Note: Transitions in Molecular Systems -- Contents -- Preface -- 1 Introduction -- 1.1 The Adiabatic Description of Molecules -- 1.1.1 Preliminaries -- 1.1.2 The Born-Oppenheimer Approximation -- 1.1.3 The Crude Born-Oppenheimer Basis Set -- 1.1.4 Correction of the Crude Adiabatic Approximation -- 1.2 Normal Coordinates and Duschinsky Effect -- 1.3 The Vibrational Wavefunctions -- 1.4 The Diabatic Electronic Basis for Molecular Systems -- 1.4.1 Preliminaries -- 1.4.2 Conical Intersection Between the States B2B2/2A' and Ã2A1/2A' of H2O+ -- 1.4.3 The Linear Model for Conical Intersection -- 2 Formal Decay Theory of Coupled Unstable States -- 2.1 The Time Evolution of an Excited State -- 2.1.1 Some Remarks About the Decay of a Discrete Molecular Metastable State -- 2.2 The Choice of the Zero-Order Basis Set -- 3 Description of Radiationless Processes in Statistical Large Molecules -- 3.1 Evaluation of the Radiationless Transition Probability -- 3.2 The Generating Function for Intramolecular Distributions I1 and I2 -- 3.2.1 The Generating Function G2(w1,w2,z1,z2) -- 3.2.2 Properties of δμ1μ2, ν1ν2, aμ1μ2, ν1ν2, and bμ1μ2, ν1ν2 -- 3.2.3 Case w1=w2=0 -- 3.2.4 Case w1 ≠ w2 ≠ 0 -- 3.2.5 Symmetry Properties of I2 -- 3.2.6 Case ф = 0 -- 3.3 Derivation of the Promoting Mode Factors Kη(t) and Iη(t) -- 3.4 Radiationless Decay Rates of Initially Selected Vibronic States in Polyatomic Molecules -- 4 Calculational Methods for Intramolecular Distributions I1, I2, and IN -- 4.1 The One-Dimensional Distribution I1(0, n -- a, b) -- 4.1.1 The Addition Theorem -- 4.2 The Distributions I1(m, n -- a, b) -- 4.2.1 Derivation of I1(m, n -- a, b) -- 4.2.2 The Addition Theorem for I1(m, n -- a, b) -- 4.2.3 The Recurrence Formula -- 4.2.4 Case b=0 -- 4.2.5 Case b ≠ 0 -- 4.2.6 Numerical Results -- 4.3 Calculation of the Multidimensional Distribution. , 4.3.1 Preliminary Consideration -- 4.3.2 Derivation of Recurrence Equations -- 4.3.3 The Calculation Procedure -- 4.3.3.1 Some Numerical Results -- 4.4 General Case of N-Coupled Modes -- 4.4.1 The Generating Function GN -- 4.4.2 Properties of δμ,ν, aμ,ν, and bμ,ν -- 4.4.3 The Distribution and its Properties -- 4.4.3.1 Symmetry Property of IN -- 4.4.4 A Special Case -- 4.4.5 Concluding Remarks and Examples -- 4.4.6 Recurrence Relations -- 4.4.7 The Three-Dimensional Case -- 4.4.8 Some Numerical Results -- 4.5 Displaced Potential Surfaces -- 4.5.1 The Strong Coupling Limit -- 4.5.2 The Weak Coupling Limit -- 4.6 The Contribution of Medium Modes -- 5 The Nuclear Coordinate Dependence of Matrix Elements -- 5.1 The q-Centroid Approximation -- 5.2 Determination of the q-Centroid -- 6 Time-Resolved Spectroscopy -- 6.1 Formal Consideration -- 6.2 Evaluation of the Radiative Decay Probability of a Prepared State -- 6.3 The Sparse Intermediate Case -- 6.3.1 Preliminary Consideration -- 6.3.2 The Molecular Eigenstates -- 6.4 Radiative Decay in Internal Conversion by Introduction of Decay Rates for {ψ1} -- 6.5 Dephasing and Relaxation in Molecular Systems -- 6.5.1 Introduction -- 6.5.2 Interaction of a Large Molecule with a Light Pulse -- 6.5.3 Free Induction Decay of a Large Molecule -- 6.5.4 Photon Echoes from Large Molecules -- 7 Miscellaneous Applications -- 7.1 The Line Shape Function for Radiative Transitions -- 7.1.1 Derivation -- 7.1.2 Implementation of Theory and Results -- 7.1.2.1 Excited-State Geometry -- 7.2 On the Mechanism of Singlet-Triplet Interaction -- 7.2.1 Phosphorescence in Aromatic Molecules with Nonbonding Electrons -- 7.2.2 Radiative T1 (ππ* ) → S0 Transition -- 7.2.3 Nonradiative Triplet-to-Ground State Transition -- 7.2.3.1 Theory and Application -- 7.2.4 Remarks on the Intersystem Crossing in Aromatic Hydrocarbons. , 7.3 Comment on the Temperature Dependence of Radiationless Transition -- 7.4 Effect of Deuteration on the Lifetimes of Electronic Excited States -- 7.4.1 Partial Deuteration Experiment -- 7.5 Theory and Experiment of Singlet Excitation Energy Transfer in Mixed Molecular Crystals -- 7.5.1 Transport Phenomena in Doped Molecular Crystals -- 7.5.2 The System Pentacene in p-Terphenyl -- 7.5.3 Techniques -- 7.5.4 Nature of the Energy Transfer: Theory -- 7.5.5 Time Evolution of the Guest Excitations -- 7.5.6 The Decay of the Transient Grating Signal -- 7.6 Electronic Predissociation of the 2B2 State of H2O+ -- 7.6.1 Evaluation of the Nonadiabatic Coupling Factor -- 7.6.2 The Basis State Functions -- 7.6.2.1 The Initial-State Wavefunction xi -- 7.6.2.2 The Final Vibrational Wavefunction xf : The Closed Coupled Equations -- 8 Multidimensional Franck-Condon Factor -- 8.1 Multidimensional Franck-Condon Factors and Duschinsky Mixing Effects -- 8.1.1 General Aspects -- 8.1.2 Derivation -- 8.2 Recursion Relations -- 8.3 Some Numerical Results and Discussion -- 8.4 Implementation of Theory and Results -- 8.4.1 The Resonance Raman Process and Duschinsky Mixing Effect -- 8.4.2 Time-Delayed Two-Photon Processes: Duschinsky Mixing Effects -- 8.4.3 Results -- 8.5 The One-Dimensional Franck-Condon Factor (N=1) -- Appendices -- Appendix A: Some Identities Related to Green.s Function -- A.1 The Green's Function Technique -- A.2 Evaluation of the Diagonal Matrix Element of Gss -- Appendix B: The Coefficients of the Recurrence Equation -- Appendix C: The Coefficients of the Recurrence Equations -- Appendix D: Solution of a Class of Integrals -- Appendix E: Quantization of the Radiation Field -- Appendix F: The Molecular Eigenstates -- Appendix G: The Effective Hamiltonian and Its Properties -- Appendix H: The Mechanism of Nonradiative Energy Transfer. , H.1 Single-Step Resonance Energy Transfer -- H.2 Phonon-Assisted Energy Transfer -- Appendix I: Evaluation of the Coefficients bμν, cμν, and bμ in the Recurrence Equations 8.28 and 8.29 -- I.1 Application -- Appendix J: Evaluation of the Position Expectation Values of xsm(qs) -- Appendix K: Vibronic Coupling Between Two Electronic States: The Pseudo-Jahn-Teller Effect -- References -- Index.