Driving and retarding forces in a chemical reaction

Insights into the variations of kinetic and potential energies in a multi-bond reaction: the reaction electronic flux perspective

CONTEXT

The debate over whether kinetic energy (KE) or potential energy (PE) are the fundamental energy components that contribute to forming covalent bonds has been enduring and stimulating over time. However, the supremacy of these energy components in reactions where multiple bonds are simultaneously formed or broken has yet to be explored. In this study, we use the reaction electronic flux (REF), an effective tool for investigating changes in driving electronic activity when bond formation or dissociation occurs in a chemical reaction, to examine the fluctuations in the KE and PE in a multi-bond reaction. To that end, the activation of CO2 by low-valent group 14 catalysts through a concerted σ -bond metathesis mechanism is analyzed. The findings of this preliminary study suggest that the REF can be utilized as a tool to rationalize alterations in the KE and PE in a multi-bond reaction. Specifically, analyses across the reaction coordinate reveal that changes in the KE and PE precede activation in the REF, stimulating the electronic activity where bond formation or dissociation processes dominate.

METHODS

The activation of CO2 by the low-valent LEH catalysts (L = N,N'-bis(2,6-diisopropyl phenyl)- β -diketiminate; E = Si, Ge, Sn, and Pb) was studied along the reaction coordinate at the M06-2X/6-31 G(d,p)-LANL2DZ(E) level of theory. The respective minimum energy path calculations were obtained using the intrinsic reaction coordinate (IRC) procedure. The reaction electronic flux (REF) was calculated through the computation of the electronic chemical potential using the frontier molecular orbital approximation. Mayer bond orders along the reaction coordinate have been determined using the NBO 3.1 program in Gaussian16. Most of the reaction coordinate quantities reported in this study (REF, KE, PE, among others) have been determined using the Kudi program and custom Python scripts.

A deeper analysis of the role of synchronicity on the Bell-Evans-Polanyi plot in multibond chemical reactions: a path-dependent reaction force constant

The role of the degree of synchronicity in the formation of the new single-bonds in a large set of 1,3-dipolar cycloadditions and its relation in the fulfilment of the classical Bell-Evans-Polanyi principle and Hammond-Leffler postulate are deeply investigated. Our results confirm that asynchronicity is an important path-dependent factor to be taken into account: (i) the Bell-Evans-Polanyi is fulfilled as the degree of (a)synchronicity is quite the same, and a linear relationship between reorganisation energy and asynchronicity is found; (ii) the asynchronicity is the origin of deviations of this classical principle of chemical reactivity since any decrease of the energy barrier is due to an increase of asynchronicity at the same exothermicity; and (iii) the less exothermic the reaction is, the more asynchronous the mechanism is, at the same energy barrier. Thus, this implies that TS imbalance decreases the reorganisation energy, consequently affecting the reaction exothermicity as well.

New Insights into the (A)Synchronicity of Diels–Alder Reactions: A Theoretical Study Based on the Reaction Force Analysis and Atomic Resolution of Energy Derivatives

In the present manuscript, we report new insights into the concept of (a)synchronicity in Diels–Alder (DA) reactions in the framework of the reaction force analysis in conjunction with natural population calculations and the atomic resolution of energy derivatives along the intrinsic reaction coordinate (IRC) path. Our findings suggest that the DA reaction transitions from a preferentially concerted mechanism to a stepwise one in a 0.10 Å window of synchronicity indices ranging from 0.90 to 1.00 Å. We have also shown that the relative position of the global minimum of the reaction force constant with respect to the TS is an alternative and quantifiable indicator of the (a)synchronicity in DA reactions. Moreover, the atomic resolution of energy derivatives reveals that the mechanism of the DA reaction involves two inner elementary processes associated with the formation of each of the two C-C bonds. This resolution goes on to indicate that, in asynchronous reactions, the driving and retarding components of the reaction force are mostly due to the fast and slow-forming C-C bonds (elementary processes) respectively, while in synchronous reactions, both elementary processes retard and drive the process concomitantly and equivalently.

The Phosphorus Bond, or the Phosphorus-Centered Pnictogen Bond: The Covalently Bound Phosphorus Atom in Molecular Entities and Crystals as a Pnictogen Bond Donor

The phosphorus bond in chemical systems, which is an inter- or intramolecular noncovalent interaction, occurs when there is evidence of a net attractive interaction between an electrophilic region associated with a covalently or coordinately bonded phosphorus atom in a molecular entity and a nucleophile in another, or the same, molecular entity. It is the second member of the family of pnictogen bonds, formed by the second member of the pnictogen family of the periodic table. In this overview, we provide the reader with a snapshot of the nature, and possible occurrences, of phosphorus-centered pnictogen bonding in illustrative chemical crystal systems drawn from the ICSD (Inorganic Crystal Structure Database) and CSD (Cambridge Structural Database) databases, some of which date back to the latter part of the last century. The illustrative systems discussed are expected to assist as a guide to researchers in rationalizing phosphorus-centered pnictogen bonding in the rational design of molecular complexes, crystals, and materials and their subsequent characterization.

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.

Diels-Alder reaction mechanisms of substituted chiral anthracene: A theoretical study based on the reaction force and reaction electronic flux

Quantum chemical calculations were used to study the mechanism of Diels-Alder reactions involving chiral anthracenes as dienes and a series of dienophiles. The reaction force analysis was employed to obtain a detailed scrutiny of the reaction mechanisms, it has been found that thermodynamics and kinetics of the reactions are quite consistent: the lower the activation energy, the lower the reaction energy, thus following the Bell-Evans-Polanyi principle. It has been found that activation energies are mostly due to structural rearrangements that in most cases represented more than 70% of the activation energy. Electronic activity mostly due to changes in σ and π bonding were revealed by the reaction electronic flux (REF), this property helps identify whether changes on σ or π bonding drive the reaction. Additionally, new global indexes describing the behavior of the electronic activity were introduced and then used to classify the reactions in terms of the spontaneity of their electronic activity. Local natural bond order electronic population analysis was used to check consistency with global REF through the characterization of specific changes in the electronic density that might be responsible for the activity already detected by the REF. Results show that reactions involving acetoxy lactones are driven by spontaneous electronic activity coming from bond forming/strengthening processes; in the case of maleic anhydrides and maleimides it appears that both spontaneous and non-spontaneous electronic activity are quite active in driving the reactions.

Real-Space Approach to the Reaction Force: Understanding the Origin of Synchronicity/Nonsynchronicity in Multibond Chemical Reactions

In this article, we present a complementary analysis based on the reaction force F(ξ)/reaction force constant κ(ξ) and noncovalent interactions (NCI) index to characterize the energetics (kinetic and thermodynamics) and mechanistic pathways of two sets of multibond chemical reactions, namely, two double-proton transfer and two Diels-Alder cycloaddition reactions. This approach offers a very straightforward and useful way to delve into a deeper understanding of this type of process. While F(ξ) allows the partition of the whole pathway into three regions or phases, κ(ξ) describes how orchestrated are the bond-breaking and bond-formation events. In turn, NCI indicates how the inter- and intramolecular bonds evolve. The most innovative aspect is the inclusion of the formation of the reactant complex along the pathway, which, by means of NCI, unveils the early molecular recognition and the comprehension of its role in determining the degree of the synchronicity/nonsynchronicity of one-step processes. This approach should be a useful and alternative tool to characterize the energetics and the mechanism of general chemical reactions.

Theoretical Study of the Mechanism of Catalytic Enanteoselective N-H and O-H Insertion Reactions

Theoretical density functional theory (DFT) calculations were carried out to study bond insertion reactions using a copper(I)-Box-carbenoid as a bond activator. In order to understand the reaction mechanism where N-H and O-H bonds actively participate, the reaction force (RF) and activation strain model (ASM) were used. Results indicate that the first step of the reaction is barrierless for both bond insertions (N-H and O-H), and the second step of the insertion reaction in the phenol (O-H bond) is favored kinetically and thermodynamically with regard to the aniline substrate (N-H bond). The enantioselectivity is driven by the ligand of the catalyst by steric repulsion, favoring the formation of the R isomer. The analysis of the reaction force and ASM exhibited that the higher energy barrier in aniline is mainly due to a higher W₂ contribution together with repulsive interactions, which hinders the insertion process.

Further understanding of the Ru-centered [2+2] cycloreversion/cycloaddition involved into the interconversion of ruthenacyclobutane using the Grubbs catalysts from a reaction force analysis

The chemical reactivity of the first- and second-generation Grubbs catalysts has always been a significant issue in olefin metathesis. In the present work, we study the [2+2] cycloreversion/cycloaddition and the alkylidene rotation involved into the interconversion of the ruthenacyclobutane intermediate, through the reaction force and reaction force constant analysis. It has been found that the structural contribution controls the barrier energy in the interconversion of ruthenacyclobutane via [2+2] cycloreversion/cycloaddition, which is slightly lower in the second generation of Grubbs catalysts while its electronic contribution is slightly higher, which unveils a major rigidity and donor/acceptor properties of the NHC. This finding explains a greater structural contribution in the rate constant. Moreover, on the basis of the reaction force constant, the process can be classified as "two-stage"-concerted reactions, noting a more asynchronous process when the first generation is used as a catalyst.Finally, a similar analysis into the alkylidene rotation was performed. It was determined that [2+2] cycloreversion and alkylidene rotations take place in a sequential manner, the energy barrier is again controlled by structural reorganization, and the pathway is less asynchronous.

Effect of the exchange–correlation functional on the synchronicity/nonsynchronicity in bond formation in Diels–Alder reactions: a reaction force constant analysis

The performance of 24 KS-DFT-based methods (GGA, MGGA, HGGA, HMGGA, and DHGGA) was assessed, finding that M11 and M06-2X (HMGGA) predicting reliable TS geometries, energetics, and (a)synchronicities in Diels–Alder reactions.

Mechanistic details of ethylene polymerization reaction using methallyl nickel(ii) catalysts

We present a mechanistic study of the ligand functionalization of bulky boron co-activators on neutral methallyl Ni(ii) catalysts for polyethylene production. This provides a blueprint for the development and design of catalysts with a high degree of tunability in a more efficient way.

Solvent effect on the degree of (a)synchronicity in polar Diels-Alder reactions from the perspective of the reaction force constant analysis

In this work, we computationally evaluated the influence of six different molecular solvents, described as a polarizable continuum model at the M06-2X/6-31+G(d,p) level, on the activation barrier/reaction rate, overall energy change, TS geometry, and degree of (a)synchronicity of two concerted Diels-Alder cycloadditions of acrolein (R1) and its complex with Lewis acid acrolein···BH₃ (R2) to cyclopentadiene. In gas-phase, we found that both exothermicity and activation barrier are only reduced by about 2.0 kcal mol^-1, and the asynchronicity character of the mechanism is accentuated when BH₃ is included. An increment in the solvent's polarity lowers the activation energy of R1 by 1.3 kcal mol^-1, while for R2 the reaction rate is enhanced by more than 2000 times at room temperature (i.e., the activation energy decreases by 4.5 kcal mol^-1) if the highest polar media is employed. Therefore, a synergistic effect is achieved when both external agents, i.e., Lewis acid catalyst and polar solvent, are included together. This effect was ascribed to the ability of the solvent to favor the encounter between cyclopentadiene and acrolein···BH₃. This was validated by the asymmetry of the TS which becomes highly pronounced when either both or just BH₃ is considered or the solvent's polarity is increased. Finally, the reaction force constant κ(ξ) reveals that an increment in the solvent's polarity is able to turn a moderate asynchronous mechanism of the formation of the new C-C σ-bonds into a highly asynchronous one. Graphical abstract A synergistic effect is achieved when both external agents, i.e., Lewis acid catalyst and polar solvent, are included together: lowered energy barriers and increased asynchronicities.

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.

Can an entirely negative fluorine in a molecule, viz. perfluorobenzene, interact attractively with the entirely negative site(s) on another molecule(s)? Like liking like!

The study presents the possibility for the formation of attractive intermolecular interactions between various entirely negative Lewis bases, leading to the formation of the thirteen isolated binary complexes examined.