Effect of the integration method on the accuracy and computational efficiency of free energy calculations using thermodynamic integration

Miguel Jorge, Nuno M. Garrido, Antonio J. Queimada, Ioannis G. Economou, Eugenia A. Macedo

Research output: Contribution to journalArticle

39 Citations (Scopus)

Abstract

Although calculations of free energy using molecular dynamics simulations have gained significant importance in the chemical and biochemical fields, they still remain quite computationally intensive. Furthermore, when using thermodynamic integration, numerical evaluation of the integral of the Hamiltonian with respect to the coupling parameter may introduce unwanted errors in the free energy. In this paper, we compare the performance of two numerical integration techniques-the trapezoidal and Simpson's rules and propose a new method, based on the analytic integration of physically based fitting functions that are able to accurately describe the behavior of the data. We develop and test our methodology by performing detailed studies on two prototype systems, hydrated methane and hydrated methanol, and treat Lennard-Jones and electrostatic contributions separately. We conclude that the widely used trapezoidal rule may introduce systematic errors in the calculation, but these errors are reduced if Simpson's rule is employed, at least for the electrostatic component. Furthermore, by fitting thermodynamic integration data, we are able to obtain precise free energy estimates using significantly fewer data points (5 intermediate states for the electrostatic component and 11 for the Lennard-Jones term), thus significantly decreasing the associated computational cost. Our method and improved protocol were successfully validated by computing the free energy of more complex systems hydration of 2-methylbutanol and of 4-nitrophenol-thus paving the way for widespread use in solvation free energy calculations of drug molecules.

LanguageEnglish
Pages1018-1027
Number of pages10
JournalJournal of Chemical Theory and Computation
Volume6
Issue number4
Early online date24 Feb 2010
DOIs
Publication statusPublished - Apr 2010

Fingerprint

Computational efficiency
Free energy
free energy
Thermodynamics
thermodynamics
Electrostatics
electrostatics
numerical integration
data integration
Hamiltonians
Data integration
Systematic errors
Methane
Solvation
complex systems
systematic errors
Hydration
solvation
Methanol
hydration

Keywords

  • integration method
  • accuracy
  • computational efficiency
  • free energy calculations
  • thermodynamic integration

Cite this

Jorge, Miguel ; Garrido, Nuno M. ; Queimada, Antonio J. ; Economou, Ioannis G. ; Macedo, Eugenia A. / Effect of the integration method on the accuracy and computational efficiency of free energy calculations using thermodynamic integration. In: Journal of Chemical Theory and Computation . 2010 ; Vol. 6, No. 4. pp. 1018-1027.
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Effect of the integration method on the accuracy and computational efficiency of free energy calculations using thermodynamic integration. / Jorge, Miguel; Garrido, Nuno M.; Queimada, Antonio J.; Economou, Ioannis G.; Macedo, Eugenia A.

In: Journal of Chemical Theory and Computation , Vol. 6, No. 4, 04.2010, p. 1018-1027.

Research output: Contribution to journalArticle

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