Solvent reaction coordinate

Abstract A mixed molecular orbital and valence bond (MOVE) method has been developed and applied to chemical reactions. In the MOVE method, a diabatic or valence bond (VE) state is defined with a block-localized wave function (ELW). Consequently, the adiabatic state can be described by the superposition of a set of critical adiabatic states. Test cases indicate the method is a viable alternative to the empirical valence bond (EVE) approach for defining solvent reaction coordinate in the combined qnantum mechanical and molecnlar mechanical (QM/MM) simulations employing exphcit molecular orbital methods. 

Therefore, X can be conveniently used to monitor the progress of the chemical reaction in the solvent reaction coordinate. Clearly, there is no single reactant structure that defines the transition state, rather, an ensemble of transition states will be obtained from the simulation, which may contain solute geometries... 

The second approach is to include explicitly solvent coordinates in the definition of the reaction coordinate because non-equilibrium solvation and solvent dynamics can play an important role in the chemical process in solution.13 A molecular dynamics simulation study of the proton transfer reaction [HO- -H- OH] in water indicated that there is considerable difference in the qualitative appearance of the free energy profile and the height of the predicted free energy barrier if the solvent reaction coordinate is explicitly taken into account.13... 

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... 

Fig. 5 Computed potential of mean force for the reaction of Cl- + CH3SHj in water along the energy-gap solvent reaction coordinate.

Figure 7 shows the free energy profile as a function of the energy-gap solvent reaction coordinate, which is compared with the PMF as a function of XR. The computed w(Xs) also has a unimodal shape and the estimated free energy barrier is 16.1 kcal/mol, in good agreement with the value from Fig. 6. Thus, for the Type 4 reaction, the use of a geometrical and a solvent reaction coordinate does not affect...

Fig. 8 Variation of the solute reaction coordinate that has been sampled by the energy-gap reference potential for the SN2 reaction of H3N + CH3SH2 in water. The figure shows that geometrical variations are closely correlated with the change of the solvent reaction coordinate.

We have described a mixed MOVB model for describing the potential energy surface of reactive systems, and presented results from applications to SN2 reactions in aqueous solution. The MOVB model is based on a BLW method to define diabatic electronic state functions. Then, a configuration interaction Hamiltonian is constructed using these diabatic VB states as basis functions. The computed geometrical and energetic results for these systems are in accord with previous experimental and theoretical studies. These studies show that the MOVB model can be adequately used as a mapping potential to derive solvent reaction coordinates for... 

We begin with an overview of the total free energy of the reacting system versus the solvent reaction coordinate, which can be usefully decomposed into two basic contributions [3, 7], as shown in Fig. 10.3(b),... 

Here AiS - AEi is the solvent reaction coordinate distance between the TS and reactant, and AE - AE is the corresponding distance between the product and reactant, (cp) is the quantum average over the proton and H-bond vibrations of Cp, the limiting product contribution to the electronic structure. The electronic structure for each critical point (c = R, P, and ) is evaluated at the respective critical point position AE (AE = AEp, AEp, or A ) along the reaction coordinate. The structural element is the quantum-averaged proton distance (over both... 

The isotope dependence of the Bronsted slope is most conveniently discussed in terms of the derivative of the expression involving force constants Eq. (10.14). These force constants certainly depend on the variation of the ZPE along the solvent reaction coordinate via Eq. (10.8). Accordingly, a can be cast in terms of these slopes plus the variation in the ZPE value at the reactant and TS positions with reaction asymmetry [4]. Since the ZPE variation is largest in the TS region, the first term in Eq. (10.14) is the most significant, and thus, the essential point is that the isotope difference is approximately proportional to... 

Figure 10.14 Proton diabatic free energy curves versus the solvent reaction coordinate for individual reactant (n ) and product (rip) proton vibrational states. Several transitions are qualitatively indicated.

Figure 3.6. Frozen solvent reaction coordinate potentials for aqueous C1 +CH3C1 reaction near standard conditions versus y = x — xK As in Figure 3.5A, the instantaneous potential V(S, x) is the sum of the gas phase potential U x) and the cage potential v S x) U x) is that of Figure 3.2 and v S x) is estimated [23] from the molcular dynamics results of ref. 14a. The parabolic approximation to V S x) of Eq. (3.48) is also shown.

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