Spectroscopy of Molecular Excitons

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Low-temperature spectroscopy of organic molecular crystals came into being in the late 20s, just when quantum physics of solids as a whole began to de velop vigorously. Already in the early works, two experimental facts of prime importance were discovered: the presence of a multitude of narrow bands in the low-temperature spectrum of a crystal, and a close relationship between the spectrum of the crystal and that of the constituent molecules. These findings immediately preceded the celebrated paper of Frenkel in which he went beyond the framework of Bloch's scheme and advanced the exciton concept. Subsequent investigations showed that the most interesting features of the spectra of molecular crystals are associated with excitons, and then the spectroscopy of molecular excitons began to form gradually on the basis of the spectroscopy of organic crystals. The molecular exciton became synonymous to the Frenkel exciton in a molecular crystal. In view of the difficulties involved in the analysis of rich spectra con taining many tens of bands, the spectroscopy of molecular crystals had long been connected most closely with the spectroscopy of molecules. It had deve loped independently, to a large extent, from the other branches of solid state physics. This was also emphasized by the difference in experimental techniques, the specific properties of the objects, etc. As a result, there was some lag in ideas and concepts.

1. Experimental Background.- 1.1 Molecular Crystals.- 1.2 Electronic Spectra of Molecules.- 1.3 Comparing the Electronic Spectrum of a Crystal and That of a Molecule.- 1.3.1 Model of an Oriented Gas.- 1.3.2 Electronic Spectra of a Crystal.- 1.4 Isotopic Effect in Electronic Spectra.- 1.5 Spectra of Doped Crystals.- 1.6 Electronic Spectra of Crystals and the Spectroscopy of Molecular Excitons.- 2. Exciton Spectra of Perfect Crystals.- 2.1 Molecular Excitons.- 2.2 Wave Functions and the Energy Spectrum of Excitons.- 2.3 Exciton Green's Function.- 2.4 Conductivity Tensor of a Crystal.- 2.5 Exciton Bands of Molecular Crystals.- 2.5.1 Benzene.- 2.5.2 Naphthalene.- 2.5.3 Anthracene.- 2.5.4 Hexamethylbenzene (Low-Temperature Modification).- 3. Exciton Spectra of Doped Crystals.- 3.1 Imperfect Crystal s.- 3.2 The Theory of the Absorption of Light by Local Excitons: Isotopic Impurities.- 3.2.1 General.- 3.2.2 Isotopic Substitution Model.- 3.2.3 Conductivity Tensor and Green's Function of a Doped Crystal.- 3.2.4 Energy Spectrum.- 3.2.5 Wave Functions.- 3.2.6 Discrete Absorption Spectrum.- 3.2.7 T Matri x.- 3.2.8 The Effect of Long-Range Interactions.- 3.2.9 Induced Absorption in the Exciton Continuum.- 3.2.10 Alternative Approach to Impurity Absorption.- 3.3 Exciton Spectra of an Isotopic Impurity.- 3.3.1 General Characteristics of Monomer Centres.- 3.3.2 Position of Impurity Bands.- 3.3.3 Polarization Ratio of the Impurity Bands.- 3.3.4 The Integral Intensities of Impurity Bands.- 3.3.5 Spectral Distribution of the Intensity of Impurity Absorpti on.- 3.3.6 The Excitation Amplitude on a Guest Molecule.- 3.3.7 The Structure of Exciton Bands as Determined from IDC Spectra.- 3.4 The Exciton Spectra of Aggregates of Isotopic Guest Molecules in IDC.- 3.4.1 The Models of Pair Centres and Their Basic Features..- 3.4.2 The General Properties of the Energy Spectra of Pair Centres.- 3.4.3 Calculation of the Spectra of Pair Centres in Naphthalene and a Comparison with Experiment.- 3.4.4 Complex Impurity Centres.- 3.5 Exciton Spectra of Defect Centres.- 3.5.1 General Characteristics of Impurity Centres.- 3.5.2 The Calculation and Comparison of the Positions of the Energy Levels and the Polarization Ratios of Defect Centres in Naphthalene.- 3.5.3 Concentration Effects.- 4. Exciton Spectra of Mixed Crystals.- 4.1 Energy Spectra of Mixed Crystals.- 4.1.1 General Features.- 4.1.2 Analytical Approach.- 4.1.3 Approximate and Numerical Methods.- 4.1.4 Choosing Methods to Calculate Spectra.- 4.2 Average-Amplitude Approximation.- 4.2.1 Elementary Theory.- 4.2.2 Average-Amplitude Approximation and Experimental Results: Mixed Crystals of d-Benzenes.- 4.3 Mixed Crystals of d-Naphthalenes. The Genesis of Exciton Bands.- 4.3.1 Spectra of Mixed Crystals of d-Naphthalene.- 4.3.2 The Naphthalene Spectra in the Average-Amplitude Approximation.- 4.3.3 The Difficulties Involved in Singling out an Exciton Multipiet.- 4.3.4 Genesis and Evolution of Exciton Multiplets.- 4.4 Methods of Calculating Mixed-Crystal Spectra.- 4.4.1 Coherent-Potential Approximation.- 4.4.2 Application of the Coherent-Potential Approximation to the Spectra of d-Naphthalenes.- 4.4.3 Shape of the Spectra in the High-Concentration Range..- 4.5 Mixed-Crystal Spectra. A Comparison of Theory with Experiment.- 4.5.1 Detailed Analysis of the Absorption and Fluorescence Spectra of a Mixed Crystal.- 4.5.2 The Experimental Shape of the Absorption Spectrum.- 4.5.3 Calculating the Shape of the Absorption Spectrum of a Mixed Crystal.- 4.5.4 Determining the Position of the Pseudobottom of the Exciton-Spectrum.- a) Mixed Crystals of hmbd0 and hmbd18.- b) Mixed Crystals of nd0 and nd8.- c) Mixed Crystals of ad0 and ad10.- 4.6 Migration of Excitons and Localization of Exciton States in Mixed Crystals.- 4.6.1 Kinetics of Excitons.- 4.6.2 Low Temperature Exciton Migration in Mixed Crystals of d-Naphthalenes and d-Benzenes.- 4.6.3 Localization and Diffusion in Disordered Systems.- 4.6.4 Discussion of Experimental Data.- 5. Band-to-Band Transition Spectra.- 5.1 Classification of Vibronic Spectra.- 5.2 Band-to-Band Transitions in Perfect Crystals.- 5.2.1 Band-to-Band Transition Theory.- 5.2.2 Experimental Investigation of Band-to-Band Spectra.- 5.3 Band-to-Band Spectra of Mixed Crystals.- 5.3.1 Calculating the Band-to-Band Spectra of Mixed Crystals.- 5.3.2 Experimental Investigation of the Band-to-Band Spectra of Mixed Crystals.- 6. Vibronic Spectra of Molecular Crystals.- 6.1 Exciton-Phonon Interaction.- 6.1.1 Vibronic Interaction Hamiltonian.- 6.1.2 Effect of the Exciton-Phonon Interaction on the Energy Spectrum of Excitons.- 6.2 Dynamical Theory of Vibronic Spectra.- 6.2.1 Dynamical Theory Hamiltonian.- 6.2.2 Conductivity Tensor.- 6.2.3 Energy Spectrum. Limiting Cases.- a) NTS Phonon.- b) TS Phonon: General Properties.- c) Weak Vibronic Coupling.- d) Strong Vibronic Coupling.- e) Molecular Limit.- f) Quasi-One-Particle States.- 6.2.4 Optical Absorption Spectrum.- 6.3 Vibronic Absorption Spectra of the Solid Aromatic Compounds.- 6.3.1 General Structure of Vibronic Spectra.- 6.3.2 Benzene.- a) One-Photon Absorpti on.- b) Two-Photon Absorption Spectrum.- 6.3.3 Naphthalene.- a) Stress-Free Crystal.- b) Stressed Naphthalene Crystal.- c) Two-Photon Absorption Spectrum.- 6.3.4 Anthracene.- 6.3.5 Alkyl benzenes.- 6.4 A Quantitative Interpretation of the Vibronic Spectra of Crystals Based on the Dynamical Theory.- 6.4.1 Calculation of the Vibronic Absorption Spectrum.- 6.4.2 Vibronic Spectra of Benzene and Naphthalene Crystals Involving NTS Phonons.- a) Benzene Crystal.- b) Naphthalene Crystal.- 6.4.3 Vibronic Absorption in Naphthalene Involving a Single TS Phonon.- 6.4.4 Composite Transitions and Overtones in a Vibronic Spectrum.- a) Composite Vibronic Transitions.- b) Overtones of the Vibronic Spectrum.- 6.5 Vibronic Spectra of Imperfect Crystals.- 6.5.1 Terms Used in the Calculation of the Spectra of Local Vibrons.- 6.5.2 Spectrum of a Local Vibron with an NTS Phonon.- 6.5.3 Spectrum of a Local Vibron with a TS Phonon.- 6.5.4 Vibronic Absorption in Doped and Mixed Crystals Involving an NTS Phonon.- a) IDC of d-Benzenes.- b) IDC of d-Naphthalenes.- c) Mixed Crystals of Naphthalenes nd0 and ndg.- d) Local Vibron on a Defect Centre.- 6.5.5 Vibronic Absorption in the IDC of Naphthalenes with a TS Phonon.- 6.5.6 Absorption Spectra of Amorphous Films.- 6.5.7 Positions of the Electronic and Vibronic Bands.- Conclusion.- Appendix A Intramolecular Vibronic Interaction in Terms of the Secondary-Quantization Representation.- Appendix B Theory of Degenerate Perturbations.- References.

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Spectroscopy of Molecular Excitons
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