Computational analysis of the mechanism of chemical reactions in terms of reaction phases: hidden intermediates and hidden transition States.

Computational approaches to understanding chemical reaction mechanisms generally begin by establishing the relative energies of the starting materials, transition state, and products, that is, the stationary points on the potential energy surface of the reaction complex. Examining the intervening species via the intrinsic reaction coordinate (IRC) offers further insight into the fate of the reactants by delineating, step-by-step, the energetics involved along the reaction path between the stationary states. For a detailed analysis of the mechanism and dynamics of a chemical reaction, the reaction path Hamiltonian (RPH) and the united reaction valley approach (URVA) are an efficient combination. The chemical conversion of the reaction complex is reflected by the changes in the reaction path direction t(s) and reaction path curvature k(s), both expressed as a function of the path length s. This information can be used to partition the reaction path, and by this the reaction mechanism, of a chemical reaction into reaction phases describing chemically relevant changes of the reaction complex: (i) a contact phase characterized by van der Waals interactions, (ii) a preparation phase, in which the reactants prepare for the chemical processes, (iii) one or more transition state phases, in which the chemical processes of bond cleavage and bond formation take place, (iv) a product adjustment phase, and (v) a separation phase. In this Account, we examine mechanistic analysis with URVA in detail, focusing on recent theoretical insights (with a variety of reaction types) from our laboratories. Through the utilization of the concept of localized adiabatic vibrational modes that are associated with the internal coordinates, q(n)(s), of the reaction complex, the chemical character of each reaction phase can be identified via the adiabatic curvature coupling coefficients, A(n,s)(s). These quantities reveal whether a local adiabatic vibrational mode supports (A(n,s) > 0) or resists (A(n,s) < 0) the curving of the path, and thus the structural changes of the reaction complex. URVA can show the mechanism of a reaction expressed in terms of reaction phases, revealing the sequence of chemical processes in the reaction complex and making it possible to determine those electronic factors that control the mechanism and energetics of the reaction. The magnitude of adiabatic curvature coupling coefficients is related to strength and polarizability of the bonds being broken. Transient points along the reaction path are associated with hidden intermediates and hidden transition states, which can be converted into real intermediates and transition states when the reaction conditions or the substitution pattern of the reaction complex are appropriately changed. Accordingly, URVA represents a theoretical tool with tremendous experimental potential, offering the chemist the ability to assert greater control over reactions.