When doing molecular dynamics simulations, there are countless sources of error (i.e. approximations and numerics).

Molecular dynamics can be used to determine intrinsic thermal properties such as Melting Point/Freezing Point/Boiling Point. What tools do give me a quantified error on these properties, and what is the underlying thechnique to quantify all these different error terms?

  • $\begingroup$ DO you mean to quantify the uncertainty due to errors other than the statistical uncertainty associated with MD? $\endgroup$
    – jheindel
    Oct 26, 2020 at 17:38
  • $\begingroup$ Yes, ideally I would like to have all possible error sources accounted for. If an error (such as it is the case for e.g. the numerical truncation error) is limited by a constant, I am ok with that. $\endgroup$ Oct 27, 2020 at 12:04

1 Answer 1


The error of a MD simulation can be roughly partitioned into four contributions:

  1. Error due to short-period statistical fluctuations;
  2. Error due to poor- or non-ergodicity (in other words, extremely long-period statistical fluctuations);
  3. Error due to numerical round-off and the use of a finite time step;
  4. Error due to the force field itself.

Quantification of 1 is trivial, for example you can compute your desired property using a series of short MD trajectories, and compute the standard deviation of their mean. 2 is very hard and basically impossible to reliably estimate, because it requires one to sample all low-barrier paths that leads the simulation to a basin with low free energy, which should be NP-hard. 3 is probably predominantly reflected in the conservation of energy, and if in doubt, you can always estimate it by using higher numerical precision (double precision instead of single precision) and a smaller time step.

4 is the most interesting (and arguably the most underrated) contribution. There are some methods for estimating it, for example https://aip.scitation.org/doi/10.1063/1.3545069. However this requires that you go into the training set of the force field, and also have knowledge of the experimental uncertainties of the training data, which can be a non-trivial amount of work. You may search for articles that cite this paper for more examples of error quantification of the force field itself.


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