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ClassicalModels

NQCModels.ClassicalModels — Module
ClassicalModels

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 ClassicalModel, which all models should subtype.

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NQCModels.ClassicalModels.ClassicalModel — Type
ClassicalModel <: Model

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

Implementation

ClassicalModels 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 Classical 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.ClassicalModels.ClassicalModel
    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
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NQCModels.ClassicalModels.Free — Type
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
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NQCModels.ClassicalModels.Harmonic — Type
Harmonic(m=1.0, ω=1.0, r₀=0.0)

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

m, ω, r₀ are the mass, frequency, and equilibrium position respectively and can be supplied as numbers or Matrices to create a compound model for multiple particles. 

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)
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