One of the major shortcomings of modern fragment-based electronic structure methods is that electron correlation (if included)
is handled at the level of individual electrons.
This project consists of two theoretical pieces.
In the first, the Hamiltonian for a supersystem is rigorously renormalized to be in terms of fluctuations of entire subsystems
(among internally correlated electronic states).
In the second part, familiar electronic structure methods, notably coupled-cluster theory, can be applied to this
renormalized Hamiltonian.
Initial tests of accuracy per cost are quite promising.
The next steps are to begin applying this model to systems of wider interest and implement the theoretically straightforward
generalization to excited states.
Project publications. Click sidebar to see all publications.
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We show here that the Hamiltonian for an electronic system may be written exactly in terms of fluctuation operators that transition constituent fragments between internally correlated states, accounting rigorously for inter-fragment electron exchange and charge transfer. Familiar electronic structure approaches can be applied to the renormalized Hamiltonian. For efficiency, the basis for each fragment can be truncated, removing high-energy local arrangements of electrons from consideration, and effectively defining collective coordinates for the fragments. For a large number of problems, this has the potential to fold the majority of electron correlation into the effective Hamiltonian, and it should provide a robust approach to incorporating difficult electronic structure problems into large systems. The number of terms in the exactly transformed Hamiltonian formally scales quartically with system size, but this can be reduced to quadratic in the mesoscopic regime, to within an arbitrary error tolerance. Finally, all but a linear-scaling number of these terms may be efficiently decomposed in terms of electrostatic interactions between a linear-scaling number of pre-computed transition densities. In a companion article, this formalism is applied to an excitonic variant of coupled-cluster theory.
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A generalized variant of coupled-cluster theory is described here, wherein the degrees of freedom are fluctuations of fragments between internally correlated states. The effects of intra-fragment correlation on the inter-fragment interaction are pre-computed and permanently folded into an effective Hamiltonian, thus avoiding many redundant evaluations of local relaxations associated with coupled fluctuations. A companion article shows that the electronic Hamiltonians of real systems may always be cast in the form required. Two proof-of-principle demonstrations are presented. One uses harmonic oscillators, for which accuracy and algorithm structure can be carefully controlled in comparisons. The other uses small electronic systems to demonstrate compelling accuracy and efficiency, also when inter-fragment electron exchange and charge transfer must be handled. This framework opens a promising path to build finely tunable, systematically improvable methods to capture precise properties of systems interacting with a large number of other systems. Since this scheme is independent of the quality of the states used for the fragments, it can be arbitrarily detailed in terms of the correlation model used for each. The extension to excited states is also straightforward.
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