ROTATIONAL SPECTROSCOPY OF DIATOMIC MOLECULES
CONTENTS 1 GENERAL INTRODUCTION 1 1 ELECTROMAGNETIC SPECTRUM 1 2 ELECTROMAGNETIC RADIATION 1 3 INTRAMOLECULAR NUCLEAR AND ELECTRONIC DYNAMICS 1 4 ROTATIONAL LEVELS 1 5 HISTORICAL PERSPECTIVES 1 6 FINE STRUCTURE AND HYPER?NE STRUCTURE OF ROTATIONAL LEVELS 1 6 1 INTRODUCTION 1 6 2 1+ STATES 1 6 3 OPEN SHELL STATES 1 6 4 OPEN SHELL STATES WITH BOTH SPIN AND ORBITAL ANGULAR MOMENTUM 1 7 THE EFFECTIVE HAMILTONIAN 1 8 BIBLIOGRAPHY APPENDIX 1 1 MAXWELL’S EQUATIONS APPENDIX 1 2 ELECTROMAGNETIC RADIATION REFERENCES 2 THE SEPARATION OF NUCLEAR AND ELECTRONIC MOTION 2 1 INTRODUCTION 2 2 ELECTRONIC AND NUCLEAR KINETIC ENERGY 2 2 1 INTRODUCTION 2 2 2 ORIGIN AT CENTRE OF MASS OF MOLECULE 2 2 3 ORIGIN AT CENTRE OF MASS OF NUCLEI 2 2 4 ORIGIN AT GEOMETRICAL CENTRE OF THE NUCLEI 2 3 THE TOTAL HAMILTONIAN IN ?ELD-FREE SPACE 2 4 THE NUCLEAR KINETIC ENERGY OPERATOR 2 5 TRANSFORMATION OF THE ELECTRONIC COORDINATES TO MOLECULE-?XED AXES 2 5 1 INTRODUCTION 2 5 2 SPACE TRANSFORMATIONS 2 5 3 SPIN TRANSFORMATIONS 2 6 SCHR¨ODINGER EQUATION FOR THE TOTAL WAVE FUNCTION 2 7 THE BORN–OPPENHEIMER AND BORN ADIABATIC APPROXIMATIONS 2 8 SEPARATION OF THE VIBRATIONAL AND ROTATIONAL WAVE EQUATIONS 2 9 THE VIBRATIONAL WAVE EQUATION 2 10 ROTATIONAL HAMILTONIAN FOR SPACE-QUANTISED ELECTRON SPIN 2 11 NON-ADIABATIC TERMS 2 12 EFFECTS OF EXTERNAL ELECTRIC AND MAGNETIC ?ELDS APPENDIX 2 1 DERIVATION OF THE MOMENTUM OPERATOR 3 THE ELECTRONIC HAMILTONIAN 3 1 THE DIRAC EQUATION 3 2 SOLUTIONS OF THE DIRAC EQUATION IN ?ELD-FREE SPACE 3 3 ELECTRON SPIN MAGNETIC MOMENT AND ANGULAR MOMENTUM 3 4 THE FOLDY–WOUTHUYSEN TRANSFORMATION 3 5 THE FOLDY–WOUTHUYSEN AND DIRAC REPRESENTATIONS FOR A FREE PARTICLE 3 6 DERIVATION OF THE MANY-ELECTRON HAMILTONIAN 3 7 EFFECTS OF APPLIED STATIC MAGNETIC AND ELECTRIC ?ELDS 3 8 RETARDED ELECTROMAGNETIC INTERACTION BETWEEN ELECTRONS 3 8 1 INTRODUCTION 3 8 2 LORENTZ TRANSFORMATION 3 8 3 ELECTROMAGNETIC POTENTIALS DUE TO A MOVING ELECTRON 3 8 4 GAUGE INVARIANCE 3 8 5 CLASSICAL LAGRANGIAN AND HAMILTONIAN 3 9 THE BREIT HAMILTONIAN 3 9 1 INTRODUCTION 3 9 2 REDUCTION OF THE BREIT HAMILTONIAN TO NON-RELATIVISTIC FORM 3 10 ELECTRONIC INTERACTIONS IN THE NUCLEAR HAMILTONIAN 3 11 TRANSFORMATION OF COORDINATES IN THE ?ELD-FREE TOTAL HAMILTONIAN 3 12 TRANSFORMATION OF COORDINATES FOR THE ZEEMAN AND STARK TERMS IN THE TOTAL HAMILTONIAN 3 13 CONCLUSIONS APPENDIX 3 1 POWER SERIES EXPANSION OF THE TRANSFORMED HAMILTONIAN 4 INTERACTIONS ARISING FROM NUCLEAR MAGNETIC AND ELECTRIC MOMENTS 4 1 NUCLEAR SPINS AND MAGNETIC MOMENTS 4 2 DERIVATION OF NUCLEAR SPIN MAGNETIC INTERACTIONS THROUGH THE MAGNETIC VECTOR POTENTIAL 4 3 DERIVATION OF NUCLEAR SPIN INTERACTIONS FROM THE BREIT EQUATION 4 4 NUCLEAR ELECTRIC QUADRUPOLE INTERACTIONS 4 4 1 SPHERICAL TENSOR FORM OF THE HAMILTONIAN OPERATOR 4 4 2 CARTESIAN FORM OF THE HAMILTONIAN OPERATOR 4 4 3 MATRIX ELEMENTS OF THE QUADRUPOLE HAMILTONIAN 4 5 TRANSFORMATION OF COORDINATES FOR THE NUCLEAR MAGNETIC DIPOLE AND ELECTRIC QUADRUPOLE TERMS 5 ANGULAR MOMENTUM THEORY AND SPHERICAL TENSOR ALGEBRA 5 1 INTRODUCTION 5 2 ROTATION OPERATORS 5 2 1 INTRODUCTION 5 2 2 DECOMPOSITION OF ROTATIONAL OPERATORS 5 2 3 COMMUTATION RELATIONS 5 2 4 REPRESENTATIONS OF THE ROTATION GROUP 5 2 5 ORBITAL ANGULAR MOMENTUM AND SPHERICAL HARMONICS 5 3 ROTATIONS OF A RIGID BODY 5 3 1 INTRODUCTION 5 3 2 ROTATION MATRICES 5 3 3 SPIN 1/2 SYSTEMS 5 3 4 SYMMETRIC TOP WAVE FUNCTIONS 5 4 ADDITION OF ANGULAR MOMENTA 5 4 1 INTRODUCTION 5 4 2 WIGNER 3- J SYMBOLS 5 4 3 COUPLING OF THREE OR MORE ANGULAR MOMENTA: RACAH ALGEBRA, WIGNER 6- J AND 9- J SYMBOLS 5 4 4 CLEBSCH–GORDAN SERIES 5 4 5 INTEGRALS OVER PRODUCTS OF ROTATION MATRICES 5 5 IRREDUCIBLE SPHERICAL TENSOR OPERATORS 5 5 1 INTRODUCTION 5 5 2 EXAMPLES OF SPHERICAL TENSOR OPERATORS 5 5 3 MATRIX ELEMENTS OF SPHERICAL TENSOR OPERATORS: THE WIGNER–ECKART THEOREM 5 5 4 MATRIX ELEMENTS FOR COMPOSITE SYSTEMS 5 5 5 RELATIONSHIP BETWEEN OPERATORS IN SPACE-?XED AND MOLECULE-?XED COORDINATE SYSTEMS 5 5 6 TREATMENT OF THE ANOMALOUS COMMUTATION RELATIONSHIPS OF ROTA- TIONAL ANGULAR MOMENTA BY SPHERICAL TENSOR METHODS APPENDIX 5 1 SUMMARY OF STANDARD RESULTS FROM SPHERICAL TENSOR ALGEBRA 6 ELECTRONIC AND VIBRATIONAL STATES 6 1 INTRODUCTION 6 2 ATOMIC STRUCTURE AND ATOMIC ORBITALS 6 2 1 THE HYDROGEN ATOM 6 2 2 MANY-ELECTRON ATOMS 6 2 3 RUSSELL–SAUNDERS COUPLING 6 2 4 WAVE FUNCTIONS FOR THE HELIUM ATOM 6 2 5 MANY-ELECTRON WAVE FUNCTIONS: THE HARTREE–FOCK EQUATION 6 2 6 ATOMIC ORBITAL BASIS SET 6 2 7 CON?GURATION INTERACTION 6 3 MOLECULAR ORBITAL THEORY 6 4 CORRELATION OF MOLECULAR AND ATOMIC ELECTRONIC STATES 6 5 CALCULATION OF MOLECULAR ELECTRONIC WAVE FUNCTIONS AND ENERGIES 6 5 1 INTRODUCTION 6 5 2 ELECTRONIC WAVE FUNCTION FOR THE H+ 2 MOLECULAR ION 6 5 3 ELECTRONIC WAVE FUNCTION FOR THE H2 MOLECULE 6 5 4 MANY-ELECTRON MOLECULAR WAVE FUNCTIONS 6 7 COUPLING OF ELECTRONIC AND ROTATIONAL MOTION: HUND’S COUPLING CASES 6 7 1 INTRODUCTION 6 7 2 HUND’S COUPLING CASE (A) 6 7 3 HUND’S COUPLING CASE (B) 6 7 4 HUND’S COUPLING CASE (C) 6 7 5 HUND’S COUPLING CASE (D) 6 7 6 HUND’S COUPLING CASE (E) 6 7 7 INTERMEDIATE COUPLING 6 7 8 NUCLEAR SPIN COUPLING CASES 6 8 ROTATIONS AND VIBRATIONS OF THE DIATOMIC MOLECULE 6 8 1 THE RIGID ROTOR 6 8 2 THE HARMONIC OSCILLATOR 6 8 3 THE ANHARMONIC OSCILLATOR 6 8 4 THE NON-RIGID ROTOR 6 8 5 THE VIBRATING ROTOR 6 9 INVERSION SYMMETRY OF ROTATIONAL LEVELS 6 9 1 THE SPACE-?XED INVERSION OPERATOR 6 9 2 THE EFFECT OF SPACE-?XED INVERSION ON THE EULER ANGLES AND ON MOLECULE-?XED COORDINATES 6 9 3 THE TRANSFORMATION OF GENERAL HUND’S CASE (A) AND CASE (B) FUNC- TIONS UNDER SPACE-?XED INVERSION 6 9 4 PARITY COMBINATIONS OF BASIS FUNCTIONS 6 10 PERMUTATION SYMMETRY OF ROTATIONAL LEVELS 6 10 1 THE NUCLEAR PERMUTATION OPERATOR FOR A HOMONUCLEAR DIATOMIC MOLECULE 6 10 3 NUCLEAR STATISTICAL WEIGHTS 6 11 THEORY OF TRANSITION PROBABILITIES 6 11 1 TIME-DEPENDENT PERTURBATION THEORY 6 11 2 THE EINSTEIN TRANSITION PROBABILITIES 6 11 3 EINSTEIN TRANSITION PROBABILITIES FOR ELECTRIC DIPOLE TRANSITIONS 6 11 4 ROTATIONAL TRANSITION PROBABILITIES 6 11 5 VIBRATIONAL TRANSITION PROBABILITIES 6 11 6 ELECTRONIC TRANSITION PROBABILITIES 6 11 7 MAGNETIC DIPOLE TRANSITION PROBABILITIES 6 12 LINE WIDTHS AND SPECTROSCOPIC RESOLUTION 6 12 1 NATURAL LINE WIDTH 6 12 2 TRANSIT TIME BROADENING 6 12 3 DOPPLER BROADENING 6 12 4 COLLISION BROADENING 6 13 RELATIONSHIPS BETWEEN POTENTIAL FUNCTIONS AND THE VIBRATION–ROTATION LEVELS 6 13 1 INTRODUCTION 6 13 2 THE JWKB SEMICLASSICAL METHOD 6 13 3 INVERSION OF EXPERIMENTAL DATA TO CALCULATE THE POTENTIAL FUNCTION (RKR) 6 14 LONG-RANGE NEAR-DISSOCIATION INTERACTIONS 6 15 PREDISSOCIATION APPENDIX 6 1 CALCULATION OF THE BORN–OPPENHEIMER POTENTIAL FOR THE H+ 2 ION 7 DERIVATION OF THE EFFECTIVE HAMILTONIAN 7 1 INTRODUCTION 7 2 DERIVATION OF THE EFFECTIVE HAMILTONIAN BY DEGENERATE PERTURBATION THEORY: GENERAL PRINCIPLES 7 3 THE VAN VLECK AND CONTACT TRANSFORMATIONS 7 4 EFFECTIVE HAMILTONIAN FOR A DIATOMIC MOLECULE IN A GIVEN ELECTRONIC STATE 7 4 1 INTRODUCTION 7 4 2 THE ROTATIONAL HAMILTONIAN 7 4 3 HOUGEN’S ISOMORPHIC HAMILTONIAN 7 4 4 FINE STRUCTURE TERMS: SPIN–ORBIT, SPIN–SPIN AND SPIN–ROTATION OPERATORS 7 4 5 ?-DOUBLING TERMS FOR A ELECTRONIC STATE 7 4 6 NUCLEAR HYPER?NE TERMS 7 4 7 HIGHER-ORDER ?NE STRUCTURE TERMS 7 5 EFFECTIVE HAMILTONIAN FOR A SINGLE VIBRATIONAL LEVEL 7 5 1 VIBRATIONAL AVERAGING AND CENTRIFUGAL DISTORTION CORRECTIONS 7 5 2 THE FORM OF THE EFFECTIVE HAMILTONIAN 7 5 3 THE N 2 FORMULATION OF THE EFFECTIVE HAMILTONIAN 7 5 4 THE ISOTOPIC DEPENDENCE OF PARAMETERS IN THE EFFECTIVE HAMILTONIAN 7 6 EFFECTIVE ZEEMAN HAMILTONIAN 7 7 INDETERMINACIES: ROTATIONAL CONTACT TRANSFORMATIONS 7 8 ESTIMATES AND INTERPRETATION OF PARAMETERS IN THE EFFECTIVE HAMILTONIAN 7 8 1 INTRODUCTION 7 8 2 ROTATIONAL CONSTANT 7 8 3 SPIN–ORBIT COUPLING CONSTANT, A 7 8 4 SPIN–SPIN AND SPIN–ROTATION PARAMETERS, ? AND ? 7 8 5 ?-DOUBLING PARAMETERS 7 8 6 MAGNETIC HYPER?NE INTERACTIONS 7 8 7 ELECTRIC QUADRUPOLE HYPER?NE INTERACTION APPENDIX 7 1 MOLECULAR PARAMETERS OR CONSTANTS 8 MOLECULAR BEAM MAGNETIC AND ELECTRIC RESONANCE 8 1 INTRODUCTION 8 2 MOLECULAR BEAM MAGNETIC RESONANCE OF CLOSED SHELL MOLECULES 8 2 1 H2, D2 AND HD IN THEIR X 1+ GROUND STATES 8 2 2 THEORY OF ZEEMAN INTERACTIONS IN 1+ STATES 8 2 3 NA2 IN THE X 1+ G GROUND STATE: OPTICAL STATE SELECTION AND DETECTION 8 2 4 OTHER 1+ MOLECULES 8 3 MOLECULAR BEAM MAGNETIC RESONANCE OF ELECTRONICALLY EXCITED MOLECULES 8 3 1 H2 IN THE C 3U STATE 8 3 2 N2 IN THE A 3+ U STATE 8 4 MOLECULAR BEAM ELECTRIC RESONANCE OF CLOSED SHELL MOLECULES 8 4 1 PRINCIPLES OF ELECTRIC RESONANCE METHODS 8 4 2 CSF IN THE X 1+ GROUND STATE 8 4 3 LIBR IN THE X 1+ GROUND STATE 8 4 4 ALKALINE EARTH AND GROUP IV OXIDES 8 4 5 HF IN THE X 1+ GROUND STATE 8 4 6 HCL IN THE X 1+ GROUND STATE 8 5 MOLECULAR BEAM ELECTRIC RESONANCE OF OPEN SHELL MOLECULES 8 5 1 INTRODUCTION 8 5 2 LIO IN THE X 2 GROUND STATE 8 5 3 NO IN THE X 2 GROUND STATE 8 5 4 OH IN THE X 2 GROUND STATE 8 5 5 CO IN THE A 3 STATE APPENDIX 8 1 NUCLEAR SPIN DIPOLAR INTERACTION APPENDIX 8 2 RELATIONSHIP BETWEEN THE CARTESIAN AND SPHERICAL TENSOR FORMS OF THE ELECTRON SPIN–NUCLEAR SPIN DIPOLAR INTERACTION APPENDIX 8 3 ELECTRON SPIN–ELECTRON SPIN DIPOLAR INTERACTION APPENDIX 8 4 MATRIX ELEMENTS OF THE QUADRUPOLE HAMILTONIAN APPENDIX 8 5 MAGNETIC HYPER?NE HAMILTONIAN AND HYPER?NE CONSTANTS 9 MICROWAVE AND FAR-INFRARED MAGNETIC RESONANCE 9 1 INTRODUCTION 9 2 EXPERIMENTAL METHODS 9 2 1 MICROWAVE MAGNETIC RESONANCE 9 2 2 FAR-INFRARED LASER MAGNETIC RESONANCE 9 3 1 STATES 9 3 1 SO IN THE A 1 STATE 9 3 2 NF IN THE A 1 STATE 9 4 2 STATES 9 4 1 INTRODUCTION 9 4 2 CLO IN THE X 2 GROUND STATE 9 4 3 OH IN THE X 2 GROUND STATE 9 4 4 FAR-INFRARED LASER MAGNETIC RESONANCE OF CH IN THE X 2 GROUND STATE 9 5 2 STATES 9 5 1 INTRODUCTION 9 5 2 CN IN THE X 2+ GROUND STATE 9 6 3 STATES 9 6 1 SO IN THE X 3?GROUND STATE 9 6 2 SEO IN THE X 3?GROUND STATE 9 6 3 NH IN THE X 3?GROUND STATE 9 7 3 STATES 9 7 1 CO IN THE A 3 STATE 9 8 4 STATES 9 8 1 CH IN THE A 4?STATE 9 9 4, 3, 2 AND 6+ STATES 9 9 1 INTRODUCTION 9 9 2 CRH IN THE X 6+ GROUND STATE 9 9 3 FEH IN THE X 4 GROUND STATE 9 9 4 COH IN THE X 3 GROUND STATE 9 9 5 NIH IN THE X 2 GROUND STATE APPENDIX 9 1 EVALUATION OF THE REDUCED MATRIX ELEMENT OF T 3(S, S, S) 10 PURE ROTATIONAL SPECTROSCOPY 10 1 INTRODUCTION AND EXPERIMENTAL METHODS 10 1 1 SIMPLE ABSORPTION SPECTROGRAPH 10 1 2 MICROWAVE RADIATION SOURCES 10 1 3 MODULATION SPECTROMETERS 10 1 4 SUPERHETERODYNE DETECTION 10 1 5 FOURIER TRANSFORM SPECTROMETER 10 1 6 RADIO TELESCOPES AND RADIO ASTRONOMY 10 1 7 TERAHERTZ (FAR-INFRARED) SPECTROMETERS 10 1 8 ION BEAM TECHNIQUES 10 2 1+ STATES 10 2 1 CO IN THE X 1+ GROUND STATE 10 2 2 HEH+ IN THE X 1+ GROUND STATE 10 2 3 CUCL AND CUBR IN THEIR X 1+ GROUND STATES 10 2 4 SO, NF AND NCL IN THEIR B 1+ STATES 10 2 5 HYDRIDES(LIH,NAH,KH,CUH,ALH,AGH)INTHEIR X 1+ GROUND STATES 10 3 2 STATES 10 3 1 CO+ IN THE X 2+ GROUND STATE 10 3 2 CN IN THE X 2+ GROUND STATE 10 4 3 STATES 10 4 1 INTRODUCTION 10 4 2 O2 IN ITS X 3? G GROUND STATE 10 4 3 SO, S2 AND NIO IN THEIR X 3?GROUND STATES 10 4 4 PF, NCL, NBR AND NI IN THEIR X 3?GROUND STATES 10 5 1 STATES 10 5 1 O2 IN ITS A 1G STATE 10 5 2 SO AND NCL IN THEIR A 1 STATES 10 6 2 STATES 10 6 1 NO IN THE X 2 GROUND STATE 10 6 2 OH IN THE X 2 GROUND STATE 10 6 3 CH IN THE X 2 GROUND STATE 10 6 4 CF, SIF, GEF IN THEIR X 2 GROUND STATES 10 6 5 OTHER FREE RADICALS WITH 2 GROUND STATES 10 7 CASE (C) DOUBLET STATE MOLECULES 10 7 1 STUDIES OF THE HEAR+ ION 10 7 2 STUDIES OF THE HEKR+ ION 10 8 HIGHER SPIN/ORBITAL STATES 10 8 1 CO IN THE A 3 STATE 10 8 2 SIC IN THE X 3 GROUND STATE 10 8 3 FEC IN THE X 3 GROUND STATE 10 8 4 VO AND NBO IN THEIR X 4?GROUND STATES 10 8 5 FEF AND FECL IN THEIR X 6 GROUND STATES 10 8 6 CRF, CRCL AND MNO IN THEIR X 6+ GROUND STATES 10 8 7 FEO IN THE X 5 GROUND STATE 10 8 8 TICL IN THE X 4 GROUND STATE 10 9 OBSERVATION OF A PURE ROTATIONAL TRANSITION IN THE H+ 2 MOLECULAR ION 11 DOUBLE RESONANCE SPECTROSCOPY 11 1 INTRODUCTION 11 2 RADIOFREQUENCY AND MICROWAVE STUDIES OF CN IN ITS EXCITED ELECTRONIC STATES 11 3 EARLY RADIOFREQUENCY OR MICROWAVE/OPTICAL DOUBLE RESONANCE STUDIES 11 3 1 RADIOFREQUENCY/OPTICAL DOUBLE RESONANCE OF CS IN ITS EXCITED A 1 STATE 11 3 2 RADIOFREQUENCY/OPTICAL DOUBLE RESONANCE OF OH IN ITS EXCITED A 2+ STATE 11 3 3 MICROWAVE/OPTICAL DOUBLE RESONANCE OF BAO IN ITS GROUND X 1+ AND EXCITED A 1+ STATES 11 4 1 INTRODUCTION 11 4 2 H2 IN THE G 1+ G STATE 11 4 3 H2 IN THE D 3U STATE 11 4 4 H2 IN THE K 3U STATE 11 5 RADIOFREQUENCY OR MICROWAVE/OPTICAL DOUBLE RESONANCE OF ALKALINE EARTH MOLECULES 11 5 1 INTRODUCTION 11 5 2 SRF, CAF AND CACL IN THEIR X 2+ GROUND STATES 11 6 RADIOFREQUENCY OR MICROWAVE/OPTICAL DOUBLE RESONANCE OF TRANSITION METAL MOLECULES 11 6 1 INTRODUCTION 11 6 2 FEO IN THE X 5 GROUND STATE 11 6 3 CUF IN THE B 3 EXCITED STATE 11 6 4 CUO IN THE X 2 GROUND STATE 11 6 5 SCO IN THE X 2+ GROUND STATE 11 6 6 TIO IN THE X 3 GROUND STATE AND TIN IN THE X 2+ GROUND STATE 11 6 7 CRN AND MON IN THEIR X 4?GROUND STATES 11 6 8 NIH IN THE X 2 GROUND STATE 11 6 9 4D TRANSITION METAL MOLECULES: YF IN THE X 1+ GROUND STATE, YO AND YS IN THEIR X 2+ GROUND STATES 11 7 MICROWAVE/OPTICAL DOUBLE RESONANCE OF RARE EARTH MOLECULES 11 7 1 RADIOFREQUENCY/OPTICAL DOUBLE RESONANCE OF YBF IN ITS X 2+ GROUND STATE 11 7 2 RADIOFREQUENCY/OPTICAL DOUBLE RESONANCE OF LAO IN ITS X 2+ AND B 2+ STATES 11 8 DOUBLE RESONANCE SPECTROSCOPY OF MOLECULAR ION BEAMS 11 8 1 RADIOFREQUENCY AND MICROWAVE/INFRARED DOUBLE RESONANCE OF HD+ IN THE X 2+ GROUND STATE 11 8 2 RADIOFREQUENCY/OPTICAL DOUBLE RESONANCE OF N+ 2 IN THE X 2+ G GROUND STATE 11 8 3 MICROWAVE/OPTICAL DOUBLE RESONANCE OF CO+ IN THE X 2+ GROUND STATE 11 9 QUADRUPOLE TRAP RADIOFREQUENCY SPECTROSCOPY OF THE H+ 2 ION 11 9 1 INTRODUCTION 11 9 2 PRINCIPLES OF PHOTO-ALIGNMENT 11 9 3 EXPERIMENTAL METHODS AND RESULTS 11 9 4 ANALYSIS OF THE SPECTRA 11 9 5 QUANTITATIVE INTERPRETATION OF THE MOLECULAR PARAMETERS