do calculations of the triplet state, there is a listing of both alpha and beta MOs. Singlet state MO diagram (only P orbital mixing shown): σ* The singlett state requires electrons in degenerate energy levels (π*) π* to pair up, that is not favorable since the pairing itself is higher in energy than the alternative unpaired triplett state due to repulsion π σ forces. Hund s rule states that for degenerate energy levels the electrons should first occupy both levels before pairing. Triplet state MO diagram (only P orbital mixing shown): _ σ* The repulsion forces are minimized in this case and Hund s rule is π* applied, so this state is energetically favorable. π σ 5
6 Q3: Display all the MOs for O2 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 using the values of the energy of the MOs from the output file. If you found the triplet state to be lower in energy, include both the spin-up and spin-down orbital energy in the diagram. Alpha orbitals (spin up): LUMO+1 E1 = Hartree = ev LUMO Antibonding σ orbitals E1 = Hartree = ev 6
7 HOMO Antibonding π orbitals E1 = Hartree = ev HOMO-1 Antibonding π orbitals E1 = Hartree = ev HOMO-2 E1 = Hartree = ev 7
8 HOMO-3 Bonding π orbitals E1 = Hartree = ev HOMO-4 Bonding π orbitals E1 = Hartree = ev HOMO-5 Antibonding σ orbitals E1 = Hartree = ev 8
9 HOMO-6 E1 = Hartree = ev HOMO-7 Antibonding σ orbitals E1 = Hartree = ev HOMO-8 E1 = Hartree = ev 9
10 Beta orbitals (spin down): LUMO+1 Antibonding π orbitals E1 = Hartree = 2.66 ev LUMO Antibonding π orbitals E1 = Hartree = 2.66 ev HOMO Bonding π orbitals E1 = Hartree = ev 10
11 HOMO-1 Bonding π orbitals E1 = Hartree = ev HOMO-2 E1 = Hartree = ev HOMO-3 Antibonding σ orbitals E1 = Hartree = ev 11
12 HOMO-4 E1 = Hartree = ev HOMO-5 Antibonding σ orbitals E1 = Hartree = ev HOMO-6 E1 = Hartree = ev 12
13 MO diagram: UP LUMO+1: ev π* UP LUMO: ev σ* DOWN LUMO+1: 2.66 ev π* DOWN LUMO: 2.66 ev π* UP HOMO: ev π* UP HOMO-1: ev π* DOWN HOMO: ev π DOWN HOMO-1: ev π UP HOMO-2: ev σ DOWN HOMO-2: ev σ UP HOMO-3: ev π UP HOMO-4: ev π UP HOMO-5: ev σ* UP HOMO-6: ev σ DOWN HOMO-3: ev σ* DOWN HOMO-4: ev σ UP HOMO-7: ev σ* UP HOMO-8: ev σ DOWN HOMO-5: ev σ* DOWN HOMO-6: ev σ 13
14 Q4: Make a plot of the energy of the H2 molecule versus the distance between the atoms (using for example Excel, Matlab or Gnuplot). 14
15 Q5: What value should the energy approach when the bond length is increased to infinity? Does the binding curve you calculated indicate this? Energy at various values of distance between H atoms (using RHF): Distance [Å]: Energy [Hartree]: When the bond distance approaches infinity the bond energy should approach zero, due to there being absolutely no interaction between the two atoms when at an infinite distance from each other, however the remaining potential energy will be for the ground state of two H atoms, that is 2*-13.6 ev = ev. So when the bond distance approaches infinity the energy will approach ev. The binding curve goes over the ev, the final calculated point (2Å) has the potential energy Hartree = ev. 15
16 Q6: Create one plot with three curves: One for the singlet state in restricted Hartree-Fock (RHF), one for the singlet state in unrestricted Hartree-Fock (UHF) and one for the triplet state. Also, add a horizontal line at the energy of two completely separated hydrogen atoms. Q7: Compare the RHF and the UHF curves. Describe the problem that occurs in the RHF calculation for large bond lengths. What is the reason for it? The reason the triplet state calculation is so different from the others is that the triplet state does not allow bond formation, so the energy plot is based on repulsion forces, eventually resulting in the non-interacting potential energy. RHF requires the atom or molecule in question to remain a closed-shell system, with all orbital levels doubly occupied. If the H atoms are separated they each need to have an electron in their 1s level, resulting in energy levels that are not doubly occupied. RHF therefore forces the 2 H atoms to bond, regardless of distance, resulting in a high energy cost for the bond at long 16
17 distances. UHF allows the two electrons to have different spatial orbitals and therefore lets the system be open-shell, this allows the electrons to separate and the H atoms to stop interacting eventually. Even though the electrons are each in their own orbital the singlet state is maintained if they still have opposite spin. Q8: Can two H-atoms form a bond in the singlet state? How about the triplet state? Is the formation of the bond(s) out of two isolated atoms exothermic or endothermic? Singlet state H2 has the following MO diagram: σ* This state forms a bond, having a σ bond order of 1. Triplet state H2 has the following MO diagram: _ _ σ* This state cannot form a bond as it has equal occupation in bonding and σ antibonding orbitals, resulting in a bond order of 0. As can be seen from the plot in Q6 (UHF singlet state) the total potential energy of the molecule is lower than if we have two non-interacting H atoms, so the bond formation is exothermic. 17
18 Q9: How does the binding curve of this calculation differ from the previous UHF calculation? Why is that? Since the orbitals for the hydrogen molecule are symmetric in this calculation, the initial guess for the orbital functions is symmetric as well. Since symmetry is a very powerful tool the next guesses will retain this symmetry. This is however not ideal in this case because it assumes complete symmetry for the spin up and spin down electrons, and thus the unrestricted HF calculation is forced into the restricted version. This results in the exact same plot as the RHF singlet in the plot from Q6. 18
Reikniefnafræði - 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
Physical 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
CHEM 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
Molecular 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
IFM Chemistry Computational Chemistry 2010, 7.5 hp LAB2. Computer laboratory exercise 1 (LAB2): Quantum chemical calculations
Computer laboratory exercise 1 (LAB2): Quantum chemical calculations Introduction: The objective of the second computer laboratory exercise is to get acquainted with a program for performing quantum chemical
Introduction to Hartree-Fock calculations in Spartan
EE5 in 2008 Hannes Jónsson Introduction to Hartree-Fock calculations in Spartan In this exercise, you will get to use state of the art software for carrying out calculations of wavefunctions for molecues,
Molecular-Orbital Theory
Prof. Dr. I. Nasser atomic and molecular physics -551 (T-11) April 18, 01 Molecular-Orbital Theory You have to explain the following statements: 1- Helium is monatomic gas. - Oxygen molecule has a permanent
Theoretical 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
Hints on Using the Orca Program
Computational Chemistry Workshops West Ridge Research Building-UAF Campus 9:00am-4:00pm, Room 009 Electronic Structure - July 19-21, 2016 Molecular Dynamics - July 26-28, 2016 Hints on Using the Orca Program
Reikniefnafræði - Verkefni 1 Haustmisseri 2013 Kennari - Hannes Jónsson
Háskóli Íslands, raunvísindasvið Reikniefnafræði - Verkefni 1 Haustmisseri 2013 Kennari - Hannes Jónsson Guðjón Henning 11. september 2013 A. Molecular orbitals and electron density of H 2 Q1: Present
Lecture 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
CHEM6085: Density Functional Theory Lecture 10
CHEM6085: Density Functional Theory Lecture 10 1) Spin-polarised calculations 2) Geometry optimisation C.-K. Skylaris 1 Unpaired electrons So far we have developed Kohn-Sham DFT for the case of paired
General Physical Chemistry II
General Physical Chemistry II Lecture 10 Aleksey Kocherzhenko October 7, 2014" Last time " promotion" Promotion and hybridization" [He] 2s 2 2p x 1 2p y 1 2p z0 " 2 unpaired electrons" [He] 2s 1 2p x 1
Organic Electronic Devices
Organic Electronic Devices Week 2: Electronic Structure Lecture 2.1: Atomic and Molecular Orbitals Bryan W. Boudouris Chemical Engineering Purdue University 1 Lecture Overview and Learning Objectives Concepts
Lecture 4: Hartree-Fock Theory
Lecture 4: Hartree-Fock Theory One determinant to rule them all, One determinant to find them, One determinant to bring them all and in the darkness bind them Second quantization rehearsal The formalism
Valence 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
Be 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,
11/29/2014. Problems with Valence Bond Theory. VB theory predicts many properties better than Lewis Theory
Problems with Valence Bond Theory VB theory predicts many properties better than Lewis Theory bonding schemes, bond strengths, bond lengths, bond rigidity however, there are still many properties of molecules
Molecular 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
The 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
In this lecture we will understand how the molecular orbitals are formed from the interaction of atomic orbitals.
Lecture 7 Title: Understanding of Molecular Orbital Page-1 In this lecture we will understand how the molecular orbitals are formed from the interaction of atomic orbitals. We will see how the electrons
Chemistry 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
Name. Chem Organic Chemistry II Laboratory Exercise Molecular Modeling Part 2
Name Chem 322 - Organic Chemistry II Laboratory Exercise Molecular Modeling Part 2 Click on Titan in the Start menu. When it boots, click on the right corner to make the window full-screen. icon in the
3: 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
Be 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,
A Computer Study of Molecular Electronic Structure
A Computer Study of Molecular Electronic Structure The following exercises are designed to give you a brief introduction to some of the types of information that are now readily accessible from electronic
This is called a singlet or spin singlet, because the so called multiplicity, or number of possible orientations of the total spin, which is
9. Open shell systems The derivation of Hartree-Fock equations (Chapter 7) was done for a special case of a closed shell systems. Closed shell means that each MO is occupied by two electrons with the opposite
Symmetry 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
PAPER :8, PHYSICAL SPECTROSCOPY MODULE: 29, MOLECULAR TERM SYMBOLS AND SELECTION RULES FOR DIATOMIC MOLECULES
Subject Chemistry Paper No and Title Module No and Title Module Tag 8: Physical Spectroscopy 29: Molecular Term Symbols and Selection Rules for Diatomic Molecules. CHE_P8_M29 TLE OF CONTENTS 1. Learning
Literature values: ΔH f, gas = % error Source: ΔH f, solid = % error. For comparison, your experimental value was ΔH f = phase:
1 Molecular Calculations Lab: Some guideline given at the bottom of page 3. 1. Use the semi-empirical AM1 method to calculate ΔH f for the compound you used in the heat of combustion experiment. Be sure
Activity Molecular Orbital Theory
Activity 201 9 Molecular Orbital Theory Directions: This Guided Learning Activity (GLA) discusses the Molecular Orbital Theory and its application to homonuclear diatomic molecules. Part A describes the
Bonding 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
Activity Molecular Orbital Theory
Activity 201 9 Molecular Orbital Theory Directions: This Guided Learning Activity (GLA) discusses the Molecular Orbital Theory and its application to homonuclear diatomic molecules. Part A describes the
Electronic structure of correlated electron systems. Lecture 2
Electronic structure of correlated electron systems Lecture 2 Band Structure approach vs atomic Band structure Delocalized Bloch states Fill up states with electrons starting from the lowest energy No
ATOMIC STRUCTURE. Atomic Structure. Atomic orbitals and their energies (a) Hydrogenic radial wavefunctions
ATOMIC STRUCTURE Atomic orbitals and their energies (a) Hydrogenic radial wavefunctions Bundet Boekfa Chem Div, Fac Lib Arts & Sci Kasetsart University Kamphaeng Saen Campus 1 2 Atomic orbitals and their
The 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
Project 3: Molecular Orbital Calculations of Diatomic Molecules. This project is worth 30 points and is due on Wednesday, May 2, 2018.
Chemistry 362 Spring 2018 Dr. Jean M. Standard April 20, 2018 Project 3: Molecular Orbital Calculations of Diatomic Molecules In this project, you will investigate the molecular orbitals and molecular
with 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
Molecular Term Symbols
Molecular Term Symbols A molecular configuration is a specification of the occupied molecular orbitals in a molecule. For example, N : σ gσ uπ 4 uσ g A given configuration may have several different states
Exchange coupling can frequently be understood using a simple molecular orbital approach.
6.4 Exchange Coupling, a different perspective So far, we ve only been looking at the effects of J on the magnetic susceptibility but haven t said anything about how one might predict the sign and magnitude
Chapter 10 Chemical Bonding II
Chapter 10 Chemical Bonding II Valence Bond Theory Valence Bond Theory: A quantum mechanical model which shows how electron pairs are shared in a covalent bond. Bond forms between two atoms when the following
Chapter 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
Chemical 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,
Symmetry 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
Molecular Structure Both atoms and molecules are quantum systems
Molecular Structure Both atoms and molecules are quantum systems We need a method of describing molecules in a quantum mechanical way so that we can predict structure and properties The method we use is
Chapter 9: Multi- Electron Atoms Ground States and X- ray Excitation
Chapter 9: Multi- Electron Atoms Ground States and X- ray Excitation Up to now we have considered one-electron atoms. Almost all atoms are multiple-electron atoms and their description is more complicated
Beyond the Hartree-Fock Approximation: Configuration Interaction
Beyond the Hartree-Fock Approximation: Configuration Interaction The Hartree-Fock (HF) method uses a single determinant (single electronic configuration) description of the electronic wavefunction. For
CHEM1901/ 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,
Electronic structure theory: Fundamentals to frontiers. 1. Hartree-Fock theory
Electronic structure theory: Fundamentals to frontiers. 1. Hartree-Fock theory MARTIN HEAD-GORDON, Department of Chemistry, University of California, and Chemical Sciences Division, Lawrence Berkeley National
Experiment 15: Atomic Orbitals, Bond Length, and Molecular Orbitals
Experiment 15: Atomic Orbitals, Bond Length, and Molecular Orbitals Introduction Molecular orbitals result from the mixing of atomic orbitals that overlap during the bonding process allowing the delocalization
General 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
Exchange Mechanisms. Erik Koch Institute for Advanced Simulation, Forschungszentrum Jülich. lecture notes:
Exchange Mechanisms Erik Koch Institute for Advanced Simulation, Forschungszentrum Jülich lecture notes: www.cond-mat.de/events/correl Magnetism is Quantum Mechanical QUANTUM MECHANICS THE KEY TO UNDERSTANDING
Molecular 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.
Chemistry 3502/4502. Final Exam Part I. May 14, 2005
Advocacy chit Chemistry 350/450 Final Exam Part I May 4, 005. For which of the below systems is = where H is the Hamiltonian operator and T is the kinetic-energy operator? (a) The free particle
Chemistry 3211 Coordination Chemistry Part 3 Ligand Field and Molecular Orbital Theory
Chemistry 3211 Coordination Chemistry Part 3 Ligand Field and Molecular Orbital Theory Electronic Structure of Six and Four-Coordinate Complexes Using Crystal Field Theory, we can generate energy level
PHYSICAL 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
AN INTRODUCTION TO QUANTUM CHEMISTRY. Mark S. Gordon Iowa State University
AN INTRODUCTION TO QUANTUM CHEMISTRY Mark S. Gordon Iowa State University 1 OUTLINE Theoretical Background in Quantum Chemistry Overview of GAMESS Program Applications 2 QUANTUM CHEMISTRY In principle,
ABC of DFT: Hands-on session 2 Molecules: structure optimization, visualization of orbitals, charge & spin densities
ABC of DFT: Hands-on session 2 Molecules: structure optimization, visualization of orbitals, charge & spin densities Tutor: Alexej Bagrets Wann? 16.11.2012, 11:30-13:00 Wo? KIT Campus Nord, Flachbau Physik,
Chemistry: 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
Valence Bond Theory Considers the interaction of separate atoms brought together as they form a molecule. Lewis structures Resonance considerations
CHEM 511 chapter 2 page 1 of 11 Chapter 2 Molecular Structure and Bonding Read the section on Lewis dot structures, we will not cover this in class. If you have problems, seek out a general chemistry text.
计算物理作业二. Excercise 1: Illustration of the convergence of the dissociation energy for H 2 toward HF limit.
计算物理作业二 Excercise 1: Illustration of the convergence of the dissociation energy for H 2 toward HF limit. In this exercise, basis indicates one of the following basis sets: STO-3G, cc-pvdz, cc-pvtz, cc-pvqz
Conformational energy analysis
Lab 3 Conformational energy analysis Objective This computational project deals with molecular conformations the spatial arrangement of atoms of molecules. Conformations are determined by energy, so the
(1/2) M α 2 α, ˆTe = i. 1 r i r j, ˆV NN = α>β
Chemistry 26 Spectroscopy Week # The Born-Oppenheimer Approximation, H + 2. Born-Oppenheimer approximation As for atoms, all information about a molecule is contained in the wave function Ψ, which is the
Molecular 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
Computational Material Science Part II. Ito Chao ( ) Institute of Chemistry Academia Sinica
Computational Material Science Part II Ito Chao ( ) Institute of Chemistry Academia Sinica Ab Initio Implementations of Hartree-Fock Molecular Orbital Theory Fundamental assumption of HF theory: each electron
Chapter 10. Structure Determines Properties! Molecular Geometry. Chemical Bonding II
Chapter 10 Chemical Bonding II Structure Determines Properties! Properties of molecular substances depend on the structure of the molecule The structure includes many factors, including: the skeletal arrangement
Exam 4 Review. Exam Review: A exam review sheet for exam 4 will be posted on the course webpage. Additionally, a practice exam will also be posted.
Chem 4502 Quantum Mechanics & Spectroscopy (Jason Goodpaster) Exam 4 Review Exam Review: A exam review sheet for exam 4 will be posted on the course webpage. Additionally, a practice exam will also be
Electronic Structure Models
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
Chapter 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
Chapter 10: Chemical Bonding II. Bonding Theories
Chapter 10: Chemical Bonding II Dr. Chris Kozak Memorial University of Newfoundland, Canada Bonding Theories Previously, we saw how the shapes of molecules can be predicted from the orientation of electron
Molecular 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
Andrew 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
Molecular Orbital Theory. Molecular Orbital Theory: Electrons are located in the molecule, not held in discrete regions between two bonded atoms
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
OVERVIEW OF QUANTUM CHEMISTRY METHODS
OVERVIEW OF QUANTUM CHEMISTRY METHODS Outline I Generalities Correlation, basis sets Spin II Wavefunction methods Hartree-Fock Configuration interaction Coupled cluster Perturbative methods III Density
Chem 263 Notes Sept. 26, 2013
Chem 263 Notes Sept. 26, 2013 Example of Predicting Stereochemistry The following example uses 2Z, 4E-hexadiene (diene) and cyclopentene (dienophile) to produce an endo product. As shown before with the
CHEM 221 section 01 LECTURE #02 Thurs., Sept.8, 2005
EM 221 section 01 LETURE #02 Thurs., Sept.8, 2005 ASSIGNED READINGS: TODAY S LASS: 1.6 Introduction to molecular orbital theory 1.7-1.9 Bonding: single, double, triple bonds 1.10 Bonding in cations, anions,
Chapter 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
5.4. 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
σ 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
π* orbitals do not Molecular Orbitals for Homonuclear Diatomics
Molecular Orbitals for Homonuclear Diatomics CHEM 2060 Lecture 26: MO theory contd L26-1 Molecular orbitals can be formed pictorially by looking at the way in which atomic orbitals overlap. Let s look
4 Diatomic molecules
s manual for Burrows et.al. Chemistry 3 Third edition 4 Diatomic molecules Answers to worked examples WE 4.1 The Lewis model (on p. 174 in Chemistry 3 ) Use the Lewis model to describe the bonding in (a)
Chapter 9. Molecular Geometry and Bonding Theories
Chapter 9. Molecular Geometry and Bonding Theories PART I Molecular Shapes Lewis structures give atomic connectivity: they tell us which atoms are physically connected to which atoms. The shape of a molecule
( ) dσ 1 dσ 2 + α * 2
Chemistry 36 Dr. Jean M. Standard Problem Set Solutions. The spin up and spin down eigenfunctions for each electron in a many-electron system are normalized and orthogonal as given by the relations, α
H 2 in the minimal basis
H 2 in the minimal basis Alston J. Misquitta Centre for Condensed Matter and Materials Physics Queen Mary, University of London January 27, 2016 Overview H 2 : The 1-electron basis. The two-electron basis
Free-Ion Terms to Ligand-field Terms
Free-Ion Terms to Ligand-field Terms! Orbital term symbols for free atoms and ions are identical to symbols for irreducible representations in R 3. " The irreducible representations of R 3 include all
CHAPTER 11 MOLECULAR ORBITAL THEORY
CHAPTER 11 MOLECULAR ORBITAL THEORY Molecular orbital theory is a conceptual extension of the orbital model, which was so successfully applied to atomic structure. As was once playfuly remarked, a molecue
Density Functional Theory Analysis of Electronic Structure Variations across the Orthoquinone/Semiquinone/Catechol Redox Series
J. Phys. Chem. A 1999, 103, 4101-4112 4101 Density Functional Theory Analysis of Electronic Structure Variations across the Orthoquinone/Semiquinone/Catechol Redox Series Daniel E. Wheeler, Jorge H. Rodriguez,
CHAPTER 8. EXPLORING THE EFFECTS OF STRUCTURAL INSTABILITIES AND OF TRIPLET INSTABILITY ON THE M-I PHASE TRANSITION IN (EDO-TTF)2PF6.
CHAPTER 8. EXPLORING THE EFFECTS OF STRUCTURAL INSTABILITIES AND OF TRIPLET INSTABILITY ON THE M-I PHASE TRANSITION IN (EDO-TTF)2PF6. The thermal metal-insulator phase transition in (EDO-TTF)2PF6 is attributed
MO theory considers the entire molecule at once not isolated electron pairs.
5. Molecular Orbital Theory READING: Chapter 2, Sections 2.7 2.10 MO theory considers the entire molecule at once not isolated electron pairs. Consequence: An electron pair can be bonding/non-bonding/anti-bonding
CHAPTER 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
CHEMISTRY Topic #1: Bonding What Holds Atoms Together? Spring 2012 Dr. Susan Lait
CHEMISTRY 2000 Topic #1: Bonding What Holds Atoms Together? Spring 2012 Dr. Susan Lait Why Do Bonds Form? An energy diagram shows that a bond forms between two atoms if the overall energy of the system
PRACTICE PROBLEMS Give the electronic configurations and term symbols of the first excited electronic states of the atoms up to Z = 10.
PRACTICE PROBLEMS 2 1. Based on your knowledge of the first few hydrogenic eigenfunctions, deduce general formulas, in terms of n and l, for (i) the number of radial nodes in an atomic orbital (ii) the
1s atomic orbital 2s atomic orbital 2s atomic orbital (with node) 2px orbital 2py orbital 2pz orbital
Atomic Orbitals 1s atomic orbital 2s atomic orbital 2s atomic orbital (with node) 2px orbital 2py orbital 2pz orbital Valence Bond Theory and ybridized Atomic Orbitals Bonding in 2 1s 1s Atomic Orbital
On the Uniqueness of Molecular Orbitals and limitations of the MO-model.
On the Uniqueness of Molecular Orbitals and limitations of the MO-model. The purpose of these notes is to make clear that molecular orbitals are a particular way to represent many-electron wave functions.
Lec20 Fri 3mar17
564-17 Lec20 Fri 3mar17 [PDF]GAUSSIAN 09W TUTORIAL www.molcalx.com.cn/wp-content/uploads/2015/01/gaussian09w_tutorial.pdf by A Tomberg - Cited by 8 - Related articles GAUSSIAN 09W TUTORIAL. AN INTRODUCTION
Excited States Calculations for Protonated PAHs
52 Chapter 3 Excited States Calculations for Protonated PAHs 3.1 Introduction Protonated PAHs are closed shell ions. Their electronic structure should therefore be similar to that of neutral PAHs, but
Performance of Hartree-Fock and Correlated Methods
Chemistry 460 Fall 2017 Dr. Jean M. Standard December 4, 2017 Performance of Hartree-Fock and Correlated Methods Hartree-Fock Methods Hartree-Fock methods generally yield optimized geomtries and molecular
Contents. 1. Building a molecular model 2. Additional Procedures and Options: 3. Selecting a calculation method
Getting started with HyperChem. Program description. In this project you will create simple organic molecules and learn how to manipulate them. However, before starting you should create your home directory
CHEM-UA 127: Advanced General Chemistry I
CHEM-UA 7: Advanced General Chemistry I I. LINEAR COMBINATION OF ATOMIC ORBITALS Linear combination of atomic orbitals (LCAO) is a simple method of quantum chemistry that yields a qualitative picture of
7. 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