My Community

Spin-Orbit-Coupling matrix elements

Ion: 1 E_soc: -0.0035306
l= 1
0.0000000 -0.0002085 -0.0002152
-0.0002085 0.0000000 -0.0002084
-0.0002152 -0.0002084 0.0000000
l= 2
0.0000000 -0.0000556 0.0000000 -0.0000526 -0.0004571
-0.0000556 0.0000000 -0.0002086 -0.0000410 -0.0000526
0.0000000 -0.0002086 0.0000000 -0.0002102 0.0000000
-0.0000526 -0.0000410 -0.0002102 0.0000000 -0.0000556
-0.0004571 -0.0000526 0.0000000 -0.0000556 0.0000000

Above is SOC matrix what is given at end of OUTCAR
what is syntax for ordering of d orbitals? (l = 2)
there are five rows and five columns of this matrix
For example, if I want to pick SOC coupling of dxy and dyz orbital from matrix, how to know which value is this in matrix
Overall, kindly mention the ordering of orbitals in row and column

Hello!

Sorry for this very late reply! The matrix dimensions within each \(l\)-block correspond to \(m\) and \(m'\) of the real spherical harmonics \(Y_{lm}\). The \(m\)-ordering is the same as in other VASP files (e.g. PROCAR):

l=1: py, pz, px 				
l=2: dxy, dyz, dz2, dxz, dx2-y2 		
l=3: fy(3x2-y2), fxyz, fyz2, fz3, fxz2, fz(x2-y2), fx(x2-3y2) 

See also the full definitions of the spherical harmonics here: wiki/index.php/Angular_functions

All the best,
Andreas Singraber