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# Difference between revisions of "LOPTICS"

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The imaginary part is determined by a summation over empty states using the equation: | The imaginary part is determined by a summation over empty states using the equation: | ||

+ | <span id="epsilon"> | ||

:<math> | :<math> | ||

\epsilon^{(2)}_{\alpha \beta}\left(\omega\right) = \frac{4\pi^2 e^2}{\Omega} | \epsilon^{(2)}_{\alpha \beta}\left(\omega\right) = \frac{4\pi^2 e^2}{\Omega} | ||

\mathrm{lim}_{q \rightarrow 0} \frac{1}{q^2} \sum_{c,v,\mathbf{k}} 2 w_\mathbf{k} \delta( \epsilon_{c\mathbf{k}} - \epsilon_{v\mathbf{k}} - \omega) | \mathrm{lim}_{q \rightarrow 0} \frac{1}{q^2} \sum_{c,v,\mathbf{k}} 2 w_\mathbf{k} \delta( \epsilon_{c\mathbf{k}} - \epsilon_{v\mathbf{k}} - \omega) | ||

\times \langle u_{c\mathbf{k}+\mathbf{e}_\alpha q} | u_{v\mathbf{k}} \rangle | \times \langle u_{c\mathbf{k}+\mathbf{e}_\alpha q} | u_{v\mathbf{k}} \rangle | ||

− | \langle u_{c\mathbf{k}+\mathbf{e}_\beta q | + | \langle u_{v\mathbf{k}} | u_{c\mathbf{k}+\mathbf{e}_\beta q} \rangle |

</math> | </math> | ||

+ | </span> | ||

here the indices ''c'' and ''v'' refer to conduction and valence band states respectively, and ''u''<sub>''c'''''k'''</sub> is the cell periodic part of the orbitals at the k-point '''k'''. The real part of the dielectric tensor ε<sup>(1)</sup> is obtained by the usual Kramers-Kronig | here the indices ''c'' and ''v'' refer to conduction and valence band states respectively, and ''u''<sub>''c'''''k'''</sub> is the cell periodic part of the orbitals at the k-point '''k'''. The real part of the dielectric tensor ε<sup>(1)</sup> is obtained by the usual Kramers-Kronig | ||

transformation | transformation | ||

+ | <span id="kramerskronig"> | ||

:<math> | :<math> | ||

\epsilon^{(1)}_{\alpha \beta} (\omega) = 1 + \frac{2}{ \pi} P \int_0^{\infty} | \epsilon^{(1)}_{\alpha \beta} (\omega) = 1 + \frac{2}{ \pi} P \int_0^{\infty} | ||

\frac{ \epsilon^{(2)}_{\alpha \beta} (\omega') \omega'}{ \omega'^2- \omega^2 + i \eta } d \omega' | \frac{ \epsilon^{(2)}_{\alpha \beta} (\omega') \omega'}{ \omega'^2- \omega^2 + i \eta } d \omega' | ||

</math> | </math> | ||

+ | </span> | ||

where ''P'' denotes the principle value. The method is explained in detail in the paper by Gajdoš ''et al.'' (see Eqs. 15, 29, and 30).<ref name="gajdos:prb:06"/> The complex shift η is determined by the parameter {{TAG|CSHIFT}}. | where ''P'' denotes the principle value. The method is explained in detail in the paper by Gajdoš ''et al.'' (see Eqs. 15, 29, and 30).<ref name="gajdos:prb:06"/> The complex shift η is determined by the parameter {{TAG|CSHIFT}}. | ||

− | Note that local field effects, i.e. changes of the cell periodic part of the potential are neglected in this approximation. These can be evaluated using either the implemented density functional perturbation theory ({{TAG|LEPSILON}}=.TRUE. | + | Note that local field effects, i.e. changes of the cell periodic part of the potential are neglected in this approximation. These can be evaluated using either the implemented density functional perturbation theory ({{TAG|LEPSILON}}=.TRUE.), or the GW routines. |

− | The method selected using {{TAG|LOPTICS}}=.TRUE. requires an appreciable number of empty conduction band states. Reasonable results are usually only obtained, if the parameter {{TAG|NBANDS}} is roughly doubled or tripled in the INCAR file with respect to the VASP default. | + | |

+ | The method selected using {{TAG|LOPTICS}}=.TRUE. requires an appreciable number of empty conduction band states. Reasonable results are usually only obtained, if the parameter {{TAG|NBANDS}} is roughly doubled or tripled in the {{FILE|INCAR}} file with respect to the VASP default. | ||

Furthermore it is emphasized that the routine works properly even for [[Hartree-Fock_and_HF/DFT_hybrid_functionals|HF and screened exchange type calculations and hybrid functionals]]. In this case, finite differences are used to determine the derivatives of the Hamiltonian with respect to '''k'''. | Furthermore it is emphasized that the routine works properly even for [[Hartree-Fock_and_HF/DFT_hybrid_functionals|HF and screened exchange type calculations and hybrid functionals]]. In this case, finite differences are used to determine the derivatives of the Hamiltonian with respect to '''k'''. | ||

Note that the number of frequency grid points is determined by the parameter {{TAG|NEDOS}}. In many cases it is desirable to increase this parameter significantly from its default value. Values around {{TAG|NEDOS}}=2000 are strongly recommended. | Note that the number of frequency grid points is determined by the parameter {{TAG|NEDOS}}. In many cases it is desirable to increase this parameter significantly from its default value. Values around {{TAG|NEDOS}}=2000 are strongly recommended. | ||

+ | |||

+ | VASP posses multiple other routines to calculate the frequency dependent dielectric function. | ||

+ | Specifically, one can use {{TAG|ALGO}} = TDHF (Casida/[[BSE calculations]]), {{TAG|ALGO}} = GW ([[GW calculations]]) and {{TAG|ALGO}} = TIMEEV ([[Time Evolution]]: apply a delta kick and follow the induced dipoles). | ||

+ | Compared to {{TAG|LOPTICS}}=.TRUE., all those routines have the advantage to include | ||

+ | effects beyond the independent particle approximation, however, they are usually | ||

+ | also much more expensive than {{TAG|LOPTICS}}=.TRUE. | ||

+ | |||

+ | *N.B: Note that {{TAG|LOPTICS}} = .TRUE. with {{TAG|ISMEAR}} = -2 is currently not supported. | ||

== Related Tags and Sections == | == Related Tags and Sections == | ||

− | {{TAG| | + | {{TAG|CSHIFT}}, |

− | {{TAG| | + | {{TAG|LNABLA}}, |

+ | {{TAG|LEPSILON}} | ||

+ | |||

+ | See also: {{sc|LOPTICS|Examples|Examples that use this tag}}, [[Time Evolution]] | ||

== References == | == References == | ||

Line 39: | Line 55: | ||

[[The_VASP_Manual|Contents]] | [[The_VASP_Manual|Contents]] | ||

− | [[Category:INCAR]][[Category: | + | [[Category:INCAR]][[Category:Dielectric Properties]][[Category:Frequency dependent dielectric properties]] |

## Latest revision as of 14:01, 8 March 2019

LOPTICS = .TRUE. | .FALSE.

Default: **LOPTICS** = .FALSE.

Description: LOPTICS=.TRUE. calculates the frequency dependent dielectric matrix after the electronic ground state has been determined.

The imaginary part is determined by a summation over empty states using the equation:

here the indices *c* and *v* refer to conduction and valence band states respectively, and *u*_{ck} is the cell periodic part of the orbitals at the k-point **k**. The real part of the dielectric tensor ε^{(1)} is obtained by the usual Kramers-Kronig
transformation

where *P* denotes the principle value. The method is explained in detail in the paper by Gajdoš *et al.* (see Eqs. 15, 29, and 30).^{[1]} The complex shift η is determined by the parameter CSHIFT.

Note that local field effects, i.e. changes of the cell periodic part of the potential are neglected in this approximation. These can be evaluated using either the implemented density functional perturbation theory (LEPSILON=.TRUE.), or the GW routines.

The method selected using LOPTICS=.TRUE. requires an appreciable number of empty conduction band states. Reasonable results are usually only obtained, if the parameter NBANDS is roughly doubled or tripled in the INCAR file with respect to the VASP default.
Furthermore it is emphasized that the routine works properly even for HF and screened exchange type calculations and hybrid functionals. In this case, finite differences are used to determine the derivatives of the Hamiltonian with respect to **k**.

Note that the number of frequency grid points is determined by the parameter NEDOS. In many cases it is desirable to increase this parameter significantly from its default value. Values around NEDOS=2000 are strongly recommended.

VASP posses multiple other routines to calculate the frequency dependent dielectric function. Specifically, one can use ALGO = TDHF (Casida/BSE calculations), ALGO = GW (GW calculations) and ALGO = TIMEEV (Time Evolution: apply a delta kick and follow the induced dipoles). Compared to LOPTICS=.TRUE., all those routines have the advantage to include effects beyond the independent particle approximation, however, they are usually also much more expensive than LOPTICS=.TRUE.

## Related Tags and Sections

See also: Examples that use this tag, Time Evolution