Gamess (US) frequently asked questions Part 5: "THE VIBRATIONAL ANALYSIS IS NOT VALID"

Gamess (US) and Firefly by default assume geometric convergence has been achieved when the maximum gradient is below 1e-4 and the RMS gradient is smaller  than 1/3 of the maximum gradient.  This convergence criterion may be changed by the user with


 $STATPT OPTTOL=<your desired convergence criterion> $END


It is well known that the vibrational analysis is strictly valid mathematically when the Hessian is computed in true stationary points (i.e when the gradient is exactly equal to zero). If the maximum gradient is sufficiently close to zero, the vibrational analysis (although not absolutely correct) is still close enough to the "true" solution for all practical purposes.



This introduction brings us to today's FAQ. A recurring question in both the Gamess-US list and the Firefly forums concerns the message often printed by the program after a vibrational analysis:

*THIS IS NOT A STATIONARY POINT ON THE MOLECULAR PES THE VIBRATIONAL ANALYSIS IS NOT VALID*

This message arises from the way gradients are analyzed by Gamess: gradients are originally computed in one set of coordinates (cartesian coordinates, I believe) , and then transformed into the  coordinate system specified by the user. Optimizations stop when the "transformed gradient" lies below OPTTOL, but Gamess uses the original, non-transformed, gradient to decide whether to consider the geometry as a stationary point on the molecular PES.  Therefore, if  the geometry is converged, the scary message in capital letters above may be safely disregarded. When in doubt, simply decrease your OPTTOL value, continue the optimization and re-compute the hessian.