Hartree-Fock on a single Oxygen atom

[Morberticus]

I'm using the TURBOMOLE program to do some basic HF calculations. They all went fine except for the single oxygen atom.

After doing an extended huckel theory guess to begin with, it recommended these occupations (d2h symmetry). That looks fine to me. The top two orbitals (4 and 5) are singly occupied so I have a triplet.

   Nr.   Orbital    Occupation       Energy
    5. o   1 b3u      1.000        -0.622769 H =       -16.946 eV
    4. o   1 b2u      1.000        -0.622769 H =       -16.946 eV
    3.      1 b1u      2.000        -0.622769 H =       -16.946 eV
    2.      2 ag       2.000        -1.234914 H  =       -33.604 eV
    1.      1 ag       2.000        -20.665490 H =      -562.337 eV

The trouble is, when I do a dscf calculation, it rearranges them to

    5.     1 b1u      2.000        -0.564167 H =       -15.352 eV
    4. o   1 b3u      1.000        -0.698996 H =       -19.021 eV
    3. o   1 b2u      1.000        -0.698996 H =       -19.021 eV
    2.      2 ag       2.000        -1.242835 H =       -33.819 eV
    1.      1 ag       2.000       -20.666663 H =      -562.369 eV

This looks completely unphysical to me, as the singly occupied orbitals should remain at the top I would imagine. For my purposes, I need to perform a restricted open hartree-fock, but I have tried an unrestricted hartree-fock calculation for comparison purposes, and it still gives me the unusual ordering above.

Is this normal?

 

[alxm]

It's normal.

 

[cgk]

The difference is that before the calculation the p orbitals are all degenerate as they most likely originate from some kind of atomic density guess. After the calculation they are not degenerate anymore, because two are singly occupied and one is doubly occupied, and they have relaxed according to that.

Apart from that, you cannot really read too much into the orbital energies. In ROHF they are not unique, and depending on your choice of defining the Fock matrix you can get rather different values for the open-shell ones.

 

[Morberticus]

It's normal.

The difference is that before the calculation the p orbitals are all degenerate as they most likely originate from some kind of atomic density guess. After the calculation they are not degenerate anymore, because two are singly occupied and one is doubly occupied, and they have relaxed according to that.

Apart from that, you cannot really read too much into the orbital energies. In ROHF they are not unique, and depending on your choice of defining the Fock matrix you can get rather different values for the open-shell ones.

Thanks. Ultimately I need orbital energies for a post-Hartree Fock CI calculation. Would they be valid to use for that purpose? I.e. Using the occupied orbitals to build a reference wavefunction for a CI calculation?

 

[cgk]

Thanks. Ultimately I need orbital energies for a post-Hartree Fock CI calculation. Would they be valid to use for that purpose? I.e. Using the occupied orbitals to build a reference wavefunction for a CI calculation?

The orbitals are fine (they are unique up to unitary transformations). The ROHF orbital energies, however, are not typically used in post-HF treatments. If you, say, put a perturbative method like RMP2 or the (T) of RHF-UCCSD(T) on top of ROHF, what happens is that the program first calculates semi-canonical alpha and beta orbitals and orbial energies, and then uses these for the actual calculation. This is done by first forming alpha and beta fock matrices (charge density Fock +/- open shell exchange) and then block-diagonalizing these in the the subspaces of the doubly/[doubly+singly] occupied and [singly+unoccupied]/unoccupied ROHF orbitals. I.e., the single set of ROHF orbitals is split into two different alpha and beta spin-orbital parts, with different (but related) spatial components.

There are also some other things to look out for. For example, ROHF wave functions do not fulfill the UHF Brillounin-Conditions, and this causes single excitations and singles energy contributions to appear in the correlation treatments.

But if you are just using a program, it will most likely do the right thing, so there is likely no need to worry about that.

 

[Morberticus]

The orbitals are fine (they are unique up to unitary transformations). The ROHF orbital energies, however, are not typically used in post-HF treatments. If you, say, put a perturbative method like RMP2 or the (T) of RHF-UCCSD(T) on top of ROHF, what happens is that the program first calculates semi-canonical alpha and beta orbitals and orbial energies, and then uses these for the actual calculation. This is done by first forming alpha and beta fock matrices (charge density Fock +/- open shell exchange) and then block-diagonalizing these in the the subspaces of the doubly/[doubly+singly] occupied and [singly+unoccupied]/unoccupied ROHF orbitals. I.e., the single set of ROHF orbitals is split into two different alpha and beta spin-orbital parts, with different (but related) spatial components.

There are also some other things to look out for. For example, ROHF wave functions do not fulfill the UHF Brillounin-Conditions, and this causes single excitations and singles energy contributions to appear in the correlation treatments.

But if you are just using a program, it will most likely do the right thing, so there is likely no need to worry about that.

Sorry, shouldn't have said orbital energies. Slip of the tongue (or fingers). I am only using the orbitals to produce Configuration State Functions, not the individual ROHF energies.

The program is in-house, but is fairly reliable.

Thanks again.