Electronic energy density in chemical reaction systems

Abstract

The energy of chemical reaction is visualized in real space using the electronic energy density nE(r⃗) associated with the electron density n(r⃗). The electronic energy density nE(r⃗) is decomposed into the kinetic energy density nT(r⃗), the external potential energy density nV(r⃗), and the interelectron potential energy density nW(r⃗). Using the electronic energy density nE(r⃗) we can pick up any point in a chemical reaction system and find how the electronic energy E is assigned to the selected point. We can then integrate the electronic energy density nE(r⃗) in any region R surrounding the point and find out the regional electronic energy ER to the global E. The kinetic energy density nT(r⃗) is used to identify the intrinsic shape of the reactants, the electronic transition state, and the reaction products along the course of the chemical reaction coordinate. The intrinsic shape is identified with the electronic interface S that discriminates the region RD of the electronic drop from the region RA of the electronic atmosphere in the density distribution of the electron gas. If the R spans the whole space, then the integral gives the total E. The regional electronic energy ER in thermodynamic ensemble is realized in electrochemistry as the intrinsic Volta electric potential φR and the intrinsic Herring–Nichols work function ΦR. We have picked up first a hydrogen-like atom for which we have analytical exact expressions of the relativistic kinetic energy density nTM(r⃗) and its nonrelativistic version nT(r⃗). These expressions are valid for any excited bound states as well as the ground state. Second, we have selected the following five reaction systems and show the figures of the nT(r⃗) as well as the other energy densities along the intrinsic reaction coordinates: a protonation reaction to He, addition reactions of HF to C2H4 and C2H2, hydrogen abstraction reactions of NH3+ from HF and NH3. Valence electrons possess their unique delocalized drop region remote from those heavily localized drop regions adhered to core electrons. The kinetic energy density nT(r⃗) and the tension density τ⃗S(r⃗) can vividly demonstrate the formation of the chemical bond. Various basic chemical concepts in these chemical reaction systems have been clearly visualized in real three-dimensional space.