[Pw_forum] homo-lumo and conductance

[Alexandre Smogunov]

Dear Sagar
I suppose you use the finite width Al wires as the leads 
as we did in our PRB paper in 2004, then you can use 1 k
point in the XY plane. But I would recommend you to use more realistic
infinite (in the XY plane) surfaces as the leads as we did in our more
recent papers, then you should use more k points as Gabriele suggests. 
21 k poins in the XY plane (perpendiculAar to the transport z axis)
corresponds to the mesh 12 12 1 1 1 1. Then you have 21 k points in the
irreducible 2D BZ = 1/8 of the full 2D BZ.

Regards, Alexander

On Sat, 13 Jun 2009, ambavale sagar wrote:

> Dear Gabriele,
Thank you for your reply. I refered to smogunov paper but I could not understand the sentence used there : "Since the system has the supercell (artificial) 2D periodicity in the xy plane, perpendicular to the transport direction, we averaged the transmission over the corresponding 2D BZ using 21 k points in the irreducible part of the BZ."  Are those 21 k-pts belong to xy plane only? what type of grid that may be? 6 6 2 1 1 1 ?
In my case supercell dimensions in x and y are 25 a.u. i.e. ~12 ang which includes nearly ~9 ang. of vaccum.

As you mentioned the limitation of DFT due to xc-functional, can I use DFT calculation to compare qualitatively the Transmission coefficient of same molecule with different geometries?

would you please mention in detail  how to find positions of HOMO, LUMO in a coupled system?


regards
Sagar Ambavale


________________________________

Message: 1
Date: Fri, 12 Jun 2009 18:14:46 +0200
From: Gabriele Sclauzero <sclauzer at sissa.it>
Subject: Re: [Pw_forum] homo-lumo and conductance
To: PWSCF Forum <pw_forum at pwscf.org>
Message-ID: <4A327EF6.7020206 at sissa.it>
Content-Type: text/plain; charset=ISO-8859-1; format=flowed


ambavale sagar wrote:
> Dear all,
> I am studying ballistic conductance through a molecule attached to Al 
> electrode.

Including Al surfaces on both sides?

> The k-pt grid used for scf calculation of scattering region 
> made of molecule and few layers of electrode, is 2 2 10 1 1 1.

If so, this k-point grid looks a bit lousy to me. Unless you use a very large supercell in 
the transverse directions (xy, since z is the transport direction in pwcond), you should 
take more k-points along that directions. Along z, instead, you need less k-points (10 
seems really too much to me). Along z you must include enough slabs before and after the 
junction with the molecule such that the scf potential at the borders of the cell is close 
enough to the scf potential of bulk Al.

You can have a look at this paper in order to get an idea:
Smogunov et al., Phys. Rev. B 78, 014423 (2008)

> I want to 
> see effect of HOMO-LUMO levels of molecule on transmission. Is it 
> sensible to find HOMO-LUMO levels of molecule using separate calculation 
> of isolated molecule with gamma point? How about bandstructure that I 
> got from 20 k-pt calculation of  scattering region periodic in z-direction?

I'm not sure I got your questions. Of course if you study the ballistic conductance 
through the molecule in the tunneling regime, the result will be very sensitive to the 
position of the HOMO and LUMO levels of the molecule. Depending on how strong is the 
binding between the molecule and the electrodes the position and width of these levels 
will be modified more or less by the hybridization with the metal states.
In order to find the position of the HOMO and LUMO in the coupled system you can look at 
the PDOS on the atoms of the molecule (if not too complex) and compare it with the 
corresponding PDOS of the isolated molecule.
Another solution might be to build Wannier functions of the HOMO and LUMO and project onto 
them, but I never tried this solution.

Anyway, you should be careful when trusting DFT results in this kind of system, since 
common XC functionals can mismatch the HOMO-LUMO gap of several eV and there could also be 
problems in getting a reliable alignment with the Fermi level of the metal. Since in 
weakly coupled junctions the conductance is very sensitive to the exact position of the 
molecular levels involved in the tunneling and to the decaying behavior of their tails, 
this issues can lead to  errors of 1 or several orders of magnitude.


Cheers

GS

> 
> Thank you.
> 
> Sagar Ambavale
> PhD student
> M.S. University of Baroda
> India
> 
>


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