Eigenstates, molecular representation

Canonical transformations from the tight-binding (atomic orbitals) representation to the eigenstate (molecular orbitals) representation play an important role, and we consider it in detail. Assume, that we find two unitary matrices SR and SR, such that the Hamiltonians of the left part Hi and of the right part Hi can be diagonalized by the canonical transformations... 

A correct representation of the molecular eigenstates, zero-order, Born-Oppenheimer states,6... 

Nano-scale and molecular-scale systems are naturally described by discrete-level models, for example eigenstates of quantum dots, molecular orbitals, or atomic orbitals. But the leads are very large (infinite) and have a continuous energy spectrum. To include the lead effects systematically, it is reasonable to start from the discrete-level representation for the whole system. It can be made by the tight-binding (TB) model, which was proposed to describe quantum systems in which the localized electronic states play an essential role, it is widely used as an alternative to the plane wave description of electrons in solids, and also as a method to calculate the electronic structure of molecules in quantum chemistry. 

Fig. 4. (a) A schematic representation of the small molecule limit. The states are the same as those represented in Fig. 1. The molecular eigenstates approximately diagonalize the effective molecular Hamiltonian (20), and each carries only a portion of the original oscillator strength to s can therefore decay radiatively to

This may result, for example, when considering electron transfer between two molecular species and working in a representation derived from the eigenstates of a system in which these species do not interact (e.g. are far from each other). The couphng results from the residual interaction that increases when the two species come closer to each other. 

Chapter 6 deals with the time evolution of radiative decaying states of polyatomic molecules with special emphasis on radiative decay in internal conversion. The decay of a manifold of closely spaced coupled states is handled by the Green s function formalism, where the matrix elements are displayed in an energy representation that involves either the Born-Oppenheimer or the molecular eigenstate basis set. The features of radiationless transitions in large, medium-sized, and small molecules are elucidated, deriving general expressions for the radiative decay times and for the fluorescence quantum yields. 

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