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How Many Conformations Need to Be Sampled to Obtain Converged QM/MM Energies? the Curse of Exponential Averaging

Ryde, Ulf LU (2017) In Journal of Chemical Theory and Computation 13(11). p.5745-5752
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.

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Please use this url to cite or link to this publication:
author
organization
publishing date
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
1549-9618
DOI
10.1021/acs.jctc.7b00826
language
English
LU publication?
yes
id
1c87b0ff-d92a-49a4-8e2f-12e68fc20652
date added to LUP
2017-12-08 08:58:27
date last changed
2018-01-16 13:27:15
@article{1c87b0ff-d92a-49a4-8e2f-12e68fc20652,
  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         = {1549-9618},
  language     = {eng},
  month        = {11},
  number       = {11},
  pages        = {5745--5752},
  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},
}