Coupling strength between electrodes and the sandwiched molecule

[zhangguangping]

Dear ATK staff and ATK users,

I want to quantitatively to describe the coupling strength between electrodes and the sandwiched molecule in a molecular junction. I have searched the forum and found this topic in 2016
https://quantumwise.com/forum/index.php?topic=4190.msg19127#msg19127

However, this topic did not give a explicit solution to this question.

I also tried to used "calculateSelfEnergy" function to get the self-energy from one electrode and then to get the energy level broadening. But I found, the self-energy and an specific energy is a matrix, which can not be used directly. Indeed, I want to use a scalar number.

Another way, as far as I know, is to used PDOS to get the broadening a specific energy, which is a scalar number.

I wonder, in ATK, is there a more convenient and reliable method to describe the coupling strength between electrodes and molecule in a molecular junction ?

With best regards,

/Guang-Ping Zhang

 

[Petr Khomyakov]

I wonder, in ATK, is there a more convenient and reliable method to describe the coupling strength between electrodes and molecule in a molecular junction ?

In QuantumATK, the coupling between the electrode and the scattering region (e.g., a molecule) is rigorously treated using the NEGF procedure for taking care of open boundary conditions. The coupling strength is reliably described by this procedure. Describing the coupling with a scalar is way less reliable compared to what is implemented in QuantumATK, since the coupling is supposed to be described with a matrix that actually depends on the energy and momentum of incoming electrons. And this is how QuantumATK treats the coupling between the electrode and the molecule.     

[zhangguangping]

I wonder, in ATK, is there a more convenient and reliable method to describe the coupling strength between electrodes and molecule in a molecular junction ?

In QuantumATK, the coupling between the electrode and the scattering region (e.g., a molecule) is rigorously treated using the NEGF procedure for taking care of open boundary conditions. The coupling strength is reliably described by this procedure. Describing the coupling with a scalar is way less reliable compared to what is implemented in QuantumATK, since the coupling is supposed to be described with a matrix that actually depends on the energy and momentum of incoming electrons. And this is how QuantumATK treats the coupling between the electrode and the molecule.   

Thanks.

[zhangguangping]

Let me introduce the question more detailly.

As figured out by our previous study (https://aip.scitation.org/doi/10.1063/1.4820237), the molecular levels (specifically LUMO) move away from the Fermi energy as the two electrodes separated (molecule-electrode coupling decreases).

This phenomenon has also been observed by other researchers (https://journals.aps.org/prb/pdf/10.1103/PhysRevB.68.115407 and https://www.nature.com/articles/nnano.2011.212).

However, this energy shift of molecular level respected to the Fermi level is not thorough understood.

The possible reasons are:

1) Coupling strength between the molecule and electrodes, which is also used in the references to explain this phenomenon.
2) Charge transfer between the electrodes and molecule.
3) ... Some other reasons

But, there is no substantial evident to confirm which above or other reason is the underlying driving force for the molecule level shift.

Now, I want to give a clear answer by using ATK package.

But, I encountered difficulty.

1) How to quantitatively describe the coupling between molecule and electrodes in a single-molecule junction in ATK?
One possible way, using the Gamma function (obtained from the broaden of PDOS).
For this way, I have tried to get the Gamma function for each molecular orbitals with the interelectrode distance. The results show that Gamma does not necessarily have relationship with the energy level shift. To be more specific, for example there are three molecular orbitals (LUMO, LUMO+1, LUMO+2) rigidly move away from the Fermi energy when the electrode distance is stretched. Gamma for LUMO decreases with electrode distance, but Gamma for LUMO+1 increases with electrode distance. This suggests that Gamma is not a good quantity to describe the molecular level shift.

On the other hand, according to the Green's function formula, the molecule energy shift is directly come from the real part of the self-energy. So, is it possible that the real part of the self-energy matrix is closely related to the electrode distance? If so, what is the physics?

2) How to get the charge for the molecule in a molecular junction with different electrode distance? I find one can not used the "Bader Charge Analysis" tool in ATK 2015.1

....

So, what can I do further, any suggestions?

With best regards,

/Guang-Ping Zhang

[Petr Khomyakov]

It is hard to give any short answers to your questions. There is a vast literature on this topic. So, I would suggest you searching and reading books and papers to learn about it.

2015.1 version is too old, so it is missing many features we have now in the code. You may still try using electron density and electron difference density to quantify the charge redistribution upon sandwiching the molecule between the two electrodes, e.g., see how that is done for covered surfaces, Eq. (2) and (3) in Phys. Rev. B 79, 195425 (2009). For your information, there is no support for 2015 version any longer. 

[zhangguangping]

It is hard to give any short answers to your questions. There is a vast literature on this topic. So, I would suggest you searching and reading books and papers to learn about it.

2015.1 version is too old, so it is missing many features we have now in the code. You may still try using electron density and electron difference density to quantify the charge redistribution upon sandwiching the molecule between the two electrodes, e.g., see how that is done for covered surfaces, Eq. (2) and (3) in Phys. Rev. B 79, 195425 (2009). For your information, there is no support for 2015 version any longer.

Dear Petr Khomyakov,

Thanks for your kind reply.

Is there any method that can directly give some evident for coupling strength between molecule and electrode in molecular junction by the recent version of ATK? We have updated our ATK-2015.1 to  ATK-2018.6 a few months ago.

With best regards.

/Guang-Ping Zhang

[Petr Khomyakov]

Width of transmission resonances related to the HOMO and LUMO energy levels of the molecule is a measure of the coupling. In the limit of fully-decoupled molecule, the  width goes to zero, as well as the coupling. This must be seen in the Transmission Spectrum, which can be computed in both 2015 and 2018 versions. If you use some simple  tight-binding model, you may then try fitting parameters of that model to ab initio data obtained from QuantumATK Transmission spectrum. As an example of how ab initio derived conductance calculations can be interpreted using a tight-binding model, see Phys. Rev. B 74, 165416 (2006).  It shows how the charge transfer and the coupling may affect the electron transport through molecule-like junctions. I also note that there must be a plenty of this kind of empirical studies on molecular junctions in the literature.

[zhangguangping]

Width of transmission resonances related to the HOMO and LUMO energy levels of the molecule is a measure of the coupling. In the limit of fully-decoupled molecule, the  width goes to zero, as well as the coupling. This must be seen in the Transmission Spectrum, which can be computed in both 2015 and 2018 versions. If you use some simple  tight-binding model, you may then try fitting parameters of that model to ab initio data obtained from QuantumATK Transmission spectrum. As an example of how ab initio derived conductance calculations can be interpreted using a tight-binding model, see Phys. Rev. B 74, 165416 (2006).  It shows how the charge transfer and the coupling may affect the electron transport through molecule-like junctions. I also note that there must be a plenty of this kind of empirical studies on molecular junctions in the literature.

Dear Petr Khomyakov,

Thanks for your kind reply. I will look into those references.

With best regards,

/Guang-Ping Zhang

[Petr Khomyakov]

Yes, and please do literature search because "molecular electronics" is a pretty old field of research by now, there must be enormous literature on that.