LORBIT: Difference between revisions
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<math> | <math> | ||
\rho^{\mu\nu}_{\alpha l} = \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 \chi_{n {\bf k}}^\mu | Y_{lm}^\alpha \rangle | ||
\langle Y_{lm}^\alpha | \chi_{n {\bf k}}^\nu \rangle | \langle Y_{lm}^\alpha | \chi_{n {\bf k}}^\nu \rangle | ||
Revision as of 17:01, 8 January 2019
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 [math]\displaystyle{ \alpha }[/math], the s, p, d,... columns correspond to the partial charges for [math]\displaystyle{ l=0,1,2,\cdots }[/math] defined as
[math]\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 }[/math]
The [math]\displaystyle{ \langle Y_{lm}^{\alpha}|\phi_{n\mathbf{k}}\rangle }[/math] are obtained from the projection of the (occupied) wavefunctions [math]\displaystyle{ |\phi_{n{\bf k}}\rangle }[/math] onto spherical harmonics that are non zero within spheres of a radius RWIGS centered at ion [math]\displaystyle{ \alpha }[/math] and the last column is the sum [math]\displaystyle{ \sum_{l}\rho_{\alpha l} }[/math].
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 [math]\displaystyle{ m^{\alpha l}_z = \rho_{\alpha l}^{\uparrow}-\rho_{\alpha l}^{\downarrow} }[/math]
In case of non-collinear calculations (LNONCOLLINEAR=.TRUE.) the lines after "total charge" correspond to the diagonal average [math]\displaystyle{ \frac{\rho_{\alpha l}^{\uparrow\uparrow} - \rho_{\alpha l}^{\downarrow \downarrow}}{2} }[/math] of the density tensor
[math]\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), }[/math]
which is determined from the projected components
[math]\displaystyle{ \rho^{\mu\nu}_{\alpha l} = \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 }[/math]
of the spinor [math]\displaystyle{ |\Psi_{n{\bf k}}\rangle=\left(\begin{matrix}\chi_{n{\bf k}}^\uparrow \\\chi_{n{\bf k}}^\downarrow \end{matrix}\right) }[/math]
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
[math]\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) }[/math]
via
[math]\displaystyle{ m_{\alpha l}^j = \frac{1}{2}\sum_{\mu,\nu=1}^2 \sigma^j_{\mu \nu} \rho_{\alpha l}^{\mu \nu}. }[/math]