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

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.