Time Evolution: Difference between revisions
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Details of the implementation are explained in Ref. <ref name="sander:prb:2015"/>. The | Details of the implementation are explained in Ref. <ref name="sander:prb:2015"/>. The | ||
time propagation algorithm | time propagation algorithm in VASP uses relatively large time steps by projecting, | ||
after each time step onto a specific number of occupied and unoccupied | after each time step, onto a specific number of occupied and unoccupied pais. The number of | ||
occupied and unoccupied pairs are | occupied and unoccupied pairs are controlled by the tags {{TAG|NBANDSO}} and {{TAG|NBANDSV}} | ||
and {{TAG|OMEGAMAX}} - | and {{TAG|OMEGAMAX}} - | ||
in the same manner as | in the same manner as done for Casida and [[BSE calculations]]. | ||
This has the advantage that the results are strictly compatible to the results | This has the advantage that the results are strictly compatible to the results | ||
obtained by the [[BSE calculations]]. | obtained by the [[BSE calculations]]. | ||
The disadvantage is that a sufficient number of unoccupied orbitals need to | The disadvantage is that a sufficient number of unoccupied orbitals need to | ||
be calculated in the preceding ground state | 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 | Per default, the time propagation code includes Hartree and local field | ||
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The number of timesteps performed in the propagation is usually inverse proportional | The number of timesteps performed in the propagation is usually inverse proportional | ||
to the value of {{TAG|CSHIFT}}. That is a small {{TAG|CSHIFT}} will require | to the value of {{TAG|CSHIFT}}. That is a small {{TAG|CSHIFT}} will require | ||
less | less time step (but yield a more strongly broadened spectrum), whereas | ||
a small shift {{TAG|CSHIFT}} will require more | a small shift {{TAG|CSHIFT}} will require more time steps. | ||
Typical values of around {{TAG|CSHIFT}}=0.1 will result in useful spectra. | Typical values of around {{TAG|CSHIFT}}=0.1 will result in useful spectra. | ||
Alternatively, the number of | Alternatively, the number of time steps can be set directly by the tag {{TAG|NELM}}. | ||
In this case, the number of | 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 | in NELM will be disregarded, and the number of time steps is determined by | ||
the tag {{TAG|CSHIFT}}. | 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 delta pulse is | 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 posses multiple other routines to calculate the frequency dependent dielectric function. | VASP posses multiple other routines to calculate the frequency dependent dielectric function. | ||
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usually fastest, whereas for hybrid functionals {{TAG|ALGO}} = TDHF is | usually fastest, whereas for hybrid functionals {{TAG|ALGO}} = TDHF is | ||
usually faster. Results of timeevolution are strictly identical to | usually faster. Results of timeevolution are strictly identical to | ||
{{TAG|ALGO}} = TDHF | {{TAG|ALGO}} = TDHF; {{TAG|ANTIRES}} = 2, if the tags {{TAG|CSHIFT}}, {{TAG|OMEGAMAX}} | ||
{{TAG|NBANDSV}}, and {{TAG|NBANDSO}} are chosen identical. | {{TAG|NBANDSV}}, and {{TAG|NBANDSO}} are chosen identical | ||
({{TAG|ANTIRES}} = 2 is required, since time propagation does not rely on | |||
the Tamm Dancoff approximation). | |||
== Related Tags and Sections == | == Related Tags and Sections == | ||
{{TAG|CSHIFT}}, | {{TAG|CSHIFT}}, | ||
{{TAG|LHARTREE}}, | {{TAG|LHARTREE}}, | ||
{{TAG|LFXC}}, | |||
{{TAG|NBANDSV}}, | {{TAG|NBANDSV}}, | ||
{{TAG|NBANDSO}}, | {{TAG|NBANDSO}}, | ||
{{TAG|OMEGAMAX}} | {{TAG|OMEGAMAX}} | ||
[[BSE calculations]] | see also [[BSE calculations]] | ||
== References == | == References == | ||
Revision as of 13:08, 28 March 2018
Description: ALGO= timeev calculates the frequency dependent dielectric matrix after the electronic ground state has been determined using the time evolution algorithm (only available in vasp.6)
The timepropagation algorithm applies a short delta puls (E field) in time, and 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 [1].
Details of the implementation are explained in Ref. [2]. The 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 NBANDSO and NBANDSV and 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 effects (LHARTREE=.TRUE. and LFXC=.TRUE.). Results in the independent particle approximation can be calculated by setting LHARTREE=.FALSE. and LFXC=.FALSE. Other combinations (LHARTREE=.TRUE. and LFXC=.FALSE. or LHARTREE=.FALSE. and LFXC=.TRUE. are presently not supported).
The number of timesteps performed in the propagation is usually inverse proportional to the value of CSHIFT. That is a small CSHIFT will require less time step (but yield a more strongly broadened spectrum), whereas a small shift CSHIFT will require more time steps. Typical values of around CSHIFT=0.1 will result in useful spectra. Alternatively, the number of time steps can be set directly by the tag NELM. In this case, the number of user supplied steps needs to exceed NELM>100 (otherwise, the value in NELM will be disregarded, and the number of time steps is determined by the tag CSHIFT.
Finally, the tag IEPSILON controls the Cartesian direction along which the delta pulse is applied. IEPSILON=4 (default) performs three independent calculations for an electric field in x, y and z direction (and is therefore most expensive).
VASP posses multiple 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 (BSE calculations equivalent to solving the Casida equation), ALGO = GW (GW calculations). For standard DFT, the timeevolution algorithm is usually fastest, whereas for hybrid functionals ALGO = TDHF is usually faster. Results of timeevolution 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 rely on the Tamm Dancoff approximation).
Related Tags and Sections
CSHIFT, LHARTREE, LFXC, NBANDSV, NBANDSO, OMEGAMAX
see also BSE calculations
References
- ↑ 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.
- ↑ T. Sander, E. Maggio, and G. Kresse, Beyond the Tamm-Dancoff approximation for extended systems using exact diagonalization. Physical Review B, 92, 045209 (2015).