### Author Topic: total energy of Green's function calculation  (Read 42 times)

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#### ypwang

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##### total energy of Green's function calculation
« on: January 25, 2023, 16:45 »
I understand that the Green's function method does not have a "total energy" equivalent to periodic calculations due to the charge transfer between leads and device. However, if I simulate a crystal using Green's function method, that is, setting the lead and the device to be the same material, there shall be no charge transfer at all; therefore the total energy from Green's function calculations shall be the same with periodic calculations. I use hexagonal BN as an example, however the results show a difference of 15.5 eV. I cannot understand why. Please give suggestions. Thank you very much!
Yun-Peng

#### Anders Blom

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##### Re: total energy of Green's function calculation
« Reply #1 on: January 25, 2023, 22:37 »
Is that 15 eV per atom or in total? Same number of atoms? Also the algorithm is quite different, so since energies are not absolute, comparing two different calculations like this does not really make sense. And anyway, why do you want to compare them?

#### ypwang

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##### Re: total energy of Green's function calculation
« Reply #2 on: January 26, 2023, 04:28 »
The difference of 15 eV is of the total energy, not per atom. The number of atoms are the same for periodic and Green's function calculations. The reason I want to do this comparison is curiosity. I am learning the Green's function method, and I am wondering on what extent does the Green's function method is equivalent to periodic calculations.
In principle, these two calculations shall be equivalent, so the difference in total energy must result from the interface between leads and the scattering region. So, could you please provide more details on how QuantumATK dealing with the lead/scattering region interface?

Best,
Yun-Peng

#### Anders Blom

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##### Re: total energy of Green's function calculation
« Reply #3 on: January 26, 2023, 20:54 »
No, the two calculations are not really the same numerically. Physically yes, kind of, but the algorithms are very different. Just to start with, there is no diagonalization of the Hamiltonian in the NEGF method, and also there are contributions to the Hamiltonian (and thus energy) from the electrodes, so one cannot even say the number of atoms is strictly the same. I honestly don't think you will find much benefit from this analysis unless you plan to write your own NEGF code...

The details of the NEGF method we use are well documented and links can be found in the manual, at the top of https://docs.quantumatk.com/manual/NEGFDevice.html, plus https://doi.org/10.1088/1361-648X/ab4007.
« Last Edit: January 26, 2023, 20:58 by Anders Blom »