libstoint

Computes atomic (one-center) 1- and 2-electron integrals over Slater-type orbitals, defined per [1] as

where is a normalization constant.

The code does not yet work! Do not use.

Capabilities

If it worked correctly, libstoint would be able to calculate all one-center one-electron integrals--overlap, nuclear attraction, and kinetic energy--and all one-center two-electron integrals up to . Unfortunately, there are bugs which I do not yet understand.

Method

All one-electron integrals are formed as linear combinations of overlap integrals, see [2]. Expressions for the two-electron integrals are calculated in Mathematica using the general formula from [1] (supplementary info) and exported as C functions. Because there is one such expression for each value of

they are accessed via a (n automatically generated) lookup table. Symmetry and selection rules cut the number of functions down, but there are still a lot. The combinatorial explosion means this method is not really appropriate for large l.

The inspiration for this approach was [3].

Building

If you have a modern C/C++ compiler and a *nix operating system you may then run make -j [jobs]; make tests. For building and running the tests, you need GoogleTest. If you don't want to install it system-wide, you may modify the Makefile to use a local copy, or just not run the tests.

To build the rudimentary Python module, make sure Python is configured the way you want, and then type make module.

References

[1] M. Lesiuk and R. Moszynski, Reexamination of the Calculation of Two-Center, Two-Electron Integrals over Slater-Type Orbitals. I. Coulomb and Hybrid Integrals, Phys. Rev. E 90, (2014).

[2] J. Fernández Rico, R. López, and G. Ramírez, Molecular Integrals with Slater Basis. I. General Approach, The Journal of Chemical Physics 91, 4204 (1989).

[3] S. Gümüş and T. Özdoǧan, Symbolic Calculation of Two-Center Overlap Integrals Over Slater-Type Orbitals, Jnl Chinese Chemical Soc 51, 243 (2004).