Density Fitted Fragment Embedding – Principles and Applications

We demonstrate how deterministic, stochastic and semistochastic density fitted fragment embedding can be constructed using both non-overlapping fragments and overlapping fragments to perform energy evaluations. We then implement the frameworks to first perform energy calculations on water clusters using a polarised 3-zeta basis set to demonstrate the observed scaling of the algorithms, which is $\mathcal{O}(N_{AO,\text{mol}}^{2.62})$ and stochastic algorithms can help to reduce the pre-factor. We then perform numerical structural optimisations on cyclic water and hydrogen fluoride clusters using the deterministic algorithm. The optimised structures' hydrogen bonding energies are then compared with results using the corresponding correlated all-electron solver, which is CCSD in this work. It turns out that if each interacting molecule is chosen as a fragment, d-BE1-DF-CCSD is able to recover almost all of the hydrogen bonding energy in both water and hydrogen fluoride clusters calculated using all-electron DF-CCSD. This work therefore provides foundations for the efficient generation and quality of fragment embedding energy data in large, weakly interacting systems.