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Lowering of the electron kinetic energy (KE) upon initial encounter of radical fragments has long been cited as the primary origin of the covalent chemical bond based on Ruedenberg’s pioneering analysis of H$${}_{2}^{+}$$${}_2^{+}$and H₂and presumed generalization to other bonds. This work reports KE changes during the initial encounter corresponding to bond formation for a range of different bonds; the results demand a re-evaluation of the role of the KE. Bonds between heavier elements, such as H₃C–CH₃, F–F, H₃C–OH, H₃C–SiH₃, and F–SiF₃behave in the opposite way to H$${}_{2}^{+}$$${}_2^{+}$and H₂, with KE often increasing on bringing radical fragments together (though the total energy change is substantially stabilizing). The origin of this difference is Pauli repulsion between the electrons forming the bond and core electrons. These results highlight the fundamental role of constructive quantum interference (or resonance) as the origin of chemical bonding. Differences between the interfering states distinguish one type of bond from another.

 

Quantum chemistry in the form of density functional theory (DFT) calculations is a powerful numerical experiment for predicting intermolecular interaction energies. However, no chemical insight is gained in this way beyond predictions of observables. Energy decomposition analysis (EDA) can quantitatively bridge this gap by providing values for the chemical drivers of the interactions, such as permanent electrostatics, Pauli repulsion, dispersion, and charge transfer. These energetic contributions are identified by performing DFT calculations with constraints that disable components of the interaction. This review describes the second-generation version of the absolutely localized molecular orbital EDA (ALMO-EDA-II). The effects of different physical contributions on changes in observables such as structure and vibrational frequencies upon complex formation are characterized via the adiabatic EDA. Example applications include red- versus blue-shifting hydrogen bonds; the bonding and frequency shifts of CO, N 2 , and BF bound to a [Ru(II)(NH 3 ) 5 ] 2 + moiety; and the nature of the strongly bound complexes between pyridine and the benzene and naphthalene radical cations. Additionally, the use of ALMO-EDA-II to benchmark and guide the development of advanced force fields for molecular simulation is illustrated with the recent, very promising, MB-UCB potential. 

Intermolecular interactions between radicals and closed-shell molecules are ubiquitous in chemical processes, ranging from the benchtop to the atmosphere and extraterrestrial space. While energy decomposition analysis (EDA) schemes for closed-shell molecules can be generalized for studying radical–molecule interactions, they face challenges arising from the unique characteristics of the electronic structure of open-shell species. In this work, we introduce additional steps that are necessary for the proper treatment of radical–molecule interactions to our previously developed unrestricted Absolutely Localized Molecular Orbital (uALMO)-EDA based on density functional theory calculations. A “polarize-then-depolarize” (PtD) scheme is used to remove arbitrariness in the definition of the frozen wavefunction, rendering the ALMO-EDA results independent of the orientation of the unpaired electron obtained from isolated fragment calculations. The contribution of radical rehybridization to polarization energies is evaluated. It is also valuable to monitor the wavefunction stability of each intermediate state, as well as their associated spin density profiles, to ensure the EDA results correspond to a desired electronic state. These radical extensions are incorporated into the “vertical” and “adiabatic” variants of uALMO-EDA for studies of energy changes and property shifts upon complexation. The EDA is validated on two model complexes, H 2 O⋯˙F and FH⋯˙OH. It is then applied to several chemically interesting radical–molecule complexes, including the sandwiched and T-shaped benzene dimer radical cation, complexes of pyridine with benzene and naphthalene radical cations, binary and ternary complexes of the hydroxyl radical with water (˙OH(H 2 O) and ˙OH(H 2 O) 2 ), and the pre-reactive complexes and transition states in the ˙OH + HCHO and ˙OH + CH 3 CHO reactions. These examples suggest that this second generation uALMO-EDA is a useful tool for furthering one's understanding of both energetic and property changes associated with radical–molecule interactions. 

Anionic molecular models for nonhydrolyzed and partially hydrolyzed aluminum and gallium framework sites on silica, M[OSi(OtBu)₃]₄⁻and HOM[OSi(OtBu)₃]₃⁻(where M=Al or Ga), were synthesized from anionic chlorides Li{M[OSi(OtBu)₃]₃Cl} in salt metathesis reactions. Sequestration of lithium cations with [12]crown‐4 afforded charge‐separated ion pairs composed of monomeric anions M[OSi(OtBu)₃]₄⁻with outer‐sphere [([12]crown‐4)₂Li]⁺cations, and hydroxides {HOM[OSi(OtBu)₃]₃} with pendant [([12]crown‐4)Li]⁺cations. These molecular models were characterized by single‐crystal X‐ray diffraction, vibrational spectroscopy, mass spectrometry and NMR spectroscopy. Upon treatment of monomeric [([12]crown‐4)Li]{HOM[OSi(OtBu)₃]₃} complexes with benzyl alcohol, benzyloxide complexes were formed, modeling a possible pathway for the formation of active sites for Meerwin–Ponndorf–Verley (MPV) transfer hydrogenations with Al/Ga‐doped silica catalysts.