As atoms obey the laws of quantum mechanics, one should in principle solve the Schrödinger equation when performing molecular simulations. On the nanoscale (tracking thousands of molecules during multiple nanoseconds) this is completely unfeasible. Even for approximate methods such as Density Functional Theory (DFT) the computational burden is too high to study phenomena such as diffusion of gas molecules in nanoporous materials (a phenomenon typical for the nanoscale). Classical force fields can resolve this issue, because atomic forces are calculated based on very simple analytical expressions, such as the Lennard-Jones potential to model van der Waals interactions between atoms. The major disadvantage is the loss of accuracy compared to ab initio methods. Indeed, determining appropriate analytical expression and corresponding parameters is a daunting task. This has lead to a situation where force fields are often deemed unreliable, as one cannot anticipate to what extent a force field is able to correctly predict certain properties for the molecular systems at hand.

In recent years, quantifying uncertainty in simulation predictions has attracted the attention of several scientific communities. The Technology Roadmap for Computational Chemistry (http://energy.gov/eere/amo/downloads/itp-chemicals-technology-roadmap-co...) ranked as most critical the “lack of methods to estimate the intrinsic accuracy of calculations, leading to a critical barrier to the more widespread use of these methods for solving practical engineering problems.” Despite the fact that the necessity for uncertainty management in constructing force-field models has been expressed some years ago, to date it has not yet been incorporated in methods to derive force fields from ab initio reference data.

Goals The goal of this thesis is to investigate how we can predict the uncertainty on simulation results obtained with force fields derived from ab initio reference data. As a test case we will focus on hydrocarbons, because of the wide availability of experimental and computational results as well as their importance in production of fuel and chemical feedstock.

The first step will be the construction of a database of ab initio results. Next, force-field parameters will be fitted to this database, where several analytical expression for the force field can be considered. The resulting force field will however never be able to precisely reproduce the reference data, and the biggest challenge is to construct a valid model for the remaining errors between force-field and ab initio results. This error model can be tested by using cross-validation techniques on the constructed database.

Traditionally, only one set of force-field parameters is considered. This approach will lead to a distribution of sets of force-field parameters. By computing hydrocarbon properties with molecular simulations (such as virial coefficients) for a sample of force-field parameter sets, we can estimate errors on the predicted properties. Finally it will be checked whether experimental values are within the predicted error bars.

This thesis requires physical insight because a thorough understanding of interactions at the atomic level is necessary to construct force fields and perform molecular simulations. The methods that will be developed are however more broadly applicable to solve general practical engineering problems where model parameters play a crucial role.