[gpaw-users] Probing the character of molecular orbitals

Tue Apr 26 11:01:37 CEST 2016

Sorry, the correct graph is this:
http://mcaroba.dyndns.org/misc/wannier_good.png

On 2016-04-26 12:00, Miguel Caro via gpaw-users wrote:
> Hi Thomas,
>
> Thanks a lot. Actually, including the projectors didn't make much of a
> difference, perhaps because the Wannier function is centered in
> between the atoms, and the core corrections are less important.
>
> However, I found a couple of issues with my script and resolved them.
> For instance, the LDOS calculator expects the WFs in ASE units
> (Bohr^-3/2), whereas the Wannier calculator dumps Wannier functions in
> units of Angstrom^-3/2. Now I get a very decent projection, with
> summed squared overlaps amounting to 0.77 for this particular example.
> So I think that it's been worth the trouble. This is the new graph
> with no scaling up: mcaroba.dyndns.org/misc/wannier_dos.png
>
> Thanks again for your help.
>
> Miguel
>
> On 2016-04-25 21:26, Thomas Olsen wrote:
>>
>> Hi Miguel
>>
>>  
>>
>> Sounds like a good solution using Wannier functions. I am not an
>> expert on the GPAW/ASE implementation, but the Wannier calculation
>> should result in a set of Unitary matrices U such that your Wannier
>> functions are:
>>
>>  
>>
>> |mR> = \sum_{nk} e^{ikR} U_{mn}|nk>
>>
>>  
>>
>> where |nk> are the Bloch states and |mR> is the Wannier function m in
>> cell R. If you do not have any k-points, then the unitary matrix
>> U_{mn} could be used to transform your set of "occupied projectirs"
>> P_ani to your Wannier function projectors such that the projector you
>> want is P_ami = \sum_n U_mn P_ani for Wannier function |mR>
>>
>>  
>>
>> This all assumes that the Wannier functions you are working with are
>> the "smooth (pseudo)" part. But I think that is true.
>>
>>  
>>
>> /Thomas 
>>
>>  
>>
>> ------------------------------------------------------------------------
>> *Fra:* Miguel Caro [miguel.caro at aalto.fi]
>> *Sendt:* 25. april 2016 20:03
>> *Til:* Thomas Olsen; gpaw-users at listserv.fysik.dtu.dk
>> *Emne:* Re: SV: [gpaw-users] Probing the character of molecular orbitals
>>
>> Hi again,
>>
>> Thanks Thomas for your email. I've kept working on this problem and I
>> think I came up with a much better solution, but I'm having trouble
>> with the implementation.
>>
>> Now, I focus on bonds between C atoms, rather than atoms themselves.
>> I pick any two C atoms in my network and calculate the Wannier
>> functions corresponding to those two atoms when they form an ethane
>> molecule: basically I put three hydrogens at the right positions from
>> each carbon so that they form a modified ethane molecule where the
>> carbons occupy the same positions as in my amorphous carbon network.
>> One of the Wannier functions is localized in between the carbons, and
>> corresponds to a sigma orbital.
>>
>> The approach can be better pictured here for the ethane
>> (mcaroba.dyndns.org/misc/ethane.png) and for the same Wannier
>> function overlayed on the amorphous carbon cell
>> (mcaroba.dyndns.org/misc/a-C.png) [sorry about the crappy rendering -
>> VMD somehow managed to mess it up]. I had to write an interpolation
>> routine for the Wannier function because my carbon network lives in a
>> hexagonal cell, and the Wannier calculator cannot handle that - that
>> explains why the orbitals don't look exactly the same.
>>
>> Now I use the LDOS calculator passing my Wannier function (wf_new)
>> instead of the KS orbitals:
>>
>>     e, dos = calc_aC.get_all_electron_ldos(mol=atoms, spin=0, npts=501,
>>                                            width=0.2, wf_k=wf_new,
>>     P_aui=P_aui)
>>
>> My problem at the moment is that I do not have the correct
>> projectors. To get a first result (quick and dirty) I simply set the
>> projectors to zero. This is a very bad solution and the summed
>> overlaps between the amorphous carbon orbitals and my Wannier
>> function are far from 1. However, qualitatively my DOS looks
>> "promising" (mcaroba.dyndns.org/misc/wannier_dos.png - note that the
>> Wannier DOS had to be scaled up by a lot). The pi orbitals that live
>> in the mobility gap of amorphous carbon (10 - 15 eV in the graph) do
>> not show in the projection onto my Wannier function, which should
>> have no pi character - exactly what I expected.
>>
>> Now my question is about how to obtain/construct the required
>> projectors. Are they readily available from the Wannier calculator?
>>
>> Many thanks,
>> Miguel
>>
>>
>> On 2016-04-21 22:03, Thomas Olsen wrote:
>>>
>>> Hi Miguel
>>>
>>>  
>>>
>>> It sounds like a tricky problem and I think that the
>>> characterization of your system in terms of pi/sigma bonds is not a
>>> completely well-defined problem - at least not quantitatively. It
>>> seems that the approach you are pursuing might give you a
>>> qualitative idea about the nature of the bonds though.
>>>
>>>  
>>>
>>> You want some measure of sigma orbitals that you can project onto
>>> everywhere and I guess the methane molecule can be used for that
>>> purpose. As you suggest, you could obtain a measure of the
>>> total "sigma" PDOS by calculating the PDOS on individual methane
>>> molecules centered on  all C atoms in your system and then add all
>>> the individual PDOS. But bear in mind that all the states you
>>> project onto does not form an orthonormal set so you will never
>>> obtain something that sums up to the total DOS in your system. Also,
>>> the result will be specific to "Methane sigma orbitals" and you
>>> would get something else if using another molecule having sigma
>>> bonds. Nevertheless, comparing the summed PDOS of sigma orbitals and
>>> pi orbitals (for some molcule) might give you a good idea of the
>>> bonding in your system
>>>
>>>  
>>>
>>> /Thomas
>>>
>>>  
>>>
>>>  
>>>
>>> ------------------------------------------------------------------------
>>> *Fra:* gpaw-users-bounces at listserv.fysik.dtu.dk
>>> [gpaw-users-bounces at listserv.fysik.dtu.dk] på vegne af Miguel Caro
>>> via gpaw-users [gpaw-users at listserv.fysik.dtu.dk]
>>> *Sendt:* 21. april 2016 15:11
>>> *Til:* gpaw-users at listserv.fysik.dtu.dk
>>> *Emne:* [gpaw-users] Probing the character of molecular orbitals
>>>
>>> Hi all,
>>>
>>> I am trying to use the scheme to project DOS onto molecular orbitals
>>> in order to probe the sigma/pi character of an amorphous carbon
>>> network. I have gone through the tutorial at
>>>
>>> https://wiki.fysik.dtu.dk/gpaw/documentation/pdos/pdos.html#molecular-orbital-pdos
>>>
>>> but still can't figure out how to do this properly.
>>>
>>> At the moment I'm calculating the Kohn-Sham orbitals for an isolated
>>> methane molecule whose C atom is centered at the same position as
>>> some C atom in my amorphous network, and in a supercell of the same
>>> size. In this way I make sure that the wave functions are
>>> commensurate (i.e. they are given on the same grid). Methane has 4
>>> sigma bonds, so I'm seeking to probe the sigma character of my
>>> amorphous carbon KS states. To achieve that, I calculate the PDOS
>>> from the overlap of the amorphous carbon KS states and the methane
>>> KS states using the method outlined in the online tutorial. The
>>> overlaps are nicely close to 1 in every case. But obviously, the
>>> methane KS orbitals are nowhere near a complete basis for my
>>> amorphous network, where I have of the order of 100s of atoms. So
>>> basically I get a very poor description of the original DOS with
>>> this approach.
>>>
>>> I was thinking about constructing the KS basis set for the
>>> projection from an array consisting of several copies of my methane
>>> orbitals shifted in space so that they are centered at each and all
>>> of the C atoms in the amorphous carbon network. But I'm not sure if
>>> this makes much sense or if it's going to work at all.
>>>
>>> I was wondering if someone has already tried to do something like
>>> this before and how they went about it.
>>>
>>> Many thanks,
>>> Miguel
>>> -- 
>>> *Dr. Miguel Caro*
>>> /Postdoctoral researcher/
>>> Department of Electrical Engineering and Automation,
>>> and COMP Centre of Excellence in Computational Nanoscience
>>> Aalto University, Finland
>>> Personal email: *mcaroba at gmail.com*
>>> Work: *miguel.caro at aalto.fi*
>>> Website: http://mcaroba.dyndns.org
>>
>> -- 
>> *Dr. Miguel Caro*
>> /Postdoctoral researcher/
>> Department of Electrical Engineering and Automation,
>> and COMP Centre of Excellence in Computational Nanoscience
>> Aalto University, Finland
>> Personal email: *mcaroba at gmail.com*
>> Work: *miguel.caro at aalto.fi*
>> Website: http://mcaroba.dyndns.org
>
> -- 
> *Dr. Miguel Caro*
> /Postdoctoral researcher/
> Department of Electrical Engineering and Automation,
> and COMP Centre of Excellence in Computational Nanoscience
> Aalto University, Finland
> Personal email: *mcaroba at gmail.com*
> Work: *miguel.caro at aalto.fi*
> Website: http://mcaroba.dyndns.org
>
>
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> gpaw-users at listserv.fysik.dtu.dk
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-- 
*Dr. Miguel Caro*
/Postdoctoral researcher/
Department of Electrical Engineering and Automation,
and COMP Centre of Excellence in Computational Nanoscience
Aalto University, Finland
Personal email: *mcaroba at gmail.com*
Work: *miguel.caro at aalto.fi*
Website: http://mcaroba.dyndns.org
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