Orbital exciton

Substituting eqns (D.4) and (D.5) into the Pariser-Parr-Pople model, eqn (D.l), we obtain the molecular orbital exciton Hamiltonian, ... 

The lowest excited states in molecular crystals are singlet and triplet excitons [3]. Since it costs coulombic energy to transfer an electron that has been excited optically from the HOMO (highest occupied molecular orbital) to the LUMC)... 

With the absorption of a quantum with an energy of more than 3.05 eV resp. 3.29 eV, an electron is lifted out of the valence band and into the conduction band, thereby forming an exciton (Fig. 5). This interpretation is also supported by the molecular orbital theory and the crystal field theory regarding the bonding conditions in the TiC lattice. 

The photoluminescence of these nanoparticles has very different causes, depending on the type of nanomaterial semiconductor QDs luminescence by recombination of excitons, rare-earth doped nanoparticles photoluminescence by atom orbital (AO) transitions within the rare-earth ions acting as luminescent centers, and metallic nanoparticles emit light by various mechanisms. Consequently, the optical properties of luminescent nanoparticles can be very different, depending on the material they consist of. 

The dependence of lifetime on temperature in the range above RT shows an activation energy in the order of 10-25 meV [Bu3, Ool]. This was proposed to be a consequence of the exchange splitting of the exciton between the singlet and the triplet state. While at RT both states are populated, only the lower triplet state is populated at temperatures below 20 K. However, it has been shown that even for crystallites of low symmetry the calculated values of the exchange splitting are too low compared with experimental observations [De3]. Calculations of the radiative lifetime of the triplet exciton that take into account spin-orbit interactions are reported to be consistent with experimental results [Nal]. 

The simplest exciton can be modeled by a hydrogen atom, with the electron and hole (equivalent to the hydrogen nucleus) in a stable orbit around each other. Within this model, two basic types of excitons can occur in crystalline materials ... 

Within the simple Bohr model used for weakly bound excitons, the radius of the electron-hole orbit is given by... 

In the present work the Cl procedure ( ) employed includes single, double, and higher excited configurations, and can treat in a natural way, using the localized monomer basis orbitals, intra- as well as inter-molecular excitations. States which arise from such monomer-based excitations can then be interpreted in terms of their locally-excited, excitonic, CT, or "mixed" character. Details as to the nature of the dimer states have been discussed in our earlier works (7, 8). 

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