Modern Optical Spectroscopy

Transcription

1 Modern Optical Spectroscopy

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3 William W. Parson Modern Optical Spectroscopy With Exercises and Examples from Biophysics and Biochemistry Second Edition

4 William W. Parson University of Washington Seattle Washington USA ISBN ISBN (ebook) DOI / Library of Congress Control Number: Springer Heidelberg New York Dordrecht London # Springer-Verlag Berlin Heidelberg 2015 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. Printed on acid-free paper Springer-Verlag GmbH Berlin Heidelberg is part of Springer Science+Business Media (

5 Preface to the Second Edition Applications of optical spectroscopy in chemistry, biochemistry, and biophysics continue to flourish. This revised edition of Modern Optical Spectroscopy includes expanded discussions of quantum optics, metal-ligand charge-transfer transitions, entropy changes during photoexcitation, electron transfer from excited molecules, normal-mode calculations, vibrational Stark effects, studies of fast processes by resonance energy transfer in single molecules, and two-dimensional electronic and vibrational spectroscopy. I have added new figures where I thought they would help and modified some of the original figures for greater clarity. The references have been updated and moved from the end of the book to the chapters where they are cited. Each chapter also has a set of exercises for students. I greatly appreciate the constructive comments from readers calling my attention to errors or points that needed clarification in the first edition. Discussions with Bill Hazelton, Bob Knox, Ross McKenzie, Nagarajan, and Steve Boxer were particularly helpful. I also thank my Springer editors Jutta Lindenborn and Sabine Schwarz for their excellent suggestions and my wife Polly for her continuing patience and encouragement. Seattle, WA April 2015 William W. Parson v

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7 Preface to the First Edition This book began as lecture notes for a course on optical spectroscopy that I taught for graduate students in biochemistry, chemistry, and our interdisciplinary programs in molecular biophysics and biomolecular structure and design. I started expanding the notes partly to try to illuminate the stream of new experimental information on photosynthetic antennas and reaction centers, but mostly just for fun. I hope that readers will find the results not only useful, but also as stimulating as I have. One of my goals has been to write in a way that will be accessible to readers with little prior training in quantum mechanics. But any contemporary discussion of how light interacts with molecules must begin with quantum mechanics, just as experimental observations on blackbody radiation, interference, and the photoelectric effect form the springboard for almost any introduction to quantum mechanics. To make the reasoning as transparent as possible, I have tried to adopt a consistent theoretical approach, minimize jargon, and explain any terms or mathematical methods that might be unfamiliar. I have provided numerous figures to relate spectroscopic properties to molecular structure, dynamics, and electronic and vibrational wavefunctions. I also describe classical pictures in many cases and indicate where these either have continued to be useful or have been supplanted by quantum mechanical treatments. Readers with experience in quantum mechanics should be able to skip quickly through many of the explanations, but will find that the discussion of topics such as density matrices and wavepackets often progresses well beyond the level of a typical 1-year course in quantum mechanics. I have tried to take each topic far enough to provide a solid stepping-stone to current theoretical and experimental work in the area. Although much of the book focuses on physical theory, I have emphasized aspects of optical spectroscopy that are especially pertinent to molecular biophysics, and I have drawn most of the examples from this area. The book therefore covers topics that receive little attention in most general books on molecular spectroscopy, including exciton interactions, resonance energy transfer, single molecule spectroscopy, high-resolution fluorescence microscopy, femtosecond pump probe spectroscopy, and photon echoes. It says less than is customary about atomic spectroscopy and about rotational and vibrational spectroscopy of vii

8 viii Preface to the First Edition small molecules. These choices reflect my personal interests and the realization that I had to stop somewhere, and I can only apologize to readers whose selections would have been different. I apologize also for using work from my own laboratory in many of the illustrations when other excellent illustrations of the same points are available in the literature. This was just a matter of convenience. I could not have written this book without the patient encouragement of my wife Polly. I also have enjoyed many thought-provoking discussions with Arieh Warshel, Nagarajan, Martin Gouterman, and numerous other colleagues and students, particularly including Rhett Alden, Edouard Alphandéry, Hiro Arata, Donner Babcock, Mike Becker, Bob Blankenship, Steve Boxer, Jacques Breton, Jim Callis, Patrik Callis, Rod Clayton, Richard Cogdell, Tom Ebrey, Tom Engel, Graham Fleming, Eric Heller, Dewey Holten, Ethan Johnson, Amanda Jonsson, Chris Kirmaier, David Klug, Bob Knox, Rich Mathies, Eric Merkley, Don Middendorf, Tom Moore, Jim Norris, Oleg Prezhdo, Phil Reid, Bruce Robinson, Karen Rutherford, Ken Sauer, Dustin Schaefer, Craig Schenck, Peter Schellenberg, Avigdor Scherz, Mickey Schurr, Gerry Small, Rienk van Grondelle, Maurice Windsor, and Neal Woodbury. Patrik Callis kindly provided the atomic coefficients used in Chaps. 4 and 5 for the molecular orbitals of 3-methylindole. Any errors, however, are entirely mine. I will appreciate receiving any corrections or suggestions for improvements. Seattle, WA October 2006 William W. Parson

9 Contents 1 Introduction Overview The Beer-Lambert Law Regions of the Electromagnetic Spectrum Absorption Spectra of Proteins and Nucleic Acids Absorption Spectra of Mixtures The Photoelectric Effect Techniques for Measuring Absorbance Pump-probe and Photon-Echo Experiments Linear and Circular Dichroism Distortions of Absorption Spectra by Light Scattering or Nonuniform Distributions of the Absorbing Molecules Fluorescence IR and Raman Spectroscopy Lasers Nomenclature Exercises References Basic Concepts of Quantum Mechanics Wavefunctions, Operators and Expectation Values Wavefunctions Operators and Expectation Values The Time-Dependent and Time-Independent Schr odinger Equations Superposition States Spatial Wavefunctions A Free Particle A Particle in a Box The Harmonic Oscillator Atomic Orbitals Molecular Orbitals Wavefunctions for Large Systems Spin Wavefunctions and Singlet and Triplet States ix

10 x Contents 2.5 Transitions Between States: Time-Dependent Perturbation Theory Lifetimes of States and the Uncertainty Principle Exercises References Light Electromagnetic Fields Electrostatic Forces and Fields Electrostatic Potentials Electromagnetic Radiation Energy Density and Irradiance The Complex Electric Susceptibility and Refractive Index Local-Field Correction Factors The Black-Body Radiation Law Linear and Circular Polarization Quantum Theory of Electromagnetic Radiation Superposition States and Interference Effects in Quantum Optics Distribution of Frequencies in Short Pulses of Light Exercises References Electronic Absorption Interactions of Electrons with Oscillating Electric Fields The Rates of Absorption and Stimulated Emission Transition Dipoles and Dipole Strengths Calculating Transition Dipoles for π Molecular Orbitals Molecular Symmetry and Forbidden and Allowed Transitions Linear Dichroism Configuration Interactions Calculating Electric Transition Dipoles with the Gradient Operator Transition Dipoles for Excitations to Singlet and Triplet States The Born-Oppenheimer Approximation, Franck-Condon Factors, and the Shapes of Electronic Absorption Bands Spectroscopic Hole Burning Effects of the Surroundings on Molecular Transition Energies The Electronic Stark Effect Metal-Ligand and Ligand-Metal Charge-Transfer Transitions and Rydberg Transitions Thermodynamics of Photoexcitation Exercises References

11 Contents xi 5 Fluorescence The Einstein Coefficients The Stokes Shift The Mirror-Image Law The Strickler-Berg Equation and Other Relationships Between Absorption and Fluorescence Quantum Theory of Absorption and Emission Fluorescence Yields and Lifetimes Fluorescent Probes and Tags Photobleaching Fluorescence Anisotropy Single-Molecule Fluorescence and High-Resolution Fluorescence Microscopy Fluorescence Correlation Spectroscopy Intersystem Crossing, Phosphorescence, and Delayed Fluorescence Exercises References Vibrational Absorption Vibrational Normal Modes and Wavefunctions Vibrational Excitation Infrared Spectroscopy of Proteins Vibrational Stark Effects Exercises References Resonance Energy Transfer Introduction The F orster Theory Using Energy Transfer to Study Fast Processes in Single Protein Molecules Exchange Coupling Energy Transfer to and from Carotenoids in Photosynthesis Exercises References Exciton Interactions Stationary States of Systems with Interacting Molecules Effects of Exciton Interactions on the Absorption Spectra of Oligomers Transition-Monopole Treatments of Interaction Matrix Elements and Mixing with Charge-Transfer Transitions Exciton Absorption Band Shapes and Dynamic Localization of Excitations Exciton States in Photosynthetic Antenna Complexes

12 xii Contents 8.6 Excimers and Exciplexes Exercises References Circular Dichroism Magnetic Transition Dipoles and n-π* Transitions The Origin of Circular Dichroism Circular Dichroism of Dimers and Higher Oligomers Circular Dichroism of Proteins and Nucleic Acids Magnetic Circular Dichroism Exercises References Coherence and Dephasing Oscillations Between Quantum States of an Isolated System The Density Matrix The Stochastic Liouville Equation Effects of Stochastic Relaxations on the Dynamics of Quantum Transitions A Density-Matrix Treatment of Absorption of Weak, Continuous Light The Relaxation Matrix More General Relaxation Functions and Spectral Lineshapes Anomalous Fluorescence Anisotropy Exercises References Pump-Probe Spectroscopy, Photon Echoes and Vibrational Wavepackets First-Order Optical Polarization Third-Order Optical Polarization and Non-linear Response Functions Pump-Probe Spectroscopy Photon Echoes Two-Dimensional Electronic and Vibrational Spectroscopy Transient Gratings Vibrational Wavepackets Wavepacket Pictures of Spectroscopic Transitions Exercises References Raman Scattering and Other Multi-photon Processes Types of Light Scattering The Kramers-Heisenberg-Dirac Theory The Wavepacket Picture of Resonance Raman Scattering Selection Rules for Raman Scattering

13 Contents xiii 12.5 Surface-Enhanced Raman Scattering Biophysical Applications of Raman Spectroscopy Coherent (Stimulated) Raman Scattering Multi-photon Absorption Quasielastic (Dynamic) Light Scattering (Photon Correlation Spectroscopy) Exercises References Appendix A A.1 Vectors A.2 Matrices A.3 Fourier Transforms A.4 Phase Shift and Modulation Amplitude in Frequency-Domain Spectroscopy A.5 CGS and SI Units and Abbreviations References Index

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15 List of Boxes Box 2.1 Operators for Observable Properties must be Hermitian Box 2.2 Commutators and Formulations of the Position, Momentum and Hamiltonian Operators Box 2.3 The Origin of the Time-Dependent Schr odinger Equation Box 2.4 Linear Momentum Box 2.5 Hermite Polynomials Box 2.6 Boltzmann, Fermi-Dirac and Bose-Einstein Statistics Box 3.1 Maxwell s Equations and the Vector Potential Box 3.2 Reflection, Transmission, Evanescent Radiation and Surface Plasmons Box 3.3 The Classical Theory of Dielectric Dispersion Box 4.1 Energy of a Dipole in an External Electric Field Box 4.2 Multipole Expansion of the Energy of a Set of Charges in a Variable External Field Box 4.3 The Behavior of the Function [exp(iy) 1]/y as y goes to Box 4.4 The Function sin 2 x/x 2 and Its Integral Box 4.5 The Oscillating Electric Dipole of a Superposition State Box 4.6 The Mean-Squared Energy of Interaction of an External Field with Dipoles in an Isotropic System Box 4.7 Physical Constants and Conversion Factors for Absorption of Light Box 4.8 Using Group Theory to Determine Whether a Transition is Forbidden by Symmetry Box 4.9 Evaluating Configuration-Interaction Coefficients Box 4.10 Box 4.11 Box 4.12 The Relationship Between Matrix Elements of the Electric Dipole and Gradient Operators Matrix Elements of the Gradient Operator for Atomic 2p Orbitals Selection Rules for Electric-Dipole Excitations of Linear Polyenes Box 4.13 Recursion Formulas for Vibrational Overlap Integrals Box 4.14 Thermally Weighted Franck-Condon Factors Box 4.15 Electronic Stark Spectroscopy of Immobilized Molecules Box 5.1 The v 3 Factor in the Strickler-Berg Equation xv

16 xvi List of Boxes Box 5.2 Creation and Annihilation Operators Box 5.3 Electron Transfer from Excited Molecules Box 5.4 Binomial, Poisson and Gaussian Distributions Box 6.1 Normal Coordinates and Molecular-Dynamics Simulations Box 6.2 Selection Rules for Vibrational Transitions Box 7.1 Dipole-Dipole Interactions Box 8.1 Why Must the Secular Determinant be Zero? Box 8.2 Real and Avoided Crossings of Energy Surfaces Box 8.3 Exciton States Are Stationary in the Absence of Further Perturbations Box 8.4 The Sum Rule for Exciton Dipole Strengths Box 9.1 Quantum Theory of Magnetic-Dipole and Electric-Quadrupole Transitions Box 9.2 Ellipticity and Optical Rotation Box 10.1 Time Dependence of the Density Matrix for an Isolated Three-State System Box 10.2 The Watched-Pot or Quantum Zeno Paradox Box 10.3 The Relaxation Matrix for a Two-State System Box 10.4 Dephasing by Static Inhomogeneity Box 10.5 Orientational Averages of Vector Dot Products Box 12.1 Quantum Theory of Electronic Polarizability