[Pw_forum] about the quantum tunneling of diffusing atoms

[lfhuang]

Dear Prof. Kohlmeyer:
   Thank you very much for your kind attention! And I appreciate your patient instruction very much!
Best Wishes!
Yours Sincerely
L. F. Huang

> From: Axel Kohlmeyer 
> Subject: Re: [Pw_forum] about the quantum tunneling of diffusing atoms
> To: PWSCF Forum 
> Message-ID: 
> Content-Type: text/plain; charset="UTF-8"
> 
> 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.

------
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L.F.Huang(黄良锋) lfhuang at theory.issp.ac.cn
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