Time Evolution: Difference between revisions
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VASP posses multiple other routines to calculate the frequency dependent dielectric function. | VASP posses multiple other routines to calculate the frequency dependent dielectric function. | ||
The simplest approach uses the independent particle approximation ({{TAG|LOPTICS}}=.TRUE). | The simplest approach uses the independent particle approximation ({{TAG|LOPTICS}}=.TRUE). | ||
Furthermore, one can use {{TAG|ALGO}} = TDHF ([[BSE calculations]] | Furthermore, one can use {{TAG|ALGO}} = TDHF (Casida/[[BSE calculations]]), {{TAG|ALGO}} = GW ([[GW calculations]]). | ||
For standard DFT, the timeevolution algorithm is | For standard DFT, the timeevolution algorithm is | ||
usually fastest, whereas for hybrid functionals {{TAG|ALGO}} = TDHF is | usually fastest, whereas for hybrid functionals {{TAG|ALGO}} = TDHF is | ||
Revision as of 13:48, 28 March 2018
Description: 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)
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 (Casida/BSE calculations), 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).
Example
A typical calculation does require two steps. First a groundstate calculation using
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 fastest
And then a second calculation performing 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 fastest
In this case, 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.
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
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).