Direct orbital selection for projection-based embedding

Projection-based embedding (PbE) has become increasingly popular in recent years due to its simplicity and robustness. It is a very promising method for highly accurate calculations of reaction barriers and reaction energies via embedding of a correlated wavefunction or sophisticated density functional theory (DFT) method for the reaction center into a more cost effective DFT description of the environment. PbE enables an arbitrary partitioning of the supersystem orbitals into subsystems. In most applications so far, the selection of orbitals for the active system was directly linked to the selection of "active atoms." We propose an inexpensive approach that automatically selects orbitals as active that change during the reaction and that assigns all remaining orbitals to the environment. This approach is directly coupled to the reaction under investigation and does not rely on any specification of active atoms. We compare different variants of this approach for the selection of orbitals along the reaction path for embedding of Adamo and Barone's hybrid functional (known as PBE0) into Perdew, Burke, and Ernzerhof's exchange-correlation functional (PBE), a method dubbed as PBE0-in-PBE embedding, based on orbitalwise partial charges and the kinetic energy. The most successful comparison scheme is based on shellwise intrinsic atomic orbital charges. We show for a set of six reactions of different types that the corresponding errors in reaction energies and barriers converge quickly to zero with the extension of the active-orbital space.