# Transiesta calculation at non-zero bias

I have followed the transiesta tutorials regarding calculations with different bias. I am now using a similar input for my calculations.

However, I found these input parameters

TS.biasContour.Eta
TS.biasContour.NumPoints


that are not reported in the manual, but rather in the old version of transiesta. I understand that these two lines are referring to the non-equilibrium contour, and in the latter version of transiesta should be referred as

%block TS.Contours.nEq
part line
from -|V|/2 - 5 kT to |V|/2 + 5 kT
delta    0.026 eV
method mid-rule
%endblock TS.Contour.nEq.neq


In the latter version of siesta, it was recommended to enlarge the number of points when increasing the bias calculated. How does this change in the last version of transiesta?

Moreover, should also

%block TBT.Contour.neq
part line
from   -1.00000 eV to    1.00000 eV
delta    0.001 eV
method mid-rule
%endblock TBT.Contour.neq


be considered in the changing?

In versions <= 4.0 the old flags:

TS.biasContour.Eta
TS.biasContour.NumPoints


were used to determine the imaginary $$\delta$$ of the Green function calculation and the number of points in the bias-window, respectively.
As mentioned having a fixed NumPoints in the input was non-ideal since for different bias one needed to manually change the NumPoints flag to achieve the same accuracy in the integration.

This was changed in versions >= 4.1 to:

%block TS.Contours.nEq
neq
%endblock
%block TS.Contour.nEq.neq
part line
from -|V|/2 - 5 kT to |V|/2 + 5 kT
delta    0.026 eV
method mid-rule
%endblock


Note that the key-point in this block is the delta 0.026 eV which tells TranSiesta to always use a splitting of 26 meV between consecutive energy points. Therefore in 4.1 and later one need not change the input file for different bias points. It will always use the same energy spacing as defined by delta.

Regarding TBtrans. Since no integration is done in the code, the new way (>= 4.1) of doing it simply allows more flexibility, i.e. to generate two different ranges of energy grids:

%block TBT.Contours
first
second
%endblock
%block TBT.Contour.first
part line
from   0. eV to 1. eV
delta    0.001 eV
method mid-rule
%endblock
%block TBT.Contour.second
part line
from -2. eV to -1. eV
delta 0.001 eV
method mid-rule
%endblock


The above could not be done in <= 4.0.

• Thanks Nick for the exhaustive answer! I think now it's clear, I have only two remaining doubts: 1. When applying bias I would expect to only give extra care to the non-equilibrium part. Since the splitting is constant when enhancing the bias in the latter version, would there be any extra parameter to consider? Or one can easily use the same input files for each bias? (changing V of course) 2. If I understood correctly, there shouldn't be problems in using a different delta for TS and TBT. I would expect to use a smaller delta in TBT if, for instance, I have sharp peaks. Is this right? Commented Jan 18, 2023 at 9:49
• 1) no other flags are necessary (generally), convergence may be more difficult, 2) sounds correct. Commented Jan 18, 2023 at 10:08
• Thanks. So, one should enhance the points in the contour (both equilibrium and non-equilibrium) only if there are problems in the convergence, but generally they could be unchanged with the bias, right? Commented Jan 18, 2023 at 10:16
• As always, convergence parameters (as these are) needs to be understood and converged for the system at hand. So one cannot say only in the case of convergence problems. Commented Jan 26, 2023 at 8:51