Variational Approaches to Free Energy Calculations
von Martin Reinhardt
Datum der mündl. Prüfung:2020-12-18
Betreuer:Prof. Dr. Helmut Grubmüller
Gutachter:Prof. Dr. Helmut Grubmüller
Gutachter:Prof. Dr. Jörg Enderlein
EnglischGradients in free energy are the driving forces of thermodynamic systems. Knowledge thereof thus enables a first-principles understanding of condensed-phase many-body systems such as macromolecular assemblies, colloids or imperfect crystals, and allows quantitative descriptions of associated processes including, for instance, molecular recognition or drug binding. To predict free energy differences computationally with high accuracy, state-of-the-art methods based on atomistic Hamiltonians use "alchemical transformations". For these, sampling is not only conducted in the two states of interest, but also in intermediate states that bridge configuration space. These intermediates are typically defined as a linear interpolation of the end state Hamiltonians. The term ‘alchemical’ refers to the fact that, in some cases, differing atoms are thereby transformed from one type into another.However, linear interpolations are still a very special case amongst all possible functional forms, and it is likely that alternative ones yield more accurate predictions. Hence, in this thesis, all possible functional forms were considered. For different schemes to calculate free energy differences, and under the assumption of independent sampling, intermediate states yielding predictions with optimal accuracy - the Variationally derived Intermediates (VI) - were derived. These differ substantially from established linear intermediates. Furthermore, as the VI derivation holds for any number of intermediate states and almost any number of sample points, it enables the generalization of several past analytical results derived under more restrictive assumptions. In the next step, the accuracy of VI was assessed: For a Lennard-Jones gas transformation, almost ten times less sampling was required for VI to achieve the same accuracy as for linear intermediates. For converting charges of molecular systems in solution, the accuracy improved by approximately a factor of two, whereas the VI calculation of solvation free energy differences yielded accuracies similar to the ones from established methods. In the latter case, limiting factors and targets for future methodological improvement were identified.
Keywords: Statistical Physics; Computational Physics; Free Energy Calculations; Molecular Dynamics Simulations