ETS-NOCV decomposition of the reaction force for double-proton transfer in formamide-derived systems

Occupied-Virtual Orbitals for Chemical Valence with Applications to Charge Transfer in Energy Decomposition Analysis

In this article, we introduce the occupied-virtual orbitals for chemical valence (OVOCV). The OVOCVs can replace or complement the closely related idea of the natural orbitals for chemical valence (NOCV). The input is a difference density matrix connecting any initial single determinant to any final determinant, at a given molecular geometry, and a given one-particle basis. This arises in problems such as orbital rearrangement or charge transfer (CT) in energy decomposition analysis (EDA). The OVOCVs block-diagonalize the density difference operator into 2 × 2 blocks, which are spanned by one level that is filled in the initial state (the occupied OVOCV) and one that is empty (the virtual OVOCV). By contrast, the NOCVs fully diagonalize the density difference matrix and therefore are orbitals with mixed occupied-virtual character. Use of the OVOCVs makes it much easier to identify the donor and acceptor orbitals. We also introduce two different types of EDA methods with the OVOCVs and, most importantly, a charge decomposition analysis method that fixes the unreasonably large CT amount obtained directly from NOCV analysis. The square of the CT amount associated with each NOCV pair emerges as the appropriate value from the OVOCV analysis. When connecting the same initial and final states, this value is identical to the CT amount obtained from the independent absolutely localized molecular orbital (ALMO) complementary occupied-virtual orbital pair (COVP) analysis. The total, summed over all pairs, is also exactly the same as the independently suggested excitation number, as proved herein. Several examples are presented to compare NOCVs and OVOCVs: stretched H2+, a strong halogen bond between tetramethylthiourea and iodine, coordination of ethene in Zeise's salt, and binding in the Cp3La···C≡NCy complex.

An ETS-NOCV-based computational strategies for the characterization of concerted transition states involving CO2

Due to the presence of both a slightly acidic carbon and a slightly basic oxygen, carbon dioxide is often involved in concerted transition states (TSs) with two (or more) different molecular events interlaced in the same step. The possibility of isolating and quantitatively evaluating each molecular event would be important to characterize and understand the reaction mechanism in depth. This could be done, in principle, by measuring the relevant distances in the optimized TS, but often distances are not accurate enough, especially in the presence of many simultaneous processes. Here, we have applied the Extended Transition State‐Natural Orbital for Chemical Valence‐method (ETS‐NOCV), also in combination with the Activation Strain Model (ASM) and Energy Decomposition Analysis (EDA), to separate and quantify these molecular events at the TS of both organometallic and organic reactions. For the former, we chose the decomposition of formic acid to CO₂ by an iridium catalyst, and for the latter, a CO₂‐mediated transamidation and its chemical variations (hydro‐ and aminolysis of an ester) as case studies. We demonstrate that the one‐to‐one mapping between the “molecular events” and the ETS‐NOCV components is maintained along the entire lowest energy path connecting reactants and products around the TS, thus enabling a detailed picture on the relative importance of each interacting component. The methodology proposed here provides valuable insights into the effect of different chemical substituents on the reaction mechanism and promises to be generally applicable for any concerted TSs.

Superatomic Ligand-Field Splitting in Ligated Gold Nanoclusters

Gold nanoclusters are attractive because of their electronic and optical properties. Many theoretical models have been proposed to explain their electronic structures through an electron-counting approach. However, subtle features may not be well explained by electron-counting rules. In this work, we have discovered a unique example of ligand-controlled skeletal bonding in two recently reported gold nanoclusters with very similar compositions and geometries. We have shown that the superatomic orbitals of the common kernel of the two clusters undergo different ligand-field splitting because of the different ligand-field strengths in the two clusters. Such a difference is clearly revealed by constructing the Jellium orbitals via an orbital alignment process, and a subsequent localization of the Jellium orbitals allows us to obtain localized bonding models. Finally, on the basis of localized bonding models, we predict the existence of a ligated gold cluster with a [Au₃₂]⁴⁺ kernel.

Bond Softening Indices Studied by the Fragility Spectra for Proton Migration in Formamide and Related Structures

Computational scheme to obtain bond softening index λ, defined within the conceptual DFT, has been obtained with the use of the reaction fragility (RF) concept. Numerical results were obtained with the RF spectra for the proton transfer reaction in formamide molecule (H₂NCHO) and the water assisted proton migration in H₂NCHO·H₂O complex. Double proton transfer reaction in the formamide dimer, (H₂NCHO)₂, and its analogues, (H₂NCHS)₂ and (H₂NCHO)·(H₂NCHS), have also been studied. The atomic and bond RF spectra clearly describe the density reorganization in the backbone of each molecule, resulting from proton displacement in the systems. The obtained softening indices have been calculated for hydrogen atoms in the reactant state (RS) and product state (PS) configuration. These indices provide fine characteristics for the local sensitivity of the reacting system to a disturbance of the position of a chosen atom.

Symmetry-Adapted Perturbation Theory Decomposition of the Reaction Force: Insights into Substituent Effects Involved in Hemiacetal Formation Mechanisms

The decomposition of the reaction force based on symmetry-adapted perturbation theory (SAPT) has been proposed. This approach was used to investigate the substituent effects along the reaction coordinate pathway for the hemiacetal formation mechanism between methanol and substituted aldehydes of the form CX₃CHO (X = H, F, Cl, and Br), providing a quantitative evaluation of the reaction-driving and reaction-retarding force components. Our results highlight the importance of more favorable electrostatic and induction effects in the reactions involving halogenated aldehydes that leads to lower activation energy barriers. These substituent effects are further elucidated by applying the functional-group partition of symmetry-adapted perturbation theory (F-SAPT). The results show that the reaction is largely driven by favorable direct noncovalent interactions between the CX₃ group on the aldehyde and the OH group on methanol.

Proton transfer in the benzimidazolone and benzimidazolthione tautomerism process catalyzed by polar protic solvents

The tautomeric equilibrium of benzimidazolone and benzimidazolthione have been studied by the density functional theory method using the CAM-B3LYP functional together with the 6-311G(d,p) basis set. Two separate mechanisms have been investigated: a direct intramolecular transfer using the polarizable continuum model and an indirect proton transfer assisted by a molecule of solvent (C6H12, H2O, CH3OH, and H2O2). In both cases, the results obtained indicate that ketone and thione are the most stable forms. However, the enhanced height of the activation barrier for the four-center mechanisms describing the tautomerism reaction as a direct intramolecular transfer implicates a relatively disadvantaged process. The participation of a polar protic solvent molecule allows the lowering of the activation energy barrier. Potential energy profiles of keto-enol and thio-enol tautomerism assisted by methanol and water are very different. The former one describes a concerted mechanism but the latter does not because it is associated with asynchronous processes that take place during the thio-enol tautomerism.