·   For a transition state structure (saddlepoint), one of the vibrational eigenvalues will be negative - it is a maximum in one direction. 

 

·   The frequency is given by the square root of the eigenvalue, so formally there will be one imaginary frequency.  If there is one, and only one, imaginary frequency, the structure really is a transition state. 

 

·   If there is more than one imaginary frequency, the structure is a higher order saddlepoint (a maximum in more than one direction), and chemically not very interesting - you would need to do more geometry optimization to find a real TS structure. 

 

·   Where the structure really is a TS structure, the atomic displacements for the imaginary frequency are very important - this normal mode corresponds to motion along the reaction coordinate. 

 

 

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