Eigenvector-Following Transition State Searches

The eigenvector to be followed `uphill' in an eigenvector-following transition state search is specified by an integer following the keyword MODE in odata. We count up from the eigenvector corresponding to the smallest eigenvalue, the one corresponding to the second smallest eigenvalue etc. using values 1, 2 and so on. The value specified by MODE is only effective on the first step: for subsequent steps the critical eigenvector is chosen by a maximum overlap criterion using the dot product with the eigenvector that was followed at the previous step. Using MODE 0 means that the eigenvector corresponding to the smallest Hessian eigenvalue is chosen at every step.

Quite often, especially if we are taking large steps in a region far from convergence, the largest modulus dot product may fall well below unity and give rise to ambiguity. At present the program takes the following action if the maximum overlap is less than 0.7. The chosen eigenvector is simply set to the same one that was followed in the last step, where the eigenvectors are numbered in terms of the corresponding eigenvalues arranged in ascending order. Zero eigenvalues are excluded from the counting. The same action is taken if the maximum overlap is with an eigenvector lying more than 8 places above the one followed at the previous step, when arranged according to ascending eigenvalue.