Occupied-Virtual Orbitals for Chemical Valence with Applications to Charge Transfer in Energy Decomposition Analysis

In this article, we introduce the occupied-virtual orbitals for chemical valence (OVOCV). The OVOCVs can replace or complement the closely related idea of the natural orbitals for chemical valence (NOCV). The input is a difference density matrix connecting any initial single determinant to any final determinant, at a given molecular geometry, and a given one-particle basis. This arises in problems such as orbital rearrangement or charge transfer (CT) in energy decomposition analysis (EDA). The OVOCVs block-diagonalize the density difference operator into 2 × 2 blocks, which are spanned by one level that is filled in the initial state (the occupied OVOCV) and one that is empty (the virtual OVOCV). By contrast, the NOCVs fully diagonalize the density difference matrix and therefore are orbitals with mixed occupied-virtual character. Use of the OVOCVs makes it much easier to identify the donor and acceptor orbitals. We also introduce two different types of EDA methods with the OVOCVs and, most importantly, a charge decomposition analysis method that fixes the unreasonably large CT amount obtained directly from NOCV analysis. The square of the CT amount associated with each NOCV pair emerges as the appropriate value from the OVOCV analysis. When connecting the same initial and final states, this value is identical to the CT amount obtained from the independent absolutely localized molecular orbital (ALMO) complementary occupied-virtual orbital pair (COVP) analysis. The total, summed over all pairs, is also exactly the same as the independently suggested excitation number, as proved herein. Several examples are presented to compare NOCVs and OVOCVs: stretched H₂⁺, a strong halogen bond between tetramethylthiourea and iodine, coordination of ethene in Zeise's salt, and binding in the Cp₃La···C≡NCy complex.