How would you model a nanoscale atomistic simulation?

If you were to investigate the interaction of two atoms, where would you start? Let’s start thinking of the most uncomplicated atom, Hydrogen. Well, the most fundamental thing we know about them is that they obey the Schrödinger equation. Here are the things that we need to take into account to solve the Schrödinger equation:

1. Kinetic energies of nuclei
2. Kinetic energies of electrons
3. Electron-ion interactions
4. Electron-Electron interaction
5. Ion-Ion interaction

And they all are the functions of three spatial coordinates. It escalated pretty quickly… What if we want to examine the Tungsten atom, which has 74 electrons? It is impossible to solve such an equation without approximations!

Since approximations we make will affect some of the quantities of the outcome, we need to determine:

• What do we want to learn about the system?
• How large should the system be?
• What time interval do we want to investigate?

There are a wide variety of models to describe the properties of atoms, molecules, materials, and rigid bodies. For example, Density Functional Theory(DFT) describes many-electron/many-body systems in terms of electron densities. It can be used to investigate the ground state electronic, optical, and chemical properties of materials in the picometer-nanometer range. However, it still is a quantum mechanical model, and the computational complexity of the systems increases with the cube of the number of electrons present in the system. DFT is practical up to a few nanometer scales but can provide a detailed description of the system.

There is a more practical method called Classical Molecular Dynamics for larger and time&temperature-dependent systems. In this method, atoms are treated as point particles, and the interaction between them is described with the interatomic potentials. The time evolution of the atoms is obtained by solving equations of motion based on Newton’s Second Law! Moreover, the thermodynamical properties are controlled with statistical methods. With this model, systems with millions of atoms can be studied!

Returning to the questions above, we want to investigate the thermal conductivity of irradiated Tungsten, which is one of the promising candidates that can be used inside Fusion Reactors because of its high melting point and endurance. The system should be large enough to simulate the damage caused by neutron bombardment and to observe a meaningful temperature gradient between the hot and cold regions. This means that we need to simulate more than a few nanometers. Finally, we want to study our system for pico-nanoseconds which is also vital for statistically valid thermodynamical properties.

In our study, we use Classical Molecular Dynamics, implemented in LAMMPS(Large-scale Atomic/Molecular Massively Parallel Simulator). The simulations contain 2.5 million atoms, and we are running them at Barcelona Supercomputing Center.