View source for Time-dependent density-functional theory calculations

VASP offers a powerful module for performing time-dependent density-functional theory (TDDFT) or time-dependent Hartree-Fock (TDHF) calculations by solving the Casida equation {{cite|casida:jomst:2009}}. This approach can be used for obtaining the frequency-dependent dielectric function with the excitonic effects and can be based on the ground-state electronic structure in the DFT, hybrid-functional or even ''GW'' approximations.  

== Solving Casida equation ==
The algorithm for solving the Casida equation can be selected by setting {{TAG|ALGO}} = TDHF. This approach is very similar to BSE but differs in the way the screening of the Coulomb potential is approximated. The TDHF approach uses the exchange-correlation kernel <math>f_{\rm xc}</math>, whereas BSE requires the <math>W(\omega \to 0)</math> from a preceding ''GW '' calculation. Thus, in order to perform a TDHF calculation, one only needs to provide the ground-state orbitals ({{FILE|WAVECAR}}) and the derivatives of the orbitals with respect to <math>k</math> ({{FILE|WAVEDER}}).
{{NB|mind|Unlike BSE, TDHF calculations do '''not''' require <math>W(\omega \to 0)</math>, i.e., {{FILE|Wxxxx.tmp}}|}}

In summary, both TDHF and BSE approaches require a preceding ground-state calculation, however, the TDHF does not need the preceding ''GW'' and can be performed with the DFT or hybrid-functional orbitals and energies.

== Time-dependent Hartree-Fock ==
The TDHF calculations can be performed in two steps: 
# ground-state calculation
# optical absorption calculation
For example, an optical absorption calculation of bulk Si can be performed using a dielectric-dependent  hybrid-functional described in Refs.{{cite|chen2018nonempirical}}{{cite|cui2018doubly}}{{cite|liu2019assessing}}.

 {{TAG|SYSTEM}}    = Si
 {{TAG|ISMEAR}}    = 0 
 {{TAG|SIGMA}}     = 0.05
 {{TAG|NBANDS}}    = 16      ! or any larger desired value
 {{TAG|ALGO}}      = D       ! Damped algorithm often required for HF type calculations, {{TAG|ALGO}} = Normal might work as well
 {{TAG|LHFCALC}}   = .TRUE. 
 {{TAG|LMODELHF}}  = .TRUE. 
 {{TAG|AEXX}}      = 0.083
 {{TAG|HFSCREEN}}  = 1.22
 {{TAG|LOPTICS}}   = .TRUE.  ! can also be done in an additional intermediate step

In the second step, the dielectric function is evaluated by solving the Casida equation 

 {{TAG|SYSTEM}}    = Si
 {{TAG|ISMEAR}}    = 0 
 {{TAG|SIGMA}}     = 0.05
 {{TAG|NBANDS}}    = 16     
 {{TAG|ALGO}}      = TDHF
 {{TAG|IBSE}}      = 0
 {{TAG|NBANDSO}}   = 4       ! number of occupied bands
 {{TAG|NBANDSV}}   = 8       ! number of unoccupied bands
 {{TAG|LHARTREE}}  = .TRUE.
 {{TAG|LADDER}}    = .TRUE.
 {{TAG|LFXC}}      = .TRUE.
 {{TAG|LMODELHF}}  = .TRUE. 
 {{TAG|AEXX}}      = 0.083
 {{TAG|HFSCREEN}}  = 1.22

THDF calculations can be performed for non-spin-polarized, spin-polarized, and noncollinear cases, as well as the case with spin-orbit coupling. There is, however, one caveat. The local exchange-correlation kernel is approximated by the density-density part only. This makes predictions for spin-polarized systems less accurate than for non-spin-polarized systems.

== Time-dependent DFT calculation ==
The TDDFT calculation using the PBE exchange-correlation kernel can be performed by disabling the ladder diagrams {{TAG|LADDER}} = .FALSE., i.e., only the PBE exchange-correlation kernel is present in the Hamiltonian.

 {{TAG|SYSTEM}}    = Si
 {{TAG|ISMEAR}}    = 0 
 {{TAG|SIGMA}}     = 0.05
 {{TAG|NBANDS}}    = 16     
 {{TAG|ALGO}}      = TDHF
 {{TAG|IBSE}}      = 0
 {{TAG|NBANDSO}}   = 4       ! determines how many occupied bands are used
 {{TAG|NBANDSV}}   = 8       ! determines how many unoccupied (virtual) bands are used
 {{TAG|LFXC}}      = .TRUE.
 {{TAG|LHARTREE}}  = .TRUE.
 {{TAG|LADDER}}    = .FALSE.
{{NB|mind|In TDDFT calculation, where the ladder diagrams are not included ({{TAG|LADDER}}{{=}}.FALSE.) or the fraction of exact exchange in the kernel is zero ({{TAG|AEXX}}{{=}}0), the resulting dielectric function lacks the excitonic effects.|}}

VASP tries to use sensible defaults, but it is highly recommended to check the {{FILE|OUTCAR}} file and make sure that the right bands are included.  The tag {{TAG|OMEGAMAX}} specifies the maximum excitation energy of included electron-hole pairs and the pairs with the one-electron energy difference beyond this limit are not included in the Hamiltonian.  

The calculated frequency-dependent dielectric function, transition energies and oscillator strength values are stored in the {{TAG|vasprun.xml}} file.

== Calculations beyond Tamm-Dancoff approximation ==
Calculations beyond Tamm-Dancoff approximation can be performed in the same manner as in the [[BSE calculations#Calculations beyond Tamm-Dancoff approximation|BSE]].

== Calculations at finite wavevectors ==
Calculations at finite wavevectors can be performed in the same manner as in the [[BSE calculations#Calculations at finite wavevectors|BSE]].
== References ==
<references/>
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[[Category:Time-dependent density functional theory]][[Category:Howto]]