[Wien] Wavefunctions and System Hamiltonian

Fri Feb 3 13:17:49 CET 2023

I guess you really have to understand the APW method first.

If you get 120 bands, this is because of the restriction that only 
eigenvalues between eg -12 to +1.5 Ry are calculated.
Depending on your RKMAX I'd estimate that the Hamiltonian is 500x500 to 
1000x1000.
-----------
You can print the eigenvectors using an option in case.in1, see UG
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The subroutine   seclr4.F solves the generalized eigenvalue problem.
You can add a print statement at the beginning to print H (and S).
(Note, that only a triangle of H is actually calculated.
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Good luck with the interpretation of these elements ...

> I do understand that the Hamiltonian is large and that I have to solve 
> it for every k-point.
> 
> If I run a calculation, I end up typically with around 120 bands. Then, 
> if I understand correctly,
> 
> I have to solve a 120x120 Hamiltonian for each k-point? That is feasible.
> 
> 
> My end goal is simply to calculate things like Berry phases, optical 
> conductivities, electron
> 
> densities, and energy bands myself. Also I want to understand the 
> band couplings at arbitrary
> 
> k-points. I could visualize these if I had the H_ij(k).
> 
> You had mentioned that it is possible to print H_ij(k) (or hopefully 
> save H_ij(k) to a file).
> 
> 
> What I had originally intended is to obtain H_ij(k) from the electron 
> density myself, once Wien2k
> 
> has finished a calculation, and thus finished approximating the electron 
> density. To do this, it should
> 
> calculate some sum of basis functions. If I had the amplitudes for this 
> sum, and the Hamiltonian as
> 
> a function of the density, I could set up very custom k-meshes, 
> or recalculate bands on any
> 
> machine without access to Wien2k, or visualize different contributions 
> to the energies like exchange
> 
> splittings or SOC resolved over k-space...or so I would think. I hope 
> I'm not being naive here.
> 
> 
> Trying to implement the latter paragraph is overkill and probably not 
> too useful.
> 
> But if you could instruct me how to save the H_ij(k) to a file, that 
> would be very helpful. Can the
> 
> eigenvectors be saved too? They are saved in the case.vector files (I 
> guess?), but these I cannot read.
> 
> I do understand that these files are massive, but I really would like to 
> use them.
> 
> 
> Kind regards,
> 
> SP.
> 
> 
> 
> 
> 
> 
> ----------------------------------------------------------------------------------------------------------------------------------------------------
> 
> Previous messages are below:
> 
> ----------------------------------------------------------------------------------------------------------------------------------------------------
> 
> 
> 
> Message: 1
> Date: Wed, 1 Jun 2022 12:22:11 +0000
> From: "Polatkan, Sascha" <sascha.polatkan at pi1.uni-stuttgart.de>
> To: "wien at zeus.theochem.tuwien.ac.at"
>          <wien at zeus.theochem.tuwien.ac.at>
> Subject: [Wien] Wavefunctions and System Hamiltonian
> Message-ID: <451a1bb20bd04cfeb04509153b4a1d29 at pi1.uni-stuttgart.de>
> Content-Type: text/plain; charset="iso-8859-1"
> 
> Greetings,
> 
> after I finished a calculation I would like to obtain the final 
> wavefunctions of my system, and if possible, also the Hamiltonian.
> I would like to do this, because I want to display system 
> characteristics with my own code. Or maybe tweak something here and
> there and observe what changes, to understand the system better. I'd 
> like to have both k-space and real space representations.
> 
> If I understand right, I should be able to extract a list of spherical 
> harmonics and interstitial orbitals for each atom, and constants
> for weighting, which the Wien2k calculates for me.
> The Hamiltonian should have a predefined set of elements from which I 
> choose when I initialize the calculation. It should be obtainable
> from the inputs already.
> But I can't quite figure out how to get to the information. I hope you 
> can help me out here.
> 
> Kind regards,
> SP
> 
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> ------------------------------
> 
> Message: 2
> Date: Wed, 1 Jun 2022 20:24:51 +0200
> From: Peter Blaha <pblaha at theochem.tuwien.ac.at>
> To: wien at zeus.theochem.tuwien.ac.at
> Subject: Re: [Wien] Wavefunctions and System Hamiltonian
> Message-ID:
>          <2bc0421b-1672-b6d5-d298-f3e109d45c8a at theochem.tuwien.ac.at>
> Content-Type: text/plain; charset=UTF-8; format=flowed
> 
> Please remember: You get  number_of_k * number_of_bands "wavefunctions
> in a solid". I.e. typically 1000-10000 wavefunctions.
> So you need to know "which wf" you want to investigate in detail.
> 
>    Otherwise, please read my respond a couple of weeks ago about wave
> functions.
> 
>  > after I finished a calculation I would like to obtain the final
>  > wavefunctions of my system, and if possible, also the Hamiltonian.
>  > I would like to do this, because I want to display system
>  > characteristics with my own code. Or maybe?tweak?something here and
>  > there and observe what changes, to understand the system better. I'd
>  > like to have both k-space and real space representations.
>  >
>  > If I understand right, I should be able to extract a list of?spherical
>  > harmonics and interstitial orbitals for each atom, and constants
>  > for weighting, which the Wien2k?calculates for me.
> 
> --------------------------------------
> I'm not sure how to understand this question. The Hamiltonian is kinetic
> energy + eff.Potential.
> 
> Or do you mean the Hamilton matrix elements, H_ij(k). In principle you
> can change the code and print this matrix. But the matrix is huge and
> depends on k !
> 
>  > The Hamiltonian should have a predefined set of elements from which I
>  > choose when I initialize the calculation. It should be obtainable
>  > from the inputs already.
>  > But I can't quite figure out how to get to?the information. I hope you
>  > can help me out here.
>  >
>  > Kind regards,
>  > SP
> 
> 
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