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| | | #Redirect [[Time-evolution_algorithm]] |
| 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
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| should be performed before selecting {{TAG|ALGO}} = TIMEEV.
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| ----
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| 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"/>.
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| 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.
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| 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.
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| 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}}.
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| 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.
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| 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).
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| == Example ==
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| A typical calculation requires two steps. First, a ground state calculation:
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| {{TAGBL|SYSTEM}} = Si
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| {{TAGBL|NBANDS}} = 12 ! even 8 bands suffice for Si
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| {{TAGBL|ISMEAR}} = 0 ; {{TAGBL|SIGMA}} = 0.05
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| {{TAGBL|ALGO}} = N
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| {{TAGBL|LOPTICS}} = .TRUE.
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| {{TAGBL|KPAR}} = 4 ! assuming we run on 4 cores, this will be the fastest
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| Second, the actual time propagation:
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| {{TAGBL|SYSTEM}} = Si
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| {{TAGBL|NBANDS}} = 12 ! even 8 bands suffice for Si
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| {{TAGBL|ISMEAR}} = 0 ; {{TAGBL|SIGMA}} = 0.05
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| {{TAGBL|ALGO}} = TIMEEV
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| {{TAGBL|IEPSILON}} = 1 ! cubic system, so response in x direction suffices
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| {{TAGBL|NBANDSO}} = 4 ; {{TAGBL|NBANDSV}} = 8 ; {{TAGBL|CSHIFT}} = 0.1
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| {{TAGBL|KPAR}} = 4 ! assuming we run on 4 cores, this will be the fastest
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| 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.
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| For standard DFT calculations, the time propagation code is so fast that very dense k-point grids can often be used.
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| == Related Tags and Sections ==
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| {{TAG|ALGO}},
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| {{TAG|CSHIFT}},
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| {{TAG|LHARTREE}},
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| {{TAG|LFXC}},
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| {{TAG|NBANDSV}},
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| {{TAG|NBANDSO}},
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| {{TAG|OMEGAMAX}}
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| see also [[BSE calculations]]
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| == References ==
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| <references>
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| <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>
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| <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).]
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| </ref>
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| </references>
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| ----
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| [[The_VASP_Manual|Contents]]
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| [[Category:INCAR]][[Category:Linear response]][[Category:VASP6]]
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