Automatic Partition of Orbital Spaces Based on Singular Value Decomposition in the Context of Embedding Theories

We present a simple approach for orbital space partitioning to be employed in the projection-based embedding theory developed by Goodpaster and coworkers [J. Chem. Theory Comput. 2012, 8, 2564]. Once the atoms are assigned to the desired subspaces, the molecular orbitals are projected onto the atomic orbitals centered on active atoms and then singular value decomposed. The right singular vectors are used to rotate the initial molecular orbitals, taking the largest gap in the singular values spectrum to define the most suitable partition of the occupied orbital space. This scheme is free from numerical parameters, contrary to the Mulliken charge threshold or the completeness criterion previously used. The performance of this new prescription is assessed in a test set of several distinct reactions, the deprotonation of decanoic acid, the torsional potential of a retinal derivative, and the critical points along the reaction coordinate of an example of the Menshutkin S_N2 reaction inside a carbon nanotube.