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Is there any software package in python or C to evaluate two electron integral repulsion integral in quantum chemistry of atoms. I am trying to solve the helium atom by constructing many body basis.Using those basis i am attempting to evaluate matrix elements.Also please suggest some references to understand more about two electron integral.

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    $\begingroup$ There are github.com/evaleev/libint and github.com/sunqm/libcint for calculating integrals over GTOs, if that is what you mean. For standard literature take a look at the books by Szabo and Ostlund as well as Helgaker, Jorgensen and Olsen, both about electronic structure theory. $\endgroup$ – Feodoran Oct 24 '18 at 13:34
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The canonical text on quantum chemistry is Modern Quantum Chemistry: Introduction to Advanced Electronic Structure Theory by Szabo and Ostlund. Every electronic structure theorist I have ever met keeps a copy of that book within arms reach of his/her desk.

As for software, I would recommend PySCF. It is an entirely free python library for quantum chemistry with the most critical routines written in C and is an excellent platform to develop on. It's also robust and fast enough to be used for large calculations should you want to scale up. (https://github.com/sunqm/pyscf)

PySCF uses libcint to perform the integrals, and contains a low-level interface to the integral evaluator. An example of how to use these methods to make a df-HF calculation is shown in the docs here: https://sunqm.github.io/pyscf/tutorial.html#molecular-integrals. A complete list of available integral routines from the libcint package is shown here (it's very comprehensive): https://sunqm.github.io/pyscf/gto.html#module-pyscf.gto.moleintor

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    $\begingroup$ github.com/sunqm/libcint is the actual library used by (and I assume written for) PySCF for these integrals. $\endgroup$ – Feodoran Oct 24 '18 at 13:40

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