Diabatic states, energy profiles

Closely related to the above merit of VB methods, the unique definition of diabatic states also allows us to derive the energy profiles for diabatic states. Since for many reactions the whole process can be described with very few resonance structures, the comparison between the diabatic and adiabatic state energy profiles can yield insight into the nature governing the reactions [22-24]. In fact, even for complicated enzymatic reactions, simple VB ideas have shown unparalleled value [25, 26]. However, the further utilization of the VB ideas at the empirical and semi-empirical levels should be carefully verified by benchmark ab initio VB... 

The diabatic free energy profile for the electronic state D is defined by the equation... 

To illustrate this theory we calculate the diabatic free energy profiles F t)) and F t]) of a complex donor-acceptor solute in two solvents of different polarity. We also examine the dependence on the charge distribution of the 5 state. 

Fig. 1 The diabatic free energy profiles for NP and IP states, o ex-RISM results, dashed line 2nd order fitting profiles, solid line 4th order fitting profiles.

The diabatic free-energy profiles of the reactant and product states provide the microscopic equivalent of the Marcus parabolas.26,27 For example, in the case of the (Cl- + CH3-CI —> CICH3 + Cl-) Sn2 reaction, one obtains23 the results shown in Fig. 2. 

The diabatic free energy profiles of the reactant and product states provide the microscopic equivalent of the Marcus parabolas [29, 30]. 

Figure 11-9. CASSCF potential-energy profiles of the ground-state So (circles), the lnjr state (triangles), the Lb state (squares), and the La state (filled squares) of the 9H-adenine along the linear interpolation reaction path from the equilibrium geometry of the nit state to the CI32 (a) and CI16 (b) conical intersections. The diabatic correlation of the states is shown in (a). (From Ref. [138])...

Note that since the profile of the lower adiabatic potential energy surface for the proton depends on the coordinates of the medium molecules, the zeroth-order states and the diabatic potential energy surfaces depend also on the coordinates of the medium molecules. The double adiabatic approximation is essentially used here the electrons adiabatically follow the motion of all nuclei, while the proton zeroth-order states adiabatically follow the change of the positions of the medium molecules. 

Figure 3. Parabolic energy profiles of two diabatic states ( (/A, reactants J/b, products) along the reaction path, displaying the crossing energy, E°aiahaUc, and the splitting of the adiabatic states ( HAb at the crossing point).

Figure 3. Computed potential energy curves for the diabatic and adiabatic state in the [HsN-H-NH ] system in the gas phase using 6-31G(d) basis set. The HF and MOVE energy profiles are overlapping.

By performing the above procedures, the solvent effect is taken into account at the VBSCF level, whereby the orbitals and structural coefficients are optimized till self-consistency is achieved. Like VBSCF, the VBPCM method is suitable for diabatic states, which are calculated with the same solvent field as the one for the adiabatic state. Thus, it has the ability to compute the energy profile of the full state as well as that of individual VB structures throughout the course of a reaction, and in so doing to reveal the individual effects of solvent on the different constituents of the wave function. In this spirit, it has been used to perform a quantitative VBSCD analysis of a reaction that exhibits a marked solvent effect, the Sn2 reaction Cl- + CH3CI —> CH3CI + Cl- (55). 

Combination of Mulliken s formalism with the Marcus quadratic representation [10] of the initial and final (diabatic) states allows the energy profile of the ET reaction coordinate to be constructed. As illustrated in Figure 8, an increase in Hab results in (i) a lowering of the ET barrier, (ii) a stabilization of the precursor and successor (CT) complexes, and (iii) a shift of their positions along the reaction coordinate (i.e. the charge is partially transferred from the... 

In the case of adiabatic electron transfer reactions, it is found that the potential energy profiles of the reactant and product sub-systems merge smoothly in the vicinity of the activated complex, due to the resonance stabilization of electrons in the activated complex. Resonance stabilization occurs because the electrons have sufficient time to explore all the available superposed states. The net result is the attainment of a steady, high, probability of electron transfer. By contrast, in the case of -> nonadiabatic (diabatic) electron transfer reactions, resonance stabilization of the activated complex does not occur to any great extent. The result is a transient, low, probability of electron transfer. Compared with the adiabatic case, the visualization of nonadiabatic electron transfer in terms of potential energy profiles is more complex, and may be achieved in several different ways. However, in the most widely used conceptualization, potential energy profiles of the reactant and product states... 

Figure 1 Free energy profiles along the reaction coordinate (77) for the initial and final diabatic states, indicating the reorganization energy if), activation free energy (G ), and reaction driving force (—...

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