Reaction coordinate defined

The reaction coordinate defined in Section 2.8 provides an algebraic method for calculating equilibrium concentrations. For a single reaction. 

The dashed line in Fig. 10.1.1 shows, in the gas phase, a calculation at the Hartree-Fock (HF) level with a 6-31G basis set. The electronic energies correspond to a minimum-energy path with a reaction coordinate defined as rc = rccv — reel, where rc = 0 corresponds to the activated complex (Cl CH3 Cl ). The minimum-energy path is optimized in Csv symmetry for fixed values of rc. 

In a simulation performed to model a chemical reaction, the parameter A corresponds to an arbitrarily chosen reaction coordinate, such as a bond length, an angle, a torsion, or a combination of these parameters. Such a reaction coordinate defines a constraint in configurational space. Constrained dynamics36 at finite temperature can be performed for a series of fixed A values, corresponding to a transition from the reactants to the product through the respective TS. 

Figure 6.3 Potential energy surface for Reaction 6.2. The energies are in kilocalories per mole and the reaction coordinate (defined as the difference between the two C-Cl distances) is in angstrom.

The degree of charge transfer is not linearly related to the reaction coordinate defined above (Section 1.3.1). 

Chorismate mutase provides an example of an enzyme where QM/MM calculations have identified an important catalytic principle at work [8], This enzyme catalyses the Claisen rearrangement of chorismate to prephenate. The reaction within the enzyme is not believed to involve chemical catalysis, and this pericylic reaction also occurs readily in solution. Lyne et al. [8] investigated the reaction in chorismate mutase in QM/MM calculations, at the AMI QM level (AMI was found to perform acceptably well for this reaction in comparisons with ab initio results for the reaction in the gas phase [8]). Different sizes of QM system were tested in the QM/MM studies (e.g. including the substrate and no, or up to three, protein side chains), and similar results found in all cases. The reaction was modelled by minimization along an approximate reaction coordinate, defined as the ratio of the forming C-C and breaking C-0 bonds. Values of the reaction coordinate were taken from the AMI intrinsic reaction coordinate for the gas-phase reaction. 

The values of Eg (st), t = 1, - , n provides a first estimate of the free energy along the LFEP. This potential is used as a bias to perform a onedimensional umbrella sampling along the generalized reaction coordinate defined by the LFEP [5,7]. The forces on the atoms of position r due to the umbrella potential are... 

A reaction coordinate, defining the barrier to reaction (activation energy) as well as the energy difference between reactants (initial state) and products (final state) or reaction energy. 

In the classical limit (hcoj k T), the reaction coordinate X t) in each quantum state can be described as a Gaussian stochastic process [203]. It is Gaussian because of the assumed linear response. As follows from the discussion in Section II.A, if the collective solvent polarization follows the linear response, the ET system can be effectively represented by two sets of harmonic oscillators with the same frequencies but different equilibrium positions corresponding to the initial and final electronic states [26, 203]. The reaction coordinate, defined as the energy difference between the reactant and the product states, is a linear combination of the oscillator coordinates, that is, it is a linear combination of harmonic functions and is, therefore, Gaussian. The mean value is = — , for state 1 and = , for state 2, respectively. We can represent Xi(r) and X2 t) in terms of a single Gaussian stochastic process x(t) with zero mean as follows ... 

In the high-temperature range (T>2T ) the most probable reaction path is the dynamically non-separable classical reaction coordinate defined by equation (203 11), which corresponds to the re-... 

That such reaction path dependent density enhancements can have a significant effect on free energy of activation barriers in compressible SCFs is shown in Fig. 7. There we present the reaction-path-dependent free energy of solvation (zeroed to the reactant value) for the symmetric Cl + CH3CI S 2 exchange reaction in supercritical water at 1.0 and pr 0.5 as a function of the reaction coordinate (defined as the difference between the two Cl-C bond lengths) rc = 0 denotes the transition state, while = 8.0X is taken as the reactant (product). The squares represent the free energies of solvation computed from a standard incompressible continuum model. 

Fig. 23 Free energy G(q, F t) as a function of the reaction coordinate defined as the pulling direction for various values of the applied force. For larger applied force, the right-hand B minimum becomes deeper dashed and dotted lines) and the equilibrium constant K Fex,t) decreases. Reprinted with permission from [108]. Copyright 2010 by the American Physical Society...

The full reaction path given by eq. (6.81) can also be compared with the MEP of the DMBE PES, Figure 6.10, using the distance along the reaction coordinate defined as... 

As discussed above, a good reaction coordinate needs to parametrize the committor, i.e., configurations with a particular value of the reaction coordinate should all have the same committor. Therefore, isosnrfaces of the reaction coordinate defined by q r) = constant should coincide, at least where they are mostly populated, with the corresponding isocommittor surfaces. This is something that can be easily tested by determining the probability distribution P(pb) of the committor for equilibrium-weighted configurations with a particular value q of the reaction coordinate [25] ... 

The normalized projection of this vector onto the normal modes at location s along the reaction coordinate defines the p mode for this straight-line path and is given by... 

---