Excitons Hamiltonian

Here Eck, (Evki) are the quasiparticle energies, calculated within the GW approximation, of the states (ck) and (vk ). In terms of the eigenvalues and eigenvectors of the excitonic Hamiltonian, namely ... 

In order to calculate ensemble averages the explicit time-dependence of the exciton Hamiltonian is replaced by stochastic processes. If drastic changes of Jmn appear due to CC conformational transitions it is hard to apply this approach (Refs. [33] and [34] introduced a dichotomically fluctuating transfer coupling to cover such large conformational transitions). Instead, as it will be demonstrated here, it is more appropriate to directly generate the time-dependence of the exciton parameters Em and Jmn by MD simulations. Then, a microscopic account for solvent effects as well as a detailed description of solvent induced conformational transitions is possible. 

The one-exciton Hamiltonian Hi mixes the monomeric site states i) to create the one-excitonic states vk> = QkiIi) (see Fig. 13). When the... 

In the next section we specify the parameters of the vibrational exciton Hamiltonian for cyclic pentapeptide and discuss the structure of one- and two-vibrational-exciton manifold. 

EM was quite extensively and successfully applied to model optical spectra of molecular crystals and aggregates. Extensions were discussed [18] to account for disorder, whose effects are particularly important in aggregates, and to include the coupling between electronic degrees of freedom and molecular vibrations [48], needed to properly describe the absorption and emission bandshapes. However, as it was already recognized in original papers [7, 46], other terms enter the excitonic Hamiltonian. Electrostatic interactions between local excitations can in fact be introduced as ... 

The one-exciton Hamiltonian for a particular polypeptide, n in a distribution of structures, was chosen as M coupled harmonic oscillators ... 

The simulation of the isotopically substituted linear and 2D-IR spectra of helices is based on one- and two-exciton Hamiltonians, Eq. (61), which describe the frequencies and delocalization of amide-1 modes of a helix with N = 25 coupled harmonic oscillators and two isotpomers. The zero-order isotope shifts were incorporated into the energy of the residues of the isotopomer modes and the naturally abundant modes also included by sampling... 

A simple model of a nano-dimensional structure in the form of a neutral spherical SNc of radius a and permittivity si, embedded in a medium with permittivity ej, has been discussed elsewhere. An electron e and hole h with elfective masses and m i were assmned to travel within this SNc (we use r and rh to denote the distances of the electron and the hole, respectively, from the center of the SNc). We assume that the two permittivites are such that E2 ei, and that the electron and hole bands are parabolic in shape. In this model, and subject to these approximations and the effective mass approximation, the exciton Hamiltonian takes the... 

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. 

To proceed further we need an equation for (A , K), which may be obtained from an effective exciton Hamiltonian. However, as the Coulomb interaction is not diagonal in fc-space, a real space basis leads to a more intuitive description. A basis state in real-space, introduced in Section 3.6.1, is... 

First we need to derive an exciton Hamiltonian in the weak-coupling limit. To do this it is necessary to recast the Pariser-Parr-Pople model (see Section 2.8.3),... 

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

The dynamic disorder stems from the stochastic coupling of the exciton states to the thermal bath. We describe this coupling in the framework of the Kubo-Anderson s theory of the stochastic resonance [20,21]. The stochastic fluctuations in the site energies are induced by the exciton-phonon coupling to the bath. They are assumed to be comparable or smaller than the energy difference in the eigenstates. We add to the excitonic Hamiltonian Hq of Eq. (1) a time... 

The 1111 F transitions give rise to the so-called high- and low-energy exciton bands of the primary donor ( P(+) and P(-), respectively ), with dipole transition moment i For simplicity we assume that the dimer is completely symmetric. Note that singling out the wavefunctions only makes sense when the 3 <-> 4 interaction is much stronger than the other interactions. Even then the P( ) bands are only a mathematical construct they do not exist in reality as the dimer bands are always mixed with the other monomer bands by the exciton hamiltonian V. 

It is easier to introduce the relative and centre-of-mass coordinates re-th and 2 = (m re + mlrh)l(m e + m ) to solve the above exciton Hamiltonian... 

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