ETS-NOCV Decomposition of the Reaction Force: The HCN/CNH Isomerization Reaction Assisted by Water

Shannon entropy variation as a global indicator of electron density contraction at interatomic regions in chemical reactions

CONTEXT

The negative of the Shannon entropy derivative is proposed to account for electron density contraction as the chemical bonds are breaking and forming during a chemical reaction. We called this property the electron density contraction index, EDC, which allows identifying stages in a reaction that are dominated by electron contraction or expansion. Four different reactions were analyzed to show how the EDC index changes along the reaction coordinate. The results indicate that the rate of change of Shannon entropy is directly related to the rate of change of the electron density at the bond critical points between all the atomic pairs in the molecular systems. It is expected that EDC will complement the detailed analysis of reaction mechanisms that can be performed with the theoretical tools available to date.

METHODS

Density functional theory calculations at the B3LYP/6-31G(d,p) level of theory were carried out using Gaussian 16 to analyze the reaction mechanisms of the four reactions studied. The reaction paths were obtained via the intrinsic reaction coordinate method, which served as the reaction coordinate to obtain the reaction force and the EDC profiles in each case. Shannon entropy and electron density at the bond critical points were calculated using the Multiwfn 3.7 package.

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.

The transition state region in nonsynchronous concerted reactions

The critical and vanishing points of the reaction force F(ξ) = -dV(ξ)/dξ yield five important coordinates (ξ_R, ξ_R^* , ξ_TS, ξ_P^* , ξ_P) along the intrinsic reaction coordinate (IRC) for a given concerted reaction or reaction step. These points partition the IRC into three well-defined regions, reactants (ξ_R→ξ_R^* ), transition state (ξ_R^* →ξ_P^* ), and products (ξ_P^* →ξ_P), with traditional roles of mostly structural changes associated with the reactants and products regions and mostly electronic activity associated with the transition state (TS) region. Following the evolution of chemical bonding along the IRC using formal descriptors of synchronicity, reaction electron flux, Wiberg bond orders, and their derivatives (or, more precisely, the intensity of the electron activity) unambiguously indicates that for nonsynchronous reactions, electron activity transcends the TS region and takes place well into the reactants and products regions. Under these circumstances, an extension of the TS region toward the reactants and products regions may occur.

The nature of stability and adsorption interactions of binary Au-Li clusters with bridge adsorption structures

Earlier findings have confirmed that CO molecules have propensities to adsorb on low-coordinated gold atoms (top sites) of Au-based clusters, which can be treated by the Blyholder model wherein the σ donation and π-back donation take place. Here, the structural features and stability of (AuLi)_n (n = 1-9) clusters were first analyzed using the GA-DFT method. The new adsorption modes, vibration frequencies and electronic interactions for Au-Li clusters with CO were investigated in detail. More excitingly, we found that CO prefers to adsorb on the bridge sites of the Au-Li clusters rather than on the top sites, which are much lower in energies than the top adsorptions, and the C-O stretching frequencies are also red-shifted. AIMD simulations show that the adsorption structures still have good thermal stability at 500 K. The density of states reveals that the electronic structures of Au-Li clusters have excellent stability for the bridge adsorptions of CO molecules. The ETS-NOCV analysis and NPA charges show that the direction of charge flow is from Au-Li clusters → CO. Our study provides an idea to elucidate the new adsorption mechanism on Au-Li clusters and the connection between the geometries and reaction properties.

Adsorption properties of pyramidal superatomic molecules based on the structural framework of the Au20 cluster

The pyramidal Au₂₀ cluster is a highly inert and stable superatomic molecule, but it is not suitable as a potential catalyst for covalent bond activations, e.g., CO oxidation reaction. Herein, the adsorption and electronic properties of CO molecules on various pyramidal clusters based on the structural framework of Au₂₀ are investigated using density functional theory. According to the SVB model, we constructed isoelectronic superatomic molecules with different pyramid configurations by replacing the vertex atoms of the Au₂₀ using metal M atoms (M = Li, Be, Ni, Cu, and Zn group atoms). After the CO molecules are adsorbed on the vertex atoms of these metal clusters, we analyzed the CO adsorption energies, C-O bond stretching frequencies, and electronic properties of the adsorption structures. It was found that the adsorption of CO molecules results in minimal changes in the parent geometries of the pyramidal clusters, and most adsorption structures are consistent with the geometry of CO adsorption at the vertex site of the Au₂₀ cluster. There are significant red shifts when CO molecules are adsorbed on the Ni/Pd/Pt atoms of the clusters, and their CO adsorption energies were also greater. The molecular orbitals and density of states reveal that there are overlaps between the frontier orbitals of the clusters and CO, and the electronic structure of NiAu₁₉^- is not sensitive to CO. The ETS-NOCV analysis shows that the increase in the density of the bonding area caused by the orbital interactions between the fragments is higher than the decrease in the density of the bonding area caused by Pauli repulsion, presenting that the direction of charge flow in the deformation density is from CO → clusters. From energy decomposition analysis (EDA) and NPA charge, we find a predominant covalent nature of the contributions in CO⋯M interactions (σ-donation). Our study indicates that the SVB model provides a new direction to expand the superatomic catalysts from the superatom clusters, which also provides inference for the extension of the single atom catalysis.

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.

Interacting Quantum Atoms Analysis of the Reaction Force: A Tool to Analyze Driving and Retarding Forces in Chemical Reactions

The analysis of the reaction force and its topology has provided a wide range of fruitful concepts in the theory of chemical reactivity over the years, allowing to identify chemically relevant regions along a reaction profile. The reaction force (RF), a projection of the Hellmann-Feynman forces acting on the nuclei of a molecular system onto a suitable reaction coordinate, is partitioned using the interacting quantum atoms approach (IQA). The exact IQA molecular energy decomposition is now shown to open a unique window to identify and quantify the chemical entities that drive or retard a chemical reaction. The RF/IQA coupling offers an extraordinarily detailed view of the type and number of elementary processes that take reactants into products, as tested on two sets of simple reactions.

Spectral Decomposition of the Reaction Force Constant

Qualitative relationships between the reaction force constant κ(ξ), the second derivative of the potential energy V(ξ), and the reactive vibrational mode that drives the reaction in the transition state region have been used in the past to measure the synchronicity of key chemical events that lead a chemical reaction. In this work, we provide a formal demonstration that κ(ξ) can be expressed in terms of the frequencies of normal modes at each point of the reaction path. This produce a decomposition of κ(ξ) that is used to analyze few representatives chemical reactions, a series of intramolecular proton transfer on formic, thioformic and dithioformic acids, and an intermolecular double proton transfer in the HNS₂:H₂O complex. It has been found that this partitioning allows to identify unambigously the reactive mode that drives the reaction at each point along the reaction coordinate thus giving relevant and detailed information about the mechanism of the chemical reactions under study.

Formation of active species from ruthenium alkylidene catalysts-an insight from computational perspective

Ruthenium alkylidene complexes are commonly used as olefin metathesis catalysts. Initiation of the catalytic process requires formation of a 14-electron active ruthenium species via dissociation of a respective ligand. In the present work, this initiation step has been computationally studied for the Grubbs-type catalysts (H₂IMes)(PCy₃)(Cl)₂Ru=CHPh, (H₂IMes)(PCy₃)(Cl)₂Ru=CH-CH=CMe₂ and (H₂IMes)(3-Br-py)₂(Cl)₂Ru=CHPh, and the Hoveyda-Grubbs-type catalysts (H₂IMes)(Cl)₂Ru=CH(o-OiPrC₆H₄), (H₂IMes)(Cl)₂Ru=CH(5-NO₂-2-OiPrC₆H₃), and (H₂IMes)(Cl)₂Ru=CH(2-OiPr-3-PhC₆H₃), using density functional theory (DFT). Additionally, the extended-transition-state combined with the natural orbitals for the chemical valence (ETS-NOCV) and the interacting quantum atoms (IQA) energy decomposition methods were applied. The computationally determined activity order within both families of the catalysts and the activation parameters are in agreement with reported experimental data. The significance of solvent simulation and the basis set superposition error (BSSE) correction is discussed. ETS-NOCV demonstrates that the bond between the dissociating ligand and the Ru-based fragment is largely ionic followed by the charge delocalizations: σ(Ru-P) and π(Ru-P) and the secondary CH^…Cl, CH^…π, and CH^…HC interactions. In the case of transition state structures, the majority of stabilization stems from London dispersion forces exerted by the efficient CH^…Cl, CH^…π, and CH^…HC interactions. Interestingly, the height of the electronic dissociation barriers is, however, directly connected with the prevalent (unfavourable) changes in the electrostatic and orbital interaction contributions despite the favourable relief in Pauli repulsion and geometry reorganization terms during the activation process. According to the IQA results, the isopropoxy group in the Hoveyda-Grubbs-type catalysts is an efficient donor of intra-molecular interactions which are important for the activity of these catalysts.

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.

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

The analysis of the electronic-structure changes along IRC paths for double-proton-transfer reactions in the formamide dimer (R1), formamide–thioformamide system (R2), and the thioformamide dimer (R3) was performed based on the extended-transition-state natural orbitals for chemical valence (ETS-NOCV) partitioning of the reaction force, considering the intra-fragments strain and the inter-fragments interaction terms, and further—the electrostatic, Pauli-repulsion and orbital interaction components, with the latter being decomposed into the NOCV components. Two methods of the system partitioning into the fragments were considered (‘reactant perspective’/bond-formation, ‘product perspective’ / bond-breaking). In agreement with previous studies, the results indicate that the major changes in the electronic structure occur in the transition state region; the bond-breaking processes are, however, initiated already in the reactant region, prior to entering the TS region. The electrostatic contributions were identified as the main factor responsible for the increase in the activation barrier in the order R1 < R2 < R3.

The influence of the metal cations and microhydration on the reaction trajectory of the N3 ↔ O2 thymine proton transfer: Quantum mechanical study

This study involves the intramolecular proton transfer (PT) process on a thymine nucleobase between N3 and O2 atoms. We explore a mechanism for the PT assisted by hexacoordinated divalent metals cations, namely Mg²⁺ , Zn²⁺ , and Hg²⁺ . Our results point out that this reaction corresponds to a two-stage process. The first involves the PT from one of the aqua ligands toward O2. The implications of this stage are the formation of a hydroxo anion bound to the metal center and a positively charged thymine. To proceed to the second stage, a structural change is needed to allow the negatively charged hydroxo ligand to abstract the N3 proton, which represents the final product of the PT reaction. In the presence of the selected hexaaqua cations, the activation barrier is at most 8 kcal/mol. © 2017 Wiley Periodicals, Inc.