From 660b7e7ca612f2979d23fd61c3d0c66164037148 Mon Sep 17 00:00:00 2001 From: James Gardner Date: Fri, 16 Jul 2021 21:01:10 +0100 Subject: [PATCH 1/2] First try with correct angular potential Derivative currently incorrect --- src/NOAu111.jl | 31 +++++++++++++++++++++---------- src/diabatic_elements.jl | 7 +++++-- 2 files changed, 26 insertions(+), 12 deletions(-) diff --git a/src/NOAu111.jl b/src/NOAu111.jl index 8e01e9e..4103f30 100644 --- a/src/NOAu111.jl +++ b/src/NOAu111.jl @@ -22,9 +22,11 @@ struct NOAu{V1,V2,V3,V4,V5,A} <: DiabaticModel AuAu::V4 image_potential::V5 atoms::A + Nindex::Int + Oindex::Int end -NOAu(jatoms) = NOAu(2, H00(), H11(), H01(), AuAu(), image(D, C, zimage), jatoms) +NOAu(jatoms, Nindex, Oindex) = NOAu(2, H00(), H11(), H01(), AuAu(), image(D, C, zimage), jatoms, Nindex, Oindex) function NOAu(symbols::AbstractVector{Symbol}, cell) jatoms = JuLIP.Atoms( @@ -34,12 +36,15 @@ function NOAu(symbols::AbstractVector{Symbol}, cell) cell=au_to_ang.(cell.vectors'), pbc=cell.periodicity ) - NOAu(jatoms) + Nindex = findfirst(isequal(7), jatoms.Z) + Oindex = findfirst(isequal(8), jatoms.Z) + NOAu(jatoms, Nindex, Oindex) end function NonadiabaticModels.potential(model::NOAu, R::AbstractMatrix) JuLIP.set_positions!(model.atoms, au_to_ang.(R)) + update_angular_potential!(model, model.atoms) Au = eV_to_au(JuLIP.energy(model.AuAu, model.atoms)) V11 = eV_to_au(JuLIP.energy(model.H00, model.atoms)) + Au V22 = eV_to_au(JuLIP.energy(model.H11, model.atoms) + ϕ - Eₐ) + Au @@ -53,16 +58,15 @@ end function NonadiabaticModels.derivative!(model::NOAu, D::AbstractMatrix{<:Hermitian}, R::AbstractMatrix) JuLIP.set_positions!(model.atoms, au_to_ang.(R)) + update_angular_potential!(model, model.atoms) Au = -JuLIP.forces(model.AuAu, model.atoms) D11 = -JuLIP.forces(model.H00, model.atoms) + Au D22 = -JuLIP.forces(model.H11, model.atoms) + Au D12 = -JuLIP.forces(model.H01, model.atoms) Oderiv, Nderiv = evaluate_image_derivative(model) - Nindex = findfirst(isequal(7), model.atoms.Z) - Oindex = findfirst(isequal(8), model.atoms.Z) - D22[Nindex] += SVector{3}(0, 0, Nderiv) - D22[Oindex] += SVector{3}(0, 0, Oderiv) + D22[model.Nindex] += SVector{3}(0, 0, Nderiv) + D22[model.Oindex] += SVector{3}(0, 0, Oderiv) for i=1:length(model.atoms) for j=1:3 @@ -78,8 +82,8 @@ end function evaluate_image_potential(model::NOAu) at = model.atoms - Nindex = findfirst(isequal(7), at.Z) - Oindex = findfirst(isequal(8), at.Z) + Nindex = model.Nindex + Oindex = model.Oindex total_mass = at.M[Oindex] + at.M[Nindex] zcom = (at[Oindex][3]*at.M[Oindex]+at[Nindex][3]*at.M[Nindex]) / total_mass image = JuLIP.evaluate(model.image_potential, zcom) @@ -88,8 +92,8 @@ end function evaluate_image_derivative(model::NOAu) at = model.atoms - Nindex = findfirst(isequal(7), at.Z) - Oindex = findfirst(isequal(8), at.Z) + Nindex = model.Nindex + Oindex = model.Oindex total_mass = at.M[Oindex] + at.M[Nindex] zcom = (at[Oindex][3]*at.M[Oindex]+at[Nindex][3]*at.M[Nindex]) / total_mass image = JuLIP.evaluate_d(model.image_potential, zcom) @@ -98,4 +102,11 @@ function evaluate_image_derivative(model::NOAu) return Oderiv, Nderiv end +function update_angular_potential!(model::NOAu, at) + O = at[model.Oindex] + N = at[model.Nindex] + cosθ = (O[3] - N[3]) / norm(O - N) + model.H11.potentials[1,2] = repulsiveAuN(B₁, β₁, r₁AuN, cosθ, rcutoff) +end + end diff --git a/src/diabatic_elements.jl b/src/diabatic_elements.jl index f727e45..fd34517 100644 --- a/src/diabatic_elements.jl +++ b/src/diabatic_elements.jl @@ -4,6 +4,11 @@ morse(F, γ, r₀) = JuLIP.@analytic r -> F*(1 - exp(-γ * (r - r₀)))^2 coupling(A2, A3, γ, r_cut) = JuLIP.@analytic r -> -A2*(1/(1+A3*exp(γ*r)) - 1/(1+A3*exp(γ*r_cut))) const zero_potential = JuLIP.@analytic r -> 0 +function repulsiveAuN(A, α, r₀, cosθ, r_cut) + JuLIP.@analytic( + r -> A*(exp(-2α*(r-r₀)) - exp(-2α*(r_cut-r₀)) - 2cosθ^2*(exp(-α*(r-r₀)) - exp(-α*(r_cut-r₀)))) + ) +end image(D, C, zimage) = JuLIP.@analytic z -> -D / sqrt(C^2 + (z-zimage)^2) struct DiabaticElement{V,Z} <: JuLIP.SitePotential @@ -47,12 +52,10 @@ end function H11() V11AuO = repulsive(A₁, α₁, rcutoff) - V11AuN = repulsive(B₁, β₁, rcutoff) V11NO = morse(F₁, γ₁, r₁NO) potentials = DefaultDict{Tuple, JuLIP.AnalyticFunction}(zero_potential) potentials[1,3] = V11AuO - potentials[1,2] = V11AuN potentials[2,3] = V11NO DiabaticElement(potentials) From 4e19d35f72a439eef1c8318e22833d37cb23274e Mon Sep 17 00:00:00 2001 From: James Gardner Date: Sat, 24 Jul 2021 13:27:08 +0100 Subject: [PATCH 2/2] Fix everything --- Project.toml | 5 +- plot/fig2.png | Bin 74913 -> 85327 bytes plot/plot.jl | 44 +++++------ src/NOAu111.jl | 44 ++--------- src/diabatic_elements.jl | 83 +++++++++++++------- src/h11.jl | 163 +++++++++++++++++++++++++++++++++++++++ test/runtests.jl | 18 +++-- 7 files changed, 257 insertions(+), 100 deletions(-) create mode 100644 src/h11.jl diff --git a/Project.toml b/Project.toml index 299dce0..67589ad 100644 --- a/Project.toml +++ b/Project.toml @@ -10,7 +10,9 @@ LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e" NonadiabaticDynamicsBase = "78c76ebc-5665-4934-b512-82d81b5cbfb7" NonadiabaticModels = "c814dc9f-a51f-4eaf-877f-82eda4edad48" StaticArrays = "90137ffa-7385-5640-81b9-e52037218182" +UnPack = "3a884ed6-31ef-47d7-9d2a-63182c4928ed" Unitful = "1986cc42-f94f-5a68-af5c-568840ba703d" +Zygote = "e88e6eb3-aa80-5325-afca-941959d7151f" [compat] julia = "1" @@ -19,6 +21,7 @@ julia = "1" ASE = "51974c44-a7ed-5088-b8be-3e78c8ba416c" PyCall = "438e738f-606a-5dbb-bf0a-cddfbfd45ab0" Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40" +UnitfulAtomic = "a7773ee8-282e-5fa2-be4e-bd808c38a91a" [targets] -test = ["Test", "PyCall", "ASE"] +test = ["Test", "PyCall", "ASE", "UnitfulAtomic"] diff --git a/plot/fig2.png b/plot/fig2.png index eaabad264022129a5043ae1622174d9087dbdda6..b5d5c11a97523f0755436bbd331276aa3588d89e 100644 GIT binary patch literal 85327 zcmb5VbyQW|7dCnj1r+I$M!FFxDFHc1cXxwycY}0ycXxM*NC*Pb-QC@Fm+$ZU#<+jo 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JuLIP.@analytic r -> 0 +image(D, C, zimage) = JuLIP.@analytic z -> -D / sqrt(C^2 + (z-zimage)^2) -function repulsiveAuN(A, α, r₀, cosθ, r_cut) - JuLIP.@analytic( - r -> A*(exp(-2α*(r-r₀)) - exp(-2α*(r_cut-r₀)) - 2cosθ^2*(exp(-α*(r-r₀)) - exp(-α*(r_cut-r₀)))) - ) +function coupling(A2, A3, γ, r_cut) + cutoff = 1/(1+A3*exp(γ*r_cut)) + JuLIP.@analytic r -> -A2*(1/(1+A3*exp(γ*r)) - cutoff) end -image(D, C, zimage) = JuLIP.@analytic z -> -D / sqrt(C^2 + (z-zimage)^2) struct DiabaticElement{V,Z} <: JuLIP.SitePotential potentials::V @@ -49,39 +51,60 @@ function H01() DiabaticElement(potentials) end -function H11() - - V11AuO = repulsive(A₁, α₁, rcutoff) - V11NO = morse(F₁, γ₁, r₁NO) - - potentials = DefaultDict{Tuple, JuLIP.AnalyticFunction}(zero_potential) - potentials[1,3] = V11AuO - potentials[2,3] = V11NO - - DiabaticElement(potentials) -end - function JuLIP.evaluate!(tmp, V::DiabaticElement, Rs, Zs, z0) Es = 0.0 i0 = JuLIP.z2i(V, z0) - for (R, Z) in zip(Rs, Zs) - i = JuLIP.z2i(V, Z) - f = select_potential(V, i0, i) - r = norm(R) + + # If X == N or O site, calculate X-Au potential + if (i0 == 2) || (i0 == 3) + for (R, Z) in zip(Rs, Zs) + i = JuLIP.z2i(V, Z) + if i == 1 + f = select_potential(V, i0, i) + r = norm(R) + Es += JuLIP.evaluate!(tmp, f, r) + end + end + end + + # If N site, calculate NO potential + if i0 == 2 + closest = find_closest(Rs, Zs, 8) + f = select_potential(V, i0, 3) + r = norm(Rs[closest]) Es += JuLIP.evaluate!(tmp, f, r) end - return Es / 2 + + return Es end function JuLIP.evaluate_d!(dEs, tmp, V::DiabaticElement, Rs, Zs, z0) i0 = JuLIP.z2i(V, z0) - for (j, (R, Z)) in enumerate(zip(Rs, Zs)) - i = JuLIP.z2i(V, Z) - f = select_potential(V, i0, i) - r = norm(R) - R̂ = R / r - dEs[j] = JuLIP.evaluate_d(f, r) * R̂ / 2 + + for i=1:length(dEs) + dEs[i] = zero(dEs[i]) end + + if (i0 == 2) || (i0 == 3) + for (j, (R, Z)) in enumerate(zip(Rs, Zs)) + i = JuLIP.z2i(V, Z) + if i == 1 + f = select_potential(V, i0, i) + r = norm(R) + R̂ = R / r + dEs[j] = JuLIP.evaluate_d(f, r) * R̂ + end + end + end + + if i0 == 2 + closest = find_closest(Rs, Zs, 8) + f = select_potential(V, i0, 3) + r = norm(Rs[closest]) + R̂ = Rs[closest] / r + dEs[closest] = JuLIP.evaluate_d(f, r) * R̂ + end + return dEs end diff --git a/src/h11.jl b/src/h11.jl new file mode 100644 index 0000000..dd17e46 --- /dev/null +++ b/src/h11.jl @@ -0,0 +1,163 @@ + +using UnPack +using Zygote + +struct H11{I,A,V} <: JuLIP.AbstractCalculator + image::I + AuN::A + potential::V +end + +function H11(jatoms) + image = ImagePotential(jatoms) + AuN = AuNCoupling() + potential = H11DiabaticElement() + H11(image, AuN, potential) +end + +function H11DiabaticElement() + V11AuO = repulsive(A₁, α₁, rcutoff) + V11NO = morse(F₁, γ₁, r₁NO) + + potentials = DefaultDict{Tuple, JuLIP.AnalyticFunction}(zero_potential) + potentials[1,3] = V11AuO + potentials[2,3] = V11NO + + DiabaticElement(potentials) +end + +function JuLIP.energy(calc::H11, at::JuLIP.AbstractAtoms; domain=1:length(at)) + e1 = JuLIP.energy(calc.image, at) + e2 = JuLIP.energy(calc.AuN, at; domain=domain) + e3 = JuLIP.energy(calc.potential, at; domain=domain) + return e1 + e2 + e3 +end + +function JuLIP.forces(calc::H11, at::JuLIP.AbstractAtoms; kwargs...) + f1 = JuLIP.forces(calc.image, at) + f2 = JuLIP.forces(calc.AuN, at; kwargs...) + f3 = JuLIP.forces(calc.potential, at; kwargs...) + return f1 + f2 + f3 +end + +struct ImagePotential{V,T} <: JuLIP.AbstractCalculator + V::V + mO::T + mN::T + mtotal::T + iN::Int + iO::Int + slab_plane::T +end + +function ImagePotential(jatoms) + iN = findfirst(isequal(7), jatoms.Z) + iO = findfirst(isequal(8), jatoms.Z) + mN = jatoms.M[iN] + mO = jatoms.M[iO] + mtotal = mO + mN + + gold_positions = jatoms.X[jatoms.Z .== 79] + slab_plane = maximum(x->x[3], gold_positions) + + V = image(D, C, zimage) + ImagePotential(V, mO, mN, mtotal, iN, iO, slab_plane) +end + +JuLIP.energy(calc::ImagePotential, at::JuLIP.AbstractAtoms) = JuLIP.evaluate(calc, at.X) +JuLIP.forces(calc::ImagePotential, at::JuLIP.AbstractAtoms) = -JuLIP.evaluate_d(calc, at.X) + +function JuLIP.evaluate(calc::ImagePotential, R) + @unpack mO, mN, mtotal, iN, iO = calc + zcom = (R[iO][3]*mO + R[iN][3]*mN) / mtotal - calc.slab_plane + return JuLIP.evaluate(calc.V, zcom) +end + +function JuLIP.evaluate_d(calc::ImagePotential, R) + @unpack mO, mN, mtotal, iN, iO = calc + zcom = (R[iO][3]*mO + R[iN][3]*mN) / mtotal - calc.slab_plane + image = JuLIP.evaluate_d(calc.V, zcom) + out = zero(R) + out[iN] = SVector{3}(0, 0, image * mN / mtotal) + out[iO] = SVector{3}(0, 0, image * mO / mtotal) + return out +end + +struct AuNCoupling{V,Z} <: JuLIP.SitePotential + V::V + zlist::Z +end + +function AuNCoupling() + V(cosθ, r) = B₁*(exp(-2β₁*(r-r₁AuN)) - exp(-2β₁*(rcutoff-r₁AuN)) + - 2cosθ^2*(exp(-β₁*(r-r₁AuN)) - exp(-β₁*(rcutoff-r₁AuN))) + ) + zlist = JuLIP.Potentials.ZList([:Au, :N, :O]) + AuNCoupling(V, zlist) +end + +function JuLIP.evaluate!(tmp, V::AuNCoupling, Rs, Zs, z0) + Es = 0.0 + i0 = JuLIP.z2i(V, z0) + if i0 == 2 # Evaluated only at N site + cosθ = calculate_cosθ(Rs, Zs) + for (R, Z) in zip(Rs, Zs) + i = JuLIP.z2i(V, Z) + if i == 1 + r = norm(R) + Es += V.V(cosθ, r) + end + end + end + return Es +end + +function calculate_cosθ(Rs, Zs) + closest = find_closest(Rs, Zs, 8) + NO_distance = Rs[closest] + cosθ = NO_distance[3] / norm(NO_distance) + return cosθ +end + +""" +Find the nearest atom with `z == ztarget`. +This is used to make sure the NO molecule interacts only with itself, +not the periodic images. +""" +function find_closest(Rs, Zs, ztarget) + target_indices = findall(isequal(ztarget), Zs) + max_dist = 100 + closest = target_indices[1] + for i in target_indices + dist = norm(Rs[i]) + if dist < max_dist + closest = i + max_dist = dist + end + end + return closest +end + +""" +This is the slowest part of the code, a hand-coded derivative would be faster, +or possibly a different autodiff package. +""" +function JuLIP.evaluate_d!(dEs, tmp, V::AuNCoupling, Rs, Zs, z0) + grad = Zygote.gradient(x -> JuLIP.evaluate!(tmp, V, x, Zs, z0), Rs)[1] + if grad === nothing + for i=1:length(dEs) + dEs[i] = zero(dEs[i]) + end + else + for i=1:length(grad) + if grad[i] === nothing + dEs[i] = zero(dEs[i]) + else + dEs[i] = grad[i] + end + end + end + return dEs +end + +JuLIP.cutoff(::AuNCoupling) = rcutoff diff --git a/test/runtests.jl b/test/runtests.jl index 96cec24..e9336f1 100644 --- a/test/runtests.jl +++ b/test/runtests.jl @@ -5,29 +5,35 @@ using PyCall using ASE using NonadiabaticDynamicsBase using NonadiabaticModels -using LinearAlgebra: norm +using Unitful, UnitfulAtomic build = pyimport("ase.build") -slab = build.fcc111("Au", size=(2,2,3), vacuum=10.0) +slab = build.fcc111("Au", size=(2,4,4), vacuum=10.0) no = build.molecule("NO") build.add_adsorbate(slab, no, 5, "ontop") at = JuLIP.Atoms(ASEAtoms(slab)) rattle!(at, 0.5) +@testset "H11" begin + @test JuLIP.Testing.fdtest(NOAu111.AuNCoupling(), at, verbose=false) + @test JuLIP.Testing.fdtest(NOAu111.H11DiabaticElement(), at, verbose=false) + @test JuLIP.Testing.fdtest(NOAu111.ImagePotential(at), at, verbose=false) +end + @testset "Components" begin @test JuLIP.Testing.fdtest(NOAu111.AuAu(), at, verbose=false) @test JuLIP.Testing.fdtest(NOAu111.H00(), at, verbose=false) @test JuLIP.Testing.fdtest(NOAu111.H01(), at, verbose=false) - @test JuLIP.Testing.fdtest(NOAu111.H11(), at, verbose=false) + @test JuLIP.Testing.fdtest(NOAu111.H11(at), at, verbose=false) end @testset "Final model" begin - R = ang_to_au.(Matrix(hcat(at.X...))) - c = PeriodicCell(ang_to_au.(cell(at)')) + R = austrip.(Matrix(hcat(at.X...))u"Å") + c = NonadiabaticDynamicsBase.PeriodicCell(austrip.(cell(at)' .* u"Å")) - model = NOAu(chemical_symbols(at), c) + model = NOAu(chemical_symbols(at), c, R) @test JuLIP.Testing.fdtest(x->potential(model, x), x->derivative(model, x), R, verbose=false) end