Same orbital energy but completely different MO coefficients

#1

Dear Psi4 users and developers,

I did an HF calculation with O2 at 6-31g* basis set with psi4 and a different QC software. In both calculations, I turned off the symmetry and reorientation. I found the final energies as well as the orbital energies match extremely well (up to 5 decimal points). However, I found something I cannot understand when I look at their MO coefficients. For some of the MOs (e.g., 1st, E=-20.7553), the coefficients from the two molden files (one from each software) match perfectly after basis function re-ordering (since each software have their own convention of ordering basis functions), but for others (e.g., 8th, E=-0.5277) the coefficients are completely different (though the energies still match). But the same thing did not happen when I switch to a smaller basis set (i.e., 6-31g). I am wondering why this would happen?

The molden files of the 6-31g* basis set from two software are attached below. I appreciate any comments and help! Thanks!

Best,
Chenru
geo.molden.txt (57.5 KB) geo-tc.molden.txt (33.9 KB)

#2

This is almost certainly due to differences in basis-function normalization factors between the codes.

#3

Thanks for your speedy reply! I think I could rationalize it if the coefficients for all the orbitals are different. But the fact that there are only some orbitals match while the others don’t seem a bit strange. Do @crawdad expect the difference in basis-function normalization factors will lead to this kind of behavior? Thanks again!

#4

Do you know the orbital type (angular momentum) of the functions whose coefficients match and those that don’t?

#5

Yes. To make a visually more clear demonstration, I just repeated the calculations with a single O atom with 6-31g*, so that the MO matrix can be visually shown (attached). I colored the places where two pragrams’ coefficients disagree by an orange background. Any insight would be appreciated!

Best,
Chenru

MOcoeff-o-hf-6-31gs
MOcoeff-o-hf-6-31gs1628×1483 296 KB

#6

This partially supports my statement because codes sometimes differ based on whether they include angular momentum contributions in the normalization factor. Contributions from s-type AOs are consistent between the programs.

Regardless, these differences are inconsequential because each code knows its normalization convention internally.

1 Like
#7

You are right! They are different only by a normalization factor for some AO. Inspired by your suggestions, I resolve this problem by doing a linear transformation for some of the orbitals, with the transforming matrix here (https://github.com/psi4/psi4/blob/master/psi4/src/psi4/libmints/writer.cc). Thanks again!