Time Evolution: Difference between revisions

From VASP Wiki
No edit summary
No edit summary
 
(15 intermediate revisions by 4 users not shown)
Line 1: Line 1:
Caution: All features presented in this tag are only available from VASP.6 or higher!


Description: {{TAG|ALGO}}= timeev calculates the frequency dependent dielectric function after the electronic ground state has been determined using the time evolution algorithm (only available in vasp.6)
Description: {{TAG|ALGO}} = TIMEEV calculates the frequency-dependent dielectric function using the time evolution algorithm. A standard DFT ground state calculation
should be performed before selecting  {{TAG|ALGO}} = TIMEEV.
----
----


The timepropagation algorithm applies a short delta puls (E field)  in time, and
The time evolution algorithm applies a short Dirac delta pulse of electric field and then follows the evolution of the dipole moments. The Green-Kubo relation allows calculating the frequency-dependent dielectric response function from the time evolution of the dipole moments {{cite|kubo:jpsj:1957}}.
then follows the evolution of the dipole moments. The Green-Kubo relation
allows to calculate the frequency dependent dielectric response function
from the time evolution of the dipole moments <ref name="kubo:57"/>.


Details of the implementation are explained in Ref. <ref name="sander:prb:2015"/>. The
Details of the implementation are explained in Ref. {{cite|sander:prb:15}}. The time evolution algorithm in VASP uses relatively large time steps by projecting, after each time step, onto a specific number of occupied and unoccupied bands. The number of occupied and unoccupied bands are controlled by the tags {{TAG|NBANDSO}}, {{TAG|NBANDSV}}, and {{TAG|OMEGAMAX}} in the same way as for Casida and [[BSE calculations]]. This has the advantage that the time evolution results are strictly compatible to the results of the BSE calculations. The disadvantage is that a sufficient number of unoccupied orbitals needs to be calculated in the preceding ground state calculation. Note, however, that unoccupied orbitals are not propagated, which saves computational time.
time propagation algorithm in VASP uses relatively large time steps by projecting,
after each time step, onto a specific number of occupied and unoccupied pais. The number of
occupied and unoccupied pairs are controlled by the tags {{TAG|NBANDSO}} and {{TAG|NBANDSV}}
and {{TAG|OMEGAMAX}} -
in the same manner as done for Casida and [[BSE calculations]].  
This has the advantage that the results are strictly compatible to the results
obtained by the [[BSE calculations]].
The disadvantage is that a sufficient number of unoccupied orbitals need to
be calculated in the preceding ground state calculations
(note however, that unoccupied orbitals are not propagated in time, which
saves compute time).  


Per default, the time propagation code includes Hartree and local field
By default, the time propagation code includes the Hartree and local-field effects ({{TAG|LHARTREE}}=.TRUE. and {{TAG|LFXC}}=.TRUE.). Results in the independent particle approximation can be calculated by setting {{TAG|LHARTREE}}=.FALSE. and {{TAG|LFXC}}=.FALSE. The two other combinations of these settings ({{TAG|LHARTREE}}=.TRUE. and {{TAG|LFXC}}=.FALSE., or {{TAG|LHARTREE}}=.FALSE. and {{TAG|LFXC}}=.TRUE.) are currently not supported.
effects ({{TAG|LHARTREE}}=.TRUE. and {{TAG|LFXC}}=.TRUE.). Results in the independent particle approximation can be calculated by setting {{TAG|LHARTREE}}=.FALSE. and {{TAG|LFXC}}=.FALSE.
Other combinations ({{TAG|LHARTREE}}=.TRUE. and {{TAG|LFXC}}=.FALSE. or
{{TAG|LHARTREE}}=.FALSE. and {{TAG|LFXC}}=.TRUE. are presently not supported).


The number of timesteps performed in the propagation is usually inverse proportional
The number of time steps is chosen usually automatically by VASP. It is inversely proportional to the value of {{TAG|CSHIFT}}. That is, a large {{TAG|CSHIFT}} requires less time steps (but yields a more strongly broadened spectrum), whereas a small shift {{TAG|CSHIFT}} requires more steps. Typically, values of {{TAG|CSHIFT}} = 0.1 result in physically meaningful spectra. Alternatively, the number of time steps can be set directly by the tag {{TAG|NELM}}. In this case, the user-defined number of steps needs to be large than 100. Otherwise, the value of {{TAG|NELM}} will be discarded, and the actual number of time steps will be determined by the tag {{TAG|CSHIFT}}.  
to the value of {{TAG|CSHIFT}}. That is a small {{TAG|CSHIFT}} will require
less time step (but yield a more strongly broadened spectrum), whereas
a small shift {{TAG|CSHIFT}} will require more time steps.  
Typical values of around {{TAG|CSHIFT}}=0.1 will result in useful spectra.
Alternatively, the number of time steps can be set directly by the tag {{TAG|NELM}}.  
In this case, the number of user supplied steps needs to exceed {{TAG|NELM}}>100 (otherwise, the value
in NELM will be disregarded, and the number of time steps is determined by  
the tag {{TAG|CSHIFT}}.


Finally, the tag {{TAG | IEPSILON}} controls the Cartesian direction along which
Finally, the tag {{TAG|IEPSILON}} controls the Cartesian direction, along which the Dirac delta pulse is applied. {{TAG|IEPSILON}} = 4 (default) performs three independent calculations for an electric field in x, y and z direction, and thus is the most expensive.
the delta pulse is applied.   {{TAG | IEPSILON}}=4 (default) performs
three independent calculations for an electric field in x, y and z direction
(and is therefore most expensive).


 
VASP provides a number of other routines to calculate the frequency-dependent dielectric function. The simplest approach uses the independent particle approximation ({{TAG|LOPTICS}} = .TRUE). Furthermore, one can use {{TAG|ALGO}} = TDHF (Casida/BSE calculations), {{TAG|ALGO}} = GW (GW calculations). For standard DFT, the time propagation algorithm ({{TAG|ALGO}} = TIMEEV) is usually the fastest, whereas for hybrid functionals {{TAG|ALGO}} = TDHF is usually faster. Results of time propagation are strictly identical to {{TAG|ALGO}} = TDHF; {{TAG|ANTIRES}} = 2, if the tags {{TAG|CSHIFT}}, {{TAG|OMEGAMAX}}, {{TAG|NBANDSV}}, and {{TAG|NBANDSO}} are chosen identical ({{TAG|ANTIRES}} = 2 is required, since time propagation does not apply the Tamm-Dancoff approximation).  
 
VASP posses multiple other routines to calculate the frequency dependent dielectric function.
The simplest approach uses the independent particle approximation ({{TAG|LOPTICS}}=.TRUE).
Furthermore, one can use {{TAG|ALGO}} = TDHF ([[BSE calculations]] equivalent to solving the Casida equation), {{TAG|ALGO}} = GW ([[GW calculations]]).  
For standard DFT, the timeevolution algorithm is
usually fastest, whereas for hybrid functionals {{TAG|ALGO}} = TDHF is
usually faster. Results of timeevolution are strictly identical to
{{TAG|ALGO}} = TDHF; {{TAG|ANTIRES}} = 2, if the tags {{TAG|CSHIFT}}, {{TAG|OMEGAMAX}}
{{TAG|NBANDSV}}, and {{TAG|NBANDSO}} are chosen identical
({{TAG|ANTIRES}} = 2 is required, since time propagation does not rely on
the Tamm Dancoff approximation).


== Example ==
== Example ==


A typical calculation does require two steps. First a groundstate
A typical calculation requires two steps. First, a ground state calculation:
calculation using


  {{TAGBL|System}} = Si
  {{TAGBL|SYSTEM}} = Si
  {{TAGBL|NBANDS}} = 12 ! even 8 bands suffice for Si
  {{TAGBL|NBANDS}} = 12 ! even 8 bands suffice for Si
  {{TAGBL|ISMEAR}} = 0 ; {{TAGBL|SIGMA}} = 0.05
  {{TAGBL|ISMEAR}} = 0 ; {{TAGBL|SIGMA}} = 0.05
  {{TAGBL|ALGO}} = N
  {{TAGBL|ALGO}} = N
  {{TAGBL|LOPTICS}} = .TRUE.
  {{TAGBL|LOPTICS}} = .TRUE.
  {{TAGBL|KPAR}} = 4    ! assuming we run on 4 cores, this will be fastest
  {{TAGBL|KPAR}} = 4    ! assuming we run on 4 cores, this will be the fastest




And then a second calculation performing the actual time propagation:
Second, the actual time propagation:  


  {{TAGBL|System}} = Si
  {{TAGBL|SYSTEM}} = Si
  {{TAGBL|NBANDS}} = 12  ! even 8 bands suffice for Si
  {{TAGBL|NBANDS}} = 12  ! even 8 bands suffice for Si
  {{TAGBL|ISMEAR}} = 0 ; {{TAGBL|SIGMA}} = 0.05
  {{TAGBL|ISMEAR}} = 0 ; {{TAGBL|SIGMA}} = 0.05
Line 75: Line 37:
  {{TAGBL|IEPSILON}} = 1 ! cubic system, so response in x direction suffices
  {{TAGBL|IEPSILON}} = 1 ! cubic system, so response in x direction suffices
  {{TAGBL|NBANDSO}} = 4  ; {{TAGBL|NBANDSV}} = 8  ;  {{TAGBL|CSHIFT}} = 0.1
  {{TAGBL|NBANDSO}} = 4  ; {{TAGBL|NBANDSV}} = 8  ;  {{TAGBL|CSHIFT}} = 0.1
  {{TAGBL|KPAR}} = 4    ! assuming we run on 4 cores, this will be fastest
  {{TAGBL|KPAR}} = 4    ! assuming we run on 4 cores, this will be the fastest
 
In this case, {{TAG|OMEGAMAX}} is set automatically to the maximum transition energy
(in this example about 25 eV). Reducing the number of considered transitions, and thus
reducing OMEGAMAX, will increase the time step, and hence reduce the number of required time steps.


In this case, {{TAG|OMEGAMAX}} is set automatically to the maximal transition energy (about 25 eV in this example). Reducing the number of considered transitions, and thus reducing {{TAG|OMEGAMAX}} will increase both the duration of time steps and their number.
   
   
For standard DFT calculations, the time propagation code is so fast that
For standard DFT calculations, the time propagation code is so fast that very dense k-point grids can often be used.  
very dense k-point grids can often be used.  


== Related Tags and Sections ==
== Related Tags and Sections ==
{{TAG|ALGO}},
{{TAG|CSHIFT}},
{{TAG|CSHIFT}},
{{TAG|LHARTREE}},
{{TAG|LHARTREE}},
Line 96: Line 55:


== References ==
== References ==
<references>
<ref name="kubo:57">[http://journals.jps.jp/doi/10.1143/JPSJ.12.570 R. Kubo, Statistical-Mechanical Theory of Irreversible Processes. I. General Theory and Simple Applications to Magnetic and Conduction Problems. In: Journal of the Physical Society of Japan. Band 12, Nr.6, 15. Juni 1957, S.570–586, doi:10.1143/JPSJ.12.57].</ref>
<ref name="sander:prb:2015">[https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.045209 T. Sander, E. Maggio, and G. Kresse, Beyond the Tamm-Dancoff approximation for extended systems using exact diagonalization. Physical Review B, 92, 045209 (2015).]


</ref>
</references>
----
----
[[The_VASP_Manual|Contents]]


[[Category:INCAR]][[Category:Linear response]][[Category:VASP6]]
[[Category:Linear response]]

Latest revision as of 09:01, 21 February 2024

Caution: All features presented in this tag are only available from VASP.6 or higher!

Description: ALGO = TIMEEV calculates the frequency-dependent dielectric function using the time evolution algorithm. A standard DFT ground state calculation should be performed before selecting ALGO = TIMEEV.


The time evolution algorithm applies a short Dirac delta pulse of electric field and then follows the evolution of the dipole moments. The Green-Kubo relation allows calculating the frequency-dependent dielectric response function from the time evolution of the dipole moments [1].

Details of the implementation are explained in Ref. [2]. The time evolution algorithm in VASP uses relatively large time steps by projecting, after each time step, onto a specific number of occupied and unoccupied bands. The number of occupied and unoccupied bands are controlled by the tags NBANDSO, NBANDSV, and OMEGAMAX in the same way as for Casida and BSE calculations. This has the advantage that the time evolution results are strictly compatible to the results of the BSE calculations. The disadvantage is that a sufficient number of unoccupied orbitals needs to be calculated in the preceding ground state calculation. Note, however, that unoccupied orbitals are not propagated, which saves computational time.

By default, the time propagation code includes the Hartree and local-field effects (LHARTREE=.TRUE. and LFXC=.TRUE.). Results in the independent particle approximation can be calculated by setting LHARTREE=.FALSE. and LFXC=.FALSE. The two other combinations of these settings (LHARTREE=.TRUE. and LFXC=.FALSE., or LHARTREE=.FALSE. and LFXC=.TRUE.) are currently not supported.

The number of time steps is chosen usually automatically by VASP. It is inversely proportional to the value of CSHIFT. That is, a large CSHIFT requires less time steps (but yields a more strongly broadened spectrum), whereas a small shift CSHIFT requires more steps. Typically, values of CSHIFT = 0.1 result in physically meaningful spectra. Alternatively, the number of time steps can be set directly by the tag NELM. In this case, the user-defined number of steps needs to be large than 100. Otherwise, the value of NELM will be discarded, and the actual number of time steps will be determined by the tag CSHIFT.

Finally, the tag IEPSILON controls the Cartesian direction, along which the Dirac delta pulse is applied. IEPSILON = 4 (default) performs three independent calculations for an electric field in x, y and z direction, and thus is the most expensive.

VASP provides a number of other routines to calculate the frequency-dependent dielectric function. The simplest approach uses the independent particle approximation (LOPTICS = .TRUE). Furthermore, one can use ALGO = TDHF (Casida/BSE calculations), ALGO = GW (GW calculations). For standard DFT, the time propagation algorithm (ALGO = TIMEEV) is usually the fastest, whereas for hybrid functionals ALGO = TDHF is usually faster. Results of time propagation are strictly identical to ALGO = TDHF; ANTIRES = 2, if the tags CSHIFT, OMEGAMAX, NBANDSV, and NBANDSO are chosen identical (ANTIRES = 2 is required, since time propagation does not apply the Tamm-Dancoff approximation).

Example

A typical calculation requires two steps. First, a ground state calculation:

SYSTEM = Si
NBANDS = 12 ! even 8 bands suffice for Si
ISMEAR = 0 ; SIGMA = 0.05
ALGO = N
LOPTICS = .TRUE.
KPAR = 4     ! assuming we run on 4 cores, this will be the fastest


Second, the actual time propagation:

SYSTEM = Si
NBANDS = 12  ! even 8 bands suffice for Si
ISMEAR = 0 ; SIGMA = 0.05
ALGO = TIMEEV
IEPSILON = 1 ! cubic system, so response in x direction suffices
NBANDSO = 4  ; NBANDSV = 8  ;  CSHIFT = 0.1
KPAR = 4     ! assuming we run on 4 cores, this will be the fastest

In this case, OMEGAMAX is set automatically to the maximal transition energy (about 25 eV in this example). Reducing the number of considered transitions, and thus reducing OMEGAMAX will increase both the duration of time steps and their number.

For standard DFT calculations, the time propagation code is so fast that very dense k-point grids can often be used.

Related Tags and Sections

ALGO, CSHIFT, LHARTREE, LFXC, NBANDSV, NBANDSO, OMEGAMAX

see also BSE calculations

References