Sampson, Christopher
(2015)
Methods for using large-scale first principles quantum mechanical calculations to compute free energies of binding.
*University of Southampton, Doctoral Thesis*, 256pp.

## Abstract

The work presented within this thesis uses quantum mechanical (QM) calculations to improve free energies of binding computed with classical (MM) force fields. Initially a direct approach was taken, where snapshots were taken at equally spaced distances throughout the classical simulation and each structure underwent a quantum single point energy calculation. This direct approach was possible by using the Zwanzig equation.However, one disadvantage of using the Zwanzig equation is it's extreme sensitivity to fluctuations in the energy difference. This led to the quantum corrected free energy being dominated by a few snapshots and convergence could not be achieved. This led to the application of an acceptance criterion, where instead of just using each evenly spaced structure from the classical simulation, each structure would have to be accepted into a target potential. In the work presented here, our target potential was a QM potential. For a simple test system of N2 in vacuum we achieved a high acceptance and converged free energies, however, for more complex systems little to no acceptance was found. The poor acceptance can be attributed to the difference between the MM and QM potential energy surfaces. Similarities were found, however, on the minima of these potential energy surfaces between the MM and QM, which led to the application of a bias to ensure that sampling was only taken from the minima. However, similar to the Zwanzig equation, this method proved to be too sensitive to difference in energy, thus convergence could not be achieved.

In order to "smooth" the transition between the MM and QM a "stepping stone" approach was used. The first step was to accept structures from a classical simulation to a QM/MM ensemble, then we used a direct approach again using the Zwanzig equation to move from the QM/MM potential to the QM. Using this approach, we find very small convergence errors (< 1 kJ/mol). This method was validated by calculating hydration free energies for a variety of ligands.

Finally, the free energy of binding was calculated for trypsin with several benzamidine derivatives using a QM-PBSA approach, which involved running QM calculations on the entire protein-ligand complex. The final results, however, showed no overall improvement of the calculated free energies between the MM and QM. It was found that the inclusion of QM methods lowered the free energy in each case.

**Thesis_corrections_v2_noSig - Version of Record**

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