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Kwok Cheik Chong

Global vs Local minima ??

Charles Grierson  Follow

In principle, you can only be 100% sure, that you would the global minimum, if you have sampled the whole potential energy surface. That, of course, is easily not possiible.
If your first and second derivatives are zero, you are at a minimum point. But you can not know, whether it is a global or local minimum.
The magnitude of the vibrational frequencies has nothing to do, with the question, whether a minimum is global or local.

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Dave Saruya  Follow

Exactly as stated above, you can be sure only of you make a full PES scan. That can be done only for very small molecules, that have a few degrees of freedom (nonlinear molecules have 3N-6 vibrational degrees of freedom, since you're not interested in translations nor rotations) and only assuming certain resolution of the scan. E.g. let's assume that you have 3 dihedral angles: you can do a 15-degree scan with all possible combinations, meaning 24*24*24 calculations and be almost sure that you found the true global minimum.
In reality and for large molecules you just scan a small part of PES and than claim that perhpas you found a reasonable structure of the global minimum.
For organic molecules we usually believe that the true global minimum in solvent lies somewhere close to the xray structure and that can be justified in your work.
For ligands and docking this is usually not an issue, since docked conformations of ligands can be (and very often are) very far from the global minimum in solution (or xray in solution).

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Andrew Wrigley  Follow

Exactly as stated above, you can be sure only of you make a full PES scan. That can be done only for very small molecules, that have a few degrees of freedom (nonlinear molecules have 3N-6 vibrational degrees of freedom, since you're not interested in translations nor rotations) and only assuming certain resolution of the scan. E.g. let's assume that you have 3 dihedral angles: you can do a 15-degree scan with all possible combinations, meaning 24*24*24 calculations and be almost sure that you found the true global minimum.
In reality and for large molecules you just scan a small part of PES and than claim that perhpas you found a reasonable structure of the global minimum.
For organic molecules we usually believe that the true global minimum in solvent lies somewhere close to the xray structure and that can be justified in your work.
For ligands and docking this is usually not an issue, since docked conformations of ligands can be (and very often are) very far from the global minimum in solution (or xray in solution).

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Barbara Forbes-Lyons  Follow

To scan PES you can try using simulated annealing. It is cheap method and help find all possible minima. Then you have to recalculate the minims with your method and basis set and voila. 

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Chief Thunder  Follow

@Bartosz Trzaskowski Thank you for clarifying for larger molecules.

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Anne Beal  Follow

In principle, you can only be 100% sure, that you would the global minimum, if you have sampled the whole potential energy surface. That, of course, is easily not possiible.
If your first and second derivatives are zero, you are at a minimum point. But you can not know, whether it is a global or local minimum.
The magnitude of the vibrational frequencies has nothing to do, with the question, whether a minimum is global or local.

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Craig 75  Follow

Some additional assurance could be brought by conformer search by some MM technique (implemented for example in Tinker) followed by QM optimization of all conformers found. Though, it can be done mainly for organic molecules.

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Bill Wald  Follow

Well, if your frequencies are not only positive, but rather large (let's say, above 50 cm-1), then it is a very convincing evidence for the global minimum.
If you are in doubt, try to run the calculations with different basis sets or functionals. The "real" minimum persists.

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Andy Carnduff  Follow

Yes, it is possible only if one samples the whole PES.

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David B?ckman  Follow

Exactly as Arnim commented, you need to scan the whole potential energy surface. i suugest you use some less computationally expensive method for this and then use DFT only around lowest energy configs. 

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