How Many Conformations Need to Be Sampled to Obtain Converged QM/MM Energies? the Curse of Exponential Averaging
(2017) In Journal of Chemical Theory and Computation 13(11). p.57455752 Abstract
Combined quantum mechanical and molecular mechanical (QM/MM) calculations is a popular approach to study enzymatic reactions. They are often based on a set of minimized structures obtained on snapshots from a molecular dynamics simulation to include some dynamics of the enzyme. It has been much discussed how the individual energies should be combined to obtain a final estimate of the energy, but the current consensus seems to be to use an exponential average. Then, the question is how many snapshots are needed to reach a reliable estimate of the energy. In this paper, I show that the question can be easily be answered if it is assumed that the energies follow a Gaussian distribution. Then, the outcome can be simulated based on a single... (More)
Combined quantum mechanical and molecular mechanical (QM/MM) calculations is a popular approach to study enzymatic reactions. They are often based on a set of minimized structures obtained on snapshots from a molecular dynamics simulation to include some dynamics of the enzyme. It has been much discussed how the individual energies should be combined to obtain a final estimate of the energy, but the current consensus seems to be to use an exponential average. Then, the question is how many snapshots are needed to reach a reliable estimate of the energy. In this paper, I show that the question can be easily be answered if it is assumed that the energies follow a Gaussian distribution. Then, the outcome can be simulated based on a single parameter, σ, the standard deviation of the QM/MM energies from the various snapshots, and the number of required snapshots can be estimated once the desired accuracy and confidence of the result has been specified. Results for various parameters are presented, and it is shown that many more snapshots are required than is normally assumed. The number can be reduced by employing a cumulant approximation to second order. It is shown that most convergence criteria work poorly, owing to the very bad conditioning of the exponential average when σ is large (more than ∼7 kJ/mol), because the energies that contribute most to the exponential average have a very low probability. On the other hand, σ serves as an excellent convergence criterion.
(Less)
 author
 Ryde, Ulf ^{LU}
 organization
 publishing date
 20171114
 type
 Contribution to journal
 publication status
 published
 subject
 in
 Journal of Chemical Theory and Computation
 volume
 13
 issue
 11
 pages
 8 pages
 publisher
 The American Chemical Society
 external identifiers

 scopus:85034260314
 wos:000415911800049
 ISSN
 15499618
 DOI
 10.1021/acs.jctc.7b00826
 language
 English
 LU publication?
 yes
 id
 1c87b0ffd92a49a48e2f12e68fc20652
 date added to LUP
 20171208 08:58:27
 date last changed
 20180506 04:38:36
@article{1c87b0ffd92a49a48e2f12e68fc20652, abstract = {<p>Combined quantum mechanical and molecular mechanical (QM/MM) calculations is a popular approach to study enzymatic reactions. They are often based on a set of minimized structures obtained on snapshots from a molecular dynamics simulation to include some dynamics of the enzyme. It has been much discussed how the individual energies should be combined to obtain a final estimate of the energy, but the current consensus seems to be to use an exponential average. Then, the question is how many snapshots are needed to reach a reliable estimate of the energy. In this paper, I show that the question can be easily be answered if it is assumed that the energies follow a Gaussian distribution. Then, the outcome can be simulated based on a single parameter, σ, the standard deviation of the QM/MM energies from the various snapshots, and the number of required snapshots can be estimated once the desired accuracy and confidence of the result has been specified. Results for various parameters are presented, and it is shown that many more snapshots are required than is normally assumed. The number can be reduced by employing a cumulant approximation to second order. It is shown that most convergence criteria work poorly, owing to the very bad conditioning of the exponential average when σ is large (more than ∼7 kJ/mol), because the energies that contribute most to the exponential average have a very low probability. On the other hand, σ serves as an excellent convergence criterion.</p>}, author = {Ryde, Ulf}, issn = {15499618}, language = {eng}, month = {11}, number = {11}, pages = {57455752}, publisher = {The American Chemical Society}, series = {Journal of Chemical Theory and Computation}, title = {How Many Conformations Need to Be Sampled to Obtain Converged QM/MM Energies? the Curse of Exponential Averaging}, url = {http://dx.doi.org/10.1021/acs.jctc.7b00826}, volume = {13}, year = {2017}, }