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Two atoms or molecules may react in many different ways (reaction channels). Even if at some conditions they do not react (e.g., the noble gases), the reason for this is that their kinetic energy is too low with respect to the corresponding reaction barrier, and the opening of their electronic closed shells is prohibitively expensive in the energy scale. If the kinetic energy increases, more and more reaction channels open up, because it is possible for higher and higher energy barriers to be overcome. Simplest chemical reactions correspond to no reaction barrier. However, for most reactants (ground-state closed-shell molecules) there is a single reaction barrier to overcome on the way from reactants to products through saddle point along the intrinsic reaction coordinate (IRC). The IRC corresponds to the steepest descent trajectory (in the mass-weighted coordinates) from the saddle point to configurations of reactants and products. Such a process may be described as the system passing from the entrance channel (reactants) to the exit channel (products) on the electronic energy map as a function of the nuclear coordinates. For reaction A+BC→AB+CA+BC→AB+C the map shows a characteristic reaction “drain-pipe”. Passing along the “drain-pipe” bottom usually requires overcoming a reaction barrier, its height being a fraction of the energy of breaking the “old” chemical bond. It is shown how to obtain accurate solution for three atomic reaction. After introducing the hyperspherical democratic coordinates it is possible to solve the Schrodinger equation (within the Ritz approach). We obtain the rate constant for the state-to-state elementary chemical reaction. For large systems such calculations are prohibitively expensive. However, a chemical reaction may be also described by the reaction path Hamiltonian method. In this method one focuses on the intrinsic reaction coordinate (IRC) measuring the motion along the “drain-pipe” bottom (reaction path) and the normal mode coordinates orthogonal to the IRC. During the reaction, energy may be exchanged between the vibrational normal modes, as well as between the vibrational modes and the motion along the IRC. Still another simple model of chemical reactions is presented, in which as the reactants’ one has an electron donor (D) and an electron acceptor (A). The molecular orbital picture of the reaction is rewritten in terms of the donor and acceptor orbitals. This approach (intermediate between the MO and VB) makes it possible to characterize the reaction path in terms of the chemical species involved. It turns out that independent of whether we consider the electrophilic or the nucleophilic substitution the chemical mechanism is very similar. On the reactants’ side one has the DA structure (no electron transfer between the donor and acceptor), while at the intermediate stage one has a superposition of the DA and D+A-D+A- (a single donor electron is already transferred to the empty antibonding acceptor orbital), structures. Finally, the product stage is in many cases best described by D+A-D+A-, D+A-∗D+A-∗ (the donor electron transferred occupies the already singly occupied antibonding acceptor orbital), and D2+A2-D2+A2- (two donor electrons are transferred to the antibonding acceptor orbital). A reaction barrier is a consequence of the “quasi-avoided crossing” of the corresponding diabatic hypersurfaces, as a result we obtain two adiabatic hypersurfaces (“lower” or electronic ground state, and “upper ” or electronic excited state). Each of the adiabatic hypersurfaces consists of two diabatic parts stitched along the border passing through the conical intersection point. On both sides of the conical intersection there are often two saddle points along the border line leading in general to two different reaction products. The two intersecting diabatic hypersurfaces (at the reactant configuration) represent the electronic ground-state DA and that electronic excited state that resembles the electronic charge distribution of the products, usually D+A-D+A-. The barrier appears therefore as the cost of opening the closed shell in such a way as to prepare the reactants for the formation of new bond(s). Some reactions are symmetry forbidden (Woodward-Hoffmann rules), because of the unfavorable amplitudes of the key molecular orbitals and the resulting high reaction barrier. In Marcus electron transfer theory, the barrier also arises as a consequence of the intersection of the two diabatic potential energy curves (taken in this model as parabolas). The barrier height depends on the reorganization energy (of the solvent and reactant) and the driving force, which is the difference in free energy between the products and the reactants. There is a surprise: too large driving force may make the reaction more difficult. |
