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1-dftk.jl
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1-dftk.jl
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### A Pluto.jl notebook ###
# v0.19.26
using Markdown
using InteractiveUtils
# This Pluto notebook uses @bind for interactivity. When running this notebook outside of Pluto, the following 'mock version' of @bind gives bound variables a default value (instead of an error).
macro bind(def, element)
quote
local iv = try Base.loaded_modules[Base.PkgId(Base.UUID("6e696c72-6542-2067-7265-42206c756150"), "AbstractPlutoDingetjes")].Bonds.initial_value catch; b -> missing; end
local el = $(esc(element))
global $(esc(def)) = Core.applicable(Base.get, el) ? Base.get(el) : iv(el)
el
end
end
# ╔═╡ 0ea37f8e-8b13-41d3-8056-25a47d763bf1
begin
using ASEconvert
using AtomsIO
using AtomsIOPython
using CUDA
using CUDA_Runtime_jll
using DFTK
using PlutoUI
using Preferences
using ForwardDiff
using Unitful
using UnitfulAtomic
using LinearAlgebra
using LazyArtifacts
Preferences.set_preferences!(CUDA_Runtime_jll, "version" => "11.8"; export_prefs=true)
end
# ╔═╡ cf8980fe-f641-11ed-099f-1534e7969056
LocalResource("Logos.png")
# ╔═╡ 4a0870f4-e653-4fc4-b91f-0144a9b1ebdd
TableOfContents()
# ╔═╡ 0c32d8e1-a4f2-4d00-aec8-d16eec012235
md"# DFTK: 4 years into a new DFT code"
# ╔═╡ 43c6a5ab-261b-4d5f-8ad0-e6f45d2b786e
md"""
As show case how Julia can be used for developing atomistic materials modelling approaches in practice, we consider in detail the density-functional toolkit (DFTK).
"""
# ╔═╡ 8acfe478-4a75-4a22-9b45-4a525b55cfba
LocalResource("dftk_overview.png")
# ╔═╡ 407a35c6-7d2e-4cc8-8aed-fe1417b61d76
md"""
More **information**:
- [dftk.org](https://dftk.org)
- [Documentation](https://docs.dftk.org)
- [Basic feature overview](https://docs.dftk.org/stable/features/)
- [Material from our 2022 summer school](https://school2022.dftk.org/)
"""
# ╔═╡ bbd486f3-bc32-4719-a9d2-e30227731307
md"## Standard calculations"
# ╔═╡ af098251-6c33-413f-9a83-e925886bead7
md"Let's revisit our iron system from before. To run in in Quantum Espresso, this was the file:"
# ╔═╡ 02b648e4-6dd2-4322-a8e8-ff18b8a5fd7d
print(read("Fe_afm.pwi", String))
# ╔═╡ 17fb9282-b52e-4523-bd4e-2e42f2ceaa4b
md"""
It works, but many will agree this is not the most intuitive way of setting up a calculation. It is almost like learning yet another programming language ;). For comparison we do the same thing using DFTK.
**1.** Via **AtomsBase** (see also next notebook) DFTK is well-integrated with **ASE** (Atomistic simulation environment), so we can just use that to build the system:
"""
# ╔═╡ 0f870a08-a05c-4a6f-b277-f7f63a4aed1d
begin
ase_system = ase.build.bulk("Fe", cubic=true) # Use ASE to build system
system = pyconvert(AbstractSystem, ase_system) # Convert it to AtomsBase
end
# ╔═╡ e635a265-034f-44b9-b254-64804d985d8d
md"""Note that we could have also just used the QE input using a
```julia
system = load_system("Fe_afm.pwi")
```
again building on a package called `AtomsIO` (next notebook) to do the parsing.
**2.** Next we select the pseudopotentials. Many standard pseudos are already available in the [PseudoLibrary](https://github.com/JuliaMolSim/PseudoLibrary), from which they can just be downloaded *on the fly*. For example:
"""
# ╔═╡ 8d126f93-58f5-4a3b-968f-738a770c2012
pseudo_sys = attach_psp(system; Fe=artifact"sg15_2022.02.06_upf/Fe_ONCV_PBE-1.2.upf");
# ╔═╡ 075c3cb8-34ef-4741-88d9-3b3702bf3131
md"Next we setup the DFT model and discretise:"
# ╔═╡ 014af448-1bc7-42aa-a7c8-a0cb7337e55a
begin
magnetic_moments = [-9.6, 9.6]
model = model_PBE(pseudo_sys; magnetic_moments,
smearing=Smearing.MarzariVanderbilt(), temperature=0.01)
basis = PlaneWaveBasis(model; Ecut=25u"Ry", kgrid=(8, 8, 8))
end
# ╔═╡ 0a3e1ce8-fb4b-4210-9b60-a3893608a8df
md"Finally we run the SCF:"
# ╔═╡ 4d11cc62-eefe-4b6f-a414-17216d4c564a
let
ρ = guess_density(basis, magnetic_moments)
scfres = @time self_consistent_field(basis; tol=1e-4, ρ);
etot_Ry = auconvert(u"Ry", scfres.energies.total)
"Total energy in Rh: $etot_Ry"
end
# ╔═╡ 85414116-6684-4243-953d-445b27caeb69
md"## Advanced features"
# ╔═╡ 266f1e46-ff20-4528-a4cf-819887313ca7
md"""
### GPU support in 500 lines of code
Using Julia's HPC abstractions, it took us 500 lines of code changes to provide initial support for GPU calculations:
"""
# ╔═╡ ad953835-a507-4bd4-9de9-824914c3aeff
let
silicon = pyconvert(AbstractSystem, ase.build.bulk("Si"))
silicon = attach_psp(silicon, Si="hgh/lda/Si-q4")
model = model_PBE(silicon)
if has_cuda()
basis = PlaneWaveBasis(model;
Ecut=30, kgrid=(5, 5, 5),
architecture=DFTK.GPU(CuArray)
)
self_consistent_field(basis; tol=1e-2, solver=scf_damping_solver())
end
end;
# ╔═╡ 53897e23-426f-4dc3-8fb5-bef6570969c3
md"This was done by a Physics Bachelor student in **10 weeks**. Performance optimisation is still to be done."
# ╔═╡ be373376-7ad5-42d2-8510-854216f22b07
md"""
### Algorithmic differentiation
Consider elastic strain engineering. We are (roughly) interested in the question:
> How does the band gap ``E_g`` change as we change the lattice parameter ``a``?
Or in other words we want the derivative ``\frac{dE_g}{da}``, so let's compute it:
"""
# ╔═╡ be57402a-6379-4688-9f58-a615fa6bdba2
function silicon_band_gap(a=10.26)
lattice = a /2 * [[0 1 1.];
[1 0 1.];
[1 1 0.]]
Si = ElementPsp(:Si, psp=load_psp("hgh/lda/Si-q4"))
atoms = [Si, Si]
positions = [ones(3)/8, -ones(3)/8]
model = model_LDA(lattice, atoms, positions)
basis = PlaneWaveBasis(model; Ecut=15, kgrid=(4, 4, 4))
scfres = self_consistent_field(basis; tol=1e-4)
# Find direct band gap
gaps = map(scfres.eigenvalues) do εk
εk_rel = εk .- scfres.εF
ε_cbm = minimum(εk_rel[εk_rel .≥ 0])
ε_vbm = maximum(εk_rel[εk_rel .< 0])
ε_cbm - ε_vbm
end
minimum(gaps)
end
# ╔═╡ 384185ac-24e3-4d55-86be-9b273186a0f5
ForwardDiff.derivative(silicon_band_gap, 10.26)
# ╔═╡ 035bd17e-fb4f-429b-872e-b56ac0fb2966
md"""
Arbitrary **user-desired derivatives** in one line of code:
* New properties / derivatives by **non-DFT experts**!
* Breaks **one PhD student per derivative** paradigm
"""
# ╔═╡ 2df9877a-6eb0-4ba6-bf63-f29043ab25ef
let
data = """
file | lines
-------------------- | -------
stres_mgga.f90 | 274
stres_loc.f90 | 148
stres_knl.f90 | 175
stres_har.f90 | 116
stres_cc.f90 | 160
stres_gradcorr.f90 | 287
stres_ewa.f90 | 243
stress.f90 | 285
"""
md"""
### Stress implementation in 20 lines
- Stress is just a post-processing step $\Rightarrow$ not performance critical
- We can **use AD** to implement it
- Comparison of implementation complexity:
- DFTK: **20 lines** [here](https://github.com/JuliaMolSim/DFTK.jl/blob/master/src/postprocess/stresses.jl)
- Quantum Espresso: **1700 lines** [here](https://github.com/QEF/q-e/tree/develop/PW/src).
- Opportunity to **keep code short** without compromising performance.
- Initial support again done by **CS Bachelor student in 10 weeks**.
"""
end
# ╔═╡ b6763a66-c0c1-4897-8e5e-57c5cf20563e
md"""
### Customising algorithms: Supplying a custom SCF solver
"""
# ╔═╡ e6cfa9d4-4c37-44a7-bf05-5765f6b30055
md"Mixing factor: $(@bind mixing_factor Slider(0.0:0.05:1.5; default=1.0, show_value=true))"
# ╔═╡ 01db705b-056b-4afe-9bb7-4e841f6e15da
function my_damped_mixing(SCF_step, ρ0, maxiter; tol)
ρin = ρ0
ρout = SCF_step(ρin)
for n = 1:maxiter
Δρ = ρout - ρin
if norm(Δρ) < tol
break
end
ρnext = ρin + mixing_factor * Δρ
ρin = ρnext
ρout = SCF_step(ρin)
end
(fixpoint=ρin, converged=norm(ρout-ρin) < tol)
end;
# ╔═╡ 08314d83-397a-476d-843a-c64071397765
md"Computational architecture: $(@bind architecture Select([DFTK.CPU(), DFTK.GPU(CuArray)]; default=DFTK.CPU()))"
# ╔═╡ abe2933c-a3e7-42e1-8f28-4476a7cf6e74
let
silicon = pyconvert(AbstractSystem, ase.build.bulk("Si"))
silicon = attach_psp(silicon; Si="hgh/lda/Si-q4")
model = model_LDA(silicon)
basis = PlaneWaveBasis(model; Ecut=20, kgrid=(4, 4, 4), architecture)
scfres = self_consistent_field(basis; tol=1e-4, solver=my_damped_mixing,
damping=1.0) # Turn off DFTK-internal damping
end;
# ╔═╡ f890362d-337d-4487-ac1d-b8a167463a49
md"""
This works immediately with MPI, GPUs, .... This works because the Julia code of `my_damped_mixing` **is compiled to CUDA bytecode** and executed as a custom CUDA kernel!
"""
# ╔═╡ 53d9f116-822c-4684-8d7f-e98fb4d9d83b
md"""
Defining custom models is equally possible, see [the DFTK documentation](https://docs.dftk.org) for examples, such as the [Gross-Pitaevskii example](https://docs.dftk.org/stable/examples/gross_pitaevskii/).
"""
# ╔═╡ dffc1540-2bf0-4a20-9d3d-12805ff2d224
md"""
## Conclusion
- Julia ecosystem crucial to
* save code
* get performance
* play with algorithms
* orchestrate calculations on a high level
- DFTK has appealing features for researchers from mathematics, computer science and method development.
"""
# ╔═╡ 00000000-0000-0000-0000-000000000001
PLUTO_PROJECT_TOML_CONTENTS = """
[compat]
ASEconvert = "~0.1.5"
AtomsIO = "~0.2.1"
AtomsIOPython = "~0.1.0"
CUDA = "~4.2.0"
CUDA_Runtime_jll = "~0.6.0"
DFTK = "~0.6.8"
ForwardDiff = "~0.10.35"
PlutoUI = "~0.7.51"
Preferences = "~1.4.0"
Unitful = "~1.14.0"
UnitfulAtomic = "~1.0.0"
[deps]
ASEconvert = "3da9722f-58c2-4165-81be-b4d7253e8fd2"
AtomsIO = "1692102d-eeb4-4df9-807b-c9517f998d44"
AtomsIOPython = "9e4c859b-2281-48ef-8059-f50fe53c37b0"
CUDA = "052768ef-5323-5732-b1bb-66c8b64840ba"
CUDA_Runtime_jll = "76a88914-d11a-5bdc-97e0-2f5a05c973a2"
DFTK = "acf6eb54-70d9-11e9-0013-234b7a5f5337"
ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
LazyArtifacts = "4af54fe1-eca0-43a8-85a7-787d91b784e3"
LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
PlutoUI = "7f904dfe-b85e-4ff6-b463-dae2292396a8"
Preferences = "21216c6a-2e73-6563-6e65-726566657250"
Unitful = "1986cc42-f94f-5a68-af5c-568840ba703d"
UnitfulAtomic = "a7773ee8-282e-5fa2-be4e-bd808c38a91a"
[preferences.CUDA_Runtime_jll]
version = "11.8"
"""
# ╔═╡ 00000000-0000-0000-0000-000000000002
PLUTO_MANIFEST_TOML_CONTENTS = """
# This file is machine-generated - editing it directly is not advised
julia_version = "1.9.0"
manifest_format = "2.0"
project_hash = "1f7dd3679f065b1c3dcb30b83e0da0904b23b50e"
[[deps.ASEconvert]]
deps = ["AtomsBase", "CondaPkg", "PeriodicTable", "PythonCall", "Unitful", "UnitfulAtomic"]
git-tree-sha1 = "2590f99b4970b99036897ed423895fba751d8633"
uuid = "3da9722f-58c2-4165-81be-b4d7253e8fd2"
version = "0.1.5"
[[deps.AbstractFFTs]]
deps = ["LinearAlgebra"]
git-tree-sha1 = "16b6dbc4cf7caee4e1e75c49485ec67b667098a0"
uuid = "621f4979-c628-5d54-868e-fcf4e3e8185c"
version = "1.3.1"
weakdeps = ["ChainRulesCore"]
[deps.AbstractFFTs.extensions]
AbstractFFTsChainRulesCoreExt = "ChainRulesCore"
[[deps.AbstractPlutoDingetjes]]
deps = ["Pkg"]
git-tree-sha1 = "8eaf9f1b4921132a4cff3f36a1d9ba923b14a481"
uuid = "6e696c72-6542-2067-7265-42206c756150"
version = "1.1.4"
[[deps.Adapt]]
deps = ["LinearAlgebra", "Requires"]
git-tree-sha1 = "76289dc51920fdc6e0013c872ba9551d54961c24"
uuid = "79e6a3ab-5dfb-504d-930d-738a2a938a0e"
version = "3.6.2"
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