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One would think that initial configuration should not significantly impact the final optimized geometry. Starting with two moieties, the final "optimized" geometry is not unique and depends highly on how they are placed initially. Is there a way to avoid this? Otherwise one could never be sure that they have ended up with the global minimum.

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Starting with two moieties, the final "optimized" geometry is not unique and depends highly on how they are placed initially. Is there a way to avoid this?

Yes and no. No, because, as OP anticipated, starting from an input geometry the optimisation algorithm will indeed find the closest (from the algorihtm point of view) local minimum and not necessarily the global one. And yes, because by performing an extensive conformational analysis, one in principle can find structures that correspond to all possible local minima and then identify the global one.

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    $\begingroup$ Operative words on that last sentence being in principle $\endgroup$ – F'x Aug 8 '16 at 15:03
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    $\begingroup$ @F'x, sad but true. In practice, even for relatively small molecules, an extensive conformational analysis requres too much (CPU) time, so that often one has to resort to the help of "chemical intuition" to reduce the cost or even avoid conformational analysis completely. $\endgroup$ – Wildcat Aug 8 '16 at 15:11
  • $\begingroup$ @Wildcat - I'm not sure I'd say that "extensive conformational analysis" requires too much time. Exhaustive (systematic) searches are exponential in the number of rotatable bonds, but there are many conformer search strategies that are pragmatic. $\endgroup$ – Geoff Hutchison Aug 8 '16 at 18:11
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    $\begingroup$ No, but "I'm not going to do any conformational sampling because I don't have a 100% guarantee of finding the global minima" seems a bit extreme. Trying some strategy is better than nothing and can at least indicate if the property of interest has much dependence on the conformer geometry. $\endgroup$ – Geoff Hutchison Aug 8 '16 at 18:31
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    $\begingroup$ @ChemInformationist - Gaussian certainly does not. To my knowledge, no standard computational package includes any type of global optimization strategies built-in. In many cases people want a local minima because they have some chemical intuition or the molecule is rigid (e.g., benzene, water). Moreover, there are many such techniques in chemistry and it's hard to have a one-size-fits-all approach because of the diversity of molecular systems and the large # of degrees of freedom. $\endgroup$ – Geoff Hutchison Aug 9 '16 at 15:16
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It is not possible to derive an algorithm that finds the global optimum independent of the initial structure. This is a general fact of non-convex optimization. The potential energy surfaces of stable compounds are not globally convex because the "dissociation" energy of any two components is finite at infinite separation.

Although there are so-called "global" optimization methods, no method that does not search every point of the search space can in general guarantee to have found the global optimum (i.e., there is always a function for which the algorithm fails to find the global optimum or visits every point in the domain).

That said, global optimization methods putatively reduce the sensitivity of the result to the initial point. There are a large number of these, some of which are deterministic (lists definitely not exhaustive since it's missing my favorite level-filling method :-).

Finally I would like to point out that the specific formulation of your problem influences how well your algorithm works, e.g., the chosen coordinate system or how any constraints are enforced. The lack of global optimization is actually useful if a certain bonding topology is supposed to be maintained; otherwise, t-butane would always optimize to n-butane, for instance.

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