A General Pythonic Framework for DFT-in-DFT and WF-in-DFT Embedding

High-level quantum mechanical (QM) simulations provide accurate electronic information of chemical systems but scale unfavourably with system size, making calculations of applied systems challenging. Hierarchical quantum mechanics in quantum mechanics embedding (QM/QM) addresses this issue by localising the highly accurate electronic structure methods to a region of chemical interest, with the wider environment represented using a less expensive embedding environment. However, implementing embedding procedures into established QM software packages can be challenging due to their monolithic design and complex software structure implemented to optimise performance. Here, we present a modular and open-source approach that extends QM/QM embedding to electronic structure codes with reduced development overhead by using the Atomic Simulation Interface (ASI) application programming interface (API) to communicate data objects between QM code invocations. We demonstrate the new software, EmbASI, by implementing the projection-based embedding (PbE) scheme into the FHI-aims electronic structure software package. Example calculations performed for pentanol and organic dimers demonstrate the efficacy of the hierarchical density functional theory (DFT) embedding approach with the charge localisation and partitioning procedures implemented in the wrapper environment. When using a truncated local atomic orbital basis, WF-in-DFT (Wavefunction-in-DFT) embedding calculations demonstrate speed-ups of 32× for RPA@PBE-in-PBE relative to a full RPA@PBE calculation while introducing minimal errors to the total energies of the embedding simulations (<1 kJ/mol).