How to improve the convergence?

[zhangguangping]

I have found that for NEG self-consistent cycle, when it is very hard to converge but near the convergence, it is useful and very helpful to restart the task with current density matrix.

My question is : if this happen, what is happening for the convergence cycle? Is there a way to solve it by adusting the parameter?

Thanks!

[Anders Blom]

The main thing that changes when you do this is the mixing. There are several parameters for the mixing algorithm, but tuning them is kind of an art in some cases The main parameter to change is the number of history steps, and the damping factor. The reason you see the behavior you do is that often it would be nice to have these two parameters different in the beginning of the loop (when the density matrix is far from the converged state) and another when it has stabilized a bit.

[zhangguangping]

The main thing that changes when you do this is the mixing. There are several parameters for the mixing algorithm, but tuning them is kind of an art in some cases The main parameter to change is the number of history steps, and the damping factor. The reason you see the behavior you do is that often it would be nice to have these two parameters different in the beginning of the loop (when the density matrix is far from the converged state) and another when it has stabilized a bit.

Dear Anders Blom,

Thanks for your reply.

I agree  with what you have mentioned. But as far as I understand, when I use a smaller mixing parameter, the convergence will be smooth but need more steps. However, the fact is not always the case: when the iteration is very near the convergence but hard to converge, I use a much smaller mixing parameter to restart the task, it will not improve the convergence.

Also, the convergence behaves very well for some bias (especially the low bias) and when the bias increase especially there are transmission peak entering the bias window, the convergence will be very difficult. However, for some system, even if there are transmission peak entering the bias window, there is no convergence problem. What does it imply for the former case? Does the corresponding state of the tranmission peak not couple to the electrodes well at that energy?


Thanks very much.

[Anders Blom]

I agree  with what you have mentioned. But as far as I understand, when I use a smaller mixing parameter, the convergence will be smooth but need more steps. However, the fact is not always the case: when the iteration is very near the convergence but hard to converge, I use a much smaller mixing parameter to restart the task, it will not improve the convergence.

I agree, not least about the observation that there are no 100% rules here. Also note that the history steps can almost have a larger influence than the mixing parameter.

Also, the convergence behaves very well for some bias (especially the low bias) and when the bias increase especially there are transmission peak entering the bias window, the convergence will be very difficult. However, for some system, even if there are transmission peak entering the bias window, there is no convergence problem. What does it imply for the former case? Does the corresponding state of the tranmission peak not couple to the electrodes well at that energy?
very much.

Since you probably climb in bias (using the 0.1 V converged state as starting guess for 0.2, etc), it seems reasonable that if the 0.2 case has a resonance peak and 0.1 doesn't, the converged 0.1-state is not, after all, a very good starting guess for 0.2. There are no shortcuts in this game

[zhangguangping]

Since you probably climb in bias (using the 0.1 V converged state as starting guess for 0.2, etc), it seems reasonable that if the 0.2 case has a resonance peak and 0.1 doesn't, the converged 0.1-state is not, after all, a very good starting guess for 0.2. There are no shortcuts in this game

[/quote]

Thanks very much for your reply. The resonance peak means there is a transmission peak which is entering the bias window?

Allow me to ask another question that is not relevant to this topic. Is there a way (or a definition for this concept) to compute the couplings between a MPSH orbital (or MPSH state) and the left or right electrodes (here the electrodes mean the left/right part of the selected MPSH region)? From this, I want to understand the shift of a MPSH orbital under the bias.

[kstokbro]

There is an indirect way.
you can calculate the DeviceDensityOfStates with either left and right contributions. From the width of the peak, you will get the coupling to the left and the right electrode.

[zhangguangping]

There is an indirect way.
you can calculate the DeviceDensityOfStates with either left and right contributions. From the width of the peak, you will get the coupling to the left and the right electrode.

Dear kstokbro,

Thanks for your reply very much.

You mean I need to calculate the DOS for the DeviceDensityOfStates using the A1(left partial spectra function) to characterize the coupling of one level to the left elelctrode, for the right electrode, using the A2(left partial spectra function)?


Thanks in advance.