AdiabaticModels

AdiabaticModels

All models defined within this module have only a single electronic state and return potentials as scalars and derivatives as simple arrays.

The central abstract type is the AdiabaticModel, which all models should subtype.

AdiabaticASEModel{A} <: AdiabaticModel

Wrapper for an ase.Atoms object that has a calculator attached. This Model will synchronise the positions with the ase object and handle the unit conversions.

Implements both potential and derivative!.

Notes on calling Python from Julia

Both PyCall.jl and PythonCall.jl can be used to create the ase.Atoms object, but PythonCall.jl is preferred.

AdiabaticModel <: Model

AdiabaticModels represent the potentials from classical molecular dynamics where the potential is a function of the position.

Implementation

AdiabaticModels should implement:

• potential(model, R)
• derivative!(model, D, R) (this is the derivative of the potential energy with respect to the positions)
• ndofs(model) (these are the degrees of freedom)

Example

This example creates a 2 dimensional adiabatic model MyModel. We implement the 3 compulsory functions then evaluate the potential. Here, the argument R is an AbstractMatrix since this is a 2D model that can accept multiple atoms.

struct MyModel{P} <: NQCModels.AdiabaticModels.AdiabaticModel
    param::P
end

NQCModels.ndofs(::MyModel) = 2

NQCModels.potential(model::MyModel, R::AbstractMatrix) = model.param*sum(R.^2)
NQCModels.derivative!(model::MyModel, D, R::AbstractMatrix) = D .= model.param*2R

model = MyModel(10)

NQCModels.potential(model, [1 2; 3 4])

# output

300

DarlingHollowayElbow()

Adiabatic elbow potential from Darling and Holloway: Faraday Discuss., 1993, 96, 43-54

DiatomicHarmonic(r₀=1.0)

Harmonic interaction between two particles.

Free()

Zero external potential everywhere. Useful for modelling free particles.

julia> model, R = Free(3), rand(3, 10);

julia> potential(model, R)
0.0

julia> derivative(model, R)
3×10 Matrix{Float64}:
 0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0
 0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0
 0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0

Harmonic(m=1.0, ω=1.0, r₀=0.0)

Adiabatic harmonic potential. $V(x) = mω^2(x-r₀)^2 / 2$

julia> using Symbolics;

julia> @variables x, m, ω, r₀;

julia> model = Harmonic(m=m, ω=ω, r₀=r₀);

julia> potential(model, hcat(x))
0.5m*(ω^2)*((x - r₀)^2)

julia> derivative(model, hcat(x))
1×1 Matrix{Num}:
 m*(x - r₀)*(ω^2)

Parameters.@with_kw struct Morse{T} <: AdiabaticModel

References

J. Chem. Phys. 88, 4535 (1988)

Eq. 43

Eq. 36

Eq. 44