Series Expansion of a Scalable Hermitian Excitonic Renormalization Method

Explicitly utilizing the sparsity of the electronic structure problem, fragmentation methods have been heavily researched for decades with great success, pushing the limits of ab initio quantum chemistry ever further. Recently, this set of methods was expanded to include a fundamentally different approach called excitonic renormalization, providing promising initial results. It builds a supersystem Hamiltonian in a second-quantized-like representation from transition-density tensors of isolated fragments, contracted with biorthogonalized molecular integrals. This makes the method fully modular in terms of the quantum chemical methods applied to each fragment and enables massive truncation of the state-space required. Proof-of-principle tests have previously shown that solving for the ground state of an excitonically renormalized Hamiltonian can efficiently scale to hundreds of fragments, but the ad hoc approach that was used to build the Hamiltonian in those tests was not scalable to larger fragments. On the other hand, initial tests of the originally proposed fully modular Hamiltonian build, presented here, have shown the accuracy to be poor on account of its non-Hermitian character. In this study we bridge the gap between these with an operator expansion that is shown to converge rapidly, tending towards a Hermitian Hamiltonian while retaining the modularity, yielding an accurate, scalable method. The accuracy of the Hamiltonian is tested here for a beryllium dimer. At distances near the equilibrium point and longer, the zeroth-order method is comparable to CCSD(T), and the first-order method to FCI. Deviations occurring at shorter bond distances are discussed along with approaches to scaling up to larger fragments.