Parallelization

• Identify the most costly function (repulsion)

function repulsion(basis, molecule::Molecule)
    n = length(basis)
    G = zeros(n, n, n, n)

    for c in CartesianIndices(G)
        i, j, t, u = c[1], c[2], c[3], c[4]

        basisᵢ, basisⱼ, basisₜ, basisᵤ = basis[i], basis[j], basis[t], basis[u]
        Rᵢ, Rⱼ, Rₜ, Rᵤ = basisᵢ.R, basisⱼ.R, basisₜ.R, basisᵤ.R
        m, p, q, r = basisᵢ.size, basisⱼ.size, basisₜ.size, basisᵤ.size

        ℓᵢ, mᵢ, nᵢ = basisᵢ.ℓ, basisᵢ.m, basisᵢ.n
        ℓⱼ, mⱼ, nⱼ = basisⱼ.ℓ, basisⱼ.m, basisⱼ.n
        ℓₜ, mₜ, nₜ = basisₜ.ℓ, basisₜ.m, basisₜ.n
        ℓᵤ, mᵤ, nᵤ = basisᵤ.ℓ, basisᵤ.m, basisᵤ.n

        for e in CartesianIndices((m, p, q, r))
            k, l, s, v = e[1], e[2], e[3], e[4]

            αᵢ, αⱼ, αₜ, αᵤ = basisᵢ.α[k], basisⱼ.α[l], basisₜ.α[s], basisᵤ.α[v]
            dᵢ, dⱼ, dₜ, dᵤ = basisᵢ.d[k], basisⱼ.d[l], basisₜ.d[s], basisᵤ.d[v]
            Nᵢ, Nⱼ, Nₜ, Nᵤ = basisᵢ.N[k], basisⱼ.N[l], basisₜ.N[s], basisᵤ.N[v]

            tei = dᵢ * dⱼ * dₜ * dᵤ * Nᵢ * Nⱼ * Nₜ * Nᵤ
            tei *= Gxyz(ℓᵢ, mᵢ, nᵢ, ℓⱼ, mⱼ, nⱼ, ℓₜ, mₜ, nₜ, ℓᵤ, mᵤ, nᵤ, αᵢ, αⱼ, αₜ, αᵤ, Rᵢ, Rⱼ, Rₜ, Rᵤ)

            G[i, j, t, u] += tei
        end
    end

    return G
end

If I parallelize the for loop, I cannot write on G in parallel form. Take G out of the for loop.