Gaussian basis calculations
For a finite system, a Gaussian basis supports direct overlap integrals and contractions of an AO density matrix into another basis. Density values can also be evaluated at quadrature points for integration or comparison in real space.
These functions use Gaussian basis definitions and remain available from elfes.physics. The resulting overlap matrix and basis integrals can be used by the density projection solver.
calculate_gaussian_overlap(
geometry: Geometry, basis_set: GaussianBasisSet
) -> HermOrbMatrix
Calculate the ordinary overlap matrix of a finite Gaussian basis.
calculate_gaussian_basis_integrals(
geometry: Geometry,
ao_basis_set: GaussianBasisSet,
basis_set: GaussianBasisSet,
density_matrix: HermOrbMatrix | HermBlockSparseOrbMatrix,
) -> OrbVector
Contract a Gaussian AO density matrix with three-center overlaps.
Three-center integrals are evaluated one target-basis shell at a time and
immediately contracted with every leading density-matrix component. The
full (n_ao, n_ao, n_basis) tensor is never materialized.
evaluate_gaussian_density(
geometry: Geometry,
ao_basis_set: GaussianBasisSet,
density_matrix: HermOrbMatrix | HermBlockSparseOrbMatrix,
grid: QuadratureGrid,
) -> QuadratureVolumetric
Evaluate physical components of a Gaussian AO density matrix at quadrature points.