Confidence in conformation search results from molecular mechanics Conformational searches using molecular mechanics can be either systematic or 'random' using Monte Carlo methods (or other non-systematic methods) to sample conformational space.

In general, my understanding is that Monte Carlo methods perform just as well as systematic searches # assuming that the right parameters are used. This is often described in (organic) computational papers along the lines of :


  A sufficient number of conformations were explored such that all low-energy conformers within  a X kj/mol window of the global minima were found at least X times. 


There is a lot of ambiguity over how many times a low energy conformer needs to be found in order to 'guarantee' that the conformational space has been fully explored. Certainly, in my own experience I can generate an ensemble that fulfils this criteria but is clearly non-complete (if I run the same search from a slightly different starting geometry I generate another ensemble with some different low-energy conformers).

My question is two-fold:


Is there any mathematical basis for the statement about finding a low energy conformation x times, or is it largely a case of convenience that works well empirically in the majority of situations ?
Is there really any way to know that a search is comprehensive without systematically exploring the entire PES ? 




#: There was a report that Ken Houk lost a bet due to his belief that systematic sampling was the only true way to explore a potential energy surface, though I cant find the paper where this was discussed.
We have published² a probabilistic treatment of this question, but for the case of MD simulations (and not MC). The principal idea is to use Good-Turing statistics to estimate the probability of unobserved species (ie conformations that have not -as yet- been observed). I have no idea whether this treatment can be transferred to MC, but there is an open source program³ -based on R- that you could try to use.

² https://pubs.acs.org/doi/10.1021/ci4005817

³ https://github.com/pkoukos/GoodTuringMD