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I learned dimer method for searching transition state in this paper: A dimer method for finding saddle points on high dimensional potential surfaces using only first derivatives.

However, I still cannot build an intuition for making sense of the method. By reading section 2 of the paper, here is my attempt:

The constructed dimer (the two ends of which are two images of the system) is used for approximating the eigenvector with the lowest eigenvalue of the Hessian matrix.

Since the direction (the eigenvector) with the smallest eigenvalue is the direction along which the curvature of PES is the smallest and the energy of the dimer directly determines the curvature of the PES, we just need to rotate the dimer in order to minimize the energy and thus the curvature.

My confusions:

  1. The rotation of the dimer is for aligning the dimer with the desired eigenvector of the Hessian matrix, but what is the purpose of translating the dimer?

  2. Why the eigenvector of the Hessian matrix with the smallest eigenvalue is so important? How the eigenvalue of which is associated with the curvature of the PES?

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