Despite the recent success of projection-based embedding, the difficulties associated with identifying proper orbital subspaces can sometimes lead to qualitatively incorrect results. In its original prescription, an orbital localization step, usually Pipek-Mezey (PM), is followed by assignment of the orbitals to the desired subspaces via a threshold in Mulliken charges. However, a chosen threshold may not be suitable for the entirety of a certain reaction coordinate, creating discontinuities in a potential energy curve. Additionally, Mulliken charges are highly dependent on the basis set and often deteriorate when the basis set is improved, which also serves as basis for the PM procedure. Here we propose a method that significantly alleviates some of these challenges as well as being free from Mulliken charges and arbitrary numerical parameters. After an SCF calculation, usually density functional theory, we perform a singular value decomposition of the occupied molecular orbital (MO) coefficients which have been projected onto the atomic orbitals of the atoms in each subsystem. The size of each orbital subspace is then obtained by partitioning the occupied space at the largest gap in the singular value spectrum, while the initial set of MOs is rotated into the basis of the associated singular vectors. This new approach, Subsystem Partitioned AO DEcomposition, SPADE, is subject to a variety of test cases, maintaining consistent orbital subspaces throughout the studied reaction coordinates and displaying superior performance to the PM/Mulliken charge combination in WFT-in-DFT calculations. To illustrate the performance of the proposed scheme, the provided figure shows the torsional potential of a retinal derivative at the MP2-in-PBE and MP2-in-B3LYP levels with the SPADE and PM/Mulliken orbital subspace construction.

Automatic partition of orbital spaces based on singular value decomposition in the context of embedding theories

2019 Spring National Meeting

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