[gpaw-users] Probing the character of molecular orbitals

Tue Apr 26 11:00:21 CEST 2016

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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