Variational Forward–Backward Charge Transfer Analysis Based on Absolutely Localized Molecular Orbitals: Energetics and Molecular Properties

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 depending 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 backward 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.