Systematically Improvable Exciton Hamiltonians in Large-scale Electronic Structure Calculations

Wavefunction-based methods for large systems are desirable for exploring problems where DFT is either uncalibrated or problematic. Existing fragment approaches typically treat the most powerful electron correlations on the same footing as dispersion forces, if at all. Our goal is a fragment-based method, in which systematic improvability is a practicable aspect, even for difficult problems embedded in environments (e.g., bond breaking in condensed phase or protein environments). In our approach, electrons are not treated individually in the global calculation. Rather, correlations between fluctuations of subunits are handled using familiar algorithms (specifically, coupled-cluster). The basis states are themselves electronically correlated excited states of the subunits, at any level of theory. This renders the Hamiltonian systematically improvable, as well as the global wavefunction. Furthermore, different parts of a system can be treated at different accuracy. Our initial investigations model a molecule as a group of strongly coupled harmonic oscillators (individual oscillators mimic electrons), and these “molecules” are then coupled to each other. For comparison, exact solutions are available for this model problem. The relative cost and accuracy are explored for calculations on the model equivalent of thousands of electrons in hundreds of fragments