Physical Methods in Inorganic Chemistry RUSSELL S. DRAGO Department of Chemistry and Chemical Engineering University of Illinois Urbana, Illinois TU Darmstadt Teiibibliothek Chemie/ Materialwissenschaft New York REINHOLD PUBLISHING CORPORATION Chapman and Hall Ltd., London Contents PART I ATOMIC A N D M O L E C U L A R S T R U C T U R E CHAPTER 1 ATOMIC STRUCTURE Wave Properties of Electrons Description of the Position and Momentum of an Electron Mathematical Description of Waves The Schrodinger Equation The Solution of the Schrodinger Equation Quantum Numbers The Physical Picture of Atomic Orbitals Extension of the Wave Equation to Atoms Other Than Hydrogen Relative Energies of the Orbitals Term Symbols and the Vector Method Term Symbols for Excited States CHAPTER 2 BONDING The Variation Principle Treatments of the Hydrogen Molecule Electron Exchange Interaction Applications of Valence Bond Theory The General Molecule XY — Electronegativity More Complicated Molecules — Resonance The Overlap of Atomic Orbitals Hybrid Orbitals Hybrids Involving d Orbitals Energetics of Hybrid Bond Formation N onequivalence of Orbitals a and TT Bonds 1 1 2 3 5 6 8 12 18 20 23 26 30 30 34 37 37 37 38 40 42 45 47 49 51 xiv CONTENTS Applications of Molecular Orbital Theory Molecular Orbitals for Homonuclear Diatomic Molecules Molecular Orbitals in Heteronuclear Diatomic Molecules Electron Deficient Molecules A Delocalized TT Electron System Molecular Orbital Description of Some Interhalogen Molecules Qualitative Comparison of the Valence Bond and Molecular Orbital Approaches Electrostatic Bonding Ionic Bonding Ion-Dipole Dipole-Dipole Dipole-Induced Dipole London Dispersion Hydrogen Bonding Covalence and Polarizability The Hydrogen Bond 53 53 58 60 62 64 64 65 65 66 67 67 68 68 68 69 CHAPTER 3 LLGAND F I E L D AND MOLECULAR ORBITAL DESCRIPTION OF BONDING IN COMPLEXES 74 Ligand Field Theory Shapes and Positions of the Orbitals Six-Coordinate Complexes Four-Coordinate Complexes Summary of the d-Level Splittings Ligand Field Strengths — Colors of Complexes The Molecular Orbital Theory of Bonding in Complexes PART II 74 74 74 82 86 86 87 SPECTROSCOP1C METHODS CHAPTER 4 SYMMETRY AND THE CHARACTER TABLES Introduction Symmetry Elements The Center of Symmetry or I nversion Center The Rotation Axis The Mirror Plane or Plane of Symmetry The Rotation-Reflection Axis; Improper Rotations The Identity Point Groups Group Theory and the Character Table Space Symmetry 99 100 100 101 103 105 106 107 111 118 CONTENTS CHAPTER 5 xv G E N E R A L INTRODUCTION TO SPECTROSCOPY Nature of Radiation Energies Corresponding to Various Kinds of Radiation Energies for Atomic and Molecular Transitions Selection Rules General Applications Determination of Concentration "Fingerprinting" I sosbestic Points CHAPTER 6 ELECTRONIC ABSORPTION SPECTROSCOPY Vibrational and Electronic Energy Levels in a Diatomic Molecule Introduction to Electronic Transitions Relationship of Potential Energy Curves to Electronic Spectra Nomenclature Assignment of Transitions Oscillator Strengths I ntensity of Electronic Transitions Polarized Absorption Spectra Charge Transfer Transitions Applications Fingerprinting Molecular Addition Compounds of Iodine Effect of Solvent Polarity on Charge Transfer Spectra Spectra of Transition Metal Complexes Selection Rules and Intensities of the Transitions Nature of Electronic Transitions in Complexes d2, d1, d3, d8 Configurations Use of Orgel Diagrams Calculation of Dq and 8 for Ni 7/ Complexes Structural Evidence from Electronic Spectra Miscellaneous Applications of the Principles Related to Electronic Transitions CHAPTER 7 VIBRATION AND ROTATION SPECTROSCOPY: INFRARED, R A M A N , AND MICROWAVE Introduction Harmonic and Anharmonic Vibrations Absorption of Radiation by Molecular Vibrations — Selection Rules Force Constant 121 121 122 124 126 127 127 130 131 135 135 137 137 139 144 147 148 150 151 151 152 155 15 8 161 161 162 164 167 168 175 181 187 187 187 189 190 xvi CONTENTS Vibrations in a Polyatomic Molecule Effects Giving Rise to Absorption Bands Normal Coordinate Analyses and Band Assignments G roup Vibrations Limitations of the G roup Vibration Concept Raman Spectroscopy Polarized and Depolarized Raman Lines Significance of the Nomenclature Used To Describe Various Species Use of Symmetry Considerations To Determine the Number of Active Infrared and Raman Lines Symmetry Requirements for Coupling Combination Bands and Fermi Resonance Microwave Spectroscopy Determination of Bond Angles and Bond Distances Measurement of the Dipole Moment of a Molecule Rotational Raman Spectra Applications of Infrared and Raman Spectroscopy Procedures Fingerprinting Spectra of Gases Application of Raman and Infrared Selection Rules to the Determination of Inorganic Structures Hydrogen Bonding Systems Changes in the Spectra of Donor Molecules upon Coordination Change in Spectra Accompanying Change in Symmetry upon Coordination CHAPTER 8 NUCLEAR MAGNETIC RESONANCE SPECTROSCOPY Theory of NMR Spectroscopy The Chemical Shift Chemical Shifts of Some Systems Studied by NMR Mechanism of Electron Shielding and Factors Contributing to the Magnitude of the Chemical Shift Chemical Shifts for Which the Local Diamagnetic Term Does Not Predominate Spin-Spin Splitting Spin-Spin Coupling Mechanism for Transmitting Nuclear Spins Applications of Spin-Spin Coupling to Structure Determination Applications Involving the Magnitude of Coupling Constants Complex Spectra Obtained When J ~ A 191 192 195 196 196 199 202 202 203 210 210 211 212 213 213 213 218 222 226 229 230 232 239 239 244 250 253 258 260 265 266 270 274 CONTENTS xvii Chemical Exchange and Other Factors Affecting Line Width Effect of Chemical Exchange on Spectra and the Evaluation of Reaction Rates for Fast Reactions Consequences of Nuclei with Quadrupole Moments in NMR The Double-Resonance Technique NMR Studies of Exchange Reactions Between Ligands and Metal Ions NMR of Paramagnetic Complexes — Contact Shifts Miscellaneous Applications of NMR to Inorganic Problems CHAPTER 9 CHAPTER 10 ELECTRON PARAMAGNETIC RESONANCE SPECTROSCOPY Introduction Presentation of the Spectrum Hyperfine Splitting in Some Simple Systems Hyperfine Splittings in Various Structures Factors Affecting the Magnitude of the g Values Interactions Affecting the Energies of Unpaired Electrons in Transition Metal Ion Complexes Zero-Field Splitting and Kramers' Degeneracy Anisotropy in the Hyperfine Coupling Constant Nuclear Quadrupole Interaction The Spin Hamiltonian Line Widths in Solid State EPR Electron Delocalization Applications Rate of Electron Exchange Reactions by EPR Miscellaneous Applications Introduction 281 290 291 294 298 303 NUCLEAR QUADRUPOLE RESONANCE SPECTROSCOPY 315 Introduction Effect of a Magnetic Field on the Spectra Relationship Between the Electric Field Gradient, q, and Molecular Structure Applications The Interpretation of eQq Data The Effects of Crystal Lattice on the Magnitude of eQq Structural Information from NQR Spectra CHAPTER 11 279 MOSSBAUER SPECTROSCOPY 315 319 320 321 321 323 323 328 328 330 331 332 338 341 342 346 348 349 350 351 352 355 356 362 362 'iii CONTENTS Resonance Line Shifts From Change In Electron Environment Quadrupole Interactions Magnetic Interactions Applications CHAPTER 12 MASS SPECTROMETRY 366 366 367 368 374 Introduction 374 Operation and Representation of Spectra 3 74 Process That Can Occur When a Molecule and a High Energy Electron Combine 378 Applications 380 Fingerprint Application and the Interpretation of Mass Spectra 380 Effect of Isotopes on the Appearance of a Mass Spectrum 382 Molecular Weight Determinations 385 Evaluation of Heats of Sublimation and Species in the Vapor over High Melting Solids 385 Appearance Potentials and Ionization Potentials 386 Appendix A. Magnetism Contributions to Magnetic Properties Effect of the Ligand Field on Spin-Orbit Coupling Measurement of Magnetic Properties Some Applications of Magnetic Data Temperature Dependence of Magnetism 389 389 391 393 394 396 Appendix B. Character Tables for Selected Point Groups 398 Appendix C. Tanabe and Sugano Diagrams for Oh Fields 403 Appendix D. Calculation of Dq(A) and j8 for OhW and TdCo" Complexes 410 Calculation of A And /3 For TdCo2+ Complexes 411 Appendix E. Normal Vibration Modes for Common Structures 414 Appendix F. Conversion of Chemical Shift Data 421 Index 423
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