Abstracts Chemistry

Path Integral Techniques in Molecular Dynamics Simulations of Open Boundary Systems

by Animesh Agarwal

In Molecular Dynamics (MD), the nuclear quantum effects induced by the spatial delocalisation of light atoms are treated via the path-integral (PI) approach of Feynman. PIMD is a powerful method to compute quantum static and dynamical properties; however the method is computationally very expensive which limits its application to fairly small systems and short time scales. This thesis deals with the extension of the recently developed Grand Canonical AdResS (GC-AdResS) method to incorporate different PIMD algorithms: A relatively small region is treated with PI formalism and is embedded into a large reservoir containing the same molecules in a coarse-grained representation. Since we are interested in calculating the quantum equilibrium (structural and dynamic) properties, there is a need to properly define these quantities in the context of open boundary systems. In this perspective, we first show the accuracy of GC-AdResS in conjunction with classical MD in calculating an important thermodynamic quantity, that is, the excess chemical potential. Next we show the correspondence between the Bergmann-Lebowitz (BL) model for open boundary systems and GC-AdResS and use the principles of BL model to define equilibrium time correlation functions in open boundary systems. We calculate these properties for liquid water and show that GC-AdResS gives the same results as reference full-atomistic simulations. Finally, since the path-integral formalism maps an atom onto a polymer ring with fictitious ``classical' beads, we use the same theoretical concepts mentioned above for the calculation of quantum properties of liquid water where GC-AdResS is merged with three different PI techniques: path-integral molecular dynamics (PIMD), ring-polymer molecular dynamics (RPMD) and centroid molecular dynamics (CMD). It is shown that the results of PI-GC-AdResS methods are fully consistent with results from full PI simulations. Mit der von Richard Feynman entwickelte Pfadintegral (PI)-Formulierung können Kern-Quanteneffekte, die durch die Delokalisierung leichter Atomkerne auftreten, mit den Methoden der Molekulardynamik (MD) behandelt werden. Allerdings ist PIMD aufgrund des hohen Rechenaufwands auf kleine Systeme und kurze Zeitskalen beschränkt. In dieser Dissertation wird eine Erweiterung der kürzlich entwickelten ``Grand Canonical AdResS''-Methode (GC-AdResS) durch verschiedene PIMD-Algorithmen behandelt. Hierbei wird der PI-Formalismus auf eine relativ kleine Region angewandt, die in eine grosses Reservoir eingebettet ist, in dem die gleichen Moleküle in einem ``coarse-grained''-Model behandelt werden. Um die strukturellen und dynamischen Eigenschaften in dem Quantengleichgewicht zu berechnen, müssen zunächst diese Eigenschaften für offener Systeme definiert werden. Hierzu zeigen wir die Genauigkeit der GC-AdResS in Verbindung mit klassischen MD, indem wir das chemische Überschusspotential berechnen. Wir zeigen die Entsprechung zwischen dem Bergmann-Lebowitz (BL) Modell…