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

Description of changes in chemical bonding along the pathways of chemical reactions by deformation of the molecular electrostatic potential

CONTEXT

The analysis of the changes in the electronic structure along intrinsic reaction coordinate (IRC) paths for model reactions: (i) ethylene + butadiene cycloaddition, (ii) prototype SN2 reaction Cl- + CH3Cl, (iii) HCN/CNH isomerization assisted by water, (iv) CO + HF → C(O)HF was performed, in terms of changes in the deformation density (Δr) and the deformation of MEP (ΔMEP). The main goal was to further examine the utility of the ΔMEP as a descriptor of chemical bonding, and to compare the pictures resulting from Δr and ΔMEP. Both approaches clearly show that the main changes in the electronic structure occur in the TS region. The ΔMEP picture is fully consistent with that based on Δρ for the reactions of the neutral species leading to the neutral products without large charge transfer between the fragments. In the case of reactions with large electron density displacements, the ΔMEP picture is dominated by charge transfer leading to more clear indication of charge shifts than the analysis of Δr.

METHODS

All the calculations were performed using the ADF package. The Becke-Perdew exchange-correlation functional was used with the Grimme's dispersion correction (D3 version) with Becke-Johnson damping. The Slater TZP basis sets defined within the ADF program were applied. For the analysed reactions, the stationary points were determined and verified by frequency calculations, and the IRC was determined. Further analysis was performed for the structures of reactants, TS, products, and the points corresponding to the minimum and maximum of the reaction force. For each point, two fragments, A and B, corresponding to the reactants were considered. The deformation density was calculated as the difference between the electron density of the system AB and the sum of densities of A and B, Δ ρ r = ρ AB r - ρ A r - ρ B r , with the same fragment definition as in the ETS-NOCV method. Correspondingly, deformation in MEP was determined as Δ V r = V AB r - V A r - V B r .

Computer-aided design of caffeic acid derivatives: free radical scavenging activity and reaction force

CONTEXT

Antioxidants are known to play a beneficial role in human health. Caffeic acid has been previously recognized as efficient in this context. However, such a capability can be enhanced through structural modification. Thus, 3829 caffeic acid derivatives were computational designed to that purpose by adding functional groups (-OH, -SH, -OCH3, -COOCH3, -F, -CF3, and -N(CH3)(C2H5)) to its framework. Promising candidates were chosen considering drug-like behavior, toxicity, and synthetic accessibility. The best candidates, dCAF-2, dCAF-16, and dCAF-82, were identified by comparison with reference antioxidants. The thermochemistry and kinetics of their reaction with •OOH are provided. The global rate coefficients were estimated to be 1.76 × 109 M-1 s-1, 3.19 × 109 M-1 s-1, and 1.79 × 109 M-1 s-1 in aqueous solution for dCAF-2, dCAF-16, and dCAF-82, respectively. In lipid medium, their total rate coefficients were estimated to be 3.65 × 103 M-1 s-1, 3.73 × 103 M-1 s-1, and 8.63 × 104 M-1 s-1 for dCAF-2, dCAF-16, and dCAF-82, respectively. These values allow predicting the designed caffeic acid derivatives as excellent antioxidants in both environments. The reaction forces for the main reaction path of the dCAF-2, dCAF-16, and dCAF-82 reactions with •OOH were explored.

METHODS

Three protocols were used: (i) CADMA-Chem (computer-assisted design of multifunctional antioxidants, based on chemical properties) to quantify ADME (absorption, distribution, metabolism, and excretion) properties, toxicity and synthetic accessibility; (ii) eH-DAMA (electron and hydrogen donating ability map) tool, to identify the derivatives expected to behave as the best antioxidants; (iii) QM-ORSA (quantum mechanics-based test for overall free radical scavenging activity), to calculate the rate constants. Electronic structure calculations were performed with Gaussian 09, at the M05-2X/6-311 + g(d,p) level of theory. Both aqueous and lipid environments were considered using the SMD continuous solvation model. Intrinsic reaction coordinate (IRC) calculations, as implemented in Gaussian 09, were used to obtain the reaction force.

Towards a complete description of the reaction mechanisms between nitrenium ions and water

CONTEXT

Nitrenium ions are intermediates in the metabolic routes producing the highly carcinogenic nitrosamines and binding to DNA molecules. The reaction mechanism of nitrenium molecules with explicit water molecules is sensibly dependent on the number of waters: when a second molecule is involved, it acts as a catalyst for the reaction, lowering intrinsic activation barriers regardless of the substituent. For all cases, the reaction force constants and reaction electron flux indicate highly synchronous reactions for n = 1 . Conversely, for n = 2 highly non-synchronous reactions are obtained, involving two separate proton transfers happening early and late in the reaction path. As a test case, for the simplest[ NH 2 ] + + 2 H 2 O reactions, orbital interactions within the NBO paradigm, bond orders, and their derivatives indicate that each individual proton transfer is highly synchronous.

METHODS

Molecular geometries were optimized and characterized at the B3LYP/6-311++G(d, p) level. Intrinsic reaction coordinates were calculated. CCSD(T) single point energies with the same basis were computed on all stationary points. The reaction force, reaction force constant, and reaction electron flux are used to study the evolution of the reacting systems. Natural bond orbitals are used to understand the primitive changes driving the reaction.

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.

Transition from synchronous to asynchronous mechanisms in 1,3-dipolar cycloadditions: a polarizability perspective

CONTEXT

This study investigates the energetic and polarizability characteristics of three 1,3-dipolar cycloaddition reactions between diazene oxide and substituted ethylenes, focusing on the transition from synchronous to asynchronous mechanisms. Synchronicity analysis, using the reaction force constant, indicates that the bond evolution process becomes increasingly decoupled as the number of cyano groups increases. Polarizability analysis reveals that isotropic polarizability reaches its maximum near the transition state in all cases, while anisotropy of polarizability shifts from the transition state toward the product direction as asynchronicity increases. The larger the shift, the more asynchronous the mechanism, as reflected by the weight of the transition region. A detailed examination of the parallel and perpendicular polarizability components to the newly formed sigma bonds shows that the evolution of the parallel component is closely aligned with the energetic changes along the reaction coordinate, particularly in the synchronous reaction. We have also identified a relationship between the displacement in the maximum state of the parallel component from the transition state and the synchronicity of the mechanism. The larger the displacement, the more asynchronous the mechanism. These findings suggest that asynchronous 1,3-dipolar cycloaddition mechanisms are characterized by a decoupling of isotropic and anisotropic polarizabilities and a shift in the maximum polarizability state of the parallel component toward the product direction.

METHODS

Density functional theory calculations were performed at the B3LYP/6-311 +  + G(d,p)//B3LYP/6-31G(d,p) level of theory. The polarizability was calculated at each point of the reaction path, obtained using the intrinsic reaction coordinate method, as implemented in Gaussian 16.

The Ehrenfest force field: A perspective based on electron density functions

The topology of the Ehrenfest force field (EhF) is investigated as a tool for describing local interactions in molecules and intermolecular complexes. The EhF is obtained by integrating the electronic force operator over the coordinates of all but one electron, which requires knowledge of both the electron density and the reduced pair density. For stationary states, the EhF can also be obtained as minus the divergence of the kinetic stress tensor, although this approach leads to well-documented erroneous asymptotic behavior at large distances from the nuclei. It is shown that these pathologies disappear using the electron density functions and that the EhF thus obtained displays the correct behavior in real space, with no spurious critical points or attractors. Therefore, its critical points can be unambiguously obtained and classified. Test cases, including strained molecules, isomerization reactions, and intermolecular interactions, were analyzed. Various chemically relevant facts are highlighted: for example, non-nuclear attractors are generally absent, potential hydrogen-hydrogen interactions are detected in crowded systems, and a bifurcation mechanism is observed in the isomerization of HCN. Moreover, the EhF atomic basins are less charged than those of the electron density. Although integration of the EhF over regions of real space can also be performed to yield the corresponding atomic forces, several numerical drawbacks still need to be solved if electron density functions are to be used for that purpose. Overall, the results obtained support the Ehrenfest force field as a reliable descriptor for the definition of atomic basins and molecular structure.

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.

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.

Proton leap: shuttling of protons onto benzonitrile

The detailed description of chemical transformations in the interstellar medium allows deciphering the origin of a number of small and medium - sized organic molecules. We present density functional theory analysis of proton transfer from the trihydrogen cation and the ethenium cation to benzonitrile, a recently discovered species in the Taurus Molecular Cloud 1. Detailed energy transformations along the reaction paths were analyzed using the interacting quantum atoms methodology, which elucidated how the proton carrier influences the lightness to deliver the proton to benzonitrile's nitrogen atom. The proton carriers' deformation energy represents the largest destabilizing effect, whereas a proton's promotion energy, the benzonitrile-proton Coulomb attraction, as well as non-classical benzonitrile-proton and carrier-proton interaction are the dominant stabilizing energy components. As two ion-molecule reactions proceed without energy barriers, rate constants were estimated using the classical capture theory and were found to be an order of magnitude larger for the reaction with the trihydrogen cation compared to that with the ethenium cation (∼10^-8 and 10^-9 cm³ s^-1, respectively). These results were obtained both with quantum chemical and ab initio molecular dynamics simulations (the latter performed at 10 K and 100 K), confirming that up to 100 K both systems choose energetically undemanding routes by tracking the corresponding minimum energy paths. A concept of a turning point is introduced, which is an equivalent to the transition state in barrierless reactions.