understanding the PROCAR file

[gjenness]

I'm trying to figure out which bands correspond to either bonding or anti-bonding states --- note that I don't really need a full COOP/COHP curve, I just need a qualitative feel for which is which. I think I can get this information from examining the PROCAR file (generated with LORBIT=12), as that contains the phase factors (amongst other things).

As a simple example, lets take a look at the PROCAR for CO in the gas-phase, with the molecular axis aligned along the z-axis. According to the MO diagram, what we should see is 4 bands below the Fermi level, corresponding to the occupied orbitals --- a 2sigma, a 2sigma*, a doubly degenerate 1pi, and a 3sigma. So if we look at the first two bands in the PROCAR file, we get the following.

band 1 # energy -28.94865556 # occ. 2.00000000

ion s py pz px dxy dyz dz2 dxz dx2 tot
1 0.160 0.000 0.124 0.000 0.000 0.000 0.000 0.000 0.000 0.284
2 0.658 0.000 0.097 0.000 0.000 0.000 0.000 0.000 0.000 0.755
tot 0.818 0.000 0.221 0.000 0.000 0.000 0.000 0.000 0.000 1.039
ion s py pz px dxy dyz dz2 dxz dx2
1 -0.980 0.000 -0.862 0.000 0.000 0.000 0.000 0.000 0.000
1 -0.124 0.000 -0.110 0.000 0.000 0.000 0.000 0.000 0.000
2 -1.716 0.000 0.679 0.000 0.000 0.000 0.000 0.000 0.000
2 -0.218 0.000 0.086 0.000 0.000 0.000 0.000 0.000 0.000

band 2 # energy -13.81786013 # occ. 2.00000000

ion s py pz px dxy dyz dz2 dxz dx2 tot
1 0.190 0.000 0.017 0.000 0.000 0.000 0.000 0.000 0.000 0.207
2 0.168 0.000 0.445 0.000 0.000 0.000 0.000 0.000 0.000 0.613
tot 0.357 0.000 0.463 0.000 0.000 0.000 0.000 0.000 0.000 0.820
ion s py pz px dxy dyz dz2 dxz dx2
1 1.180 0.000 0.379 0.000 0.000 0.000 0.000 0.000 0.000
1 0.147 0.000 0.047 0.000 0.000 0.000 0.000 0.000 0.000
2 -0.937 0.000 -1.512 0.000 0.000 0.000 0.000 0.000 0.000
2 -0.117 0.000 -0.188 0.000 0.000 0.000 0.000 0.000 0.000

Now as I understand it, the first table (highlighted in blue) for each band is some sort of charge/occupancy, and the second table (highlighted in red) corresponds to the phase factors. In addition, the table with the phase factors, the first row for each ion corresponds to the real part, and the second row corresponds to the imaginary part.

Using a simple COOP picture, we know that if there is a positive overlap, then the band is bonding, but if the overlap is negative, the band is anti-bonding. My question is, how can we use the phase factors in PROCAR file to determine, at least from a qualitative standpoint, which bands are bonding and anti-bonding?

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