Frenkel exciton Hamiltonian

In Section II, we describe the CEO computational approach combined with semiempirical molecular Hamiltonian. Section III presents a real space analysis of electronic excitations and optical response of different conjugated molecules. In Section IV, we compute interchromophore interactions to derive an effective Frenkel exciton Hamiltonian for molecular aggregates. Finally, summary and discussion are presented in Section V. 

The problem is simplified considerably for chromophores. spatially well-separated, whose interactions are purely Coulombic (electron-exchange is negligible).Each chromophore then retains its own electrons and the aggregate may be described using the Frenkel exciton Hamiltonian for an assembly of two-level systems ... 

The term Davydov splitting usually refers to the splitting of degenerate states in molecular aggregates and crystals in which intermolecular interactions are electrostatic, and are described by the Frenkel exciton Hamiltonian. In contrast, the coupling between electronic modes in dimers includes electrostatic as well as exchange interactions, which result in interchromophore electronic coherence. These may not be described by Frenkel exciton Hamiltonian. 

MBE Schemes for the Calculation of Electronic Excitation Energies The Frenkel Exciton Hamiltonian Formalism... 

The Frenkel exciton Hamiltonian formalism with energies calculated with MBE schemes was recently applied to investigate the electronic absorption spectrum of liquid HCN [34], water [35], and liquid and supercritical CO2 [36]. 

The concept of Frenkel excitons (molecular excitons) [54] provides a good starting point for the description of the electronically excited states of the LH complexes. The respective model Hamiltonian reads in Heitler-London approximation... 

Let us assume that every molecule in the crystal has only two states, ground and excited. Then a general Hamiltonian for Frenkel excitons in the Heitler-London approximation (neglecting the particle nonconserving terms) including pair interaction may be written as (1), (6)... 

In these relations the operator B (Bn) describes the creation (annihilation) of a molecular excitation at lattice site n. We assume below that n 1,2,. ..,Ar, where N is the number of molecules in the chain and we consider one electronically excited molecular state. Then E-p is the on-site energy of a Frenkel exciton and Mnni is the hopping integral for molecular excitation transfer from molecule n to molecule n. In the summation in HF the terms with n = n are omitted. The Hamiltonian HF describes the Frenkel excitons in the Heitler-London approximation. 

In the same way as in the theory of Frenkel exciton mixing (Ch. 3), we have to diagonalize the total Hamiltonian H to consider the mixing of Frenkel and CT states and to find the new mixed states. We use the linear transformation to new operators ( and where... 

The quantity N 2 gives us the Wannier-Mott exciton component, A f 2 the part of the Frenkel exciton, and Np 2 the part of the cavity photon mode in the (p,k) cavity polariton state with energy hup(k). The diagonal Hamiltonian is... 

When speaking of kinematic interaction, it should be noted that the problem of its separation in connection with the transition from Pauli operators to Bose operators is far from new. This problem arises, in particular, for the Heisenberg Hamiltonian, which corresponds, for example, to an isotropic ferromagnet with spin a = 1/2 when spin waves whose creation and annihilation operators obey Bose commutation relations are introduced. This problem was dealt with by many people, including Dyson (6), who obtained the low-temperature expansion for the magnetization. However, even before Dyson s paper, Van Kranendonk (7) proposed to take into account of the kinetic interaction by starting from a picture where one spin wave produces an obstacle for the passage of another spin wave, since two flipped spins cannot be located at the same site (for Frenkel excitons this means that two excitons cannot be localized simultaneously on one and the same molecule). 

Experimentally observed polariton [spectra in polymer crystals have mostly been analyzed in terms of phenomenological models, treating the solid as a continuum (ISIS). Microscopic treatments for molecular crystals have been proposed within the framework of the Frenkel-exciton model (19-22) using semiempirical Hamiltonians to represent the matter field. 

Hamiltonians formally similar to Eq. (2.4) are encountered not only in the central problems of lattice dynamics and electron propagation, but also in a large variety of other problems. Among them we mention the Frenkel theory of excitons, the coupled electron-lattice impurities in the entire range of coupling, the Jahn-Teller (or pseudo-Jahn-Teller) systems, interacting spins, and so on. 

To evaluate the matrix element F(k) determining the resonance interaction between Frenkel and Wannier-Mott excitons we write down the interaction Hamiltonian as... 

In this subsection we take into account the exciton-phonon interaction and show that the exciton-cavity photon interaction also gives rise to a nonelastic Wannier-Frenkel interaction with phonons. Let us begin with the exciton-phonon interaction Hamiltonian... 

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