Electronic structure calculations - the algebraic approach

Most of the electronic structure calculations performed today axe based on expansions in terms of analytical basis functions with = r — 

The application of a modified electron-nucleus potential together with analytical basis functions requires the evaluation of appropriate matrix elements (nuclear attraction integrals)  

This notation covers both the non-relativistic and relativistic cases (scalar orbitals and 4-component spinors, respectively), the indices i and j carry information to identify the basis functions imambiguously. The integrals in Eq. (122) may involve only a single centre A = B — C [ atomic integrals ]), two centres, or three centres A, B, C all different). The difficulty of their evaluation increases with the number of centres. In addition, every type of basis functions requires its own implementation of nuclear attraction integrals. This task has been accomplished, at least to some paxt, for various potentials and Slater-type or Gauss-type basis functions. For technical reasons (ease of evaluation of multi-centre integrals) the latter type is usually preferred. 

Since the introduction of the Gauss-t3q e finite nucleus model (see Sect. 4.4) into relativistic quantum chemistry by Visser et al. [96], the combination of this model with Gauss-type basis functions has been most widely distributed, see, e.g., the programs developed by Dyall et al. [97], by Viss-cher et al. [98,99] (MOLFDIR), and by Saue et al. [100] (DIRAC). 

Nuclear attraction integrals for the combination of the homogeneous finite nucleus model (see Sect. 4.3) with Gauss-type basis functions were implemented by Ishikawa et al. [101], by Matsuoka et al. [102,103], and by dementi et al. [104-106]. 

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