Meaning and ordering of f-orbitals in DOS

Message

ehftz943315 · #1 Post by **ehftz943315** » Wed Oct 19, 2011 8:10 am

I am working with actinide compounds and need to understand better DOS. Could somebody help with clarification what set of f-orbitals is really used in calculation of the density of states? If spin-orbit interaction is not included in calculations, then the set of orbitals should be real. I found that VASP writes projected DOS set

s, p_y, p_z, p_x, d_xy, d_yz, d_z2-r2, d_xz, d_x2-y2

for spd-orbitals to DOSCAR file. I cannot find similar information for f-orbitals. I need to know meaning of the components of f-orbitals provided in DOSCAR file with the same kind of reference to REAL (not complex) atomic orbitals. Which set of f-orbitals is used (general or cubic)? What is the order of component written in DOSCAR?

Another similar question is about the DOS for calculations WITH account for spin-orbit interactions. What functions are used to calculate DOS in this case? How are they ordered in DOSCAR? Could you describe these functions?

Thanks!

hatdau · #2 Post by **hatdau** » Fri Oct 21, 2011 1:01 am

Look at the PROCAR you will see:

ion s py pz px dxy dyz dz2 dxz dx2 f-3 f-2 f-1 f0 f1 f2 f3 tot

ehftz943315 · #3 Post by **ehftz943315** » Sat Oct 22, 2011 2:36 am

Sorry, but this is precisely the form of reply, which I asked to avoid!

It is misleading:
The reference like this is the reference to orbitals with COMPLEX angular part for f-functions .

I asked for reference to orbitals with REAL angular part (see, for example, http://winter.group.shef.ac.uk/orbitron ... index.html . I need this information with reference to functions in this fashion for calculations without spin-orbit interactions, whatever in cubic or general set .

My guess is that the general set of real f-orbitals is used. It seems that following order is used in DOSCAR:

5fy(3x2-y2), 5fxyz, 5fyz2, 5fz3, 5fxz2, 5fz(x2-y2), 5fy(3x2-y2), 5fx(x2-3y2)

Is this correct?
(see http://winter.group.shef.ac.uk/orbitron ... tions.html for definitions of general set (!) )

Please, describe what functions are used in calculations with account for SOI as well.

I appreciate your help!

<span class='smallblacktext'>[ Edited Sat Oct 22 2011, 06:15AM ]</span>

#4 Post by **admin** » Mon Oct 24, 2011 2:28 pm

YLM(:,1) -> s
YLM(:,2:4) -> p:= y, z, x
YLM(:,5:9) -> d:= xy, yz, z2, xz, x2
YLM(:,10:16) -> f:= y(3x2-y2), xyz, yz2, z3, xz2, z(x2-y2), x(x2-3y2)

FAK=1/(2._q * SQRT(PI))

1: YLM = FAK

2: YLM= (FAK*SQRT(3._q))*Y
3: YLM= (FAK*SQRT(3._q))*Z
4: YLM= (FAK*SQRT(3._q))*X

5: YLM= (FAK*SQRT(15._q)) *X*Y
6: YLM= (FAK*SQRT(15._q)) *Y*Z
7: YLM= (FAK*SQRT(5._q)/2._q)*(3*Z*Z-1)
8: YLM= (FAK*SQRT(15._q)) *X*Z
9: YLM= (FAK*SQRT(15._q)/2._q)*(X*X-Y*Y)

10: YLM= (FAK*SQRT(35._q/2._q)/2._q) *Y*(3*X*X-Y*Y)
11: YLM= (FAK*SQRT(105._q)) *X*Y*Z
12: YLM= (FAK*SQRT(21._q/2._q)/2._q) *Y*(4*Z*Z-X*X-Y*Y)
13: YLM= (FAK*SQRT(7._q)/2._q) *Z*(2*Z*Z-3*X*X-3*Y*Y)
14: YLM= (FAK*SQRT(21._q/2._q)/2._q) *X*(4*Z*Z-X*X-Y*Y)
15: YLM= (FAK*SQRT(105._q)/2._q) *Z*(X*X-Y*Y)
16: YLM= (FAK*SQRT(35._q/2._q)/2._q) *X*(X*X-3*Y*Y)

ehftz943315 · #5 Post by **ehftz943315** » Wed Oct 26, 2011 1:54 am

Thank you very much! This answers on my 1st question. This means that in DOSCAR we have 33 columns for collinear calculation without SOI : one-electron energy + 32 components, considering we have spin-down and spin-up cases.

Could you, please, describe definition of the components for case with account for spin-orbit interactions (SOI)? It seems DOSCAR contains 64 components in this case. Do you use orbitals with complex angular functions for this? How are they combined with spin functions? How are they ordered in DOSCAR?

In your reply to my collaborator you mentioned:

in the non-collinear case, there ar 4 numbers for each of these terms,
total, m_x, m_y, m_z

I understand that you described non-collinear case without SOI. If we consider spin projections as well, should we have double that number of spin components:
[total, m_x, m_y, m_z ] for spin projection opposite to atom's spin - 4 columns;
[total, m_x, m_y, m_z ] for spin projection along to atom's spin - other 4 columns ?

This means 8 columns per orbital component. Therefore, I would expect 129 columns for each atom in DOSCAR (energy+128 components). Is my understanding correct? Will the number of components double again for calculations with SOI ?

I appreciate your assistance!