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Schemes to include a treatment of torsional anharmonicity in the conformational analysis of biological molecules are introduced. The approaches combine ab initio electronic energies and harmonic frequencies with unharmonic torsional partition functions calculated using the torsional path integral Monte Carlo method on affordable potential energy surfaces.

Theuse of the Zwanzig equation in the calculation of single-stepperturbations to provide first-principles (ab initio) quantum mechanics (QM) correction terms to molecular mechanics(MM) free energy cycles is well established. A rigorous test of theability to converge such calculations would be very useful in thiscontext. In this work, we perform a direct assessment of the convergenceof the MM to QM perturbation, by attempting the reverse QM to MM perturbation.This required the generation of extensive QM molecular dynamics trajectories,using density functional theory (DFT), within the representative biologicalsystem of a DNA adenosine–thymidine dimer. Over 100 ps of dynamicswith the PBE functional and 6.25 ps with the LDA functional were generated.We demonstrate that calculations with total potential energies arevery poorly convergent due to a lack of overlap of phase space distributionsbetween ensembles. While not theoretically rigorous, the use of interactionenergies provides far superior convergence, despite the presence ofnonclassical charge transfer effects within the DFT trajectories.The source of poor phase space overlap for total energies is diagnosed,the approximate quantification of overlaps suggesting that even forthe comparatively simple system considered here convergence of totalenergy calculations within a reasonable simulation time is unfeasible. [ABSTRACT FROM AUTHOR]

We present a method which uses DFT (quantum, QM) calculations to improve free energies of binding computed with classical force fields (classical, MM). To overcome the incomplete overlap of configurational spaces between MM and QM, we use a hybrid Monte Carlo approach to generate quickly correct ensembles of structures of intermediate states between a MM and a QM/MM description, hence taking into account a great fraction of the electronic polarization of the quantum system, while being able to use thermodynamic integration to compute the free energy of transition between the MM and QM/MM. Then, we perform a final transition from QM/MM to full QM using a one-step free energy perturbation approach. By using QM/MM as a stepping stone toward the full QM description, we find very small convergence errors (<1 kJ/mol) in the transition to full QM. We apply this method to compute hydration free energies, and we obtain consistent improvements over the MM values for all molecules we used in this study. This approach requires large-scale DFT calculations as the full QM systems involved the ligands and all waters in their simulation cells, so the linear-scaling DFT code ONETEP was used for these calculations.

Schemes of increasing sophistication for obtaining free energies of binding have been developed over the years, where configurational sampling is used to include the all-important entropic contributions to the free energies. However, the quality of the results will also depend on the accuracy with which the intermolecular interactions are computed at each molecular configuration. In this context, the energy change associated with the rearrangement of electrons (electronic polarization and charge transfer) upon binding is a very important effect. Classical molecular mechanics force fields do not take this effect into account explicitly, and polarizable force fields and semiempirical quantum or hybrid quantum-classical (QM/MM) calculations are increasingly employed (at higher computational cost) to compute intermolecular interactions in free-energy schemes. In this work, we investigate the use of large-scale quantum mechanical calculations from first-principles as a way of fully taking into account electronic effects in free-energy calculations. We employ a one-step free-energy perturbation (FEP) scheme from a molecular mechanical (MM) potential to a quantum mechanical (QM) potential as a correction to thermodynamic integration calculations within the MM potential. We use this approach to calculate relative free energies of hydration of small aromatic molecules. Our quantum calculations are performed on multiple configurations from classical molecular dynamics simulations. The quantum energy of each configuration is obtained from density functional theory calculations with a near-complete psinc basis set on over 600 atoms using the ONETEP program.