Molecular dynamics simulation of simple fluids

Let us consider a system of N monoatomic particles interacting with Lennard-Jones interactions. The molecular model construction has been described in Chapter 14. 

The classical equations of motion for particles of mass m are 3N second-order differential equations 

Equivalently, we can write the following 6N first-order differential equations 

In practice, numerical integration of 6N first-order differential equations is less challenging and computationally demanding than numerical integration of 3N second-order differential equations. Thus, the set of Eq. 16.3 is the preferred one for MD simulations. 

We should note that in the absence of any external fields, the total energy of the system is conserved. In other words, numerical integration of Newton s equations of motion simulates the microcanonical ensemble. The forces are then called conservative. 

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Molecular Dynamics Simulations of Simple Fluids with Three-Body Interactions Included... 

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