William W. Parson Modern Optical Spectroscopy Student Edition

Transcription

1 William W. Parson Modern Optical Spectroscopy Student Edition

2 William W. Parson Modern Optical Spectroscopy With Exercises and Examples from Biophysics and Biochemistry Student Edition 123

3 WILLIAM W. PARSON University of Washington Department of Biochemistry Box Seattle, WA USA ISBN e-isbn DOI / Springer Dordrecht Heidelberg London New York Library of Congress Control Number: c Springer-Verlag Berlin Heidelberg 2007, First student edition 2009 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable to prosecution under the German Copyright Law. The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the rele-vant protective laws and regulations and therefore free for general use. Cover design: WMXDesign, Heidelberg, Germany Printed on acid-free paper Springer is part of Springer Science+Business Media (

4 Preface to the Student Edition The student edition of Modern Optical Spectroscopy includes a new set of exercises for each chapter. The exercises and problems generally emphasize basic points, and often include simplified absorption or emission spectra or molecular orbitals that can be evaluated easily with the aid of a calculator or spreadsheet. Students who are adept at computer programming will find it instructive to try to write algorithms that also could be applied to larger, more complicated sets of data. SpectraintroducedinsomeoftheproblemsforChaps.4and5areusedagain in later chapters to illustrate how quantities calculated from the spectra can be applied to topics such as resonance energy transfer and exciton interactions. Seattle, November, 2008 William W. Parson

5 Preface 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. Oneofmygoalshasbeentowriteinawaythatwillbeaccessibletoreaders 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 steppingstone 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, singlemolecule 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 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

6 VIII Preface 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, October 2006 William W. Parson

7 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 Basic Concepts of Quantum Mechanics Wavefunctions, Operators, and Expectation Values Wavefunctions Operators and Expectation Values The Time-Dependent and Time-Independent Schrödinger Equations Superposition States Spatial Wavefunctions A Free Particle A Particle in a Box The Harmonic Oscillator Atomic Orbitals Molecular Orbitals Approximate Wavefunctions for Large Systems Spin Wavefunctions and Singlet and Triplet States Transitions Between States: Time-Dependent Perturbation Theory Lifetimes of States and the Uncertainty Principle... 68

8 X Contents 3 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 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 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 238

9 Contents XI 6 Vibrational Absorption Vibrational Normal Modes and Wavefunctions Vibrational Excitation IR Spectroscopy of Proteins Vibrational Stark Effects Resonance Energy Transfer Introduction The Förster Theory Exchange Coupling Energy Transfer to and from Carotenoids in Photosynthesis 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 Excimers and Exciplexes 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 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 Steady-State Absorption The Relaxation Matrix More General Relaxation Functions and Spectral Lineshapes Anomalous Fluorescence Anisotropy Pump Probe Spectroscopy, Photon Echoes, and Vibrational Wavepackets First-Order Optical Polarization

10 XII Contents 11.2 Third-Order Optical Polarization and Nonlinear Response Functions Pump Probe Spectroscopy Photon Echoes Transient Gratings Vibrational Wavepackets Wavepacket Pictures of Spectroscopic Transitions Raman Scattering and Other Multiphoton Processes Types of Light Scattering The Kramers Heisenberg Dirac Theory The Wavepacket Picture of Resonance Raman Scattering Selection Rules for Raman Scattering Surface-Enhanced Raman Scattering Biophysical Applications of Raman Spectroscopy Coherent Raman Scattering Multiphoton Absorption Quasielastic (Dynamic) Light Scattering (Photon Correlation Spectroscopy) Appendix 1 Vectors 447 Appendix 2 Matrices 451 Appendix 3 Fourier Transforms 455 Appendix 4 Fluorescence Phase Shift and Modulation 459 Appendix 5 CGS and SI Units and Abbreviations 463 References 465 Exercises 505 Subject Index 523