Problem with diatomic molecules where both atoms have orbitals different than s

[aromanro]

Hi,

I think I found a problem with such setup. For example for N2 molecule, with the following configuration:

basis = sto-3g charge = 0 atoms = 2 units = bohr N 0.0000 0.0000 0.0000 N 2.147932 0.0000 0.0000

the given result is:

Total energy [Hartree]: -144.1995252

This is with the fix of the bug I previously signaled.

According to some paper I was looking into, the Hartree-Fock limit for N2 is -108.994.

I am comparing your results with a program I've written. It has different basis sets than yours but the values are quite similar. I too have issues with diatomic molecules for this kind of configuration. It works nicely for example for H2O or any diatomic molecule I tried that has a hydrogen in it, but fails once I put two atoms with both more than s orbitals.

I'm using recurrence relations (I think they are called Hamilton & Schaefer) to solve the integrals, for this described case I could spot different terms in both the nuclear matrix and in electron-electron integrals than given by your program. Most of the values are basically identical, but some come out differently.

It doesn't mean yours are wrong since I am also getting bad results for such molecules, but it seems that I'm getting results closer to the expected value, for example for the above molecule I get -113.677. Still wrong :(

Thanks, Adrian

[aromanro]

As a help to diagnose this, I just compared with the values my program gives for N2, the overlap and kinetic matrices are basically identical, despite the different methods of calculating them, so I suppose the problems originate elsewhere. I'll let you know if I found more about this.

[aromanro]

For the core matrix, I found only one difference - it comes out from the nuclear matrix, since the kinetic matrix is ok. I don't know which one is correct (they could be both wrong), the matrix element corresponding to a px orbital from one N and the px orbital from the other N comes out different, all other matrix values seem to match. There are also electron-electron integral differences :(

[ifilot]

I have calculated N2 using the geometry as you described above in Gaussian; the result with a STO-3G basis set is -107.50 a.u.; which is within the HF limit as you mentioned above. HFCXX indeed gives -144.20 a.u., which is clearly wrong. Interestingly, also PyQuante is off with a value of -149.46 a.u.

I am still in the dark where the problem originates from.

[aromanro]

Could you please look at the value PyQuante gives for the above matrix element (line 3, col 8, numbering starting with 1 or the symmetric correspondent)? I'm curious if I have the wrong value...

[aromanro]

Your program has -3.44603 there, mine gives 3.487057. If I have it wrong, probably e-e integrals are also wrong in a similar manner, since the calculations have similarities.

[ifilot]

I make a mistake with PyQuante; I now get -106.82 a.u. for the total energy (yay!). That number is correct.

Furthermore, PyQuante gives

<2px | hcore | 2px> = 3.487

So I probably have some error in my code or in my definition for the basis set.

For reproduction of the PyQuante calculation, see below:

from PyQuante.Molecule import Molecule
from PyQuante.hartree_fock import rhf

n2 = Molecule('n2',[(7,(0,0,0)),(7,(2.147932,0,0))])

en,orbe,orbs = rhf(n2, basis="sto-3g")
print en

[aromanro]

Thank you! That should help me a lot!

[aromanro]

By the way, by looking at your code it seems that you use some code similar with the one discussed here: http://chemistry.stackexchange.com/questions/40958/computing-two-electron-integrals-with-an-sto-3g-basis-set There is an errata here: http://spider.shef.ac.uk/ It's unlikely that you have that mistake, but it's worth a try...

[aromanro]

Here is more info about the bug: I simply forced H[2][7] = H[7][2] = 3.487; With this change, the code converges to -107.5005469, which seems to be correct. So you have an issue somewhere with the nuclear matrix, I have an issue with the e-e integrals :(

I tried replacing the Boys functions calculations with mine with the same result, so it's not originating from Boys/Fgamma implementation. Anyway, I think I can rely on your code for e-e integrals values to check against mine.

[aromanro]

Hi,

Now I have more info. I used your program to check the electron-electron integrals results from my program. Now I get basically identical results for the N2 molecule. I had a nasty bug in the electron transfer relation implementation combined with a mistake in the way I stored integral computation results :(

So the issue with the N2 molecule in your program is certain to originate only from the nuclear matrix computation.

[ifilot]

OK; it turned out to be a really stupid mistake. See: https://github.com/ifilot/hfcxx/blob/master/src/nuclear.cpp#L65

That line had arrA[iI] = A_term(... instead of arrA[iI] += A_term(...

@aromanro : I am very grateful that you found this mistake. Many thanks again!