[Pw_forum] about the quantum tunneling of diffusing atoms

[Axel Kohlmeyer]

On Tue, 2009-03-31 at 08:07 +0200, Stefano Baroni wrote:
> Dear LF Huang,
> 
> 
> no code will ever be a substitute of common sense. What you need is
> simply the potential energy (i.e. "total energy" in the usual DFT
> parlance) of a system, as a function of the coordinates of the
> diffusing atom. As simple (or as complicated) as that!

please let me add my 2 cents to this.

you can go back to a quantum mechanics text book and look up 
for example the discussions of quantum particle vs. wall cases.
the potential doesn't change whether the particle is quantum
or classical!

what you seem to be looking for is some kind of  
"barrier crossing probability". now, wrt to that i'd have several
concerns:

 - how accurate is your "classical" barrier potential to begin with?
   you are doing graphite and hydrogen and use plain DFT. the   
   interaction between a benzene molecule and a hydrogen molecule is
   a frequently used test case for methods that add dispersion 
   interactions corrections to DFT. hmmm...

 - is tunneling relevant at all? at T > 0K the carbon atoms move and
   your barrier will fluctuate, that will affect the crossing 
   probability. similarly, if your hydrogen has enough kinetic energy,
   tunneling is irrelevant.

 - what is the correlation length of your system? only if it is long 
   quantum effects of the atom core matter. since you seem to be
   doing a solid state vacuum system, you should be good on that.

after you've made sure that all of the above is not rendering any 
further studies of the quantum effects pointless, _then_ i would look
into path-integral methods (e.g. the works of mark tuckerman and dominik
marx) that allow studying probability distributions at finite
temperature, albeit mostly in imaginary time. mind you, those
calculations are hugely expensive and you may be best off to first
make some tests with a classical potential. in fact, i would not
be surprised if a suitably chosen classical potential would give 
you a better representation of the potential barrier than DFT.

cheers,
   axel.




> 
> 
> Stefano
> 
> On Mar 31, 2009, at 7:38 AM, lfhuang wrote:
> 
> > Dear Tone Kokalj: 
> > First thank you for your kind attention to my previous poster:
> > "about the logical parameter use_masses in IONS 
> > card" Now I have another question: How to calculate the potential
> > barrier for the quantum tunneling of diffusing 
> > atoms in PWSCF? Any technical method suggested ? If PWSCF can't
> > calculate this kind of things, where should I 
> > get a start to edit the code ? 
> > PS: In an excellent paper: P. G. Sundell etc., PRL 92, 155901, the
> > authors found a "symmetrically weighted" method 
> > to calculate the "coincidence configuration". 
> > 
> > Best Wishes! 
> > 
> > Yours Sincerely 
> > L. F. Huang 
> > ------ 
> > ====================================================================== 
> > L.F.Huang(黄良锋) lfhuang at theory.issp.ac.cn 
> > ====================================================================== 
> > Add: Research Laboratory for Computational Materials Sciences, 
> > Instutue of Solid State Physics,the Chinese Academy of Sciences, 
> > P.O.Box 1129, Hefei 230031, P.R.China 
> > Tel: 86-551-5591464-328(office) 
> > Fax: 86-551-5591434 
> > Web: http://theory.issp.ac.cn> (website of our theory group) 
> > http://www.issp.ac.cn> (website of our institute) 
> > ====================================================================== 
> > 
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> 
> ---
> Stefano Baroni - SISSA  &  DEMOCRITOS National Simulation Center -
> Trieste
> http://stefano.baroni.me [+39] 040 3787 406 (tel) -528 (fax) /
> stefanobaroni (skype)
> 
> 
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-- 
=======================================================================
Axel Kohlmeyer   akohlmey at cmm.chem.upenn.edu   http://www.cmm.upenn.edu
   Center for Molecular Modeling   --   University of Pennsylvania
Department of Chemistry, 231 S.34th Street, Philadelphia, PA 19104-6323
tel: 1-215-898-1582,  fax: 1-215-573-6233,  office-tel: 1-215-898-5425
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If you make something idiot-proof, the universe creates a better idiot.