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# LORBIT

LORBIT = 0 | 1 | 2 | 5 | 10 | 11 | 12
Default: LORBIT = None

Description: LORBIT, together with an appropriate RWIGS, determines whether the PROCAR or PROOUT files are written.

 LORBIT RWIGS tag files written 0 required DOSCAR and PROCAR 1 required DOSCAR and lm-decomposed PROCAR 2 required DOSCAR and lm-decomposed PROCAR + phase factors 5 required DOSCAR and PROOUT 10 ignored DOSCAR and PROCAR 11 ignored DOSCAR and lm-decomposed PROCAR 12 ignored DOSCAR and lm-decomposed PROCAR + phase factors

### Remark:

For LORBIT = 11 and ISYM = 2 the partial charge densities are not correctly symmetrized and can result in different charges for symmetrically equivalent partial charge densities. This issue if fixed as of version >=6. For older versions of vasp a two-step procedure is recommended:

• 1. Self-consistent calculation with symmetry switched on (ISYM=2)
• 2. Recalculation of the partial charge density with symmetry switched off (ISYM=0)

To avoid unnecessary large WAVECAR files it recommended to set LWAVE=.FALSE. in step 2

• If LORBIT is set the partial charge densities can be found in the OUTCAR
total charge

# of ion       s       p       d       tot
------------------------------------------
1        1.514   0.000   0.000   1.514
2        0.123   0.345   0.000   0.468


Here the first column corresponds to the ion index $\alpha$  , the s, p, d,... columns correspond to the partial charges for $l=0,1,2,\cdots$  defined as

$\rho _{{\alpha l}}={\frac {1}{N_{{{\bf {k}}}}}}\sum _{{n{{\bf {k}}}}}f_{{n{{\bf {k}}}}}\sum _{{m=-l}}^{{l}}|\langle Y_{{lm}}^{{\alpha }}|\phi _{{n{\mathbf {k}}}}\rangle |^{2}$  The $\langle Y_{{lm}}^{{\alpha }}|\phi _{{n{\mathbf {k}}}}\rangle$  are obtained from the projection of the (occupied) wavefunctions $|\phi _{{n{{\bf {k}}}}}\rangle$  onto spherical harmonics that are non zero within spheres of a radius RWIGS centered at ion $\alpha$  and the last column is the sum $\sum _{{l}}\rho _{{\alpha l}}$  .

Note that depending on the system an "f" column can be found as well.

• In case of collinear calculations (ISPIN=2) the magnetization densities are written to the OUTCAR
magnetization (x)

# of ion       s       p       d       tot
------------------------------------------
1        0.000   0.000   0.000   0.000
2        0.000   0.245   0.000   0.245


Here the magnetization density (projection axis is the z-axis) is calculated from the difference in the up and down spin channel $m_{z}^{{\alpha l}}=\rho _{{\alpha l}}^{{\uparrow }}-\rho _{{\alpha l}}^{{\downarrow }}$  • In case of non-collinear calculations (LNONCOLLINEAR=.TRUE.) the lines after "total charge" correspond to the diagonal average

${\frac {\rho _{{\alpha l}}^{{\uparrow \uparrow }}-\rho _{{\alpha l}}^{{\downarrow \downarrow }}}{2}}$  of the density tensor

$\rho _{{\alpha l}}=\left({\begin{matrix}\rho _{{\alpha l}}^{{\uparrow \uparrow }}&\rho _{{\alpha l}}^{{\uparrow \downarrow }}\\\rho _{{\alpha l}}^{{\downarrow \uparrow }}&\rho _{{\alpha l}}^{{\downarrow \downarrow }}\\\end{matrix}}\right),$  which is determined from the projected components

$\rho _{{\alpha l}}^{{\mu \nu }}={\frac {1}{N_{{{\bf {k}}}}}}\sum _{{n{{\bf {k}}}}}f_{{n{{\bf {k}}}}}\sum _{{m=-l}}^{{l}}\langle \chi _{{n{{\bf {k}}}}}^{\mu }|Y_{{lm}}^{\alpha }\rangle \langle Y_{{lm}}^{\alpha }|\chi _{{n{{\bf {k}}}}}^{\nu }\rangle$  of the spinor $|\Psi _{{n{{\bf {k}}}}}\rangle =\left({\begin{matrix}\chi _{{n{{\bf {k}}}}}^{\uparrow }\\\chi _{{n{{\bf {k}}}}}^{\downarrow }\end{matrix}}\right)$  Similarly, the lines after "magnetization (x)" correspond to the partial magnetization density projected onto the x direction and two additional entries "magnetization (y)", "magnetization (z)" are written for the y and z direction and are calculated from the three Pauli matrices

$\sigma ^{x}=\left({\begin{matrix}0&1\\1&0\\\end{matrix}}\right),\quad \sigma ^{y}=\left({\begin{matrix}0&-i\\i&0\\\end{matrix}}\right),\quad \sigma ^{z}=\left({\begin{matrix}1&0\\0&-1\\\end{matrix}}\right)$  via

$m_{{\alpha l}}^{j}={\frac {1}{2}}\sum _{{\mu ,\nu =1}}^{2}\sigma _{{\mu \nu }}^{j}\rho _{{\alpha l}}^{{\mu \nu }}.$  