Quantifying individual (anti)bonding molecular orbitals' contributions to chemical bonding

Keto-enol tautomerism from the electron delocalization perspective

The equilibrium between keto and enol forms in acetylacetone and its derivatives is studied using electron delocalization indices and delocalization tensor density. We demonstrate how electron delocalization governs the equilibrium between keto and enol forms. The less stable enols have more distinct double and single bond character in the CCC fragment, while electron delocalization in this fragment is more pronounced in more stable enols. Looking for the origin of such behavior, we considered the one-electron potentials entering the Euler equation for the electron density. We found that electron delocalization is mainly governed by the static exchange potential, which depends on the three-dimensional atomic structure. It, however, does not distinguish differences in electron delocalization in more and less stable enols, the effect arising from the kinetic exchange contribution, which reflects spin-dependent effects in the electron motion. The local depletion of kinetic exchange in the conjugated fragment yields the enhanced electron delocalization along the CCC bonds in more stable enols. Thus, a combination of considered descriptors allowed us to reveal the influence of electron delocalization on the equilibrium between keto and enol forms and showed the significant features of this phenomenon.

Two, Three, or Not to Be? Elucidating Multiple Bonding in d6 Pseudotetrahedral Oxo and Imide Complexes

Late-transition-metal oxo and imide complexes play an important role in the catalytic functionalization and activation of small molecules. An emerging theme in this area over the past few decades has been the use of lower coordination numbers, and pseudotetrahedral geometries in particular, to stabilize what would otherwise be highly reactive species. However, the bonding structure in d⁶ oxo and imide complexes in this geometry is ambiguous. These species are typically depicted with a triple bond; however, recent experimental evidence suggests significant empirical differences between these complexes and other triply bonded complexes with lower d counts. Here we use a suite of computational orbital localization methods and electron density analyses to probe the bonding structure of isoelectronic d⁶ Co^III oxo and imide complexes. These analyses suggest that a triple-bond description is inaccurate because of a dramatically weakened σ interaction. While the exact bond order in these cases is necessarily dependent on the model used, several metrics suggest that the strength of the metal-O/N bond is most similar to that of other formally doubly bonded complexes.

Dual XH-π Interaction of Hexafluoroisopropanol with Arenes

The dual XH (OH and CH) hydrogen-bond-donating property of 1,1,1,3,3,3-hexafluoroisopropanol (HFIP) and the strong dual XH-π interaction with arenes were firstly disclosed by theoretical studies. Here, the high accuracy post-Hartree-Fock methods, CCSD(T)/CBS, reveal the interaction energy of HFIP/benzene complex (-7.22 kcal/mol) and the contribution of the electronic correlation energy in the total interaction energy. Strong orbital interaction between HFIP and benzene was found by using the DFT method in this work to disclose the dual XH-π intermolecular orbital interaction of HFIP with benzene-forming bonding and antibonding orbitals resulting from the orbital symmetry of HFIP. The density of states and charge decomposition analyses were used to investigate the orbital interactions. Isopropanol (IP), an analogue of HFIP, and chloroform (CHCl₃) were studied to compare them with the classical OH-π, and non-classical CH-π interactions. In addition, the influence of the aggregating effect of HFIP, and the numbers of substituted methyl groups in benzene rings were also studied. The interaction energies of HFIP with the selected 24 common organic compounds were calculated to understand the role of HFIP as solvent or additive in organic transformation in a more detailed manner. A single-crystal X-ray diffraction study of hexafluoroisopropyl benzoate further disclosed and confirmed that the CH of HFIP shows the non-classical hydrogen-bond-donating behavior.

The CH···HC interaction in biphenyl is a delocalized, molecular-wide and entirely non-classical interaction: Results from FALDI analysis

In this study we aim to determine the origin of the electron density describing a CH···HC interaction in planar and twisted conformers of biphenyl. In order to achieve this, the fragment, atomic, localized, delocalized, intra- and inter-atomic (FALDI) decomposition scheme was utilized to decompose the density in the inter-nuclear region between the ortho-hydrogens in both conformers. Importantly, the structural integrity, hence also topological properties, were fully preserved as no 'artificial' partitioning of molecules was implemented. FALDI-based qualitative and quantitative analysis revealed that the majority of electron density arises from two, non-classical and non-local effects: strong overlap of ortho CH σ-bonds, and long-range electron delocalization between the phenyl rings and ortho carbons and hydrogens. These effects resulted in a delocalized electron channel, that is, a density bridge or a bond path in a QTAIM terminology, linking the H-atoms in the planar conformer. The same effects and phenomena are present in both conformers of biphenyl. We show that the CH···HC interaction is a molecular-wide event due to large and long-range electron delocalization, and caution against approaches that investigate CH···HC interactions without fully taking into account the remainder of the molecule.

Characterization of bonding modes in metal complexes through electron density cross-sections

Qualitative inspection of molecular orbitals (MOs) remains one of the most popular analysis tools used to describe the electronic structure and bonding properties of transition metal complexes. In symmetric coordination complexes, the use of group theory and the symmetry-adapted linear combination (SALC) of fragment orbitals allows for a very accurate and informative interpretation of MOs, but the same procedure cannot be performed for asymmetric complexes, such as Schrock and Fischer carbenes. In this work, we present a straight-forward approach for classifying and quantifying MO contributions to a particular metal-ligand interaction. Our approach utilizes the topology of MO density contributions to a cross-section of an inter-nuclear region, and is computationally inexpensive and applicable to symmetric and asymmetric complexes alike. We also apply the same approach with similar decompositions using Natural Bond Orbitals (NBO) and the recently developed Fragment, Atomic, Localized, Delocalized and Interatomic (FALDI) density decomposition scheme. In particular, FALDI analysis provides additional insights regarding the multi-centric nature of metal-carbene bonds without resorting to expensive multi-reference calculations.

Molecular Orbitals Support Energy-Stabilizing "Bonding" Nature of Bader's Bond Paths

Our MO-based findings proved a bonding nature of each density bridge (DB, or a bond path with an associated critical point, CP) on a Bader molecular graph. A DB pinpoints universal physical and net energy-lowering processes that might, but do not have to, lead to a chemical bond formation. Physical processes leading to electron density (ED) concentration in internuclear regions of three distinctively different homopolar H,H atom-pairs as well as classical C-C and C-H covalent bonds were found to be exactly the same. Notably, properties of individual MOs are internuclear-region specific as they (i) concentrate, deplete, or do not contribute to ED at a CP and (ii) delocalize electron-pairs through either in- (positive) or out-of-phase (negative) interference. Importantly, dominance of a net ED concentration and positive e^--pairs delocalization made by a number of σ-bonding MOs is a common feature at a CP. This feature was found for the covalently bonded atoms as well as homopolar H,H atom-pairs investigated. The latter refer to a DB-free H,H atom-pair of the bay in the twisted biphenyl (Bph) and DB-linked H,H atom-pairs (i) in cubic Li₄H₄, where each H atom is involved in three highly repulsive interactions (over +80 kcal/mol), and (ii) in a weak attractive interaction when sterically clashing in the planar Bph.