Is there a way by which we can know the optimized geometry of a molecule is local minima without actually performing the frequency calculations. I just want to know is there any alternative way other than forces/Hessian matrix.
If you are talking about systematic procedures that cover all possible atomic coordinates in your molecule, and stick to the method that you used to optimize your structure, then I would say no, there is no other way.
Basically, you want to know if there is any atom displacement that will make your energy become even lower than in your current structure. When the optimizer finishes, all first derivatives of the energy with respect to the atom coordinates are zero - finding that point is basically its job. So any small displacement of a single atom along one of its coordinates will (in theory) not even change your energy at all. Therefore, the next thing that could actually hold any information are the second derivatives - but those are exactly what the Hessian matrix contains and where you get your frequencies from.
So, doing a frequency calculation after your optimization is essentially the same as looking at the first non-vanishing set of energy derivatives to see if any of them imply a lower energy somewhere in the vicinity of your optimized structure. That's as simple as you can make it.
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