Overlap matrix elements

[awvwgk]

Calculation of overlap integral related terms in xTB Hamiltonian. The aim is to calculate diatomic blocks (off-site elements) of matrix elements, usually containing up to three shells with angular momenta up to l=2 (d-orbitals).

Fortran implementation reference

• storage type for basis set used in tblite (array of structures style via cgto_type): src/tblite/basis/type.f90
• expansion of Slater type orbitals to contracted Gaussian type orbitals: src/tblite/basis/slater.f90
• horizontal Obara–Saika recursion for overlap integral evaluation in Cartesian atomic orbitals: src/tblite/integral/overlap.f90
• transformation from Cartesian atomic orbitals to spherical atomic orbitals: src/tblite/integral/trafo.f90
• Gram-Schmidt orthonormalization (mainly for GFN1-xTB 1s2s basis on H): src/tblite/basis/ortho.f90
• atomic block wise calculation of matrix elements (buildDiatomicBlocks): src/dftbp/extlibs/tblite.F90

Relevant test cases:

• self-overlap of contracted Gaussian type orbitals should be unity

[hoelzerC]

First version: https://github.com/grimme-lab/xtbML/commit/c8318430835e8c95fda54dcc5a632ce07eb5bff1

Some open TODOs including docstring, some index checks and minor stuff.

Requires testing! So far only "translation" from fortran to python. However, code has not been run and checked yet.

[hoelzerC]

Added tests for overlap. https://github.com/grimme-lab/xtbML/commit/d8cd6af67eaf95fe8a66e3a51b072f68a5d24abf

Apart from minor documentation, overlap is complete.