HOMO/LUMO wavefunctions and Fermi Energy

Asked by Tristan Zaborniak on 2019-02-08

To whom it may concern:

In running Denchar, using the version bundled with the 4.0 version of Siesta, I've produced 3-dimensional .cube files containing wavefunction information for a scattering region sandwiched between two electrodes.

My questions are simply: how do I know which of these wavefunctions correspond to the HOMO and LUMO? and: where can I find the Fermi energy of the scattering region?

Cheers,

Tristan

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Last query:
2019-03-05
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2019-03-06
Launchpad Janitor (janitor) said : #2

This question was expired because it remained in the 'Needs information' state without activity for the last 15 days.

Nick Papior (nickpapior) said : #3

You have figure this out manually.

I.e. compare the EIG file with the wavefunctions requested.

I.e. if the eig file looks something like this:

 -0.450041854E+01
         17 1 1
         1 -0.187478176E+02 -0.173838754E+02 -0.108292318E+02 -0.682593296E+01 -0.275335945E+01 0.264601683E+01 0.105186869E+02 0.111270254E+02 0.120793547E+02 0.139033171E+02

then HOMO would be index 4 and LUMO would be index 5. for the first k-point.

Tristan Zaborniak (tristanz) said : #4

Hi Nick;

Thank-you for your response.

Perhaps I have set up my .fdf files wrong, as it is only in the running of an electrode calculation (with a diagonal solution method) that a .EIG file is produced. (The manual states that the WriteEigenvalues option requires that the solution method be diagonal.)

It is possible to generate .CUBE files for the wavefunctions corresponding to each biased system (if multiple are being tested). These should differ between each bias, but with the .EIG file being specific to the electrode, the indices mapping to the HOMO and LUMO as you describe will be the same, regardless of the bias.

So: despite this, is it the electrode .EIG file that you are referring to? Will the HOMO and LUMO indices be the same across all biases (with just the shapes of them between biases differing)?

I would appreciate your thoughts on this.

Cheers.

Tristan

Nick Papior (nickpapior) said : #5

There is no "eigenstate" for the biased systems (they are connected to leads and thus infinite).

Hence you cannot plot wavefunctions corresponding to a specific state. What you can do is plot the density matrix for a given energy, see the tbtrans manual in 4.1-b4.

Tristan Zaborniak (tristanz) said : #6

Hi again;

Thank-you again for your response.

I just have one more question: I've been running calculations on the same structure at different bias voltages to create an I-V curve for it, one of which is 0.00.

Surely at zero bias the scattering region could have its wavefunctions plotted, no? I understand that the 'system' including the leads is infinite, but feel as if it should be possible to plot the HOMO and LUMO of the scattering region at zero bias. My thought is that at this zero bias, the .EIG file method you mentioned in your initial response would be appropriate.

Please let me know if I am wrong in thinking this.

Thanks.

Tristan

Nick Papior (nickpapior) said : #7

No it doesn't matter. We cannot calculate the eigenstate for an infinite system, even at zero bias the system is infinite.

You can, however, say that the EIG method would(should) correspond roughly to an eigenstate in the infinite system, provided the electrodes are good at screening.

Note that analysis based on subset eigenstates may still be indicative and important analysis tools, search e.g. for MPSH, molecular projected self-consistent Hamiltonian. We used it in https://pubs.acs.org/doi/abs/10.1021/acs.nanolett.7b03066 for analysis on eigenstates. These are particularly useful when the coupling between the "molecule" and electrodes are weak.

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