Optimization of Fragment State Spaces within the Excitonic Renormalization Framework

TL;DR

This paper introduces an efficient algorithm to optimize fragment state spaces within the excitonic renormalization framework, enabling scalable and accurate electronic structure calculations for weakly interacting fragments.

Contribution

It develops a bottom-up optimization algorithm using monomer gradients and pre-screening, completing the excitonic renormalization methodology with a polynomially scaling framework.

Findings

The algorithm produces compact model state spaces closely matching optimal ones.

Optimized zeroth-order spaces can accurately recover first-order results.

Numerical tests on the beryllium dimer validate the approach.

Abstract

The recently proposed excitonic renormalization framework presents an alternative ansatz to elec- tronic structure theory of weakly interacting fragments. It makes use of absolutely localized orbitals and correlated states evaluated on isolated fragments, which are then used to recover the interaction in an ab-initio manner based on a biorthogonal framework. The correlated monomer information can be heavily truncated, and the Hamiltonian can be expanded in a rapidly converging series, allow- ing the Hamiltonian to be built and diagonalized in a scalable fashion. However, the methodology still lacks an efficient bottom-up procedure, capable of producing optimized model state spaces for the isolated fragments, without ever building the Hamiltonian in the full monomer state spaces. In order to address this issue, this work presents an algorithm utilizing monomer gradients at three different levels as well as an efficient pre-screening of the determinant space, ensuring compact model state spaces and intermediates. Numerical results are presented for the beryllium dimer, showing that the algorithm is indeed capable of building compact model state spaces, yielding results that closely resemble those of the optimal model state spaces. Furthermore, it is shown that model state spaces, optimized at the zeroth order of the Hamiltonian expansion, can also be used to accurately recover first order results, enabling very efficient optimization, as the optimization can be conducted at a lower order than the targeted final level. Hence, the presented solver completes the excitonic renormalization methodology, forming a polynomially scaling framework.