Traits used for potentials

As mentioned above, potential functions can be used to model all kinds of interactions between particles such as bonded and non-bonded interactions. In Lumol, Potential is a trait. To further distinguish between bonded interactions (bond lengths, angles and dihedrals) and non-bonded interactions, we use another trait (often called marker traits). Your possible options to further specialise a Potential are

• PairPotential for non-bonded two body interactions;
• BondPotential for covalent bonds interactions;
• AnglePotential for covalent angles interactions;
• DihedralPotential for covalent dihedral angles interactions.

For our Mie potential implementation, we will have to implement both the Potential as well as the PairPotential traits. If we wanted to implement a function that can be used as non-bonded as well as bond-length potential, we’d have to implement Potential, PairPotential as well as BondPotential. “Implementing a trait” means that we will define a struct for which we will add functions to satisfy the traits’ requirements.

Let’s start by having a look at the documentation for Potential: open the API documentation. As you can see from the trait, a Potential defines two functions, energy and force (we ignore the Sync + Send statement for now):

pub trait Potential: Sync + Send {
    fn energy(&self, x: f64) -> f64;
    fn force(&self, x: f64) -> f64;
}

energy will compute the interaction energy between atoms as a function of x. The force is defined as the negative derivative of the energy function with respect to x.

Both functions take a single, scalar argument and return a single scalar value. In our case x stands for the distance between two interaction sites. Note that only the function definitions – without a function body – are specified. We will have to implement these functions for our potential.