BSEPREC: Difference between revisions
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{{TAGDEF|BSEPREC|Low {{!}} Medium {{!}} High {{!}} Accurate | Medium}} | {{TAGDEF|BSEPREC|Low {{!}} Medium {{!}} High {{!}} Accurate | Medium}} | ||
Description: | Description: Determines the precision of the [[:Category:Bethe-Salpeter_equations#Time_evolution|time-evolution algorithm]], where it controls the timestep and the number of steps, and the precision of the [[:Category:Bethe-Salpeter_equations#Lanczos_algorithm |Lanczos algorithms]], where it sets the convergence threshold for the dielectric function. | ||
----- | |||
==Time-evolution algorithm== | ==Time-evolution algorithm== | ||
The timestep in the time-evolution calculation is inversely proportional to the maximum transition energy {{TAG|OMEGAMAX}} and the number of steps is inversely proportional to the broadening {{TAG|CSHIFT}}. Depending on the {{TAG|BSEPREC}} stable these parameters are scaled depending on the precision tag {{TAG|BSEPREC}}. | The timestep in the time-evolution calculation is inversely proportional to the maximum transition energy {{TAG|OMEGAMAX}} and the number of steps is inversely proportional to the broadening {{TAG|CSHIFT}}. Depending on the {{TAG|BSEPREC}} stable these parameters are scaled depending on the precision tag {{TAG|BSEPREC}}. | ||
{| cellpadding="5" cellspacing=" | ::{| cellpadding="5" cellspacing="5" style="width: 50%; border-spacing: 5px;" | ||
| style="text-align:center; background-color:#DEC4EB;"| {{TAG|BSEPREC}} || style="text-align:center; background-color:#DEC4EB;"| {{TAG|OMEGAMAX}} || style="text-align:center; background-color:#DEC4EB;"| {{TAG|CSHIFT}} | |||
|- | |- | ||
| Accurate (a) || <math>\times 4</math> || <math>\times 1/10</math> | |style="background-color:#D9F8F5;"| Accurate (a) ||style="background-color:#D9F8F5;"| <math>\times 4</math> ||style="background-color:#D9F8F5;"| <math>\times 1/10</math> | ||
|- | |- | ||
| High (h) || <math>\times 3</math> || <math>\times 1/7.5</math> | |style="background-color:#D9F8F5;"| High (h) ||style="background-color:#D9F8F5;"| <math>\times 3</math> ||style="background-color:#D9F8F5;"| <math>\times 1/7.5</math> | ||
|- | |- | ||
| Medium (m) || <math>\times 2.5</math> || <math>\times1/6.25</math> | |style="background-color:#D9F8F5;"| Medium (m) ||style="background-color:#D9F8F5;"| <math>\times 2.5</math> ||style="background-color:#D9F8F5;"| <math>\times1/6.25</math> | ||
|- | |- | ||
| Low (l) || <math>\times 2</math> || <math>\times1/5</math> | |style="background-color:#D9F8F5;"| Low (l) ||style="background-color:#D9F8F5;"| <math>\times 2</math> ||style="background-color:#D9F8F5;"| <math>\times1/5</math> | ||
|} | |} | ||
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==Lanczos algorithm== | ==Lanczos algorithm== | ||
{{NB|mind|Replaces {{TAG|LANCZOSTHR}} as of version 6.5.1}} | |||
The Lanczos algorithm stops once the imaginary part of the dielectric function computed in two consecutive iterations differs bellow a certain threshold for the root-mean-square, i.e. once after <math>n</math> iterations the value of | The Lanczos algorithm stops once the imaginary part of the dielectric function computed in two consecutive iterations differs bellow a certain threshold for the root-mean-square, i.e. once after <math>n</math> iterations the value of | ||
<math> | ::<math> | ||
\mathrm{RMS}[\epsilon_n] = \sqrt{\frac{1}{N_\omega}\sum_{i=1}^{N_\omega}\left(\Im[\epsilon_n(\omega_i)]-\Im[\epsilon_{n-1}(\omega_i)]\right)^2} | \mathrm{RMS}[\epsilon_n] = \sqrt{\frac{1}{N_\omega}\sum_{i=1}^{N_\omega}\left(\Im[\epsilon_n(\omega_i)]-\Im[\epsilon_{n-1}(\omega_i)]\right)^2} | ||
</math> | </math> | ||
is below a certain value defined by '''BSEPREC'''. | is below a certain value defined by '''BSEPREC'''. | ||
{| cellpadding="5" cellspacing=" | |||
::{| cellpadding="5" cellspacing="5" style="width: 50%; border-spacing: 5px;" | |||
| style="text-align:center; background-color:#DEC4EB;"| BSEPREC || style="text-align:center; background-color:#DEC4EB;"| <math>\mathrm{RMS}[\epsilon_n]</math> | |||
|- | |- | ||
| Accurate (a) || <math>10^{-5}</math> | |style="background-color:#D9F8F5;"| Accurate (a) ||style="background-color:#D9F8F5;"| <math>10^{-5}</math> | ||
|- | |- | ||
| High (h) || <math>10^{-4}</math> | |style="background-color:#D9F8F5;"| High (h) ||style="background-color:#D9F8F5;"| <math>10^{-4}</math> | ||
|- | |- | ||
| Medium (m) || <math>10^{-3}</math> | |style="background-color:#D9F8F5;"| Medium (m) ||style="background-color:#D9F8F5;"| <math>10^{-3}</math> | ||
|- | |- | ||
| Low (l) || <math>10^{-2}</math> | |style="background-color:#D9F8F5;"| Low (l) ||style="background-color:#D9F8F5;"| <math>10^{-2}</math> | ||
|} | |} | ||
| Line 47: | Line 51: | ||
{{TAG|NBANDSO}}, | {{TAG|NBANDSO}}, | ||
{{TAG|CSHIFT}}, | {{TAG|CSHIFT}}, | ||
{{TAG|OMEGAMAX}} | {{TAG|OMEGAMAX}} | ||
[[BSE calculations]] | |||
[[Time-dependent density-functional theory calculations]] | [[BSE calculations]] | ||
[[Time-dependent density-functional theory calculations]] | |||
[[Bethe-Salpeter equations]] | [[Bethe-Salpeter equations]] | ||
---- | ---- | ||
[[Category:INCAR tag]] [[Category:Many-body perturbation theory]][[Category:Bethe-Salpeter equations]] | [[Category:INCAR tag]] [[Category:Many-body perturbation theory]][[Category:Bethe-Salpeter equations]] | ||
Latest revision as of 08:53, 17 October 2025
BSEPREC = Low | Medium | High | Accurate
Default: BSEPREC = Medium
Description: Determines the precision of the time-evolution algorithm, where it controls the timestep and the number of steps, and the precision of the Lanczos algorithms, where it sets the convergence threshold for the dielectric function.
Time-evolution algorithm
The timestep in the time-evolution calculation is inversely proportional to the maximum transition energy OMEGAMAX and the number of steps is inversely proportional to the broadening CSHIFT. Depending on the BSEPREC stable these parameters are scaled depending on the precision tag BSEPREC.
BSEPREC OMEGAMAX CSHIFT Accurate (a) [math]\displaystyle{ \times 4 }[/math] [math]\displaystyle{ \times 1/10 }[/math] High (h) [math]\displaystyle{ \times 3 }[/math] [math]\displaystyle{ \times 1/7.5 }[/math] Medium (m) [math]\displaystyle{ \times 2.5 }[/math] [math]\displaystyle{ \times1/6.25 }[/math] Low (l) [math]\displaystyle{ \times 2 }[/math] [math]\displaystyle{ \times1/5 }[/math]
For example, the number of steps [math]\displaystyle{ N_{\rm steps} }[/math] for BSEPREC = Low can be found via [math]\displaystyle{ N_{\rm steps}=\frac{{\rm OMEGAMAX}\times 2}{{\rm CSHIFT}/5} }[/math]
Lanczos algorithm
| Mind: Replaces LANCZOSTHR as of version 6.5.1 |
The Lanczos algorithm stops once the imaginary part of the dielectric function computed in two consecutive iterations differs bellow a certain threshold for the root-mean-square, i.e. once after [math]\displaystyle{ n }[/math] iterations the value of
- [math]\displaystyle{ \mathrm{RMS}[\epsilon_n] = \sqrt{\frac{1}{N_\omega}\sum_{i=1}^{N_\omega}\left(\Im[\epsilon_n(\omega_i)]-\Im[\epsilon_{n-1}(\omega_i)]\right)^2} }[/math]
is below a certain value defined by BSEPREC.
BSEPREC [math]\displaystyle{ \mathrm{RMS}[\epsilon_n] }[/math] Accurate (a) [math]\displaystyle{ 10^{-5} }[/math] High (h) [math]\displaystyle{ 10^{-4} }[/math] Medium (m) [math]\displaystyle{ 10^{-3} }[/math] Low (l) [math]\displaystyle{ 10^{-2} }[/math]
To prevent the algorithm from being too slow, the number of frequencies during the convergence loop is set to [math]\displaystyle{ N_\omega }[/math] = INT(SQRT(NOMEGA)), where NOMEGA is set in the INCAR.
Related tag and articles
IBSE, NBANDSV, NBANDSO, CSHIFT, OMEGAMAX
Time-dependent density-functional theory calculations