InteratomicPotentials.jl

This repository implements some basic language and syntax for manipulating interatomic potentials in Julia. The primary purpose of this package is to design a flexible package for use with data-driven and parameter-fitted interatomic potentials. This package is also being designed in order to allow users to define custom potentials and forces for use in molecular dynamics. This package also supports the Spectral Neighbor Analysis Potential (SNAP) potential of Thompson et al. 2015 (see documentation for bibliography) and a naive hacking of the Atomic Cluster Expansion of Drautz 2019 through the ACE1.jl julia package. We are working toward more complete implementation of these machine learning or data-driven potentials in the context of the CESMIX julia suite that seeks to fit and run these potentials for molecular dynamics. For additional details, see the CESMIX ecosystem.

This package is part of the CESMIX molecular modeling suite. This package is also intended to be used with Atomistic.jl (for molecular dynamics, with Molly.jl), and PotentialLearning.jl (for fitting potentials from data).

This package is a work in progress.

WARNING: As of v0.2.8, SNAP implementation is inconsistent with ACE implementation, and additionally, may produce incorrect values! (See this issue). Use at your own risk!

Working Example

In order to compute the interatomic energy of a system, or the forces between atoms in a system, the user has to

• 1. define an AbstractSystem using AtomsBase and
• 2. construct a potential (subtype of an ArbitraryPotential).

Once these two structures have ben instantiated, the quantity of interest can be computed using the signature func(system, potential).

First, let's create a configuration:

using InteratomicPotentials, StaticArrays
using AtomsBase, Unitful, UnitfulAtomic
# Define an atomic system
elem = :Ar
atom1     = Atom(elem, ( @SVector [1.0, 0.0, 0.0] ) * 1u"Å")
atom2    = Atom(elem, ( @SVector [1.0, 0.25, 0.0] ) * 1u"Å")
atoms = [atom1,atom2]
box = [[1., 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 1.0]] * 1u"Å"
bcs = [DirichletZero(), Periodic(), Periodic()]
system   = FlexibleSystem(atoms, box , bcs)

Now we can define the parameters of our interatomic potential:

ϵ = 1.0 * 1u"eV"
σ = 0.25 * 1u"Å"
rcutoff  = 2.25 * 1u"Å"
lj       = LennardJones(ϵ, σ, rcutoff, [elem])           # <: EmpiricalPotential <: AbstractPotential

Now we can compute a variety of quantities of the system:

pe       = potential_energy(system, lj)               # <: Float64 (Hartree)
f        = force(system, lj)                          # <: Vector{SVector{3, Float64}} (Hartree/Bohr)
v        = virial(system, lj)                         # <: Float64 (Hartree)
v_tensor = virial_stress(system, lj)                  # <: SVector{6, Float64} (Hartree)

When computing the force, the energy is already available. A convenience implementation that returns both quantities is given by:

pe, f    = energy_and_force(system, lj)

See "/test/" for further examples.

Utility functions

There are a growing number of features designed to allow handle of potential parameter easier. For example, one can retrieve the parameters of a potential via:

get_rcutoff(lj) # Gets radial cutoff (here: 2.25 * 1u"Angstrom")
get_species(lj) # Returns the species the potential is defined for (here: [:Ar])
get_parameters(lj) # Returns the parameters (here: [ϵ, σ])
set_parameters(lj, (ϵ = 2.0 * 1u"eV", σ = 1.0 * 1u"Å")) # Set parameters (returns a new potential)

Potential Types

All interatomic potentials listed in this project are subtypes of ArbitraryPotential. There are three types of potentials currently implemented: EmpiricalPotential, BasisPotential, and combination potentials via MixedPotentials.

EmpiricalPotentials include two-body potentials like BornMayer, LennardJones. MixedPotential is a convenience type for allowing the linear combination of potentials. An example would be:

lj1 = LennardJones(1.0 * u"eV", 1.0 * u"Angstrom", 2.5 * u"Angstrom", [:Ar]) # Ar-Ar Interactions
lj2 = LennardJones(1.0 * u"eV", 1.5 * u"Angstrom", 3.0 * u"Angstrom", [:Xe]) # Xe-Xe Interactions
lj3 = LennardJones(1.5 * u"eV", 1.3 * u"Angstrom", 2.5 * u"Angstrom", [:Ar, :Xe]) # Ar-Xe Interactions
lj = lj1 + lj2 + lj3# Potential defined for all interactions in an Ar-Xe system.

EmpiricalPotential <: AbstractPotential
BornMayer <: EmpiricalPotential
LennardJones <: EmpiricalPotential
Coulomb     <: EmpiricalPotential
ZBL         <: EmpiricalPotential

LinearCombinationPotential <: MixedPotential

BasisPotential <: AbstractPotential
SNAP           <: BasisPotential
ACE            <: BasisPotential