[Pw_forum] homo-lumo and conductance

Gabriele Sclauzero sclauzer at sissa.it
Mon Jun 15 09:04:03 CEST 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.

Here Alexander already replied you. So your k_perpendicular points sampling depends if you 
want to study an isolated wire (thick or monoatomic), or a wire/molecule between realistic 
electrodes (modeled as surfaces or surfaces+tips attached to them). In the former case, if 
your supercell is large enough in the directions perpendicular to the transport the 
transmission should not depend on k_perp and you need only one k_perp-point. In the latter 
you need to sample accurately the 2D BZ, since the transmission depends (a lot in some 
cases) on k_perp.

> 
> 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?

I cannot say, actually. It depends on the coupling and other details. You can have a look 
to the recent work by Thygesen and Rubio, which try to include a GW correction in this 
kind of calculations.

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

What I would do (but fur sure there are many better methods) if I want to put, say, O_2 
between electrodes is to look at the PDOS (computed by projwfc.x in the QE suite) 
projected onto the O atoms and compare it with the PDOS of the isolated O_2. It would give 
an idea of the level of hybridization between molecule and electrodes and of the position 
of the HOMO(LUMO)-derived levels.
It could also be useful to look at the PDOS on the electrode atoms to understand which 
metallic states/atoms are more involved in the coupling.

regards,

GS


> 
> regards
> Sagar Ambavale
> ------------------------------------------------------------------------
> **
> Message: 1
> Date: Fri, 12 Jun 2009 18:14:46 +0200
> From: Gabriele Sclauzero <sclauzer at sissa.it <mailto:sclauzer at sissa.it>>
> Subject: Re: [Pw_forum] homo-lumo and conductance
> To: PWSCF Forum <pw_forum at pwscf.org <mailto:pw_forum at pwscf.org>>
> Message-ID: <4A327EF6.7020206 at sissa.it <mailto: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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> | Gabriele Sclauzero, PhD Student                  |
> | c/o:  SISSA & CNR-INFM Democritos,              |
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o ------------------------------------------------ o
| Gabriele Sclauzero, PhD Student                  |
| c/o:   SISSA & CNR-INFM Democritos,              |
|        via Beirut 2-4, 34014 Trieste (Italy)     |
| email: sclauzer at sissa.it                         |
| phone: +39 040 3787 511                          |
| skype: gurlonotturno                             |
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