6.3 How to set the initial pathway in the VC-NEB calculation

The VC-NEB method is very efficient for finding the phase transition path, but we must also carefully prepare the initial path. The cell rotations happen near the initial and final structures during the VC-NEB calculation, where the pathway includes a lot of identical structures near the initial and finial images. To remove these useless rotations, our improved Variable-Image-Number method will prevent cell rotations automatically, which saves quite a lot of time.

Alternatively, you can apply the rotation-avoiding technique before you apply the VC-NEB method when generating the initial image set. The general $3 \times 3$ rotation matrix with Euler angles $R(\phi , \theta , \psi )$ and the lattice mirror operator $M(x, y, z)$ matrix are defined. Before performing a VC-NEB calculation, the global numerical search in space of Euler angles and mirror operator are used to find the minimal lattice cell transformation distance $\Delta h$:

  \begin{equation}  \Delta h = \left| {h_{initial} - R(\phi ,\theta ,\psi ) M(x,y,z)h_{final}}\right|. \end{equation}   (13)

The rotation-avoiding lattice vector of the final image $\tilde h_{final}$ is assigned as the endpoint image:

  \begin{equation}  \tilde h_{final} = R(\phi ,\theta ,\psi )M(x,y,z)h_{final}. \end{equation}   (14)

More important, we need to prevent the arbitrariness assigning the atomic fractional coordinates $\mathbf{r}_{v}$ of the initial and finial images (correctly mapping the atoms at the initial and final structures). Otherwise, the calculation will be hard to converge or several identical paths can be found in a calculation, as shown in Fig. 16. For more complicated systems, you will get some unreasonable or messy pathways if you don’t have a good initial pathway. Global numerical search for minimizing the distance between the atoms from two endpoint images helps the VC-NEB method to reassign the atom sequence. The ability to automatically create model paths before the VC-NEB calculation is crucial for the stability and convergence of the algorithm, and is a prerequisite for studying large and complex systems.

\includegraphics[scale=0.8]{pic/VCNEB_pathway}
Figure 16: Identical pathways found when setting up a “bad” initial Image file. The pathway is for the B3$\rightarrow $B1 phase transition in GaN at the equilibrium pressure 45.0 GPa. At Images 11 and 21, B1 and B3 structures in a monoclinic cell are found during the MEP searching, respectively. The Ga atoms move along the arrow directions during the phase transition.