About the obara saika integral method about hartree-fock-in-cpp

[Walter-Feng]

It's more like My historical reason for learning & writing Hartree-Fock. The Obara-Saika part is inherited from my C version of Hartree-Fock, and it was written when I was being an RA in University of Bristol, and thus the thesis mentioned in the comments, instead of directly implementing the Obara-Saika scheme.

So it is relatively unrelated to the performance - the codes should be slower and ill-optimized. To implement a faster one, maybe the first step is to parse RRs before runtime, or simply use good libraries. This repo is more intended for tutorials, so I believe less-optimized code can promote better understanding.

The implementation is not fixed yet- I was thinking I have correct implemention in Rys quadrature method, maybe not a hurry for me to fix the ERI in Obara-Saika. Maybe it's good chance I give it a look and probably directly implement the OS scheme.

[Walter-Feng]

But overall it will require less computation to sum over all the function pairs, as these pairs can be utilized for both sides of the integrals (which I didn't do in my code).

By the way, the thesis I was referencing has some errors. I recall it was \xi -> \zeta in ERI, if you really want to check it.

[mavenlin]

Thanks for the clarification!

[Walter-Feng]

Obara-Saika scheme of ERI is now correctly implemented. Super slow though :(