Diatomic Molecules. Atom -> Molecule. Diatomic Molecules - Lukas Schott
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1 Diatomic Molecules Atom -> Molecule
2 Outline 1. Introduction and motivation 1. Overview of natural molecules (and sneak preview) 2. Reasons of interest 2. A Brief History of Molecules 3. Born Oppenheim approximation 4. Examples for electron orbits 1. Linear Combination of Atomic Orbits (LCAO) with H2+ 2. LCAO of Molecular Orbits with H2 3. Short introduction to other Approximations 5. Nuclei vibration and rotation levels 6. Current research 7. Summary 8. Sources
3 1.1 Overview of natural molecules Mr. Brinclhof (Br I N Cl H O F)
4 1.2 Reasons of interest LEGO bricks of all molecules e.g. amino acid, sugar, gasoline (chemistry and biology) Mathematical basics for large molecules Experimental tests of theoretical approximations Further possible bindings Basic of complex structures (astrobiophysics)
5 2 A Brief History of Molecules Etymology: molecule from moles (=mass barrier) ~400 B.C. Platon and Empedocles: Elements: Water, Fire ~350 B.C. Democritus Leucippus : atoms = small particles with properties 1625 Descartes: Resurgence of atomic theory
6 2 A Brief History of Molecules Etymology: molecule from moles (=mass barrier) ~400 B.C. Platon and Empedocles: Elements: Water, Fire ~350 B.C. Democritus Leucippus : atoms = small particles with properties Descartes: Resurgence of atomic theory Daltons law of Definite and Multiple Proportions Avogadro: atoms->molecules-> particles
7 2 A Brief History of Molecules Etymology: molecule from moles (=mass barrier) ~400 B.C. Platon and Empedocles: Elements: Water, Fire ~350 B.C. Democritus Leucippus : atoms = small particles with properties Descartes: Resurgence of atomic theory Daltons law of Definite and Multiple Proportions Avogadro: atoms->molecules-> particles Gilbert N. Lewis cube modulation
8 2 A Brief History of Molecules Etymology: molecule from moles (=mass barrier) ~400 B.C. Platon and Empedocles: Elements: Water, Fire ~350 B.C. Democritus Leucippus : atoms = small particles with properties Descartes: Resurgence of atomic theory Daltons law of Definite and Multiple Proportions Avogadro: atoms->molecules-> particles Gilbert N. Lewis cube modulation Lewis structure -> electron pair bond
9 2 A Brief History of Molecules Etymology: molecule from moles (=mass barrier) ~400 B.C. Platon and Empedocles: Elements: Water, Fire ~350 B.C. Democritus Leucippus : atoms = small particles with properties description 2009 Descartes: Resurgence of atomic theory Daltons law of Definite and Multiple Proportions Avogadro: atoms->molecules-> particles Gilbert N. Lewis cube modulation Lewis structure -> electron pair bond Born, Oppenheimer, London, Heitler, Pauling QM IMB first picture of Pentacene with chem. Bonds
10 2 A Brief History of Molecules Pentacene AFM Atomic Force Microscope IBM picture on molecular level of nano tube using AFM (atomic force microscope
11 3 Born Oppenheimer Approximation Estimations & principle: No spin Not relativistic: Bohr: => terms negligible for the electrons Nuclei velocity relative to electron movement very slow: Plan: Hamiltonian Neglect nuclei velocity Solve electron wave equa. Separation & rewrite Born Oppenheimer Negelct Matrix elements
12 Hamiltonian Neglect nuclei velocity Solve electron wave equa. Separation & rewrite Born Oppenheimer Negelct Matrix elements Configuration: Hamiltonian SGE:
13 Hamiltonian Neglect nuclei velocity Solve electron wave equa. Separation & rewrite Born Oppenheimer Negelct Matrix elements Neglect for now! (Electronic SGE)
14 Hamiltonian Neglect nuclei velocity Solve electron wave equa. Separation & rewrite Born Oppenheimer Negelct Matrix elements Neglect for now! (Electronic SGE) Examples later Now pretend to know a solution : orthonormal & complete set
15 Hamiltonian Neglect nuclei velocity Solve electron wave equa. Separation & rewrite Born Oppenheimer Negelct Matrix elements Separation: Sum convention New rewritten SGL Multiply by and integrate over r Born Oppenheimer Equation Matrix elements: Non-adiabatic coupling terms (NACT)
16 Hamiltonian Neglect nuclei velocity Solve electron wave equa. Separation & rewrite Born Oppenheimer Negelct Matrix elements Born Oppenheimer Equation Vibration levels Rotation levels
17 Hamiltonian Neglect nuclei velocity Solve electron wave equa. Separation & rewrite Born Oppenheimer Negelct Matrix elements Non adiabatic coupling terms Collapse of the BO approximation Both:
18 The underlying physical laws necessary for the mathematical theory of a large part of physics and the whole of chemistry are thus completely known, and the difficulty is only finding the right approximation.» Paul Adrien M. Dirac
19 To solve: 4.1 LCAO-Linear Combination of Atomic Orbits with H2+ Step overview: A. Neglect nuclei movement B. Estimate a wave function C. Set the distance of nuclei to parameter R D. Normalisation -> interaction integral E. Energy expectation value <H> F. Minimize Energy
20 4.1 LCAO precision Exact values LCAO values E(R) for the stable symmetric and unstable asymmetri c Overview of effects on the LCAO
21 Nothing is solved» Me
22 4.2 Other approximations for H2+ Adjusted wave function +λz: charge distribution drawn out in z- direction -> polarisation +radial probability density η(r). η<1 contraction 1. LCAO simple 2. LCAO contraction η 3. LCAO contraction & polarisation 4. James & Coolidge
23 4.3 Approximation for H2 LCAO Hamiltonian Solving Idea? Linear combination of atomical Orbits
24 4.3 Approximation for H2 LCAO Symmetric position, asymmetric spin Antisymmetric position, symmetric spin i) - for two 1-s H-atom functions - for includes two H- atoms ii) - Contains non binding factor -higher energy
25 4.4 Heitler London Approximation Heitler London
26 5.Vibration and rotation levels Born Oppenheimer for nuclei & two body problem Rotational symmetry We know the solution
27 5.Vibration and rotation levels This reduces the equation to New: For small l, depending on l at rl. has a minima Setting leads to an harmonic oscillator
28 5.Vibration and rotation levels Solving this leads us to: Effective electrical energy Visible light 1 Vibration energy infrared 2 Rotation energy far infrared µwaves ~100nm ~µm ~mm -> cm
29 6. Current Research - conceptual MPIK nuclear physics early Universe H2 formation Star origin
30 6. Current Research - conceptual MPIK nuclear physics early Universe H2 formation Star origin, small-particle clouds, fast ion neutral reactions -> molecules
31 6. Current Research - conceptual MPIK nuclear physics early Universe H2 formation Star origin, small-particle clouds, fast ion neutral reactions -> molecules
32 6. Current Research - conceptual MPIK nuclear physics early Universe H2 formation Star origin, small-particle clouds, fast ion neutral reactions -> molecules
33 6. Current Research - conceptual MPIK nuclear physics early Universe H2 formation Star origin, molecular clouds, fast ion neutral reactions -> molecules Atom-molecule dark state from Bose-Einstein-Condensate BEC ( a>) + Laser beam -> frees Rb atoms to Rb2 molecules (photoassociation) Second laser beam: certain frequency ->suppression of photoassociation Dark state ~ c1 g> - c2 a>
34 7. Summary Natural diatomic molecules Br I N Cl H O F Born Oppenheimer LCAO (H2+) Heitler London Vibration & rotation levels Current research H2 formation main coolant, Rb superposition
35 Thank you for your Attention!
36 Introduction - History - Born Oppenheimer - Electron orbits - Vibration and rotation Summary - Sources 8. References Literature Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character, Vol. 123, No. 792 (6 April 1929) Schwabl, Franz (2002). Quantenmechanik. 6. Auflage, Berlin: Springer Verlag Born, Max & Oppenheimer, Robert (1927), Analen der Physik Zur Quantenheorie der Molekeln. Vierte Folge Band 84, Leipzig: Verlag von Joh. Ambrosius Barth Lewis, Gilbert. N., (April 1916), The Atom and the Molecule. Boston. Verlag unklar Demtröder, Wolfgang, (Februar 2005), Experimentalphysik 3- Atome Moleküle und Festkörper. Auflage 3, New York: Springer Verlag Lector of Jack Simpson, PhD in Toronto, Canada Area, Lecture to Born and Oppenheimer Approximation History Gilbert N. Lewis Original Work: BBC News Penatacine AFM Image Born Oppenheimer & solutions Technische Universität Braunschweig: University of Oxford Department of Physics: New York University: Universität Jena: Paul Dirac Quote: Current research MPIK HEIDELBERG & Ultra Cold Gases and Molekular Superposition University of Innsbruck:
37 Outtakes
38 Introduction - History - Born Oppenheimer - Electron orbits - Vibration and rotation - Summary Hamiltonian Neglect nuclei velocity Solve electron wave equa. Separation & rewrite Born Oppenheimer Negelct Matrix elements Justification of neglecting the first NACT term insignifican t
39 Introduction - History - Born Oppenheimer - Electron orbits - Vibration and rotation - Summary Hamiltonian Neglect nuclei velocity Solve electron wave equa. Separation & rewrite Born Oppenheimer Negelct Matrix elements Justification for the second NACT term Estimation with oscillation wave function: Let be a typical nucleus amplitude terms of size insignifica nt
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The Unshifted Atom-A Simpler Method of Deriving Vibrational Modes of Molecular Symmetries
Est. 1984 ORIENTAL JOURNAL OF CHEMISTRY An International Open Free Access, Peer Reviewed Research Journal www.orientjchem.org ISSN: 0970-020 X CODEN: OJCHEG 2012, Vol. 28, No. (1): Pg. 189-202 The Unshifted
The content is based on the National Science Teachers Association (NSTA) standards and is aligned with state standards.
Literacy Advantage Physical Science Physical Science Literacy Advantage offers a tightly focused curriculum designed to address fundamental concepts such as the nature and structure of matter, the characteristics
List the 3 main types of subatomic particles and indicate the mass and electrical charge of each.
Basic Chemistry Why do we study chemistry in a biology course? All living organisms are composed of chemicals. To understand life, we must understand the structure, function, and properties of the chemicals
Unit 2 Lesson 1 Introduction to Energy. Copyright Houghton Mifflin Harcourt Publishing Company
Get Energized! What are two types of energy? Energy is the ability to cause change. Energy takes many different forms and causes many different effects. There are two general types of energy: kinetic energy
Concept 2. A. Description of light-matter interaction B. Quantitatities in spectroscopy
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LAGUARDIA COMMUNITY COLLEGE CITY UNIVERSITY OF NEW YORK NATURAL SCIENCES DEPARTMENT
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(1) The size of a gas particle is negligible as compared to the volume of the container in which the gas is placed.
Gas Laws and Kinetic Molecular Theory The Gas Laws are based on experiments, and they describe how a gas behaves under certain conditions. However, Gas Laws do not attempt to explain the behavior of gases.
Contents. Goldstone Bosons in 3He-A Soft Modes Dynamics and Lie Algebra of Group G:
... Vlll Contents 3. Textures and Supercurrents in Superfluid Phases of 3He 3.1. Textures, Gradient Energy and Rigidity 3.2. Why Superfuids are Superfluid 3.3. Superfluidity and Response to a Transverse
KE A = PE MAX 1/2M v 2 = k q1 q2 /R
CHAPTER 13 NUCLEAR STRUCTURE NUCLEAR FORCE The nucleus is help firmly together by the nuclear or strong force, We can estimate the nuclear force by observing that protons residing about 1fm = 10-15m apart
Boyle s law - For calculating changes in pressure or volume: P 1 V 1 = P 2 V 2. Charles law - For calculating temperature or volume changes: V 1 T 1
Common Equations Used in Chemistry Equation for density: d= m v Converting F to C: C = ( F - 32) x 5 9 Converting C to F: F = C x 9 5 + 32 Converting C to K: K = ( C + 273.15) n x molar mass of element
Atoms, Ions and Molecules The Building Blocks of Matter
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Electrons in Atoms & Periodic Table Chapter 13 & 14 Assignment & Problem Set
Electrons in Atoms & Periodic Table Name Warm-Ups (Show your work for credit) Date 1. Date 2. Date 3. Date 4. Date 5. Date 6. Date 7. Date 8. Electrons in Atoms & Periodic Table 2 Study Guide: Things You