[WIP] Additional exx kernels: Voxel averaged and Wigner-Seitz truncation by toschaefer · Pull Request #1282 · JuliaMolSim/DFTK.jl

toschaefer · 2026-03-11T08:03:44Z

Two additional useful strategies for the Coulomb kernel for electron repulsion integrals (e.g. for exx).

Wigner-Seitz truncation
R. Sundararaman, T. A. Arias. Phys. Rev. B 87, 165122 (2013)

Voxel averaged (mean potential)
T. Schaefer et al, J. Chem. Phys. 160, 051101 (2024)
This requires Gauss-Legendre quadrature points, hence I added the package FastGaussQuadrature to the dependencies.

Sync with upstream

antoine-levitt · 2026-04-27T16:17:37Z

Nice! Particularly interested in the Wigner-Seitz truncation - is there any reason to do anything else? It seems to me this is the superior approach? Do we really want to support the voxel averaged? Also maybe some opportunities to share code with ewald.jl, but I haven't looked too closely.

It'd be nice to have a generalized API for all these functions that return centered functions (we have a couple of those: densities guesses, local pseudos, projectors, coulomb kernels, etc.). I think long-term we want the ability to get their real-space and partial Fourier transforms (wrt 1 or 2 dimensions), so we can do eg 2D materials. But maybe it's not worth unifying since they have quite different requirements (numerical psp vs analytic but singular coulomb really are quite different computationally)

CC @denizunel

mfherbst · 2026-04-28T06:45:01Z

Also maybe some opportunities to share code with ewald.jl,

I think so, but I'd keep that for later, same as the generalized API. I'm currently looking at this on the side to streamline the code a bit, will hopefully push a review in the next week.

toschaefer · 2026-05-16T15:47:05Z

Nice! Particularly interested in the Wigner-Seitz truncation - is there any reason to do anything else? It seems to me this is the superior approach?

For EXX of gapped systems Wigner-Seitz truncation is probably the best approach to reach the thermodynamic llimit.
But for beyond-EXX stuff like many-electron correlation methods (MP2, CC, ...) it may not be quite as superior. In particular when we consider relatively small cells where a truncation is simply too rough (no matter if spehrically or Wigner-Seitz).

Do we really want to support the voxel averaged?

We need it for surface science (strongly anisotropic cells) with coupled cluster theory. Since our plan is to make DFTK a standard workflow, voxel averaged would be essential.
It would also be nice to have it for tests with the new (planned) mixers for SCF calculations with EXX. In particular for metals, voxel averaged could be advantageous.

toschaefer · 2026-05-21T06:46:08Z

rebased to make merge easier

antoine-levitt · 2026-05-22T13:24:01Z

Is this still WIP or ready for review?

toschaefer · 2026-05-22T13:56:34Z

from my end, ready for review

antoine-levitt

Very nice!

antoine-levitt · 2026-05-27T09:31:50Z

 - [`SphericallyTruncatedCoulomb`](@ref): θ(R-r)/r
+- [`WignerSeitzTruncatedCoulomb`](@ref): χ(r)/r where χ(r)=1 inside Wigner-Seitz cell, otherwise 0.

 If an interaction model features a singularity, that requires some special treatment,


no comma after singularity (germanism)

features a singularity -> is long-range

antoine-levitt · 2026-05-27T09:35:48Z

-#      where Γ is BZ volume) is used.
+#      (where Γ is BZ volume) is used.
 #   _compute_kernel_fourier(::InteractionKernel, basis, qpt, q)
 #      The single q-point version of compute_kernel_fourier


there's compute_ and eval_, should all these be merged?

(we really need to have a unified API for localized functions that can be evaluated in real or reciprocal space)

also should we have a eval_kernel_real? This is often useful for debug purposes (can be left as TODO if you don't feel like doing it)

compute_ sets up and returns the full vector with all the complexity of how the sampling points (including the singularity) are defined for each G+q while eval_ is more the mathematical evaluation of the kernel at a given point G+q.

I added a TODO for eval_kernel_real.

antoine-levitt · 2026-05-27T09:38:33Z


 See also: [`compute_kernel_fourier`](@ref)
 """
 abstract type InteractionKernel end


AbstractCoulombKernel? Interaction seems a bit generic (these are all Coulomb-like)

After some back-and-forth we called it InteractionKernel in #1223 (comment)

antoine-levitt · 2026-05-27T09:39:09Z

 If an interaction model features a singularity, that requires some special treatment,
 the following are available:
 - [`ProbeCharge`](@ref): Gygi-Baldereschi probe charge method
 - [`ReplaceSingularity`](@ref): Set G+q=0 component to given value (default is zero)


I think we use relatively consistently (or at least we wanted to) p for the Fourier-space variable in \R^3 (so usually things like p=G+k, and q=k-k'). Why mention G at all in this file? Can't you just use p?

Principally, I am happy to follow your stylistic preferences. I don't think we've mentioned this yet during the EXX development, and if I shall change it, I would prefer to postpone it for now, since I'm already working on the next PR (which also includes some changes in src/coulomb.jl).

antoine-levitt · 2026-05-27T09:41:50Z

 Base.Broadcast.broadcastable(k::InteractionKernel) = Ref(k)

 # Each InteractionKernel should support the following functions:
 #   eval_kernel_fourier(::InteractionKernel, Gsq)


give the equation defining this. Gsq -> p? Or ps?)

Gsq refers to G squared so psq? But I am not sure if I understand correctly...

antoine-levitt · 2026-05-27T10:15:13Z

+            d_min = min(d_min, d)
+        end
+        if d_min > sqrt(eps(T))
+            V_lr_real[idx] = erf(ω * d_min) / d_min


as above, define a erf(x)/x function?

Hm I think we should have a general way of doing f(x)/x stably and AD-friendly, this is coming up pretty frequently (also with @Technici4n in the spherical harmonics stuff)

Ah but of course it's my old friend the divided difference (high order in the case of f(x)/x^l). We have a general solution in https://github.com/xuequan818/MatrixFuns.jl but it might be a bit overkill...?

(the reason I want to get this right is otherwise it will come up to bite us in the ass with AD)

I want to do things like

function expm1_over_x(x) if abs(x) < 1000floatmin(Float64) x = 1000floatmin(Float64) end expm1(x) / x end

but of course this screws up AD at 0. We can have a cutoff point and switch to a finite order taylor expansion. This is ugly and getting good precision of higher derivatives is annoying, but I'm not sure what else to do.

antoine-levitt · 2026-05-27T10:24:23Z

+    V_lr_real = zeros(Complex{T}, basis.fft_size...)
+    for idx in CartesianIndices(V_lr_real)
+        r_frac = r_vectors[idx]
+        r_centered = r_frac .- round.(r_frac) # MIC


write it out explicitly (I had to think to get what it was referring to)

antoine-levitt · 2026-05-27T10:27:11Z

+        r_centered = r_frac .- round.(r_frac) # MIC
+        r_cart = model.lattice * r_centered
+        d_min = norm(r_cart)
+        for dx in -nx:nx, dy in -ny:ny, dz in -nz:nz # Check neighbors for non-orthorhombic cells


I have to say I don't understand what's going on here, why isn't this just erf(r)/r for r in r_vectors?, maybe factor out the geometry stuff to another function?

antoine-levitt · 2026-05-27T10:28:31Z

+        Gnorm2 = sum(abs2, G_cart)
+        found_singularity = (iG==1 && iszero(q))
+        Rcut = cbrt(basis.model.unit_cell_volume*3/4/π)
+        if !found_singularity


why don't you just write the condition here? Also why not iszero(G_cart)?

(also same comment as above, hopefully we can avoid this special casing)

antoine-levitt · 2026-05-27T10:30:18Z

    end
    kernel_fourier
 end
+


Running out of time today, note to self to resume the review from here.

toschaefer added 3 commits March 6, 2026 08:25

Merge pull request #8 from JuliaMolSim/master

2db40bc

Sync with upstream

Merge branch 'JuliaMolSim:master' into master

2d8936e

Merge branch 'JuliaMolSim:master' into master

e2135a3

toschaefer added 2 commits May 19, 2026 17:10

Merge branch 'JuliaMolSim:master' into master

aba4d00

reintroduce WignerSeitzTruncatedCoulomb and VoxelAveraged

e92b7d8

toschaefer force-pushed the exx_kernels branch from ec14222 to e92b7d8 Compare May 21, 2026 06:44

antoine-levitt reviewed May 27, 2026

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toschaefer commented Mar 11, 2026 •

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