[gpaw-users] Probing the character of molecular orbitals

Mon Apr 25 20:26:40 CEST 2016

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<mailto:gpaw-users-bounces at listserv.fysik.dtu.dk> [gpaw-users-bounces at listserv.fysik.dtu.dk<mailto:gpaw-users-bounces at listserv.fysik.dtu.dk>] på vegne af Miguel Caro via gpaw-users [gpaw-users at listserv.fysik.dtu.dk<mailto:gpaw-users at listserv.fysik.dtu.dk>]
Sendt: 21. april 2016 15:11
Til: gpaw-users at listserv.fysik.dtu.dk<mailto: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<mailto:mcaroba at gmail.com>
Work: miguel.caro at aalto.fi<mailto: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<mailto:mcaroba at gmail.com>
Work: miguel.caro at aalto.fi<mailto:miguel.caro at aalto.fi>
Website: http://mcaroba.dyndns.org
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