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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 13 ignored DOSCAR and lm-decomposed PROCAR + phase factors, choose best projector for each band 14 ignored DOSCAR and lm-decomposed PROCAR + phase factors, choose single projector for interval EMIN,EMAX

### Remarks:

LORBIT=13 and LORBIT=14 are only supported by version >=5.4.4. 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 is 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

The phase factors written by VASP can usually only be used as a qualitative measure of the projection of the orbitals into the atomic sphere. The main issue is that most VASP POTCAR files have two or three projectors per l-quantum number, and projecting an orbital onto two projectors will obviously yield two complex numbers. VASP combines these two numbers into a single number. The precise algorithms differ in different versions of VASP, and we recommend that you inspect the source code for more details. From vasp.6 onward, a new improved scheme has been implemented and can be selected using LORBIT=14. In this case, VASP first selects a single projector for each l-quantum number by linearly combining all projectors with the same l-quantum number. This is done in such a way that the new projector is optimally chosen to represent the calculated orbitals in the energy interval specified by ENMAX and ENMIN. In the second step, VASP projects onto these optimized projectors yielding a single complex number for each orbital, site and l-quantum number, which is written to the PROCAR file. For details we also refer to [1]. LORBIT=12 should no longer be used except for qualitative calculations. LORBIT=13 chooses the projectors also automatically, but allows for different optimal linear combinations for each orbital. Note that this is generally not desirable, since the resultant projection is not compatible with the required properties of a projection operator (a projection operator needs to use energy and orbital independent projectors). Hence do not use LORBIT=13 for anything but a qualitative analysis.

• 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 ${\displaystyle \alpha }$, the s, p, d,... columns correspond to the partial charges for ${\displaystyle l=0,1,2,\cdots }$ defined as

${\displaystyle \rho _{{\alpha l}}={\frac {1}{N_{{{\bf {k}}}}}}\sum _{{n{{\bf {k}}}}}f_{{n{{\bf {k}}}}}\sum _{{m=-l}}^{{l}}|\langle Y_{{lm}}^{{\alpha }}|\phi _{{n{\mathbf {k}}}}\rangle |^{2}}$

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

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 ${\displaystyle m_{z}^{{\alpha l}}=\rho _{{\alpha l}}^{{\uparrow }}-\rho _{{\alpha l}}^{{\downarrow }}}$

• In case of non-collinear calculations (LNONCOLLINEAR=.TRUE.) the lines after "total charge" correspond to the diagonal average

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

${\displaystyle \rho _{{\alpha l}}=\left({\begin{matrix}\rho _{{\alpha l}}^{{\uparrow \uparrow }}&\rho _{{\alpha l}}^{{\uparrow \downarrow }}\\\rho _{{\alpha l}}^{{\downarrow \uparrow }}&\rho _{{\alpha l}}^{{\downarrow \downarrow }}\\\end{matrix}}\right),}$

which is determined from the projected components

${\displaystyle \rho _{{\alpha l}}^{{\mu \nu }}={\frac {1}{N_{{{\bf {k}}}}}}\sum _{{n{{\bf {k}}}}}f_{{n{{\bf {k}}}}}\sum _{{m=-l}}^{{l}}\langle \chi _{{n{{\bf {k}}}}}^{\mu }|Y_{{lm}}^{\alpha }\rangle \langle Y_{{lm}}^{\alpha }|\chi _{{n{{\bf {k}}}}}^{\nu }\rangle }$

of the spinor ${\displaystyle |\Psi _{{n{{\bf {k}}}}}\rangle =\left({\begin{matrix}\chi _{{n{{\bf {k}}}}}^{\uparrow }\\\chi _{{n{{\bf {k}}}}}^{\downarrow }\end{matrix}}\right)}$

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

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

via

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