Time Evolution - Revision history

Huebsch: Redirected page to Time-evolution algorithm

2025-02-07T12:33:54Z

Redirected page to Time-evolution algorithm

← Older revision		Revision as of 12:33, 7 February 2025
Line 1:		Line 1:
	~~Caution: All features presented in this tag are only available from VASP.6 or higher!~~		#Redirect [[Time-evolution_algorithm]]

	~~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 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}}.

	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.

	~~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.

	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}}.

	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.

	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).

	~~== Example ==~~

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

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


	~~Second, the actual time propagation:~~

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

	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 very dense k-point grids can often be used.~~

	~~== Related Tags and Sections ==~~
	~~{{TAG\|ALGO}},~~
	~~{{TAG\|CSHIFT}},~~
	~~{{TAG\|LHARTREE}},~~
	~~{{TAG\|LFXC}},~~
	~~{{TAG\|NBANDSV}},~~
	~~{{TAG\|NBANDSO}},~~
	~~{{TAG\|OMEGAMAX}}~~

	~~see also [[BSE calculations]]~~

	~~== References ==~~

	~~----~~

	~~[[Category:Linear response~~]]

Huebsch at 09:01, 21 February 2024

2024-02-21T09:01:51Z

← Older revision		Revision as of 09:01, 21 February 2024
Line 58:		Line 58:
	----		----

	[[Category:Linear response~~]][[Category:VASP6~~]]		[[Category:Linear response]]

Ftran at 08:54, 20 October 2023

2023-10-20T08:54:05Z

← Older revision		Revision as of 08:54, 20 October 2023
Line 7:		Line 7:
	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}}.		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}}.

	Details of the implementation are explained in Ref. {{cite\|sander:prb:~~2015~~}}. 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.		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.

	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.		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.

Ftran at 08:52, 20 October 2023

2023-10-20T08:52:44Z

← Older revision		Revision as of 08:52, 20 October 2023
Line 55:		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>~~
	~~</references>~~
	----		----

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

Ftran at 08:52, 20 October 2023

2023-10-20T08:52:19Z

← Older revision		Revision as of 08:52, 20 October 2023
Line 5:		Line 5:
	----		----

	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 ~~<ref name="~~kubo:~~57"/>~~.		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}}.

	Details of the implementation are explained in Ref. ~~<ref name="~~sander:prb:2015~~"/>~~. 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.		Details of the implementation are explained in Ref. {{cite\|sander:prb:2015}}. 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.

	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.		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.
Line 57:		Line 57:
	<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="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>		</ref>

Ftran at 08:34, 20 October 2023

2023-10-20T08:34:39Z

← Older revision		Revision as of 08:34, 20 October 2023
Line 63:		Line 63:
	</references>		</references>
	----		----
	~~[[The_VASP_Manual\|Contents]]~~
	[[Category:Linear response]][[Category:VASP6]]		[[Category:Linear response]][[Category:VASP6]]

Karsai at 20:09, 3 March 2019

2019-03-03T20:09:48Z

← Older revision		Revision as of 20:09, 3 March 2019
Line 64:		Line 64:
	----		----
	[[The_VASP_Manual\|Contents]]		[[The_VASP_Manual\|Contents]]
			[[Category:Linear response]][[Category:VASP6]]
	~~[[Category:INCAR]]~~[[Category:Linear response]][[Category:VASP6]]

Karsai at 11:22, 15 February 2019

2019-02-15T11:22:08Z

← Older revision		Revision as of 11:22, 15 February 2019
Line 1:		Line 1:
	All features presented in this tag are only available from VASP.6 or higher!		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 using the time evolution algorithm. A standard DFT ground state calculation		Description: {{TAG\|ALGO}} = TIMEEV calculates the frequency-dependent dielectric function using the time evolution algorithm. A standard DFT ground state calculation

Karsai at 11:21, 15 February 2019

2019-02-15T11:21:45Z

← Older revision		Revision as of 11:21, 15 February 2019
Line 1:		Line 1:
			All features presented in this tag are only available from VASP.6 or higher!

	Description: {{TAG\|ALGO}} = TIMEEV calculates the frequency-dependent dielectric function using the time evolution algorithm ~~(only available in VASP v6)~~. A standard DFT ground state calculation		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.		should be performed before selecting {{TAG\|ALGO}} = TIMEEV.
	----		----

Stkr at 14:36, 30 March 2018

2018-03-30T14:36:18Z

← Older revision		Revision as of 14:36, 30 March 2018
Line 4:		Line 4:
	----		----

	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 <ref name="kubo:57"/>.		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 <ref name="kubo:57"/>.

	Details of the implementation are explained in Ref. <ref name="sander:prb:2015"/>. 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.		Details of the implementation are explained in Ref. <ref name="sander:prb:2015"/>. 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.

← Older revision		Revision as of 12:33, 7 February 2025
Line 1:		Line 1:
	~~Caution: All features presented in this tag are only available from VASP.6 or higher!~~		#Redirect [[Time-evolution_algorithm]]

	~~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 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}}.

	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.

	~~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.

	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}}.

	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.

	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).

	~~== Example ==~~

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

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


	~~Second, the actual time propagation:~~

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

	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 very dense k-point grids can often be used.~~

	~~== Related Tags and Sections ==~~
	~~{{TAG\|ALGO}},~~
	~~{{TAG\|CSHIFT}},~~
	~~{{TAG\|LHARTREE}},~~
	~~{{TAG\|LFXC}},~~
	~~{{TAG\|NBANDSV}},~~
	~~{{TAG\|NBANDSO}},~~
	~~{{TAG\|OMEGAMAX}}~~

	~~see also [[BSE calculations]]~~

	~~== References ==~~

	~~----~~

	~~[[Category:Linear response~~]]

← Older revision		Revision as of 08:54, 20 October 2023
Line 7:		Line 7:
	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}}.		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}}.

	Details of the implementation are explained in Ref. {{cite\|sander:prb:~~2015~~}}. 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.		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.

	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.		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.