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**1 - 3**of**3**### An Introduction to Ab Initio Molecular Dynamics Simulations

- COMPUTATIONAL NANOSCIENCE: DO IT YOURSELF!
, 2006

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### Engineering and Aerodynamics,

"... Abstract. In this paper we present the results of utilizing scientific computing methodologies to address an engineering problem from nano technologies. In nano and microscale, the calculation could only be done with some particle based representation method. One of them is Molecular Dynamics (MD) m ..."

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Abstract. In this paper we present the results of utilizing scientific computing methodologies to address an engineering problem from nano technologies. In nano and microscale, the calculation could only be done with some particle based representation method. One of them is Molecular Dynamics (MD) method. In the paper we describe the construction of the Molecular Dynamics Method and we present some results of the MD simulation of the water nanoflows [13, 14].

### O F E E

"... Within the framework of equilibrium statistical mechanics the free energy of a phase gives a measure of its associated probabilistic weight. In order to determine phase boundaries one must then determine the conditions under which the free energy difference (FED) between two phases is zero. The unde ..."

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Within the framework of equilibrium statistical mechanics the free energy of a phase gives a measure of its associated probabilistic weight. In order to determine phase boundaries one must then determine the conditions under which the free energy difference (FED) between two phases is zero. The underlying complexity usually rules out any analytical approaches to the problem, and one must therefore adopt a computational approach. The focus of this thesis is on (Monte Carlo) methodologies for FEDs. In order to determine FEDs via Monte Carlo, the simulation must (in principle) be able to visit the regions of configuration space associated with both phases in a single simulation. Generally however one finds that these regions are significantly dissimilar, and are separated by an intermediate region of configuration space of intrinsically low probability, so that a simulation initiated in either of the phases will tend to remain in that phase. This effect is generally referred to as the overlap problem and is the most significant obstacle that one faces in the task of estimating FEDs. In chapter 2 we start by formulating the FED problem using the Phase Mapping (PM) technique of [1]. This technique allows one to circumvent the intermediate regions of configuration space altogether by mapping configurations of one phase directly onto those of the other. Despite the improvement that one gets when formulating the problem via the PM, the overlap problem persists, albeit to a lesser degree. In chapter 2 we define precisely what we mean by overlap and then discuss a range of methods that are available to us for calculating the FEDs within the PM formalism. In the subsequent chapters we then focus on the three generic strategies that arise in addressing the overlap problem.