What are Atomistic Simulations?

A bold answer is “in principle all properties,” provided that we have a sufficiently accurate description of the underlying physics. In reality, the answer is of course more limited, since an exact solution to the quantum-mechanical problem is computationally not possible except for very small molecules, and force fields are difficult to parametrize accurately for arbitrary systems.

In order to provide a more detailed answer, we will consider each category separately, depending on how the interactions between atoms are described.

Force fields can be used to study the energy, forces, and stress of a collection of atoms. Force field calculations are computationally efficient, since the force on a particular atom only depends on the type and position of the other atoms in its close vicinity, through parametrized relationships. This means that systems with several million atoms can be studied.

However, the force field requires fitting to either experimental data or higher level simulations, and the domain of usage is generally limited to systems of similar structure as the ones used for the fitting. Modern force fields are often developed (or trained) using machine learning such as the moment tensor potentials (MTPs) in Synopsys QuantumATK, which often achieves similar quality of results as density functional theory calculations, provided that the structures are sufficiently close to the training structures.

One of the most used simulation types performed with force fields is molecular dynamics (MD), which essentially solves Newton’s second law whereby the acceleration of an atom is given by the force on it divided by its mass. Numerically integrating the acceleration over time yields the velocity and position of the atoms for each time step, with different MD simulations relating to the thermodynamic ensemble of interest.

MD simulations can thus provide a wide range of structural, thermal, and mechanical information. Just a few examples include the formation of grain boundaries or dislocations in crystals and how this affects the hardness of a material; phase transitions such as the melting point of a material; or thermal transport across an interface.

The other main type of atomistic simulations, electronic structure methods, employ a much more detailed physical description of how atoms interact, specifically via the electrons, based on quantum mechanics. These methods can further be divided into two categories: ab initio or first-principles methods (where density functional theory, DFT, is the most widely used in materials science), and semi-empirical models.

As the name implies, first-principles methods do not require any a prior knowledge of the interactions between the atoms. In essence, the only necessary input for these calculations are the positions of all the atoms in the system, a model for how atoms generally interact (which usually involves certain numerical approximations to reduce the calculation time), and an electronic description of each chemical element. Semi-empirical methods are also quantum-mechanical, but less general, since they (akin to force fields) use predefined parameters for some terms in the interactions between atoms.

First-principles methods can be used for the same studies as force fields, but with a much broader application range, as atoms of different elements can be combined in all possible, arbitrary ways, without a need to adjust any parameters for each case. In practice, however, the simulations are limited to much smaller systems, typically below 10,000 atoms, due to increased computational complexity of the governing equations. Semi-empirical electronic structure methods can handle larger systems, even up to millions of atoms, but are often hard to parametrize for systems with many different chemical elements, and each parameter set is usually only valid for a particular type of material.

Electronic structure methods allow for studying a large number of material properties, including electrical properties such as resistivity and mobility, and whether a material is a metal, semiconductor, or an insulator, by estimating the band gap. Optical and magnetic properties can also be obtained, and one can investigate effects that derive purely from quantum mechanics, such as superconductivity, topological invariants, tunnelling, and many others. Additionally, it is equally possible to perform ab initio MD (AIMD) simulations to obtain thermal and mechanical properties, but these are generally very time-consuming calculations.

Atomistic simulations help understand the billions of transistors inside devices like a smartphone, which consist of multiple different materials in extremely thin layers, sometimes just a few atomic layers thick. Even if these materials are well characterized experimentally, their properties can be strongly modified when the thickness is reduced down to the atomic scale.

Another very important technology example is interfaces (and the related field of surface physics) where the assumptions of a continuum description of a material fundamentally break down. The chemical bonding between atoms in the two different materials creates an intermediate region which cannot be described correctly by just using the properties of the individual materials involved in the interface.

Modern electronic devices also often involve novel materials for which experimental observations are limited or expensive to obtain. In these cases, atomistic simulations are highly valuable in order to predict the behavior of the materials before they are even manufactured, and to calculate properties that can be used as input parameters to continuum simulations.

While in silico “experiments” can never fully replace actual measurements, atomistic simulations are a very powerful tool to reduce the number of candidates through computational screening and by helping to interpret experimental results. This can save significant amounts of time and money in the development of novel materials and devices.