How small are atoms and molecules?

Sodium ions (Na+) are about a fifth of a nanometer across, while chloride ions (Cl^-) have a diameter of about a third of a nanometer.  By comparison, a red blood cell is between 6,000 and 8,000 nanometers, and the width of a human hair is around 40,000 nanometers!

A teaspoon of salt contains 5.86 x 10²² (58,600,000,000,000,000,000,000) molecules of NaCl. A single grain of salt contains 1.44 x 10¹⁸ (1,440,000,000,000,000,000) NaCl molecules.

What is a simulation?

A simulation is an imitation of how a real-world process or system operates over time. Simulations are used to study, understand, and predict how something works. They are especially useful tools to investigate nanoscale phenomena, which are often difficult to observe directly (because, you know, small...).

What is molecular dynamics?

Molecular dynamics applies the same laws that describe the trajectories of visible objects, like soccer balls and planets in orbit, to understand the trajectories of atoms and how their collisions result in particular diffusion paths or chemical reactions. Since observing and measuring the motions of individual atoms is difficult, we often use thermodynamic averages, which correlate the behavior of individual atoms with measurable macroscopic properties like energy, pressure, and volume.

How do you make a molecular dynamics simulation?

Molecular dynamics simulations allow us to predict how atoms will interact, what materials they will form, and what properties those materials will have. To create such a simulation, we need a mathematical expression that describes how atoms behave and interact.  We start with Newton's second law of motion, which states that the force applied to any object is equal to the product of the object's mass and its acceleration (Force = mass x acceleration, or F=ma). Since an atom contains both positively charged protons and negatively charged electrons, two different forces combine to give the value of F: one is an attractive force between particles of opposite charge, and the other is a repulsive force between particles of the same charge. The strength of each force will vary with the distance between atoms, and we can combine these patterns into a potential, or an equation that calculates the total force on an atom as a function of its distance away from other atoms.

How does a molecular dynamics simulation work?

1. Start with each atom in a fixed position.
2. Once we know the position of the atom, the potential (from Step 3) allows us to calculate the force on the atom.
3. Once we know the force on the atom, Newton's second law (F = ma) allows us to calculate its acceleration.
4. Once we know the atom's acceleration, we can calculate its new velocity after a time interval Δt.
5. Once we know the atom's velocity, we can calculate its new position.
6. Based on its new position, we can repeat steps 1-5, and continue to repeat to find out how the system evolves with time.

What are the criteria a good molecular dynamics simulation must meet?

It is important that a molecular dynamics simulation be both accurate and efficient. Both momentum and energy must be conserved, in accordance with the laws of mechanics and thermodynamics, and the calculated trajectories of the atoms should be correct for as long a time as possible, and with the time step Δt as large as possible. At the same time, it should minimize the calculations and memory required for each time step.