How to calculate the parity of a particular band?

[sandeep.kumar]

Dear all,

I was trying to calculate the parity of a band at a particular KPOINT using PROCAR file which i obtained by using LORBIT = 12 in non self consistent calculations. I just want to know whether i am doing it in a correct way or not.
Suppose i have two two degenerate bands having the following data:

band 1 # energy -12.16749851 # occ. 1.00000000

ion s py pz px dxy dyz dz2 dxz dx2 tot
1 0.392 0.000 0.007 0.000 0.000 0.000 0.002 0.000 0.000 0.401
2 0.392 0.000 0.007 0.000 0.000 0.000 0.002 0.000 0.000 0.401
tot 0.783 0.000 0.015 0.000 0.000 0.000 0.004 0.000 0.000 0.802
1 0.144 0.000 0.003 -0.000 -0.000 0.000 0.001 -0.000 0.000 0.148
2 0.144 0.000 0.003 -0.000 -0.000 0.000 0.001 -0.000 0.000 0.148
tot 0.289 0.000 0.005 -0.000 -0.000 0.000 0.002 -0.000 0.000 0.296
1 0.137 -0.000 0.003 0.000 0.000 -0.000 0.001 0.000 -0.000 0.140
2 0.137 -0.000 0.003 0.000 0.000 -0.000 0.001 0.000 -0.000 0.140
tot 0.274 -0.000 0.005 0.000 0.000 -0.000 0.002 0.000 -0.000 0.281
1 0.337 -0.000 0.006 -0.000 -0.000 -0.000 0.002 -0.000 -0.000 0.345
2 0.337 -0.000 0.006 -0.000 -0.000 -0.000 0.002 -0.000 -0.000 0.345
tot 0.674 -0.000 0.013 -0.000 -0.000 -0.000 0.004 -0.000 -0.000 0.691
ion s py pz px dxy dyz dz2 dxz dx2
1 -0.846 ****** ****** ****** -2.955 -2.694 -2.653 -0.859 -0.859
1 -0.979 -0.000 0.148 -0.002 -0.000 -0.000 0.047 -0.000 -0.000
2 -0.466 0.923 0.793 2.228 ****** ****** -6.019 -6.060 -3.678
2 -0.979 0.000 -0.148 0.002 -0.000 -0.000 0.047 -0.000 -0.000

band 2 # energy -12.16749822 # occ. 1.00000000

ion s py pz px dxy dyz dz2 dxz dx2 tot
1 0.392 0.000 0.007 0.000 0.000 0.000 0.002 0.000 0.000 0.401
2 0.392 0.000 0.007 0.000 0.000 0.000 0.002 0.000 0.000 0.401
tot 0.783 0.000 0.015 0.000 0.000 0.000 0.004 0.000 0.000 0.802
1 -0.144 -0.000 -0.003 0.000 0.000 -0.000 -0.001 0.000 -0.000 -0.148
2 -0.144 -0.000 -0.003 0.000 0.000 -0.000 -0.001 0.000 -0.000 -0.148
tot -0.289 -0.000 -0.005 0.000 0.000 -0.000 -0.002 0.000 -0.000 -0.296
1 -0.137 0.000 -0.003 -0.000 -0.000 0.000 -0.001 -0.000 0.000 -0.140
2 -0.137 0.000 -0.003 -0.000 -0.000 0.000 -0.001 -0.000 0.000 -0.140
tot -0.274 0.000 -0.005 -0.000 -0.000 0.000 -0.002 -0.000 0.000 -0.281
1 -0.337 0.000 -0.006 0.000 0.000 0.000 -0.002 0.000 0.000 -0.345
2 -0.337 0.000 -0.006 0.000 0.000 0.000 -0.002 0.000 0.000 -0.345
tot -0.674 0.000 -0.013 0.000 0.000 0.000 -0.004 0.000 0.000 -0.691
ion s py pz px dxy dyz dz2 dxz dx2
1 -0.261 ****** ****** ****** -2.955 -2.694 -2.681 -0.858 -0.859
1 0.239 -0.007 -0.036 0.000 0.000 -0.000 -0.011 0.000 -0.000
2 0.120 0.921 0.881 2.222 ****** ****** -6.047 -6.060 -3.678
2 0.239 0.007 0.036 -0.000 0.000 -0.000 -0.011 0.000 -0.000


At the end of band 1 data, i have real as well as imaginary component of each orbital contribution to the band for each ion. I am considering it as taking the magnitude of one orbital say for band #1, s = (-0.846 - i 0.979), so magnitude = sqrt(0.846^2+0.979^2).
Overall parity of the band i am calculating as =
(-1)^(magnittude of s-orbital of 1st ion * 0 + magnittude of px-orbital of 1st ion * 1 + magnittude of py-orbital of 1st ion * 1 + magnittude of pz-orbital of 1st ion * 1 + magnittude of dxy-orbital of 1st ion * 2 + magnittude of dyz-orbital of 1st ion * 2 + magnittude of dxz-orbital of 1st ion * 2 + magnittude of dz2-orbital of 1st ion * 2 +magnittude of dx2-y2-orbital of 1st ion * 2 + magnittude of s-orbital of 2nd ion * 0 + magnittude of px-orbital of 2nd ion * 1 + magnittude of py-orbital of 2nd ion * 1 + magnittude of pz-orbital of 2nd ion * 1 + magnittude of dxy-orbital of 2nd ion * 2 + magnittude of dyz-orbital of 2nd ion * 2 + magnittude of dxz-orbital of 2nd ion * 2 + magnittude of dz2-orbital of 2nd ion * 2 +magnittude of dx2-y2-orbital of 2nd ion * 2)

Same i do for 2nd degenerate band, and multiply the parity of these two bands, to get the overall parity at this energy.

Can somebody please tell me whether i am going in right direction or not?
and suppose if (-1)^26.01, then should i round off this value to 26 or not?

Kindly help me for the same, i would be extremely thankful to you.

[GangBi]

You can infer the parity of the orbital at time reversal invariant momentum (TRIM) point by calculate the partial charge density of that orbital. From the point group and which atom contribute to the orbital is at least sometimes enough to judge the parity. see e.g. J.O. Dimmock, G.B. Wright, Phys. Rev., 135, A821-A830 (1964).

[sandeep.kumar]

Dear Sir,

Thank you so much for your response. Can you please tell me that which file i have to look into for finding the partial charge density? and can you please explain by giving some example?
I would be extremely thankful to you for the same.