Diabatic energy hypersurfaces

The diabatic potential-energy hypersurfaces U(Q [([).]) are of use to examine the energy reshuffling in neighborhoods of a crossing point Q, where U(Q [([)]]) = U(Q [(t)j>]). This may look like a conic intersection but it should not be confused with that the domain where this condition holds can be named a seam as it is common practice in the adiabatic scheme, see vol.127 of Faraday Discussions... 

A rigorous electro-nuclear separability scheme has been examined. Therein, an equivalent positive charge background replaces the nuclear configuration space the coordinates of which form, in real space, the -space. Diabatic potential energy hypersurfaces for isomers of ethylene in -space were calculated by adapting standard quantum chemical packages. 

The barrier always results from the intersection of diabatic potential energy hypersurfaces. We may think of diabatic states as preserving the electronic state (e.g., the qfstem of chemical bonds) I and II, respectively. 

The conical intersection plays a fundamental role in the theory of chemical reactions (Chapter 14). The lower (ground-state) as well as the higher (excited-state) hypersurfaces are composed of two diabatic parts, which in polyatomics correspond to different patterns of chemical bonds. This means that the system (represented by a point) when moving on the ground-state adiabatic hypersurface toward the join of the two parts, passes near the conical intersection point, over the energy barrier, and goes to the products. This is the essence of a chemical reaction. 

Reaction barriers appear because the reactants have to open their valence shells and prepare the electronic structure to he able to form new bonds. This means that their energy goes up until the right excited structure lowers its energy so much that the system slides down the new diabatic hypersurface to the product configuration. 

Fig. 14.27. Electron transfer in the reaction DA D+A , as well as the relation of the Marcus parabolas to the concepts of the conical intersection, diabatic and adiabatic states, entrance and exit channels and the reaction barrier. Panel (a) shows two diabatic surfaces as functions of the f i and I2 variables that describe the deviation from the comical intersection point (within the bifurcation plane cf., p. 312). Both surfaces are shown schematically in the form of the two intasecting paraboloids one for the reactants (DA), and the second for products (D A ). (b) The same as (a), but the hypersurfaces are presented more realistically. The upper and lower adiabatic surfaces touch at the conical intersection point, (c) A ma-e detailed view of the same surfaces. On the ground-state adiabatic surface (the lower one), we can see two reaction channels I and 11, each with its reaction barrier. On the upper adiabatic surface, an energy valley is visible that symbolizes a bound state that is separated from the conical intersection by a reaction barrier, (d) The Marcus parabolas represent the sections of the diabatic surfaces along the corresponding reaction channel, at a certain distance from the conical intersection. Hence, the parabolas in reality cannot intersect (undergo an avoided crossing).

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