Integrals

Electron-repulsion (and other) integrals

n_ao4cartshell(id::Integer, info::ILibcint)

Return the number of AOs for a given cartesian shell id.

n_ao4sphshell(id::Integer, info::ILibcint)

Return the number of AOs for a given spherical shell id.

eri_2e2idx!(out, basis::BasisSet)

Compute the two-electron 2-index electron-repulsion integral matrix. The result is stored in out.

eri_2e2idx(basis::BasisSet)

Compute the two-electron 2-index electron-repulsion integral matrix.

kinetic!(out, basis::BasisSet)

Compute the kinetic integral matrix. The result is stored in out.

kinetic(basis::BasisSet)

Compute the kinetic integral matrix.

nuclear!(out, basis::BasisSet)

Compute the nuclear integral matrix. The result is stored in out.

nuclear(basis::BasisSet)

Compute the nuclear integral matrix.

overlap!(out, basis::BasisSet)

Compute the overlap integral matrix. The result is stored in out.

overlap(basis::BasisSet)

Compute the overlap integral matrix.

eri_2e3idx!(out, buffer, batch::BasisBatch)

Compute the two-electron three-index electron-repulsion integral in batch mode (see BasisBatcher). The result is stored in out. buffer is a preallocated buffer [MAlloc]Buffer{Cdouble} of size buffer_size_3idx(batch.bb).

eri_2e3idx!(out, ao_basis::BasisSet, fit_basis::BasisSet)

Compute the two-electron three-index electron-repulsion integral. The result is stored in out.

eri_2e3idx(ao_basis::BasisSet, fit_basis::BasisSet)

Compute the two-electron three-index electron-repulsion integral.

BasisBatch

A structure to represent a batch of basis functions. The structure is used to loop over basis functions in a batched manner. The structure is used in conjunction with BasisBatcher.

BasisBatcher

A structure to loop of basis functions in a batched manner. This is useful for computing integrals in batches. The structure is initialized with two basis sets and provides a method to loop over all basis functions of the second basis in a batched manner:

function BasisBatcher(basis1::BasisSet, basis2::BasisSet, target_length::Int=100)

The batch length is determined by the target_length parameter. The actual batch length depends on the number of basis functions in the shells of the second basis set and can be smaller or larger than the target_length. One can use the max_batch_length function to determine the maximum batch length.

Example

bbatches = BasisBatcher(basis1, basis2)
for batch in bbatches
  range = range(batch) # range of basis functions in the batch
  eri_2e3idx!(@view(pqP[:,:,range]), batch)
end

buffer_size_3idx(bb::BasisBatcher)

Return the buffer size needed in the 3-index integral calculation.

The buffer has to be of type [MAlloc]Buffer{Cdouble}(lenbuf) or [MAlloc]ThreadsBuffer{Cdouble}(lenbuf).

max_batch_length(bb::BasisBatcher)

Return the maximum batch length.

range(bb::BasisBatch)

Return the range of basis functions in the batch.

eri_2e2idx!(out, ash1::AngularShell, ash2::AngularShell, basis::BasisSet)

Compute the two-electron 2-index electron-repulsion integral between two angular shells. The result is stored in out.

eri_2e2idx_cart!(out, i::Int, j::Int, basis::BasisSet)

Compute the two-electron 2-index electron-repulsion integral between two angular shells. The result is stored in out.

eri_2e2idx_cart(ash1::AngularShell, ash2::AngularShell, basis::BasisSet)

Compute the two-electron 2-index electron-repulsion integral between two angular shells.

eri_2e2idx!(out, ash1::AngularShell, ash2::AngularShell, basis::BasisSet)

Compute the two-electron 2-index electron-repulsion integral between two angular shells. The result is stored in out.

eri_2e2idx_sph!(out, i::Int, j::Int, basis::BasisSet)

Compute the two-electron 2-index electron-repulsion integral between two angular shells. The result is stored in out.

eri_2e2idx_sph(ash1::AngularShell, ash2::AngularShell, basis::BasisSet)

Compute the two-electron 2-index electron-repulsion integral between two angular shells.

eri_2e3idx!(out, ash1ao::AngularShell, ash2ao::AngularShell, ashfit::AngularShell, basis::BasisSet)

Compute the two-electron three-index electron-repulsion integral $v_{a_1}^{a_2 P}$ for given angular shells. basis has to contain ao and fit bases. The result is stored in out.

eri_2e3idx_cart!(out, i::Int, j::Int, P::Int, basis::BasisSet)

Compute the two-electron three-index electron-repulsion integral $v_i^{j P}$ for given angular shells. basis has to contain ao and fit bases. The result is stored in out.

eri_2e3idx_cart(ash1ao::AngularShell, ash2ao::AngularShell, ashfit::AngularShell, basis::BasisSet)

Compute the two-electron three-index electron-repulsion integral $v_{a_1}^{a_2 P}$ for given angular shells. basis has to contain ao and fit bases.

eri_2e3idx!(out, ash1ao::AngularShell, ash2ao::AngularShell, ashfit::AngularShell, basis::BasisSet)

Compute the two-electron three-index electron-repulsion integral $v_{a_1}^{a_2 P}$ for given angular shells. basis has to contain ao and fit bases. The result is stored in out.

eri_2e3idx_sph!(out, i::Int, j::Int, P::Int, basis::BasisSet)

Compute the two-electron three-index electron-repulsion integral $v_i^{j P}$ for given angular shells. basis has to contain ao and fit bases. The result is stored in out.

eri_2e3idx_sph(ash1ao::AngularShell, ash2ao::AngularShell, ashfit::AngularShell, basis::BasisSet)

Compute the two-electron three-index electron-repulsion integral $v_{a_1}^{a_2 P}$ for given angular shells. basis has to contain ao and fit bases.

kinetic!(out, ash1::AngularShell, ash2::AngularShell, basis::BasisSet)

Compute the kinetic integral between two angular shells. The result is stored in out.

kinetic_cart!(out, i::Int, j::Int, basis::BasisSet)

Compute the kinetic integral between two angular shells. The result is stored in out.

kinetic_cart(ash1::AngularShell, ash2::AngularShell, basis::BasisSet)

Compute the kinetic integral between two angular shells.

kinetic!(out, ash1::AngularShell, ash2::AngularShell, basis::BasisSet)

Compute the kinetic integral between two angular shells. The result is stored in out.

kinetic_sph!(out, i::Int, j::Int, basis::BasisSet)

Compute the kinetic integral between two angular shells. The result is stored in out.

kinetic_sph(ash1::AngularShell, ash2::AngularShell, basis::BasisSet)

Compute the kinetic integral between two angular shells.

nuclear!(out, ash1::AngularShell, ash2::AngularShell, basis::BasisSet)

Compute the nuclear integral between two angular shells. The result is stored in out.

nuclear_cart!(out, i::Int, j::Int, basis::BasisSet)

Compute the nuclear integral between two angular shells. The result is stored in out.

nuclear_cart(ash1::AngularShell, ash2::AngularShell, basis::BasisSet)

Compute the nuclear integral between two angular shells.

nuclear!(out, ash1::AngularShell, ash2::AngularShell, basis::BasisSet)

Compute the nuclear integral between two angular shells. The result is stored in out.

nuclear_sph!(out, i::Int, j::Int, basis::BasisSet)

Compute the nuclear integral between two angular shells. The result is stored in out.

nuclear_sph(ash1::AngularShell, ash2::AngularShell, basis::BasisSet)

Compute the nuclear integral between two angular shells.

overlap!(out, ash1::AngularShell, ash2::AngularShell, basis::BasisSet)

Compute the overlap integral between two angular shells. The result is stored in out.

overlap_cart!(out, i::Int, j::Int, basis::BasisSet)

Compute the overlap integral between two angular shells. The result is stored in out.

overlap_cart(ash1::AngularShell, ash2::AngularShell, basis::BasisSet)

Compute the overlap integral between two angular shells.

overlap!(out, ash1::AngularShell, ash2::AngularShell, basis::BasisSet)

Compute the overlap integral between two angular shells. The result is stored in out.

overlap_sph!(out, i::Int, j::Int, basis::BasisSet)

Compute the overlap integral between two angular shells. The result is stored in out.

overlap_sph(ash1::AngularShell, ash2::AngularShell, basis::BasisSet)

Compute the overlap integral between two angular shells.

Libcint

Minimal wrap around the integral library libcint. This module exposes libcint functions to the Julia interface.

(adapted from GaussianBasis.jl)