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When conducting a minimization on Gaussian software, What are the procedures used to eliminate imaginary frequencies if we have already found a stationary point? Are there any keywords that would help to find the minimum?

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Use tighter convergence criteria.

If the geometry is already converged with default convergence criteria, then just using tighter convergence thresholds should work. Look at the tight option in the gaussian manual.

Sometimes one will just almost always have one small imaginary frequency (like a few wavenumbers) and it can be very hard to eliminate these, especially when any finite differences are used in calculating the gradient or hessian. This is because there is inherent noise/uncertainty associated with the iterative processes involved in both geometry optimizations and solving the relevant electronic structure equations (both have somewhat arbitrary convergence criteria).

In rare cases where you are optimizing a very floppy molecule, you might need to increase the step size used in the optimization as the potential surface can be too flat along some coordinate leading the optimization to erroneously stop because the geometry changes so little that the convergence criteria seem to be met when not at a minimum. I've only seen this happen once though, so that's unlikely to be the problem.

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