Development and Application of Hamiltonian Adaptive Resolution Simulations for Systems having Long-range Interactions
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Abstract
Computer simulations have proven to be a powerful tool in soft matter research since they have helped to elucidate microscopic details of many phenomena observed in experiments that would otherwise have remained unclear. Therefore, the high demand for computer simulations on one hand, and the emergence of very fast computational units on the other hand, have led to development of a great variety of computational methods. These techniques have provided the possibility to investigate phenomena occurring within a wide range of length and time scales, from chemical reactions at the quantum scale to self-assembly at the macroscale.
However, the computational costs of studying these phenomena in a single, highly detailed resolution are often too expensive. Hence, provided the locality of the phenomenon, it is advantageous to develop multi-resolution techniques. In these approaches, the system is divided into a high resolution subregion, described by an accurate but computationally expensive model, and a low resolution region, where the rest of the system is treated by means of a coarse but computationally efficient model. One of such multi-resolution techniques is the Hamiltonian Adaptive Resolution Simulations (H-AdResS) method. In this approach, the two resolutions are smoothly coupled through a transition layer in which compensating forces are applied on the molecules, and a constant chemical potential throughout the resolutions is enforced.
In this work, we first explain the challenges of implementing long-ranged elec- trostatic interactions in H-AdResS. We then propose and validate the usage of a short-range modification of Coulomb potential, the Damped Shifted Force model, in the context of the H-AdResS scheme. We validate this approach by reproducing the structural and dynamical properties of liquid water. Next, we take advantage of the constant chemical potential inherent to H-AdResS to introduce a new and efficient method to compute the chemical potential of liquids and mixtures. The method has been named spatially resolved thermodynamic integration (SPARTIAN). Subsequently, we employ the same approach to compute the free energy of solids by coupling the real crystals with their corresponding ideal Einstein crystals. Afterwards, we use the Jarzynski equality to obtain the solvation free energy of molecules by using steered molecular dynamics to pull the molecule from the atomistic (solvated state) into the ideal gas (unsolvated state) region. Lastly, we discuss the spatial block analysis (SBA) method to efficiently extrapolate thermodynamic quantities such as bulk isothermal compressibility from finite-size computer simulations, and discuss different types of finite-size effects in the SBA context. This study is designed to target the problems involving sampling in grand canonical ensembles which is also crucial for the extension and development of the SPARTIAN method into a new grand canonical molecular dynamics framework.