## Locating transit state ### Dimer method Nice day's create a timer, evaluate at both ends, rotate and translate to minimize. The dimmer energy (i.e., its direction along the most unstable mode or lowest curvature mode, *minimum force direction*) Then reversed the force along dimer direction, translated to saddle points. ![[Drawing 2023-09-27 21.50.44.excalidraw.svg]] >[!Note] > This method does not need initial/final points (i.e. reactant and products) and Hessians. ### Band method This is the method to find minimal energy path, which passes through the saddle point. It connects the images with springs and when natural length of the spring $\rightarrow 0$ and set target function for certain of certain form ($E_k$), Then the final configuration of the chain would be MEP. - A problem with this is *corner cutting*. It cannot sample the saddle point at the corner. This is due to the component of the spring force, which is perpendicular to the path, tend to pull the image of the MEP. >[!Notice] >MEP is minimum energy path. $E_k$ is a summation of potential (from [[Potential energy surface]]) energy and harmonic oscillator energy. And to get minimum $E_k$ we get minimum action. > This method gets its name for its good parallel to the elastic band. ![[Drawing 2023-09-27 22.10.12.excalidraw.svg]] ### NEB, nudged elastic band Here we change the minimization function, to compute only the force along the spring and the force perpendicular to the potential gradient, i.e., $\vec{F_i^o}=-\nabla V(R_i)|_\perp + \vec{F_i^s}\cdot\tau_\parallel\tau_\parallel$ >[!Note] >$\nabla V(R_i)$ is potential perpendicular. >$\vec{F_i^s}$ is spring force. >$\tau_\parallel$ gives parallel, or say, tangential result. Problem: College of the two reactant/product are important. (must be known) ### Improved NEB Clever choice of tangent of spring may lead to better convergence.