Effective diabatic states

Having defined the effective diabatic states, the wave function for a reacting system, Q[R. X], along the entire reaction path can be described by the resonance of these state functions ... 

The use of the energy-gap reaction coordinate allows us to calculate solvent reorganization energies in a way analogous to that in the Marcus theory for electron transfer reactions.19 The major difference here is that the diabatic states for electron transfer reactions are well-defined, whereas for chemical reactions, the definition of the effective diabatic states is not straightforward. The Marcus theory predicts that... 

In the empirical valence bond model [31], the potential energy surface is typically non-linearly related to two model states, called effective diabatic states corresponding to the reactant and the product bonding characters, Eq. 9. Although additional diabatic states, important for describing the transition state, can be included and have often been discussed, the computational complexity makes it difficult in practical use for the study of enzyme reactions. 

As written, Eq. (52) depends on all the (infinite number of) adiabatic electronic states. Fortunately, the inverse dependence of the coupling strength on energy separation means that it is possible to separate the complete set of states into manifolds that effectively do not interact with one another. In particular, Baer has recently shown [54] that Eq. (57), and hence Eq. (58) also holds in the subset of mutually coupled states. This Ending has important consequences for the use of diabatic states explored below. 

It is prerequisite to define localized, diabatic state wave fimctions, representing specific Lewis resonance configurations, in a VB-like method. Although this can in principle be done using an orbital localization technique, the difficulty is that these localization methods not only include orthorgonalization tails, but also include delocalization tails, which make contribution to the electronic delocalization effect and are not appropriate to describe diabatic potential energy surfaces. We have proposed to construct the locahzed diabatic state, or Lewis resonance structure, using a strictly block-localized wave function (BLW) method, which was developed recently for the study of electronic delocalization within a molecule.(28-3 1)... 

From a fundamental point of view, one may prefer to determine the electron donor-acceptor coupHng directly from diabatic states. This procedure has certain advantages [36], in particular when one is interested in a detailed investigation of electron correlation effects. Computational strategies that rely on adiabatic (delocahzed) states are in general simpler to apply and thus more common [27]. 

The solvent sensitivity of the diabatic quantities (//DA and AfiDA) is an interesting manifestation of a solvent-driven non-Condon effect, in which the solute polarizability, responding to the RF as the solvent is varied, changes the effective two-state electronic space used to model the ET process [29],... 

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). 

One of the most valuable features of theoretical methods based on classical VB structures is their ability to calculate the energy of a diabatic state. For practical uses, some diabatic bond energy curves of chemical interest can be, for example, the separate dissociation energy curves of the ionic and covalent components of a bond, or the energy curves of the effective VB structures of a... 

To express the collective solvent reaction coordinate as in equation (6), it is necessary to define the specific diabatic potential surface for the reactant and product state. This, however, is not a simple task, and there is no unique way of defining such diabatic states. What is needed is a method that allows the preservation of the formal charges of the fragments of reactant and product resonance states. At the same time, solvent effects can be incorporated into electronic structure calculations in molecular dynamics and Monte Carlo simulations. Recently, we developed a block-localized wave function (BLW) method for studying resonance stabilization, hyperconjugation effects, and interaction energy decomposition of organic molecules.20-23 The BLW method can be formulated to specify the effective VB states.14... 

Thus, for a given diabatic state, z is the free energy difference between the minimum energy point and the point corresponding to the minimum energy of the other state. The effective z value for the two-state system can be taken as the arithmetic mean of z, and z/ [47] (i.e., one-half of the Stokes shift for the optical ET process). 

Figure 4. Qualitative illustration of the effects of configurational mixing in an A D-A complex, a) Diabatic states with degenerate acceptors b) Effect of mixing between the three states it is assumed that only MLCTi mixes with the ground state.

Warshel and coworkers have employed the empirical valence-bond (EVB) method [49] to simulate FERs for PT [50] and other reactions [51]. The PT step between two water molecules in the mechanism of the reaction catalysed by carbonic anhy-drase was described as an effective two-state problem involving reactant-like (H0H)(0H2) and product-like (HO )(HOH2+) VB structures [50a], Diabatic energy curves for these two VB structures were calibrated to reproduce the experimental free energy change for autodissociation in water, and the mixing of the... 

For arbitrary triangles (the Q point group), the angle 6 is not uniquely defined, but can be obtained by an analysis of the wave function in a way similar to that used to construct the diabatic states from the adiabatic ones [180,181]. It should also be noted that for arbitrary trimer configurations, the resulting two A states are coupled nonadiabatically. This coupling can be viewed as a pure three-body effect. 

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