Diabatic Energy Surfaces

Since the TS is given in terms of the diabatic energy surfaces for the reactant and product, it is also clear that activation energies will be too high. For evaluating relative"... 

In these sections the classical, semiclassical, and quantum-mechanical models of electron transfer are outlined. In all three treatments the nuclear factors determining the rate are calculated using the zero-order or diabatic-energy surfaces. Interaction of these surfaces is necessary for the electronic factor to be nonzero. This interaction is introduced as a correction to the zero-order surfaces and determines the degree of adiabaticity of the reaction. 

BJ theory replaces the classically derived energy surfaces and transition-state model of the MH treatment (Figs. 1 and 2) with a quantum-mechanical tunneling model. The BJ diabatic energy surfaces are shown in Fig. 990 Only the solvent is treated classically, and the X-axis now only represents solvent reorganization. Both energy... 

Fig. 11. Intersection of diabatic energy surfaces for hydrogen moving 1.1 A above a rigid atlyl radical framework. The full grid corresponds to the closed-shell surface (packet A) and the broken grid to the diradical surface (packet B). (Reprinted with permission from Bernardi et al. Copyright 1984 American Chemical Society.)...

In Section 4.7.1, we found that if the diabatic energy surfaces, Hu and H22, interact with the interaction matrix element, H12, we may approximately write the secular equation... 

States Definition, Computation, and Applications). Methods for the ab initio computation of diabatic electronic energy surfaces and coupling elements are available (see, e.g.. Ref. 19 and references therein), although complete ab initio calculations of multi-dimensional diabatic energy surfaces are still scarce. 

Here the transition state is approximated by the lowest crossing pomt on the seam intersecting the diabatic (non-interacting) potential energy surfaces of the reactant and product. The method was originally developed... 

At this point, it is important to note that as the potential energy surfaces are even in the vibrational coordinate (r), the same parity, that is, even even and odd odd transitions should be allowed both for nonreactive and reactive cases but due to the conical intersection, the diabatic calculations indicate that the allowed transition for the reactive case ate odd even and even odd whereas in the case of nomeactive transitions even even and odd odd remain allowed. 

The adiabatic picture is the standard one in quantum chemistry for the reason that, not only is it mathematically well defined, but it is also that used in ab initio calculations, which solve the electronic Hamiltonian at a particular nuclear geometry. To see the effects of vibronic coupling on the potential energy surfaces one must move to what is called a diabatic representation [1,65,180, 181]. 

H3 (and its isotopomers) and the alkali metal triiners (denoted generally for the homonuclears by X3, where X is an atom) are typical Jahn-Teller systems where the two lowest adiabatic potential energy surfaces conically intersect. Since such manifolds of electronic states have recently been discussed [60] in some detail, we review in this section only the diabatic representation of such surfaces and their major topographical details. The relevant 2x2 diabatic potential matrix W assumes the fomi... 

In Chapter VI, Ohm and Deumens present their electron nuclear dynamics (END) time-dependent, nonadiabatic, theoretical, and computational approach to the study of molecular processes. This approach stresses the analysis of such processes in terms of dynamical, time-evolving states rather than stationary molecular states. Thus, rovibrational and scattering states are reduced to less prominent roles as is the case in most modem wavepacket treatments of molecular reaction dynamics. Unlike most theoretical methods, END also relegates electronic stationary states, potential energy surfaces, adiabatic and diabatic descriptions, and nonadiabatic coupling terms to the background in favor of a dynamic, time-evolving description of all electrons. 

The previous treatment relied on the assumption that the transition occurs on a single potential energy surface V(x) characterized by a barrier separating two wells. This potential is actually created from the terms of the initial and final electronic states. The separation of electron and nuclear coordinates in each of these states gives rise to the diabatic basis with nondiagonal Hamiltonian matrix... 

On the potential energy surfaces thus obtained 2D wavepacket dynamics calculations have been performed in the diabatic state representation. The reduced massses are regarded as those of CH2-ethylene system. The validity was examined by using on-the-fly ab initio molecular dynamics that were supplementarily performed. The dynamics calculations performed are composed of the following steps ... 

Let us consider the possible relations of LS and HS potential energy surfaces as shown schematically in Fig. 9. As long as the zero-order or diabatic surfaces are considered, the eleetrons remain localized on the particular spin state, no eleetron transfer being possible. In order that a conversion between the LS and HS state takes place, electronic coupling of the states is required. This coupling effectively removes the degeneracy at the interseetion of the zero-order surfaces... 

While MOVB can yield reasonable energetic results and an excellent description of the overall potential energy surface on diabatic states and the adiabatic ground... 

Song L, Gao J (2008) On the construction of diabatic and adiabatic potential energy surfaces based on ab initio valence bond theory. J Phys Chem A ASAP... 

Figure 11-1. Cartoon of ground and excited state potential energy surfaces, indicating points where nona-diabatic transitions can occur...

Introducing the diabatic free energy surfaces of the initial and final states,... 

Figure 6. Diabatic potential energy surfaces for electron transfer reactions in the system AL/B.

---