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<div>Dear Prof. Kohlmeyer:
<BR>
Thank you very much for your kind attention! And I appreciate your patient instruction very much!
<BR>
Best Wishes!
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Yours Sincerely
<BR>
L. F. Huang
<BR>
<BR>
</FONT><FONT color=#444444>> From: Axel Kohlmeyer
<BR>
</FONT><FONT color=#444444>> Subject: Re: [Pw_forum] about the quantum tunneling of diffusing atoms
<BR>
</FONT><FONT color=#444444>> To: PWSCF Forum
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</FONT><FONT color=#444444>> Message-ID:
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</FONT><FONT color=#444444>> Content-Type: text/plain; charset="UTF-8"
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</FONT><FONT color=#444444>>
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</FONT><FONT color=#444444>> On Tue, 2009-03-31 at 08:07 +0200, Stefano Baroni wrote:
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</FONT><FONT color=#444444>> </FONT><FONT color=#444444>> Dear LF Huang,
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</FONT><FONT color=#444444>> </FONT><FONT color=#444444>>
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</FONT><FONT color=#444444>> </FONT><FONT color=#444444>>
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</FONT><FONT color=#444444>> </FONT><FONT color=#444444>> no code will ever be a substitute of common sense. What you need is
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</FONT><FONT color=#444444>> </FONT><FONT color=#444444>> simply the potential energy (i.e. "total energy" in the usual DFT
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</FONT><FONT color=#444444>> </FONT><FONT color=#444444>> parlance) of a system, as a function of the coordinates of the
<BR>
</FONT><FONT color=#444444>> </FONT><FONT color=#444444>> diffusing atom. As simple (or as complicated) as that!
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</FONT><FONT color=#444444>>
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</FONT><FONT color=#444444>> please let me add my 2 cents to this.
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</FONT><FONT color=#444444>>
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</FONT><FONT color=#444444>> you can go back to a quantum mechanics text book and look up
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</FONT><FONT color=#444444>> for example the discussions of quantum particle vs. wall cases.
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</FONT><FONT color=#444444>> the potential doesn't change whether the particle is quantum
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</FONT><FONT color=#444444>> or classical!
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</FONT><FONT color=#444444>>
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</FONT><FONT color=#444444>> what you seem to be looking for is some kind of
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</FONT><FONT color=#444444>> "barrier crossing probability". now, wrt to that i'd have several
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</FONT><FONT color=#444444>> concerns:
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</FONT><FONT color=#444444>>
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</FONT><FONT color=#444444>> - how accurate is your "classical" barrier potential to begin with?
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</FONT><FONT color=#444444>> you are doing graphite and hydrogen and use plain DFT. the
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</FONT><FONT color=#444444>> interaction between a benzene molecule and a hydrogen molecule is
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</FONT><FONT color=#444444>> a frequently used test case for methods that add dispersion
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</FONT><FONT color=#444444>> interactions corrections to DFT. hmmm...
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</FONT><FONT color=#444444>>
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</FONT><FONT color=#444444>> - is tunneling relevant at all? at T </FONT><FONT color=#444444>> 0K the carbon atoms move and
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</FONT><FONT color=#444444>> your barrier will fluctuate, that will affect the crossing
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</FONT><FONT color=#444444>> probability. similarly, if your hydrogen has enough kinetic energy,
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</FONT><FONT color=#444444>> tunneling is irrelevant.
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</FONT><FONT color=#444444>>
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</FONT><FONT color=#444444>> - what is the correlation length of your system? only if it is long
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</FONT><FONT color=#444444>> quantum effects of the atom core matter. since you seem to be
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</FONT><FONT color=#444444>> doing a solid state vacuum system, you should be good on that.
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</FONT><FONT color=#444444>>
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</FONT><FONT color=#444444>> after you've made sure that all of the above is not rendering any
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</FONT><FONT color=#444444>> further studies of the quantum effects pointless, _then_ i would look
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</FONT><FONT color=#444444>> into path-integral methods (e.g. the works of mark tuckerman and dominik
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</FONT><FONT color=#444444>> marx) that allow studying probability distributions at finite
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</FONT><FONT color=#444444>> temperature, albeit mostly in imaginary time. mind you, those
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</FONT><FONT color=#444444>> calculations are hugely expensive and you may be best off to first
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</FONT><FONT color=#444444>> make some tests with a classical potential. in fact, i would not
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</FONT><FONT color=#444444>> be surprised if a suitably chosen classical potential would give
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</FONT><FONT color=#444444>> you a better representation of the potential barrier than DFT.
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</FONT><FONT color=#444444>>
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</FONT><FONT color=#444444>> cheers,
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</FONT><FONT color=#444444>> axel.
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<BR>
------
<BR>
======================================================================
<BR>
L.F.Huang(黄良锋) <A href=mailto:lfhuang@theory.issp.ac.cn>lfhuang@theory.issp.ac.cn</A>
<BR>
======================================================================
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Add: Research Laboratory for Computational Materials Sciences,
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Instutue of Solid State Physics,the Chinese Academy of Sciences,
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P.O.Box 1129, Hefei 230031, P.R.China
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Tel: 86-551-5591464-328(office)
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Web: <A href=http://theory.issp.ac.cn target=_blank>http://theory.issp.ac.cn</A</FONT><FONT color=#444444>> (website of our theory group)
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