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

Abstract

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 1 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 (BH 3 , BeO/BeCO 3), and complexes of the N 2 , CO, and BF isoelectronic series with [Ru(II)(NH 3) 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.

The Nature of Nonclassical Carbonyl Ligands Explained by Kohn–Sham Molecular Orbital Theory

“…This electronic density shift is not only revealed by the electrostatic potential surfaces, but also by the molecular dipole moment of CO, which goes from 0.25 D with its positive side on C to 0.58 D with its positive side on O (Figure 4 b). The latter is in line with recent work by Head‐Gordon et al., who identified the change in dipole moment as one of the drivers behind C−O contraction [27, 28] . The main reason for this density shift is that C−O contraction increases the antibonding overlap between the 2s orbital on C with the 2p z orbital on O in the 5σ HOMO, [37] resulting in a larger lobe on the carbon atom pointing away from the oxygen atom (Figure S4).…”

“…The latter is in line with recent work by Head-Gordone tal.,w ho identified the change in dipole moment as one of the drivers behindC ÀOc ontraction. [27,28] The main reason for this density shift is that CÀO contraction increases the antibonding overlap between the 2s orbitalo nCwitht he 2p z orbital on Oi nt he 5s HOMO, [37] resulting in al arger lobe on the carbon atom pointing away from the oxygen atom ( Figure S4).…”

“…[19][20][21][22] In contrast to classical carbonyls, nonclassical carbonyls are less straightforwardt oe xplaina nd have therefore been as ubjecto fo ngoing research in which different explanations have been proposed. [18,[22][23][24][25][26][27][28] In one explanation, the CO ! TM s-donation strengthens the CÀOb ond because the 5s HOMO is slightly antibonding in nature.…”

Revealing the Nature of Electron Correlation in Transition Metal Complexes with Symmetry-Breaking and Chemical Intuition

“…The original scheme decomposes the interaction energy into frozen, polarization, and charge transfer contributions. 75,76 In order to reveal more insight into the nature of the bidirectional charge transfer of some metal-ligand bonds, we augmented the analysis with a further decomposition of the CT energy using the newly developed variational forward-backward (VFB) decomposition 77 .…”

Dissociation of HCl in water nanoclusters: an energy decomposition analysis perspective

“…The changes due to charge-transfer can be further analyzed by separating the overall charge-transfer into contributions from forward and backward donations using the variational forward-backward (VFB) scheme. 89 In order to isolate the effect of charge-transfer between HCl and the water tetramer, the two-fragment reference (HCl)((H 2 O) 4 ) is employed for the VFB analysis. Selected distances and angles are collected in Table S1.…”