The Fragment Hamiltonian recasts the electronic Hamiltonian into a sum of Hamiltonians for the individual fragments (i.e. atoms, functional groups, sites, etc.) plus fragment-fragment interactions. In this way, the emphasis is placed on the electronic states of the fragments, rather than on the states of the individual electrons. One choice for the many-electron wave function of the system is one where there is an integer number of electrons on each fragment. We need to allow the number electrons on a fragment to fluctuate. This can be accomplished by taking a linear combination of such many-electron wave functions, or valence states, where the number of electrons on a particular fragment is not necessarily the same for each valence state. For instance, suppose that we have a system of three fragments in an equilateral triangle configuration, each with nuclear charge Z. Let a valence state be designated by | N1 N2 N3 &gt;, where the Ni are the numbers of electrons on the ith fragment. One possible valence state assigns each of the three fragments Ni = Z electrons. Then that valence state is | Z Z Z &gt;. If the system is neutral, then another possible valence state might be one where the first fragment has transferred an electron to the second. Then the valence state would be | Z-1 Z+1 Z &gt;. However, the first fragment might instead transfer an electron to the third fragment. To construct a trial state, one takes a linear combination of the valence states that are deemed important to the system and properties of interest. In transitioning from one of these valance states to another, we suppose that a charge-transfer hopping process is involved. For instance, the transition | Z Z Z &gt; → | Z-1 Z+1 Z &gt; puts the system into an excitonic state having one electron-hole pair. For charge separation problems, we are starting from a bound exciton and transitioning to another excitonic state with the charges separated by a different distance. If the distance exceeds a prescribed limit, the exciton is dissociated and the electron and hole can migrate independently. If the electron migrates to the hole site, the pair annihilates. We adopt a standard hopping model and perform Monte Carlo simulations to estimate the escape probability for selected fragment properties and geometries. The Fragment Hamiltonian results are compared with simulations using standard, one-electron hopping models.

Charge-separation models from the fragment-Hamiltonian approach

255th National Meeting (2018)

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