title: Development of Iterative Methods for Coarse-Graining Molecular Liquids
Creators: name: Bernhardt, Marvin P.
Publisher: name: UNSPECIFIED
Year: 2022

description: The enormous number of atoms in biological and macromolecular systems can prohibit the direct application of atomistic molecular dynamics (MD) simulations. This limitation motivates the construction of coarser models for molecular systems. Bottom-up coarse-graining methods derive potentials between coarse-grained (CG) beads, which represent groups of atoms, by matching properties of a reference atomistic force field. By developing reliable and well-understood models, time and length scales inaccessible by atomistic MD simulations become reachable. Finding effective pair potentials that represent a certain radial distribution function (RDF) is an inverse problem that needs to be solved iteratively, e.g. by Newton's method. In every iteration, a potential is used in an MD simulation to calculate the RDF. From the mismatch of the RDF and the target RDF, a potential update is calculated and a new iteration starts. The same technique can also be used to obtain atomistic force fields from ab initio MD simulations. Besides the primary challenge of matching structure, the dynamic and thermodynamic properties are altered when changing resolution. It is of interest how those properties are changing and how some of them might be retained. The first topic in this work is the use of integral equation theory for bottom-up coarse-graining. The theory provides an approximate link between structure and potential, e.g. via the reference interaction site model (RISM) and the hypernetted chain (HNC) closure relation. This link can be used to provide a good initial guess for the pair potential and an approximation to the Jacobian matrix for an iteration in Newton's method. While the exact Jacobian is in principle accessible from sampling certain covariances, as done in the inverse Monte Carlo (IMC) method, the HNC Newton's method is distinctly faster. The integral equation coarse-graining theory is in two steps generalized, such that is finally applicable to any molecular mixture. Instabilities in the iterative RDF matching process are examined and a modification for their avoidance is developed. By changing from a Newton to a Gauss-Newton method, constraints can be included in the potential updates. Thermodynamic constraints, such as pressure, osmotic pressure in implicit solvent models, and the enthalpy of vaporization, are developed and the combination of multiple constraints is explored. All methodological advancements are implemented in the open-source coarse-graining software package VOTCA. Secondly, iterative methods are applied to derive ion-water pair potentials from AIMD data. Instead of using a fixed parametric form for the ion-water potential, a free-form tabulated potential is derived. By comparing the derived potentials with the parametric Lennard-Jones (LJ) form, which is typically used in electrolyte force fields, it is found that the latter has an overly steep repulsion flank. This directly affects dynamical properties such as vibrational frequencies of the ions in the solvation shell. With the derived potentials, experimental frequencies are closely matched, while the LJ potentials fail to do so. Also, the solvation entropy is in better agreement with experimental values when departing from the LJ form. Thirdly, the dynamic and thermodynamic effects of coarse-graining molecular liquids with different levels of resolution are assessed. By comparing the vibrational density of states (VDOS) of a mapped atomistic trajectory with that of a derived CG model, acceleration of translational and rotational dynamics as well as washing out of vibrational dynamics with decreasing resolution are made visible. The two-phase thermodynamic model is used to connect the VDOS of the liquid systems to their entropy. This allows for a detailed investigation into the contributions to the entropy and how they change with the resolution of the CG model. The loss in entropy is found to happen in several steps, where the loss of rotational degrees of freedom plays a larger role than the loss of vibrations.