Reaction force analysis
A chemical reaction is mainly expressed in terms of geometrical changes
of structural parameters and rearranging of the electron densities
involved in the chemical process. But, the relative energy profile does
not give us complete information about the chemical reaction. Hence, the
reaction force concept is applied for finding structural and electronic
changes existing along the complete chemical reaction process[32–35]. The reaction force F(ξ)[36] is defined as
\(F\left(\xi\right)=-\frac{\text{dE}}{\text{dξ}}\) (5)
On the other hand, the reaction force profile provides an energy
partition of the activation and reaction energies Δ\(E^{\neq}\) and
Δ\(E\) respectively. Therefore (ΔE°) and
(Δ\(E^{\neq}\)) takes the following form [37–39]
\(\left(\text{ΔE}\right)=W_{1}+W_{2}+W_{3}+W_{4}\) (6)
\(\left(\Delta E^{\neq}\right)=W_{1}+W_{2}\) (7)
From equation (6) and (7), W1, W2,
W3, and W4 are the reaction works
involved in the mechanism.
\begin{equation}
W_{1}=-\int_{\xi_{R}}^{\xi_{1}}{F\left(\xi\right)d\xi>0}\text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }W_{2}=-\int_{\xi_{1}}^{\xi_{\text{TS}}}{F\left(\xi\right)d\xi>0}\nonumber \\
\end{equation}\begin{equation}
W_{3}=-\int_{\xi_{\text{TS}}}^{\xi_{2}}{F\left(\xi\right)d\xi<0}\text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }W_{4}=-\int_{\xi_{2}}^{\xi_{p}}{F\left(\xi\right)d\xi<0}\nonumber \\
\end{equation}