[WIP] InteratomicPotentials.jl

This module implements methods (energies, forces, and virial tensors) for a variety of interatomic potentials, including the SNAP Potential (Thompson et al. 2014, see notes for current limitations).

Project goals:

• Having a defined structure for each potential
  • The potential structure will hold the trainable and nontrainable parameters
  • The potential structure will naturally plug-and-play with fitting and uncertainty quantification codes (PotentialLearning.jl and PotentialUQ.jl)
  • Todo: Develop a struct and interface for Interatomic Potentials that allows the creation of more complex potentials (i.e., sums of potentials or mixed type potentials for systems with multiple elements.)
• Allow for easy use of automatic differentiation through framework.

Right now, this module contains the framework for the following potentials

• Lennard Jones
• SNAP (explicit multi-element support (chem flag) is nominally supported but not currently tested.)

To Dos:

• Improve neighborlist framework for multi-element systems (i.e. allowing potentials to differentiate based on the element of atom i and atom j).
• Finish testing SNAP potential for explicit multi-element flag.
• Create a structure that allows for the complexification and combination of interatomic potentials.
  • Ideally this would allow for the specification of which potential should be used in multi-element systems for each pair of elements.
• Add zbl potential.
• Interface with MDP.
• See issues for more topics.

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).

# Define an atomic system
atom1     = Atom(element, ( @SVector [1.0, 0.0, 0.0] ) * 1u"Å")
atom2    = Atom(element, ( @SVector [1.0, 0.25, 0.0] ) * 1u"Å")
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)

ϵ = 1.0
σ = 0.25 * 1u"Å"
rcutoff  = 2.0 * 1u"Å"
lj       = LennardJones(ϵ, σ, rcutoff)           # <: EmpiricalPotential <: ArbitraryPotential
pe       = potential_energy(system, lj)               # <: Float64
f        = force(system, lj)                          # <: Vector{SVector{3, Float64}}
v        = virial(system, lj)                         # <: Float64
v_tensor = virial_stress(system, lj)                  # <: SVector{6, Float64}

See "/test/" for further examples.

Potential Types

All interatomic potentials listed in this project are subtypes of ArbitraryPotential. At this point, as of v0.11, there are two branches of potentials: EmpiricalPotential and BasisPotential. EmpiricalPotentials include two-body potentials like BornMayer, LennardJones. BasisPotential require the expansion of the configration of atoms using some basis set of functions and a set of coefficients for each of the members of the expansion in order to calculate energies and forces (i.e. SNAP).

EmpiricalPotential <: ArbitraryPotential
BornMayer <: EmpiricalPotential
LennardJones <: EmpiricalPotential
Coulomb     <: EmpiricalPotential
ZBL         <: EmpiricalPotential

BasisPotential <: ArbitraryPotential
SNAP           <: BasisPotential

BasisPotential are associated with the functions that evaluate the basis set with parameters necessary for the particular basis expansion used. For example,

SNAP_parameters = SNAPParams(...)
basis_evaluation = evaluate(system, SNAP_parameters)
gradient_basis_evaulation = evaluate_d(system, SNAP_parameters)

For linear basis expansions, the energies and forces are dot products between the potential coefficients and the results of evaulate and evalulate_d, respectively.