What happens when you want to do charge-fitting on large molecules?


Electronic energy transfer (EET) plays an important role in natural systems, most prominently as an essential step in photosynthesis(Scholes 2003). Related to EETs are excitonic interactions, i.e. the interaction between excited states on different chromophores. Of particular recent interest are excitonic resonance states that arise when an excitation is a combination of locally excited states on different chromophores giving rise to a delocalized excited state.

The quantity of interest in EETs are the electronic couplings that determines how much the different chromophores interact. The larger this coupling is, the more delocalized the excited state can be. In order to understand the photophysics in large multichromophoric systems, the electronic coupling are essential to evaluate and understand.

There are essentially two ways to calculate the couplings:

  • taking into accout Coulomb, exchange and overlap terms.
  • transformation to diabatic state.

In this work, we use the first approach.

Theoretical Background

Coupling between excited states

For two chromophores \(A\) and \(B\), the upper limit to the electronic coupling between adiabatic states \(i\) and \(j\) is one half of the splitting energy \(\Delta E_{ij}\) \[\label{eqn:halfsplit} |J_{ij}| = \frac{|\Delta E_{ij}|}{2} = \frac{|E_i - E_j|}{2}.\] For symmetry-equivalent chromophores, the couplings in eq \ref{eqn:halfsplit} is the exact coupling.(Blancafort 2014) Computing the coupling through eq \ref{eqn:halfsplit} is impractical for large chromophores because of the computational demand and especially if surroundings needs to be taken into account also.

It is possible to partition the couplings into three contributions: Coulombic, exchange and overlap. Commonly, the chromophores are separed enough such that the latter two terms can be ignored. The resulting Coulomb-couplings are usually evaluated using transition densities of each chromophore. That is, the electronic coupling, \(J_{ij}\), between the excited state \(i\) on chromophore \(A\) and the excited state \(j\) on chromophore \(B\), \(J_{ij}\), is related to the transition densities \(\rho(\mathbf{r})_{A,i}^T\) and \(\rho(\mathbf{r}')_{B,j}^T\) of chromophore \(A\) and \(B\)