Recently I run an PSI4 RHF calculation of hydrogen molecule, using STO-3G basis. When bond length is set at 1.40 AU, the total energy given by PSI4 is -1.11673832869.

In Szabo/Ostlund page 167, the expected energy is -1.11672.

Just wondering if anyone know what might be the causes of the small difference (0.000018 AU)?

PSI4’s SCF code uses density-fitting by default, so that accounts for some of the differences in the integrals used to obtain the final energy. If you turn off DF with, e.g.,

```
set scf_type pk
```

Then you get an energy of -1.116714 a.u., which difference from the Szabo & Ostlund value by less than $10^{-5}$ a.u. Not sure why there’s a difference in rounding. Perhaps the number of significant figures retained in the basis set exponents and contraction coefficients? I don’t have my copy of S&O at home with me.

I was able to get the same energy -1.116714 a.u. with a different program, the small remaining difference must be caused by a rounding error. Thank you for the answer.