Converging ligand-binding free energies obtained with free-energy perturbations at the quantum mechanical level

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In this article, the convergence of quantum mechanical (QM) free-energy simulations based on molecular dynamics simulations at the molecular mechanics (MM) level has been investigated. We have estimated relative free energies for the binding of nine cyclic carboxylate ligands to the octa-acid deep-cavity host, including the host, the ligand, and all water molecules within 4.5 Å of the ligand in the QM calculations (158-224 atoms). We use single-step exponential averaging (ssEA) and the non-Boltzmann Bennett acceptance ratio (NBB) methods to estimate QM/MM free energy with the semi-empirical PM6-DH2X method, both based on interaction energies. We show that ssEA with cumulant expansion gives a better convergence and uses half as many QM calculations as NBB, although the two methods give consistent results. With 720,000 QM calculations per transformation, QM/MM free-energy estimates with a precision of 1 kJ/mol can be obtained for all eight relative energies with ssEA, showing that this approach can be used to calculate converged QM/MM binding free energies for realistic systems and large QM partitions.


Research areas and keywords

Subject classification (UKÄ) – MANDATORY

  • Biophysics
  • Physical Chemistry


  • host-guest systems, ligand binding, non-Boltzmann Bennett acceptance ratio method, octa-acid host, QM/MM free-energy perturbation, quantum mechanics, semi-empirical methods, single-step exponential averaging
Original languageEnglish
Pages (from-to)1589-1600
Number of pages12
JournalJournal of Computational Chemistry
Issue number17
Publication statusPublished - 2016 Jun 30
Publication categoryResearch

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