MolecularIntegrals.jl

Status	Coverage

The goal of MolecularIntegrals.jl is to supply fast and hackable one- and two-electron integrals for computational chemistry calculations. There are many excellent molecular integral packages available to Julia programmers, but few are written in Julia. This project will explore how fast we can make these integrals while maintaining a readable and hackable code base.

The code is released under a MIT License.

If you're only interested in using molecular integral code, we highly recommend using one of these existing projects:

• libints and its Julia bindings Lints.jl
• Pyscf, the libcint package.
• JuliaChem.jl's JERI bindings

Briefly, the libints packages implement Obara-Saiko and Head-Gordon/Pople recurrence relations, and the libcints packages implement Rys quadrature based methods. Both are excellent, and, more importantly, are well-tested by being used in many current projects.

What we hope MolecularIntegrals.jl will provide is simple, easily understandable methods that are nonetheless fast enough for production use and that will be valuable for people interested in understanding how these integration techniques work, and in modifying and improving them.

Timing comparison

As a starting point to motivate the development, we will consider Table 5 from the paper Libcint: an efficient general integral library for Gaussian basis functions written by Qiming Sun, the author of Libcint and Pyscf, reporting the time required to compute electron repulsion integrals for ethane using different programs and different basis sets.

Basis	size	Psi4	Molpro	Libcint w/o	w/SSE3
6-31G	30	0.10	0.09	0.09	0.07
6-311G**	72	0.64	0.49	0.49	0.41
ANO	238	2527.6	51.13	53.59	37.78
cc-pVDZ	58	0.45	0.34	0.24	0.21
aug-cc-pVDZ	100	1.87	1.18	1.02	0.85
cc-pVTZ	144	4.98	4.82	2.65	2.05
aug-cc-pVTZ	230	26.03	23.12	12.40	9.27
cc-pVQZ	290	81.24	65.12	31.51	22.60
aug-cc-pVQZ	436	444.23	324.29	151.04	107.24

Preliminary Julia Timings for Ethane/6-31G

Compare to roughly 0.1 sec albeit on completely different hardware. This is mostly just to set a crude benchmark to compare coding improvements.

Results using a single thread:

Basis	size	Huz	HGP	Rys
sto-3G	16	1.71	0.041	0.415
6-31G	30	6.56	0.202	1.550
cc-pVDZ	58	115.4	2.451	25.94

With 4 threads:

Basis	size	Huz	HGP	Rys
sto-3G	16	0.814	0.021	0.186
6-31G	30	3.723	0.131	0.803
cc-pVDZ	58	62.60	1.727	16.31

These results hopefully still have lots of room for speedups.