ULTRAFAST INFRARED AND RAMAN SPECTROSCOPY

By EMILY MOORE

CONTENTS CHAPTER 1 GENERALITIES ON DIATOMIC MOLECULES 11 GENERALITIES ON DETECTING DIATOMIC MOLECULES 111 RADIATION–MATTER INTERACTION FOR DETECTION 112 DIATOMIC MOLECULES: OBSERVATION, ANALYSIS AND INTERPRETATION 12 HAMILTONIAN OF A DIATOMIC MOLECULE 13 SYMMETRY PROPERTIES OF A DIATOMIC MOLECULE 131 GROUP OF SYMMETRY 132 SYMMETRY OF THE ELECTRONIC STATES 133 SYMMETRY OF THE TOTAL WAVE FUNCTIONS 14 EXAMPLE OF THE DIATOMIC MOLECULE WITH TWO ELECTRONS H2, HD, D2 141 HAMILTONIAN OF THE ISOTOPOLOGUES 142 BO APPROXIMATION 143 ADIABATIC REPRESENTATION 144 DIABATIC REPRESENTATION 15 CONCLUSION 16 APPENDIX CHAPTER 2 ENERGY LEVELS OF A DIATOMIC MOLECULE IN GASEOUS PHASE 21 INTRODUCTION 22 PURE VIBRATION MOVEMENT OF A DIATOMIC MOLECULE 221 HARMONIC OSCILLATOR: CLASSICAL PROCESSING 222 HARMONIC OSCILLATOR: QUANTUM ASPECT 223 TRANSITIONS BETWEEN TWO VIBRATIONAL LEVELS: SELECTION RULES 224 “CREATION” AND “ANNIHILATION” OPERATORS 225 ANHARMONIC OSCILLATOR 226 CONTACT TRANSFORMATION METHOD 23 ROTATION MOVEMENT OF A RIGID DIATOMIC MOLECULE 231 FREE RIGID ROTOR: CLASSICAL PROCESSING 232 FREE RIGID ROTOR: QUANTUM ASPECT 233 TRANSITIONS BETWEEN ROTATIONAL LEVELS: SELECTION RULES 24 VIBRATION–ROTATION COUPLING OF A FREE DIATOMIC MOLECULE 241 NON-RIGID ROTOR 242 ROVIBRATIONAL TRANSITIONS: SELECTION RULES 25 APPENDIX 251 THE COMMUTATORS 252 EXPRESSIONS OF PN AND QN IN TERMS OF THE OPERATORS A AND A† 253 MATRIX ELEMENTS OF PN AND QN 254 MATRIX OF ROTATION AND ROTATIONAL TRANSITIONS CHAPTER 3 PROFILE AND SHAPE OF SPECTRAL LINES 31 INTRODUCTION 32 SEMICLASSICAL MODEL OF CALCULATING THE BROADENING PARAMETERS OF SPECTRAL LINES 321 GENERAL DESCRIPTION OF THE INTERACTING PHYSICAL SYSTEM 322 GENERAL EXPRESSION OF THE PROFILE OF A SPECTRAL LINE 323 CONSEQUENCES OF THE INVARIANCE OF THE ZWANZIG RELAXATION OPERATOR UNDER ROTATION 324 SEMICLASSICAL CONTEXT FOR CALCULATING THE RELAXATION MATRIX 325 BROADENING PARAMETER ACCORDING TO THE DIFFUSION OPERATOR 326 CALCULATION OF THE DIFFERENTIAL CROSS-SECTION S(B, V) 327 INTERACTION POTENTIAL ENERGY 328 RELATIVE TRAJECTORY OF THE MOLECULES 329 EXPRESSION OF S(B,V) IN TERMS OF RESONANCE FUNCTIONS 33 TRUE SHAPE, PROFILE AND INTENSITY OF AN ABSORPTION LINE 34 LINE PROFILE 341 LORENTZ PROFILE 342 GAUSS PROFILE 343 VOIGT PROFILE 344 GALATRY, NELKIN–GHATAK AND RAUTIAN–SOBELMANN PROFILES 35 CONCLUSION 36 APPENDIX 361 LIOUVILLE FORMALISM 362 THE CLEBSCH–GORDAN COEFFICIENTS AND THE WIGNER 3J SYMBOLS 363 THE TERMS OF THE DIFFERENTIAL CROSS-SECTION EXPANSION S(B,V) CHAPTER 4 ENERGY LEVELS AND SPECTRAL PROFILE OF A DIATOMIC MOLECULE IN CONDENSED PHASE 41 INTRODUCTION 42 INCLUSION MODEL 421 BINARY INTERACTION ENERGY 422 LAKHLIFI–DAHOO INCLUSION MODEL 43 RARE GAS NANOCAGE 431 THE RARE GASES IN THE SOLID STATE 432 DYNAMICS OF THE PERFECT FCC LATTICE (BRAVAIS LATTICE) 433 GREEN FUNCTION OF THE PERFECT MONOATOMIC CRYSTAL 44 INCLUSION OF A MOLECULE IN A RARE GAS MATRIX 441 DEFORMATION METHOD 442 EQUILIBRIUM OF THE DOPED CRYSTAL 45 GENERAL HAMILTONIAN AND SEPARATION OF THE MOVEMENTS 451 HAMILTONIAN OF THE SYSTEM 452 SEPARATION OF THE OPTICAL SYSTEM’S MOVEMENTS AND THE BATH IN THE RIGID MATRIX APPROXIMATION 453 VIBRATIONAL MODE 454 ORIENTATIONAL MODES 455 ACTIVE OPTICAL SYSTEM 456 TRANSLATIONAL MODES 457 OPTICAL MODES – BATH COUPLING 46 INFRARED ABSORPTION COEFFICIENT 461 GENERAL EXPRESSION 462 HEISENBERG REPRESENTATION 463 AVERAGES AND CORRELATION FUNCTIONS 464 BAR SPECTRUM OR DIRAC SPECTRUM 465 SPECTRAL PROFILE 47 CONCLUSION 48 APPENDIX 481 EXPRESSION OF THE DISPERSION–REPULSION CONTRIBUTION OF THE ENERGY OF TRUNCATED BINARY INTERACTION IN THE FOURTH ORDER 482 ROTATION MATRIX 483 EIGENVALUES CORRECTION OF THE ORIENTATION HAMILTONIAN 484 EIGENVALUES CORRECTION OF THE ORIENTATION HAMILTONIAN CHAPTER 5 APPLICATIONS TO HCL, CO, O2 AND N2 51 THE HCL HETERONUCLEAR MOLECULE ISOLATED AND TRAPPED IN A MATRIX 511 MOLECULE IN THE GASEOUS PHASE 512 MOLECULE TRAPPED IN RARE GAS MATRIX 52 LIDAR PROBING OF TERRESTRIAL HOMONUCLEAR MOLECULES N2 AND O2 53 THE HETERONUCLEAR MOLECULE CO TRAPPED IN A MATRIX AND ABSORBED ON GRAPHITE SUBSTRATE (1000) AT A LOW TEMPERATURE 531 MOLECULE TRAPPED IN A RARE GAS MATRIX 532 MOLECULE ADSORBED ON THE GRAPHITE SUBSTRATE 533 MOLECULE–GRAPHITE INTERACTION ENERGY 534 ADSORPTION OBSERVABLES AT A LOW TEMPERATURE 54 CONCLUSION GENERALITIES ON DIATOMIC MOLECULES A DIATOMIC MOLECULE IS THE SIMPLEST POSSIBLE ASSEMBLY BASED ON A SYSTEM OF ATOMS THAT LEAD TO MOLECULES, WHETHER HOMONUCLEAR OR HETERONUCLEAR ITS SPECTRAL SIGNATURE IS THE RESULT OF THE INTERACTION OF AN ELECTROMAGNETIC RADIATION WITH THE ELECTRONS, GIVEN THE MOVEMENT OF ITS CHARGED CONSTITUENTS, NUCLEI AND ELECTRONS THIS INTERACTION IS MODELED BY AN OPERATOR, THE N-POLAR MOMENT, WHICH LEADS TO A TRANSITION BETWEEN THE DIATOMIC MOLECULE’S ENERGY STATES, THE EIGENFUNCTIONS OF THE HAMILTONIAN, ITS ENERGY OPERATOR BUILT ON THE CLASSICAL (ELECTRONIC, VIBRATION AND ROTATION) AND QUANTUM (ELECTRONIC AND NUCLEAR SPIN) DEGREES OF FREEDOM THE RESOLUTION OF THE SCHRÖDINGER EIGENVALUES EQUATION OF THE MOLECULAR SYSTEM IS BASED ON THE BORN– OPPENHEIMER (BO) APPROXIMATION, WHICH ALLOWS THE ELECTRONS’ FAST MOVEMENT TO BE DECOUPLED FROM THAT OF THE NUCLEI, WHICH IS MUCH SLOWER, AND TO SEPARATELY PROCESS ITS ELECTRONIC AND VIBRATION–ROTATION DEGREES OF FREEDOM IN SPECTROSCOPY THE CHARACTERISTICS OF THE ELECTRONIC, VIBRATIONAL AND ROTATIONAL SPECTRA DEPEND ON THE MOLECULE’S SYMMETRIES AND ITS ELECTRONIC AND NUCLEAR SPIN PROPERTIES WE CAN USE GROUP THEORY FOR PREDICTING THE ABSORPTION SPECTRA PROFILES AND THE TRANSITION RULES EXPECTED IN INFRARED OR RAMAN SPECTROSCOPY THUS, MOLECULAR SPECIES ARE DIVIDED INTO PARA AND ORTHO VARIETIES FOR THE H2 MOLECULE, FOR INSTANCE IN THE RAMAN ROTATIONAL SPECTRUM, H2 PRESENTS AN INTENSITY ALTERNATION WHICH IS DIFFERENT TO THAT OF N2 AS A FUNCTION OF THE ROTATIONAL QUANTUM NUMBER, WHEREAS FOR O2, ONE LINE OUT OF TWO IS ABSENT IN THE SPECTRUM