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<p>To facilitate the understanding of charge transfer (CT) effects in dative complexes,
we propose a variational forward-backward (VFB) approach to decompose the overall
CT stabilization energy into contributions from forward and backward donation in the framework of energy decomposition analysis based on absolutely localized molecular orbitals (ALMO-EDA). Such a decomposition is achieved by introducing two additional
constrained intermediate states in which only one direction of CT is permitted. These
two “one-way” CT states are variationally relaxed such that the associated nuclear
forces can be readily obtained. This allows for a facile integration into the previously
developed adiabatic EDA scheme so that the molecular property changes arising from forward and back donation can be separately assigned. Using ALMO-EDA augmented
by this VFB model, we investigate the energetic, geometric, and vibrational features of
complexes composed of CO and main group Lewis acids (BH3, BeO/BeCO3), and complexes of the N2, CO, and BF isoelectronic series with [Ru(II)(NH3)5]2+. We identify
that the shift in the stretching frequency of a diatomic π-acidic ligand (XY), such as
CO, results from a superposition of the shifts induced by permanent electrostatics and
backward CT: permanent electrostatics can cause an either red or blue shift depend-
ing on the alignment of the XY dipole in the dative complex, and this effect becomes
more pronounced with a more polar XY ligand; the back-donation to the antibonding
π orbital of XY always lowers the X−Y bond order and thus red-shifts its stretching
frequency, and the strength of this interaction decays rapidly with the intermolecular
distance. We also reveal that while σ forward donation contributes significantly to energetic stabilization, it affects the vibrational feature of XY mainly by shortening the
intermolecular distance, which enhances both the electrostatic interaction and back-
ward CT but in different rates. The synergistic effect of the forward and backward
donations appears to be more significant in the transition metal complexes, where the
forward CT plays an essential role in overcoming the strong Pauli repulsion. These
findings highlight that the shift in the XY stretching frequency is not a reliable metric
for the strength of π back-donation. Overall, the VFB-augmented EDA scheme that
we propose and apply in this work provides a useful tool to characterize the role played
by each physical component that all together lead to the frequency shift observed. </p>
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Conjugation and Hyperconjugation Effects: Comparative Studies Through Localized Molecular Orbitals Energy Decomposition Analysis (LMO-EDA) and Natural Bond Orbitals (NBO)
