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For pedagogical reasons, I am looking for ways to calculate quantum-mechanical quantities such as $\langle m | \dot{m}\rangle, \langle m | \dot{n}\rangle, \langle m | \ddot{n}\rangle$ using wavefunctions $m,n$ output from DFT calculations (Quantum Espresso, specifically). The overhead dots denote derivatives. Ideally, I would be able to calculate the Berry phase for custom loops as well.

So far, I have tried using some Python tools (z2Pack, PythTB) to try and post-process wannier90 output, but as a beginner, it doesn't seem as if these tools allow us to calculate our own matrix elements. They seem to be just for intra-level quantities such as $\langle m | \dot{m}\rangle$.

Does anyone more-experienced have any advice on what existing software might be easiest to work with to calculate these custom-defined quantities? I would rather try messing with some software that is more likely to support these kinds of calculations. PythTB seems to be one of the best options I have, but Python may not be the best for large datasets (compared to Fortran, etc). Thank you for your time.

Edit: The issue also seems to be that several post-processing software tend to use the numerical method where one takes $\arg$ of some product of complex phases corresponding to each $k$ point. However to do something like $\langle m | \dot{n}\rangle$, it might be better to use a central difference method to carry out the derivative of the wavefunction (as opposed to an established discretized method for the Berry phase, as in section 4.5 in Ref [1]).

[1]: Tight-Binding Formalism in the Context of the PythTB Package, https://www.physics.rutgers.edu/pythtb/_downloads/915304f3240dca549efa8f491463a797/pythtb-formalism.pdf

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  • $\begingroup$ I gave my +1 to this a long time back! But @TribalChief I just wanted to let you know that your question has been mentioned here: mattermodeling.stackexchange.com/q/6422/5 Do you think you're able to help that (new) user with their first question on the entire Stack Exchange network? $\endgroup$ Aug 9 at 16:59
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    $\begingroup$ @NikeDattani, thanks for bringing this to my attention. I was able to make a MATLAB implementation a while back. I am away for a few days but can get to the question sometime Thursday. The user will probably have to process things further from there using Python. $\endgroup$ Aug 9 at 17:15
  • $\begingroup$ Beautiful! I think a MATLAB implementation would be good enough, especially if it works in Octave! I have more experience with MATLAB than Python, so perhaps I could help the user if they need further help after your answer. $\endgroup$ Aug 9 at 17:20
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You can use QE.6xxx with the support of the hdf5 library. To realize that purpose, you should add the following command when you compile QE:

--with-hdf5=yes

or take a look at the official guide.

Then the saved wavefunction can be manipulated with the python package h5py.

import h5py
read_wf=h5py.File("wfc1.hdf5")
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  • $\begingroup$ Thanks for the answer. Would you mind confirming that if I compile QE with that flag, QE will automatically save hdf5 files (with wf_collect = .true. in pw.x)? I ask because I see only wfc1.dat. I tried looking in the documentation for more on this, but all I see is how to enable hdf5. I just want to make sure that's all that is needed to be done. Additionally, do you know of any references/links that demonstrate manipulation of these QE hdf5 files? Perhaps I am looking at the wrong documentation... $\endgroup$ Jan 25 at 2:01
  • $\begingroup$ @TribalChief You should add that tag in your configure file. Take a look section 2.3 in this link: quantum-espresso.org/Doc/user_guide.pdf $\endgroup$
    – Jack
    Jan 25 at 7:14

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