Multiscale Computational Modeling of Biomolecular Systems

This thesis presents new theoretical developments within the polarizable embedding (PE) and polarizable density embedding (PDE) models, focused on improvements of the capabilities and efficiency of the two models. The PE model is an advanced polarizable environment model that allows for an accurate inclusion of environmental effects in hybrid QM/MM calculations. It describes environments atomistically through a combination of a multi-center multipole expansion and distributed atomic polarizabilities. The PE model has a particular focus on molecular response properties and spectroscopy and has been used extensively for the modeling of solvents and biomolecular environments. The PDE model is an extension of the PE model with an improved description of permanent electrostatics. Further, PDE includes an account of non-electrostatic Pauli repulsion, which is highly useful in dealing with the so-called electron spill-out problem. The theoretical background of the PE and PDE models is outlined, and examples of their practical performance are discussed.


For the PDE model, an extension towards large biomolecular environments is developed. With this theoretical advancement, the PDE model can be used to model large biomolecular environments, such as proteins. The computational efficiency of the PE model is examined, and improvements to the efficiency of the most time-consuming parts of the embedding calculation are suggested, implemented, and benchmarked. These improvements address the accelerated solution of the polarization equations by introducing a linear-scaling evaluation of the classical fields with the Fast Multipole Method (FMM). Additionally, approximations to the QM/MM interaction are proposed and tested for accuracy and efficiency. With these advancements, the computational performance of PE calculations is greatly improved, and routine calculations on sizable biomolecular systems are finally possible.