I was comparing the two-electron integrals (electron repulsion integrals, ERI) printed by various well-established packages (Gaussian, GAMESS, Molpro etc.) and observed that Gaussian is the oddball in including the factors coming from permutational symmetry ("redundancy factors").
Here I use water as an example, with the Huzinaga minimal basis set taken from bse.pnl.gov for consistency (built-ins in some packages had different primitive terms or number of decimal places).
\begin{array}{|c|c|}\hline O&0.0&0.0&0.1173\\\hline H&0.0&0.7572&-0.4692\\\hline H&0.0&-0.7572&-0.4692\\\hline \end{array}
I assumed no spatial symmetry (xyz coordinates) and used cartesian functions (not that it makes a difference with Huzinaga, but for later changes).
After the runs, the easiest one to understand was the output from GAMESS (option NPRINT=4) which left the integrals uncorrected for redundancy. Molpro (INT,SPRI=2) printed some numbers that are off by factors of 2, 4, 8 but otherwise agree with GAMESS.
But I fail to understand the output from Gaussian (SCF(Conventional) IOp(3/33=6) ExtraLinks=L316 Symmetry=None). Some of the numbers are off by factors of 2 or 4 (but not in the same entries as in Molpro) and some other numbers seem completely unrelated, even having opposite signs.
Q: Does anyone know the reason for this and how to read it correctly (to confirm agreement with other packages)?
Here are my outputs: GAMESS (line ~292), Molpro (line ~187), Gaussian 09 (line ~4810)
The indices of $[ij|k\ell]$ are in "canonical" order, ie. $i\ge j$, $k \ge \ell$, and ${i\choose2} + j \ge {k\choose 2} + \ell$.
