HOMO/LUMO wavefunctions and Fermi Energy

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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.

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

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.

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

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.

Hello Nick,

I had a follow up question regarding this discussion. I am trying to visualise HOMO/LUMO of the BDT molecule.
After generating the .EIG file using 5 k-points, I have 5 sets of points and I am unsure which particular value will serve as the HOMO.
If, using your example, the HOMO is -0.682593296E+01 for the first k-point and -0.7E+01 for the second k-point, and a different value for all the other k-points, does that mean that the molecule has different HOMO values? and how would I determine the exact HOMO value to use for orbital visualisations?

Thank you,
Ebere.

If it is a molecule you don't need k-points, and if you use them anyways you should get the same eigenstates.
If as in your case you get different values for different k-points then you are not simulating a molecule.

Hello Nick,

Thank you for your response.

Thanks,
Ebere.

Thank you, Professor Papior,
And how about finding Homo\lumo in spin polarized calculation?
If it is possible please provide an example.

Finding HOMO/LUMO for a polarized calculation is the same as for an unpolarized calculation.

Excuse me, for my case I have 624 eigenvalues for each spin 1248 in total. In the EIG file, there is a gap between eigenvalues number 112 and 113 and also 736 and 737. So my wavefunction block is as follow
%block wavefunckpoints
0.000 0.000 0.000 112 113 736 737
% endblock wavefunckpoints
But after the calculation has been done for wavefunctions denchar has printed wavefunctions for eigenstate number 112 113 0 0. Could you please help me to find the error?