## Molecular Dynamics

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Molecular Dynamics (MD) simulations are a collection of computational experiments conducted on a collection of atoms for understanding the atomistic behavior of matter. These methods are now widely used in every field of science and engineering to understand microscopic behavior of materials to predict the macroscopic properties of interest. The computational experiments conducted using MD simulations guide both experimental work and theoretical predictions for discovering causes of the well know transitions in the matter.

The power of MD simulations comes from the statistical mechanical ensembles that allow simulations and study of large collection of physical phenomena, such as, phase transition, deformation, elastic behavior, electrical properties, vibration properties and structural properties of matter under a variety of physical conditions. For new discoveries in science the MD simulations have become power tools at the hands of scientist and engineers paving the way for experimental investigations and development of theories.

### Topics

In this topic you will learn about the Ergodic behavior of atoms where the long time trajectories sample the entire phase-space necessary for thermodynamic ensemble behavior.

In this topic you will learn about the force field models that describe the inter-atomic forces of attraction and repulsion and intra-atomic forces between collections of atoms forming molecules. These idealized potential functions, such as, Lenard Jones function provide simple pair-potentials used for solving Newton's second law of motion for the computational evolution of atomic trajectories.

In this topic, you will learn four laws of thermodynamics. The laws of thermodynamics define the relationship between the temperature, pressure and volume. The zeroth law defines the equilibrium of temperature, first law defines the relation between hear and work, second law describes the quality of heat and entropy and third law describes that the entropy behavior as we reach absolute zero temperature.

In this topic you will learn about the Ergodic behavior of atoms where the long time trajectories sample the entire phase-space necessary for thermodynamic ensemble behavior.

The study in the computational science is done based on physical systems that describe the thermodynamic systems. The open and close systems, reversible and irreversible systems, and thermodynamic processes describe the properties of the physical systems. Once these physical systems are described in terms of thermodynamic intensive and extensive properties, then you can perform computational molecular dynamics on collection of atoms for discoveries in science.

In this topic you will learn about statistical mechanics, a branch of Physics that deals with the ensemble of microstates. These ensembles of microstates are connected with the thermodynamics variable, such as, micro canonical ensembles, canonical ensemble, and constant pressure ensemble and grand-canonical ensembles. Using the machinery of statistical mechanical under these ensembles molecular dynamics method can perform computational experiments.

The statistical thermodynamics connects collection of microstates for statistical calculation of bulk properties. With collection of small number atoms in a given force field described by a potential function, molecular dynamics method can successfully calculate bulk properties of a matter. You will learn how to use statistical thermodynamics of partition functions for your MD experiments.

In this topic you will learn how thermodynamic variables that drive the thermodynamic processes. For example you will learn about temperature as thermodynamic driver for phase change from solid to liquid.

In this topic you will learn about thermodynamics processes, such as, isothermal, isochoric, isobaric and adiabatic to define the work done in a thermodynamic cycle. The degree of freedom defines as number of possible dimensions for the motion of particles in a thermodynamic ensemble. The degrees of freedom also define the how we can apply equipartition theorem for the calculation of partition function and calculate bulk thermodynamic properties for the ensemble of atoms.

There are four fundamental processes that describe the thermodynamic state of a system. In this topic you will learn change in internal energy U of the systems under isothermal (constant temperature T), isochoric (constant V), isobaric (constant pressure P), and adiabatic (constant heat Q) processes. The processes then define the thermodynamics ensemble to study thermodynamic processes using Molecular Dynamic simulations.