ENERGY TRANSFER IN THE WEAK AND STRONG COUPLING REGIME


 Noah York
 2 years ago
 Views:
Transcription
1 ERC Starting Grant 2011 Dipar)mento di Scienze Chimiche Università degli Studi di Padova via Marzolo 1, Padova Italy ENERGY TRANSFER IN THE WEAK AND STRONG COUPLING REGIME [1] Vekshin, N. L. Energy transfer in macromolecules; Society of Photo op)cal Instrumenta)on Engineers: Bellingham, Washington state, [2] May, V.; Kuhn, O. Charge and Energy Transfer Dynamics in Molecular Systems; Wiley VCH: Berlin, 1 ed., ElisabeEa Collini
2 ERC Starting Grant 2011 isolated system of two two levels chromophores (molecular dimer): ΔE A e A e B ΔE B g A A B g B System Hamiltonian: H = H A +H B + V Interac(on
3 ERC Starting Grant ) When the chromophores do not interact (V=0), the dimer is described by: a ground state: two singly excited states: a double excited state: 2) When V 0 g A g B g A e B ; e A g B e A e B Neglec)ng (i) exchange correla)ons; (ii) electrosta)c interac)ons between electron clouds and (iii) strongly off resonant coupling terms (Heitler London approx.) Considering the chromophores far apart enough  > point dipole approxima)on The interac)on V may be wrieen as: V = µ A µb * R 3 3 R µ A R 5 ( )( R * µ ) B R = vector connec)ng the point dipoles
4 ERC Starting Grant 2011 STRONG COUPLING (1) system ini)ally in the state e A g B for arbitrarily strong coupling V. The energies of the sta)onary states of such a system may be solved by expanding them in the states with one of the sites excited: ψ i = C A e A g B +C B g A e B, and then solving the matrix eigenvalue equa)on : " ΔE A V %" C % " $ ' $ A ' $ # V * ΔE B ' &# $ C B &' = E C % A $ ' # $ C B &' The eigenvalues of this equa)on are the new energies E + and E of the coupled states, which from the secular equa)ons are found to be: ( ) Δ = 1 ΔE 2 ( ΔE B A) ΔE ± = K + Δ 2 + V 2 where K = 1 ΔE + ΔE 2 A B Note that the coupling splits up the energies of the states; wri)ng V as V e iφ and using the normaliza)on condi)on C A 2 + C B 2 = 1, the eigenvectors are: ψ ± = 1 2 ( g A e B ± e A g B ) If V real and V>>Δ (strong coupling)
5 ERC Starting Grant 2011 STRONG COUPLING (2) P B (t): probability that the excita)on resides on B at the )me t, if at t=0 was ini)ally on A: P B (t) = V 2 Δ 2 + V 2 sin2 Δ 2 + V 2 with P A (t) = 1 C B (t) 2. This shows that the new states are coherent superposi)ons of the A excited and B excited states and that the excita)on will coherently oscillate back and forth between chromophores A and B at the frequency: Ω = ( ΔE + ΔE ) / = 2 Δ 2 + V 2 /
6 ERC Starting Grant 2011 WEAK COUPLING In the weak coupling regime, the electronic levels of the single chromophores are liele perturbed by V and the spectrum of the dimer is iden)cal to the sum of the spectra of the two chromophores. In this case the energy transfer probability can be calculated using perturba)on theory: P B (t) = C B (t) 2 = V 2 " sin 2 1 Ω 2 0 t 2 $ 1 # ( 2 Ω 0 t) 2 ( ) % ' & where Ω 0 Ω( V 0) = ( ΔE B ΔE A ) / = 2Δ / which is the limit for small V of the expression obtained previously in the strong coupling regime. Note that for long t, significant ET occurs only when and then we can write: Ω 0 0 P B (t) = V 2 t 2 # sin 2 1 dω 2 Ω 0 t 0 % 1 $ ( 2 Ω 0 t) 2 ( ) & ( = 2π ' V 2 t
7 ERC Starting Grant 2011 Dipar)mento di Scienze Chimiche Università degli Studi di Padova via Marzolo 1, Padova Italy Strong coupling regime: Frenkel excitons model [1] S. Davydov, Theory of molecular excitons, Plenum Press, New York, [2] H. Van Amerongen, L. Valkunas and R. Van Grondelle, Photosynthe=c Excitons, World Scien)fic, Singapore, ElisabeEa Collini
8 ERC Starting Grant 2011 Frenkel excitons In the Frenkel exciton model, a system of N chromophores is represented by the Hamiltonian: n is molecular excited state at site n with energy ε n, and J nm is the excitonic coupling between the n th and m th chromophore. Diagonaliza)on of H e gives rise to eigenstates α, called exciton states, such that: Exciton states form a new basis for the descrip)on of op)cal proper)es and energy transfer dynamics. site basis exciton basis (eigenbasis)
9 ERC Starting Grant 2011 DETAILS: If one neglects addi)onal (e.g., nuclear) degrees of freedom, the calcula)on of eigenstates and eigenfrequencies can be performed analy)cally. q If each of the N molecules can be in two states, the Hamiltonian has 2 N eigenstates, linear combina)ons of single molecule s states, each with a fixed number of single molecule excita)ons present. They separate into groups (manifolds) according to the number of excita)ons they contain (ν). q The nondegenerate ground state is the direct product of the N molecular ground state wave func)ons q there are N excited state manifolds, each labelled by ν; the ν th manifold contains N/(N ν) ν independent ν exciton states in which ν molecules are excited and N ν molecules are unexcited. q the one exciton band (ν = 1) is formed by N eigenstates, know as Frenkel excitons, characterized by a single quantum number k. The exact expression of eigenstates and eigenenergies of the Hamiltonian describing this system can be calculated by diagonaliza)on under suitable boundary condi)ons. E.Collini, PCCP, 14 (2012) 3725 and references therein
10 ERC Starting Grant 2011 Example: diagonaliza)on for a linear assembly of N molecules: E.Collini, PCCP, 14 (2012) 3725 and references therein
11 ERC Starting Grant 2011 Including also the environment, the hamiltonian reads: H TOT =H e + HB +H SB Linear system bath coupling: where q n = collec)ve bath coordinate It is usually assumed that the bath modes modula)ng different chromophores are independent, so H SB represents independent phonon induced fluctua)ons of the site energies. The dynamics is related to spectral density ρ n (ω) which represents the coupling strength and density of states of the phonon bath. The strenght of the system bath coupling is measured by the reorganiza)on energy λ n :
PCV Project: Excitons in Molecular Spectroscopy
PCV Project: Excitons in Molecular Spectroscopy Introduction The concept of excitons was first introduced by Frenkel (1) in 1931 as a general excitation delocalization mechanism to account for the ability
More informationTeoretisk Fysik KTH. Advanced QM (SI2380), test questions 1
Teoretisk Fysik KTH Advanced QM (SI238), test questions NOTE THAT I TYPED THIS IN A HURRY AND TYPOS ARE POSSIBLE: PLEASE LET ME KNOW BY EMAIL IF YOU FIND ANY (I will try to correct typos asap  if you
More informationPHY4604 Introduction to Quantum Mechanics Fall 2004 Practice Test 3 November 22, 2004
PHY464 Introduction to Quantum Mechanics Fall 4 Practice Test 3 November, 4 These problems are similar but not identical to the actual test. One or two parts will actually show up.. Short answer. (a) Recall
More informationProblem Set 3 Solutions CH332 (SP 06) 1. Skoog problem 151 (omit terms (j), (k) and (m)). Draw diagrams as necessary.
Problem Set 3 Solutions CH332 (SP 06) 1. Skoog problem 151 (omit terms (j), (k) and (m)). Draw diagrams as necessary. a) fluorescence Relaxation of an excited state by emission of a photon without a change
More informationRaman Spectroscopy Basics
Raman Spectroscopy Basics Introduction Raman spectroscopy is a spectroscopic technique based on inelastic scattering of monochromatic light, usually from a laser source. Inelastic scattering means that
More informationNMR and IR spectra & vibrational analysis
Lab 5: NMR and IR spectra & vibrational analysis A brief theoretical background 1 Some of the available chemical quantum methods for calculating NMR chemical shifts are based on the HartreeFock selfconsistent
More informationThe Role of Electric Polarization in Nonlinear optics
The Role of Electric Polarization in Nonlinear optics Sumith Doluweera Department of Physics University of Cincinnati Cincinnati, Ohio 45221 Abstract Nonlinear optics became a very active field of research
More informationDesign of 2D waveguide networks for the study of fundamental properties of Quantum Graphs
Design of 2D waveguide networks for the study of fundamental properties of Quantum Graphs Introduction: what is a quantum graph? Areas of application of quantum graphs Motivation of our experiment Experimental
More informationInstability, dispersion management, and pattern formation in the superfluid flow of a BEC in a cylindrical waveguide
Instability, dispersion management, and pattern formation in the superfluid flow of a BEC in a cylindrical waveguide Michele Modugno LENS & Dipartimento di Fisica, Università di Firenze, Italy Workshop
More informationNMR for Physical and Biological Scientists Thomas C. Pochapsky and Susan Sondej Pochapsky Table of Contents
Preface Symbols and fundamental constants 1. What is spectroscopy? A semiclassical description of spectroscopy Damped harmonics Quantum oscillators The spectroscopic experiment Ensembles and coherence
More informationNMR SPECTROSCOPY. Basic Principles, Concepts, and Applications in Chemistry. Harald Günther University of Siegen, Siegen, Germany.
NMR SPECTROSCOPY Basic Principles, Concepts, and Applications in Chemistry Harald Günther University of Siegen, Siegen, Germany Second Edition Translated by Harald Günther JOHN WILEY & SONS Chichester
More informationInfrared Spectroscopy: Theory
u Chapter 15 Infrared Spectroscopy: Theory An important tool of the organic chemist is Infrared Spectroscopy, or IR. IR spectra are acquired on a special instrument, called an IR spectrometer. IR is used
More informationImportance of the singleparticle continuum in BCS pairing with a pseudostate basis
EPJ Web of Conferences 117, Importance of the singleparticle continuum in BCS pairing with a pseudostate basis J. A. Lay 1,C.E.Alonso 2,L.Fortunato 1, and A. Vitturi 1 1 Dipartimento di Fisica e Astronomia
More information1. The quantum mechanical state of a hydrogen atom is described by the following superposition: ψ = (2ψ 1,0,0 3ψ 2,0,0 ψ 3,2,2 )
CHEM 352: Examples for chapter 2. 1. The quantum mechanical state of a hydrogen atom is described by the following superposition: ψ = 1 14 2ψ 1,, 3ψ 2,, ψ 3,2,2 ) where ψ n,l,m are eigenfunctions of the
More informationDetermining the Structure of an Organic Compound
Determining the Structure of an Organic Compound The analysis of the outcome of a reaction requires that we know the full structure of the products as well as the reactants In the 19 th and early 20 th
More informationHigh frequency low intensity current effects: biostimulation and cellular regeneration
UNIVERSITA DEGLI STUDI DI PADOVA Dipartimento di Anatomia e Fisiologia Umana Department of Human Anatomy and Physiology High frequency low intensity current effects: biostimulation and cellular regeneration
More informationFoundations of Chemical Kinetics. Lecture 20: The master equation
Foundations of Chemical Kinetics Lecture 20: The master equation Marc R. Roussel Department of Chemistry and Biochemistry Transition rates Suppose that Ps (t) is the probability that a system is in a state
More informationConcept 2. A. Description of lightmatter interaction B. Quantitatities in spectroscopy
Concept 2 A. Description of lightmatter interaction B. Quantitatities in spectroscopy Dipole approximation Rabi oscillations Einstein kinetics in twolevel system B. Absorption: quantitative description
More informationSection 6 Raman Scattering (lecture 10)
Section 6 Scattering (lecture 10) Previously: Quantum theory of atoms / molecules Quantum Mechanics Valence Atomic and Molecular Spectroscopy Scattering The scattering process Elastic (Rayleigh) and inelastic
More informationOrbital Dynamics coupled with JahnTeller phonons in Strongly Correlated Electron System
The 5 th Scienceweb GCOE International Symposium 1 Orbital Dynamics coupled with JahnTeller phonons in Strongly Correlated Electron System Department of Physics, Tohoku University Joji Nasu In collaboration
More informationMicrocavity Quantum Electrodynamics:
Microcavity Quantum Electrodynamics: From atoms to quantum dots Boris Anghelo Rodríguez Rey Grupo de Física Atómica y Molecular Instituto de Física, Universidad de Antioquia September 26, IWQCD 2012 Universidad
More informationMolecular vibrations: Iterative solution with energy selected bases
JOURNAL OF CHEMICAL PHYSICS VOLUME 118, NUMBER 8 22 FEBRUARY 2003 ARTICLES Molecular vibrations: Iterative solution with energy selected bases HeeSeung Lee a) and John C. Light Department of Chemistry
More informationNMR Nuclear Magnetic Resonance
NMR Nuclear Magnetic Resonance Nuclear magnetic resonance (NMR) is an effect whereby magnetic nuclei in a magnetic field absorb and reemit electromagnetic (EM) energy. This energy is at a specific resonance
More information1 The water molecule and hydrogen bonds in water
The Physics and Chemistry of Water 1 The water molecule and hydrogen bonds in water Stoichiometric composition H 2 O the average lifetime of a molecule is 1 ms due to proton exchange (catalysed by acids
More informationSpectroscopy. The Interaction of Electromagnetic Radiation (Light) with Molecules
Spectroscopy. The Interaction of Electromagnetic Radiation (Light) with Molecules (1) Electromagnetic Radiationwave description propagation c = 3 x 10 10 cm/sec magnetic () and electric (E) field vectors
More informationThe Central Equation
The Central Equation Mervyn Roy May 6, 015 1 Derivation of the central equation The single particle Schrödinger equation is, ( H E nk ψ nk = 0, ) ( + v s(r) E nk ψ nk = 0. (1) We can solve Eq. (1) at given
More informationPotential Energy Surfaces C. David Sherrill School of Chemistry and Biochemistry Georgia Institute of Technology
Potential Energy Surfaces C. David Sherrill School of Chemistry and Biochemistry Georgia Institute of Technology Potential Energy Surfaces A potential energy surface is a mathematical function that gives
More informationTime dependence in quantum mechanics Notes on Quantum Mechanics
Time dependence in quantum mechanics Notes on Quantum Mechanics http://quantum.bu.edu/notes/quantummechanics/timedependence.pdf Last updated Thursday, November 20, 2003 13:22:3705:00 Copyright 2003 Dan
More informationNuclear Magnetic Resonance
Nuclear Magnetic Resonance NMR is probably the most useful and powerful technique for identifying and characterizing organic compounds. Felix Bloch and Edward Mills Purcell were awarded the 1952 Nobel
More informationSemiconductor Laser Diode
Semiconductor Laser Diode Outline This student project deals with the exam question Semiconductor laser diode and covers the following questions: Describe how a semiconductor laser diode works What determines
More informationLecture 3: Optical Properties of Bulk and Nano. 5 nm
Lecture 3: Optical Properties of Bulk and Nano 5 nm The Previous Lecture Origin frequency dependence of χ in real materials Lorentz model (harmonic oscillator model) 0 e  n( ) n' n '' n ' = 1 + Nucleus
More informationCHAPTER 13 MOLECULAR SPECTROSCOPY
CHAPTER 13 MOLECULAR SPECTROSCOPY Our most detailed knowledge of atomic and molecular structure has been obtained from spectroscopy study of the emission, absorption and scattering of electromagnetic radiation
More informationProton Nuclear Magnetic Resonance Spectroscopy
Proton Nuclear Magnetic Resonance Spectroscopy Introduction: The NMR Spectrum serves as a great resource in determining the structure of an organic compound by revealing the hydrogen and carbon skeleton.
More informationEuropean Benchmark for Physics Bachelor Degree
European Benchmark for Physics Bachelor Degree 1. Summary This is a proposal to produce a common European Benchmark framework for Bachelor degrees in Physics. The purpose is to help implement the common
More informationIntroduction OLEDs OTFTs OPVC Summary. Organic Electronics. Felix Buth. Walter Schottky Institut, TU München. Joint Advanced Student School 2008
Felix Buth Joint Advanced Student School 2008 Outline 1 Introduction Difference organic/inorganic semiconductors From molecular orbitals to the molecular crystal 2 Organic Light Emitting Diodes Basic Principals
More informationIntroduces the bra and ket notation and gives some examples of its use.
Chapter 7 ket and bra notation Introduces the bra and ket notation and gives some examples of its use. When you change the description of the world from the inutitive and everyday classical mechanics to
More informationNonlinear normal modes of three degree of freedom mechanical oscillator
Mechanics and Mechanical Engineering Vol. 15, No. 2 (2011) 117 124 c Technical University of Lodz Nonlinear normal modes of three degree of freedom mechanical oscillator Marian Perlikowski Department of
More informationChemistry 102 Summary June 24 th. Properties of Light
Chemistry 102 Summary June 24 th Properties of Light  Energy travels through space in the form of electromagnetic radiation (EMR).  Examples of types of EMR: radio waves, xrays, microwaves, visible
More information thus, the total number of atoms per second that absorb a photon is
Stimulated Emission of Radiation  stimulated emission is referring to the emission of radiation (a photon) from one quantum system at its transition frequency induced by the presence of other photons
More informationarxiv:condmat/9811359v1 [condmat.disnn] 25 Nov 1998
arxiv:condmat/9811359v1 [condmat.disnn] 25 Nov 1998 Energy Levels of Quasiperiodic Hamiltonians, Spectral Unfolding, and Random Matrix Theory M. Schreiber 1, U. Grimm, 1 R. A. Römer, 1 and J. X. Zhong
More informationTheory of Light Scattering in Condensed Matter
Proceedings of the First Joint USA USSR Symposium Theory of Light Scattering in Condensed Matter Edited by Bernard Bendow Solid State Sciences Division Rome Air Development Center Hanscom AFB, Massachusetts
More informationTime out states and transitions
Time out states and transitions Spectroscopy transitions between energy states of a molecule excited by absorption or emission of a photon hn = DE = E i  E f Energy levels due to interactions between
More informationSinglet fission for solar energy conversion A theoretical insight. David Casanova
Singlet fission for solar energy conversion A theoretical insight David Casanova Quantum Days in Bilbao July 16, 2014 Harvesting Solar Energy Solar energy 1h = 1 year human consumption We use ~ 0.07% Earth
More informationExcitation transfer and energy exchange processes for modeling the FleischmannPons excess heat effect
Hagelstein, P.L. and I. Chaudhary. Excitation transfer and energy exchange processes for modeling the FleischmannPons excess heat effect. in ICCF14 International Conference on Condensed Matter Nuclear
More informationGroup Theory and Chemistry
Group Theory and Chemistry Outline: Raman and infrared spectroscopy Symmetry operations Point Groups and Schoenflies symbols Function space and matrix representation Reducible and irreducible representation
More informationElectromagnetic Radiation
Activity 17 Electromagnetic Radiation Why? Electromagnetic radiation, which also is called light, is an amazing phenomenon. It carries energy and has characteristics of both particles and waves. We can
More information2. Atomic Structure. 2.1 Historical Development of Atomic Theory. Remember!? Dmitri I. Mendeleev s Periodic Table (17 Feb. 1869 )
2. Atomic Structure 2.1 Historical Development of Atomic Theory Remember!? Dmitri I. Mendeleev s Periodic Table (17 Feb. 1869 ) 1 2.1.1 The Periodic Table of the Elements 2.1.2 Discovery of Subatomic Particles
More informationH NMR (proton NMR): determines number and type of H atoms 13. C NMR (proton NMR): determines number and type of C atoms
14.1 An Introduction to NMR Spectroscopy A. The Basics of Nuclear Magnetic Resonance (NMR) Spectroscopy nuclei with odd atomic number have a S = ½ with two spin states (+1/2 and 1/2) 1 H NMR (proton NMR):
More information2. Introduction to quantum mechanics
2. Introduction to quantum mechanics 2.1 Linear algebra Dirac notation Complex conjugate Vector/ket Dual vector/bra Inner product/bracket Tensor product Complex conj. matrix Transpose of matrix Hermitian
More informationProbing the Vacuum Induced Coherence in a Λsystem
Probing the Vacuum Induced Coherence in a Λsystem Sunish Menon and G. S. Agarwal Physical Research Laboratory, Navrangpura, Ahmedabad 380 009, India. (February 8, 1999) We propose a simple test to demonstrate
More informationThe Essentials of Quantum Mechanics
The Essentials of Quantum Mechanics Prof. Mark Alford v7, 2008Oct22 In classical mechanics, a particle has an exact, sharply defined position and an exact, sharply defined momentum at all times. Quantum
More information2. Molecular stucture/basic
2. Molecular stucture/basic spectroscopy The electromagnetic spectrum Spectral region for atomic and molecular spectroscopy E. Hecht (2nd Ed.) Optics, AddisonWesley Publishing Company,1987 Spectral regions
More informationProton Nuclear Magnetic Resonance ( 1 HNMR) Spectroscopy
Proton Nuclear Magnetic Resonance ( 1 HNMR) Spectroscopy Theory behind NMR: In the late 1940 s, physical chemists originally developed NMR spectroscopy to study different properties of atomic nuclei,
More informationSymmetric Stretch: allows molecule to move through space
BACKGROUND INFORMATION Infrared Spectroscopy Before introducing the subject of IR spectroscopy, we must first review some aspects of the electromagnetic spectrum. The electromagnetic spectrum is composed
More informationThomson and Rayleigh Scattering
Thomson and Rayleigh Scattering Initial questions: What produces the shapes of emission and absorption lines? What information can we get from them regarding the environment or other conditions? In this
More informationTime out states and transitions
Time out states and transitions Spectroscopy transitions between energy states of a molecule excited by absorption or emission of a photon hν = E = E i E f Energy levels due to interactions between parts
More informationContents. Goldstone Bosons in 3HeA 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
More informationElectronic Structure Methods. by Daniel Rohr Vrije Universiteit Amsterdam
Electronic Structure Methods by Daniel Rohr Vrije Universiteit Amsterdam drohr@few.vu.nl References WFT Szaboo & Ostlund Modern Quantum Chemistry Helgaker, Jørgensen & Olsen Molecular ElectronicStructure
More informationAccuracy of the coherent potential approximation for a onedimensional array with a Gaussian distribution of fluctuations in the onsite potential
Accuracy of the coherent potential approximation for a onedimensional array with a Gaussian distribution of fluctuations in the onsite potential I. Avgin Department of Electrical and Electronics Engineering,
More informationThe Quantum Harmonic Oscillator Stephen Webb
The Quantum Harmonic Oscillator Stephen Webb The Importance of the Harmonic Oscillator The quantum harmonic oscillator holds a unique importance in quantum mechanics, as it is both one of the few problems
More informationLecture 1: Microscopic Theory of Radiation
253a: QFT Fall 2009 Matthew Schwartz Lecture : Microscopic Theory of Radiation Blackbody Radiation Quantum Mechanics began on October 9, 900 with Max Planck s explanation of the blackbody radiation spectrum.
More informationFrequency Doubling and Second Order Nonlinear Optics
Frequency Doubling and Second Order Nonlinear Optics Paul M. Petersen DTU Fotonik, Risø campus Technical University of Denmark, Denmark (email: paul.michael.petersen@risoe.dk) Outline of the talk The first
More informationSection 5 Molecular Electronic Spectroscopy (lecture 9 ish)
Section 5 Molecular Electronic Spectroscopy (lecture 9 ish) Previously: Quantum theory of atoms / molecules Quantum Mechanics Vl Valence Molecular Electronic Spectroscopy Classification of electronic states
More informationChapter 8 Molecules. Some molecular bonds involve sharing of electrons between atoms. These are covalent bonds.
Chapter 8 Molecules (We have only three days for chapter 8!) 8.1 The Molecular Bond A molecule is an electrically neutral group of atoms held together strongly enough to behave as a single particle. A
More informationElectromagnetic Radiation (EMR) and Remote Sensing
Electromagnetic Radiation (EMR) and Remote Sensing 1 Atmosphere Anything missing in between? Electromagnetic Radiation (EMR) is radiated by atomic particles at the source (the Sun), propagates through
More informationDiatomic Molecules. Atom > Molecule. Diatomic Molecules  Lukas Schott
Diatomic Molecules Atom > Molecule 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
More information1D 3D 1D 3D. is called eigenstate or state function. When an operator act on a state, it can be written as
Chapter 3 (Lecture 45) Postulates of Quantum Mechanics Now we turn to an application of the preceding material, and move into the foundations of quantum mechanics. Quantum mechanics is based on a series
More informationInstrumental Lab. Nuclear Magnetic Resonance. Dr Alex J. Roche
Instrumental Lab Nuclear Magnetic Resonance Dr Alex J. Roche 1 Nuclear Magnetic Resonance (NMR) Spectroscopy NMR is the most powerful analytical tool currently available to an organic chemist. NMR allows
More information5. Scanning NearField Optical Microscopy 5.1. Resolution of conventional optical microscopy
5. Scanning NearField Optical Microscopy 5.1. Resolution of conventional optical microscopy Resolution of optical microscope is limited by diffraction. Light going through an aperture makes diffraction
More informationPROTON NUCLEAR MAGNETIC RESONANCE SPECTROSCOPY (HNMR)
PROTON NUCLEAR MAGNETIC RESONANCE SPECTROSCOPY (HNMR) WHAT IS HNMR SPECTROSCOPY? References: Bruice 14.1, 14.2 Introduction NMR or nuclear magnetic resonance spectroscopy is a technique used to determine
More informationPigment Organization and Transfer of Electronic Excitation in the Photosynthetic Unit of Purple Bacteria
3854 J. Phys. Chem. B 1997, 101, 38543871 Pigment Organization and Transfer of Electronic Excitation in the Photosynthetic Unit of Purple Bacteria Xiche Hu, Thorsten Ritz, Ana Damjanović, and Klaus Schulten*
More informationSpectrum Scarcity and Free Space Op1cal Communica1ons. Mohamed Slim Alouini KAUST January 2014
Spectrum Scarcity and Free Space Op1cal Communica1ons Mohamed Slim Alouini KAUST January 2014 Agenda Spectrum Scarcity RF spectrum Mobile traffic growth and spectrum scarcity Cogni1ve Radio Networks (CRNs)
More informationStructural Health Monitoring Tools (SHMTools)
Structural Health Monitoring Tools (SHMTools) Parameter Specifications LANL/UCSD Engineering Institute LACC14046 c Copyright 2014, Los Alamos National Security, LLC All rights reserved. May 30, 2014
More information1 Variational calculation of a 1D bound state
TEORETISK FYSIK, KTH TENTAMEN I KVANTMEKANIK FÖRDJUPNINGSKURS EXAMINATION IN ADVANCED QUANTUM MECHAN ICS Kvantmekanik fördjupningskurs SI38 för F4 Thursday December, 7, 8. 13. Write on each page: Name,
More informationModule 3 : Molecular Spectroscopy Lecture 13 : Rotational and Vibrational Spectroscopy
Module 3 : Molecular Spectroscopy Lecture 13 : Rotational and Vibrational Spectroscopy Objectives After studying this lecture, you will be able to Calculate the bond lengths of diatomics from the value
More informationOptics and Spectroscopy at Surfaces and Interfaces
Vladimir G. Bordo and HorstGunter Rubahn Optics and Spectroscopy at Surfaces and Interfaces WILEY VCH WILEYVCH Verlag GmbH & Co. KGaA Contents Preface IX 1 Introduction 1 2 Surfaces and Interfaces 5
More informationElectronic Structure and Transition Intensities in RareEarth Materials
Electronic Structure and Transition Intensities in RareEarth Materials Michael F Reid Department of Physics and Astronomy and MacDiarmid Institute for Advanced Materials and Nanotechnology University
More information6) How wide must a narrow slit be if the first diffraction minimum occurs at ±12 with laser light of 633 nm?
Test IV Name 1) In a single slit diffraction experiment, the width of the slit is 3.1 105 m and the distance from the slit to the screen is 2.2 m. If the beam of light of wavelength 600 nm passes through
More informationRaman Spectroscopy. 1. Introduction. 2. More on Raman Scattering. " scattered. " incident
February 15, 2006 Advanced Physics Laboratory Raman Spectroscopy 1. Introduction When light is scattered from a molecule or crystal, most photons are elastically scattered. The scattered photons have the
More informationMolecularOrbital Theory
MolecularOrbital Theory 1 Introduction Orbitals in molecules are not necessarily localized on atoms or between atoms as suggested in the valence bond theory. Molecular orbitals can also be formed the
More informationThree Pictures of Quantum Mechanics. Thomas R. Shafer April 17, 2009
Three Pictures of Quantum Mechanics Thomas R. Shafer April 17, 2009 Outline of the Talk Brief review of (or introduction to) quantum mechanics. 3 different viewpoints on calculation. Schrödinger, Heisenberg,
More informationAmplification Atomic (or molecular, or semiconductor) system has energy levels Some higher energy states are stable for a short time (ps to ms)
Part 5: Lasers Amplification Atomic (or molecular, or semiconductor) system has energy levels Some higher energy states are stable for a short time (ps to ms) Incident photon can trigger emission of an
More informationBy far the most important and useful technique to identify organic molecules. Often the only technique necessary.
Chapter 13: NMR Spectroscopy 39 NMR Spectroscopy By far the most important and useful technique to identify organic molecules. Often the only technique necessary. NMR spectrum can be recorded for many
More informationVibrations of Carbon Dioxide and Carbon Disulfide
Vibrations of Carbon Dioxide and Carbon Disulfide Purpose Vibration frequencies of CO 2 and CS 2 will be measured by Raman and Infrared spectroscopy. The spectra show effects of normal mode symmetries
More informationModule 1: Quantum Mechanics  2
Quantum Mechanics  Assignment Question: Module 1 Quantum Mechanics Module 1: Quantum Mechanics  01. (a) What do you mean by wave function? Explain its physical interpretation. Write the normalization
More informationMASTER OF SCIENCE IN PHYSICS MASTER OF SCIENCES IN PHYSICS (MS PHYS) (LIST OF COURSES BY SEMESTER, THESIS OPTION)
MASTER OF SCIENCE IN PHYSICS Admission Requirements 1. Possession of a BS degree from a reputable institution or, for nonphysics majors, a GPA of 2.5 or better in at least 15 units in the following advanced
More informationChapter 13 Mass Spectrometry and Infrared Spectroscopy
Chapter 13 Mass Spectrometry and Infrared Spectroscopy Copyright 2011 The McGrawHill Companies, Inc. Permission required for reproduction or display. 1 Overview of Mass Spectrometry Mass spectrometry
More informationLecture 29. Introduction to Fluorescence Spectroscopy
Lecture 29 Introduction to Fluorescence Spectroscopy Introduction When a molecule absorbs light, an electron is promoted to a higher excited state (generally a singlet state, but may also be a triplet
More informationConvec'on, Humidity, and Predictability in a Near Global Aquaplanet CRM
S11 S12 Convec'on, Humidity, and Predictability in a Near Global Aquaplanet CRM Chris Bretherton, University of Washington Marat Khairoutdinov, Stony Brook University Goals of study Use a near global
More informationRaman Scattering Theory David W. Hahn Department of Mechanical and Aerospace Engineering University of Florida (dwhahn@ufl.edu)
Introduction Raman Scattering Theory David W. Hahn Department of Mechanical and Aerospace Engineering University of Florida (dwhahn@ufl.edu) The scattering of light may be thought of as the redirection
More informationGIANT FREQUENCY SHIFT OF INTRAMOLECULAR VIBRATION BAND IN THE RAMAN SPECTRA OF WATER ON THE SILVER SURFACE. M.E. Kompan
GIANT FREQUENCY SHIFT OF INTRAMOLECULAR VIBRATION BAND IN THE RAMAN SPECTRA OF WATER ON THE SILVER SURFACE M.E. Kompan Ioffe Institute, SaintPeterburg, Russia kompan@mail.ioffe.ru The giant frequency
More informationIR Applied to Isomer Analysis
DiscovIRLC TM Application Note 025 April 2008 Deposition and Detection System IR Applied to Isomer Analysis Infrared spectra provide valuable information about local configurations of atoms in molecules.
More informationStephen Hill National High Magnetic Field Lab Florida State University, Physics. nationalmaglab.org
Stephen Hill National High Magnetic Field Lab Florida State University, Physics nationalmaglab.org Outline of talk: What is Electron Magnetic Resonance (EMR) Spinspin interactions and structure measurements
More informationFrom lowest energy to highest energy, which of the following correctly orders the different categories of electromagnetic radiation?
From lowest energy to highest energy, which of the following correctly orders the different categories of electromagnetic radiation? From lowest energy to highest energy, which of the following correctly
More informationBlackbody radiation derivation of Planck s radiation low
Blackbody radiation derivation of Planck s radiation low 1 Classical theories of Lorentz and Debye: Lorentz (oscillator model): Electrons and ions of matter were treated as a simple harmonic oscillators
More informationEnergia da vibrazioni
Energy harves,ng Energia da vibrazioni Luca Gammaitoni Dipar,mento di Fisica, Università di Perugia www.nipslab.org Energy required to operate the portable devices Energy available from portable sources
More informationCROP CLASSIFICATION WITH HYPERSPECTRAL DATA OF THE HYMAP SENSOR USING DIFFERENT FEATURE EXTRACTION TECHNIQUES
Proceedings of the 2 nd Workshop of the EARSeL SIG on Land Use and Land Cover CROP CLASSIFICATION WITH HYPERSPECTRAL DATA OF THE HYMAP SENSOR USING DIFFERENT FEATURE EXTRACTION TECHNIQUES Sebastian Mader
More informationChapter 15 NMR Spectroscopy
Chempocalypse Now! Chapter 15 NMR Spectroscopy Page 1 Chapter 15 NMR Spectroscopy Parts of Topics A5 and A9 from the IB HL Chemistry Curriculum A5 A.5.1 Nuclear magnetic resonance (NMR) spectrometry (2
More informationRCNP. 1. Complex scaling method (CSM) to describe manybody unbound states. 2. Spectroscopy of resonances 3. Reactions using CSM 2009.2.
RCNP 1. Complex scaling method (CSM) to describe manybody unbound states. 2. Spectroscopy of resonances 3. Reactions using CSM 2009.2.2728 1 CSM 8 Be C O α α Borromean 6 He 11 Li unbound 5 He 10 Li 10
More informationSimulation of infrared and Raman spectra
Simulation of infrared and Raman spectra, 1 Bernard Kirtman, 2 Michel Rérat, 3 Simone Salustro, 1 Marco De La Pierre, 1 Roberto Orlando, 1 Roberto Dovesi 1 1) Dipartimento di Chimica, Università di Torino
More information