Variational Energy Decomposition Analysis of Charge-Transfer Interactions between Metals and Ligands in Carbonyl Complexes

Abstract

Variational energy decomposition analyses have been presented to quantify the σ-dative, ligand-to-metal forward charge transfer (CT) and the π-conjugative, metal-to-ligand backward charge delocalization on a series of isolelectronic transition-metal carbonyl complexes M­(CO)6, including M = Ti2–, V–, Cr, Mn+, and Fe2+. Although the qualitative features of these energy terms are understood, well-defined quantitative studies have been scarce. Consistent with early findings, electrostatic and Pauli exchange effects play a key role in σ-donation, resulting in blue shifts in ligand vibrational frequency in the complex geometries. Excluding chemical bonding interactions between the CO ligand and the metal fragments in the energy decomposition analysis, we found that loosely bound electrostatic complexes can be formed at a longer metal-to-ligand distance due to the exponential decay of Pauli exchange. In all complexes, the overall binding stabilization can be attributed to CT effects, with opposing trends between σ-donation and π-back bonding that follows an order of Ti2– (4.4) > V1– (2.6) > Cr (1.5) > Mn1+ (1.1) > Fe2+ (0.5) in π-to-σ CT ratio. These electronic and energetic features are mirrored in the vibrational frequency shifts induced by different factors. The present investigation may help stimulate the use of energy decomposition techniques to understand the structure and activity of metallocatalysts using density functional theory.

DFT exchange: sharing perspectives on the workhorse of quantum chemistry and materials science

“…These configurations, obtained either through fragmental block-localization or by local electronic excitations, correspond to well-defined Lewis resonance structures, whose variational optimization can be directly used for block-localized wave-function interaction energy-decomposition analysis (BLW-EDA) to provide a quantitative interpretation of DFT results, such as aromaticity, hyperconjugation, and the Dewar-Chatt-Duncanson s-dative donation and p-backbonding in transition-metal complexes. 739 Furthermore, these localized electronic structures can be used to define diabatic states by orthogonal projection, 740 Recently, a general approach was introduced for treating spin-coupling interactions of open-shell molecules by MSDFT. 458 The TDF energies that determine spin coupling are obtained by enforcing the multiplet degeneracy of the S + 1 state in the M S = S manifold.…”

Multistate Energy Decomposition Analysis of Molecular Excited States

“…Energy decomposition analysis (EDA) is widely used and plays an important role in the understanding of intermolecular interactions in molecular systems. − These studies provide insights into the interplay of Pauli exclusion, polarization and charge transfer effects that contribute to intermolecular forces. In turn, the information gained from these investigations can be useful to designing and optimizing empirical potential energy functions for condensed-phase and biomolecular simulations. , A large number of EDA models have been proposed, but they are almost exclusively limited to molecular complexes in the ground state. ,,− On the other hand, a major current frontier of theoretical chemistry is to study chemical processes taking place in electronically excited states in areas such as photochemistry, photovoltaic devices, photosynthesis and photoreception in biology, − catalysis, and even reactions in fuel cells and at the electrodes . Electronic coupling among local states in these systems can be used to determine the rate of excited-state energy transfer.…”

“…EDA models belonging to the second category were developed with certain elements of variational optimization of key reference intermediate states for energy partition. In Mo’s block-localized wave function (BLW) approach and the absolutely localized molecular orbital analysis, , the strictly block-localized orbitals for every intermediate in the EDA are fully variationally optimized, providing a set of well-defined diabatic intermediate states for interpretation of the resonance energies of aromaticity, anomeric effects and forward-and-backward bonding interactions. ,, Other illustrative examples include the early constrained space orbital variations (CSOV) method by successively mixing occupied and virtual orbitals of different molecules, ,, and the reduced variational space self-consistent-field (RVS-SCF) model in which the orbitals of one fragment is optimized in the presence of the frozen orbitals of other fragments . Another class of EDA theory features the extended transition state (ETS) scheme, ,, along with natural orbitals for chemical valence (NOCV) theory, in which not only noncovalent intermolecular interactions are decomposed, but also the energy of a chemical bond can be separated into unpaired electron contributions. , The ETS-NOCV method allows the analysis of bonding characteristics such as σ,π,δ bond types …”

Excimer Energies

“…Energy decomposition analysis (EDA) is a useful tool for understanding intermolecular interactions. − Although methods for molecular complexes in the ground state have been thoroughly developed, − few approaches are currently available for analyzing energy terms of excimers and exciplexesmolecular aggregates formed in the electronic excited states. One exception is a study by Ge et al, , who used the same energy terms in ground-state EDA, , including frozen (frz), polarization (pol), and charge transfer (CT) terms, to describe intermolecular interactions in the excited states Δ E int * = Δ E frz * + Δ E pol * + Δ E CT * .…”