Bjola, Antoniu; (2025) Mean Force Integration: A Unified Framework for Merging Independent Simulations subject to Various Bias Potentials. Doctoral thesis (Ph.D), UCL (University College London).

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Abstract

Molecular dynamics (MD) simulation has become a powerful tool for studying and predicting molecular properties due to significant algorithm advances and the explosive growth of computational capabilities. Moreover, molecular dynamics enables the direct evaluation of free energy surfaces (FESs), offering atomistic insight that complements experimental studies and enables the prediction of numerous thermodynamic properties. Yet MD remains constrained by system size and accessible time scales. Furthermore, many processes of interest, such as nucleation or protein folding, are characterised by rare events, where considerable energy barriers impede transitions between stable states. Nevertheless, transitions must be sampled multiple times for statistically significant predictions of free energies, rendering brute force simulations unfeasible. To address this issue, numerous methods have been proposed to enhance the sampling of rare events. Two widely used methods are umbrella sampling and metadynamics. The former makes use of parallel simulations that sample local predefined regions of configuration space, while the latter continually constructs a bias potential that facilitates the sampling of high-energy configurations. A new method called mean force integration (MFI), which works on the basis of metadynamics, computes the mean force rather than the FES directly, thereby simplifying reweighting and accelerating convergence. Additionally, it can be used to combine independent simulations, turning a serial problem into a parallel one, which increases computational efficiency. This thesis advances MFI to a versatile framework: A general formulation is presented, accommodating the combination of arbitrary static and history-dependent biases. This is complemented by an on-the-fly uncertainty metric that estimates the convergence of the mean force, and a bootstrap analysis that provides a quantitative assessment of the error of the FES. These advances are validated with complex chemical systems, including the nucleation of supersaturated argon vapour, the two-step crystallisation of a colloidal system, and the beta-scission reaction of butyl acrylate. It is shown how the computational cost of excessively expensive simulations can be reduced by employing several shorter simulations subject to diverse biasing parameters. The resulting under-converged trajectories were analysed and combined with MFI, resulting in converged FESs. For the beta-scission reaction, the FES was used to predict reaction rates, which agreed with experimental rates. Additionally, novel reinitialisation protocols are introduced, dividing simulations into diverse biasing stages and recycling interim FES estimates as starting static biases, thereby consistently enhancing convergence of the FES. This was further developed into a framework where simulations are analysed in real time, terminated and reinitialised automatically, as biasing parameters are optimised iteratively. To encourage a wider adoption of MFI, all the Python code used in this work is made openly accessible at github.com/mme-ucl/MFI. By unifying data from independent biased trajectories, enabling an iterative improvement of biasing parameters, and providing reliable convergence metrics, MFI broadens the range of phenomena that researchers can tackle.

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