I have a minimum and a transition state structure and I would like to determine the normal mode which leads to the transition state from the minimum. How to perform it numerically? I am thinking about that the frequency of this normal mode is in the same position in the diagonalized (mass-weighted) force constant matrix as the imaginary one if the structures of the Min. and the TS are optimally rotated and shifted into each other (as in case of RMSD calculation). Is it true?
You could define a 3N-dimensional vector that connects your minimum and TS structures, and compute its scalar product with each eigenvector of the hessian matrix (this is proportional to the projection on each eigenvector as they are typically normalized). The one with maximum absolute value (sign is arbitrary) should be the one you're looking for.
"You could define a 3N-dimensional vector that connects your minimum and TS structures." Could you please help me how? Is it necessary that the Min. and the TS structures are optimally rotated and shifted?
Alignment would be necessary, then you just subtract respective coordinates.
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