[Pw_forum] second energy parameter setting in RRKJ USPP

Tue Aug 12 08:33:55 CEST 2008

I am too old too remember, and too lazy to search in the library ... ;-)
Actually, the matter is probably treated in "old" math phys books,  
such as Courant & Hilbert or Morse & Feshbach. The chapter where this  
is dealt with is on Sturm Liouville theory (http://en.wikipedia.org/wiki/Sturm-Liouville_theory 
). You do not need to dig very much in math. All I know I learnt why I  
wrote a solver for the 1D Schroedinger equation, which is the ancestor  
of the solvers presently included in the QE distribution ...  
("practice is the Mother of learning")
Cheers - SB

On Aug 11, 2008, at 10:43 PM, Prasenjit Ghosh wrote:

> Dear Stefano,
>
> Thanks for the nice explanation.
> Can you please suggest some "old" quantum mechanics books or some  
> other reading materials where they deal with such issues?
>
> With regards,
> Prasenjit.
>
> 2008/8/11 Stefano Baroni <baroni at sissa.it>
> Dear Wenmei:
>
> besides the very sound suggestion by Hande, I would also recommend
> that you take a glance at any (possibly, old) textbook in elementary
> quantum mechanics. Why old? Because modern texts often given
> elementary stuff for granted, which usually it is not.
>
> Coming to the specific issue that you raise. The number of nodes in
> the solution of a 1D Schroedinger equation depends on the energy
> parameter. The lower the energy, the fewer the nodes.  Of course, for
> an arbitrary energy parameter the resulting wavefunction is not
> normalizable, that is why it has to be discarded, but for very
> special, discrete, values, and energy is quantized. It is interesting
> to understand "intuitively" how quantization of energy comes about. As
> you rise the energy from any given value, the outer node moves out
> furthhr and futher from the origin, but the number of nodes stays
> constant if you do not change the energy too much. If the energy is
> raised too much, a further node will appear. For some critical value
> of the energy, the "extra" node will be at infinity: that's when an
> energy eigenvalue is crossed.
>
> I do not expect that, if you have never heard about similar
> arguments,  you will understand mine, which have been stated rather
> sloppily. Actually, if you decide to study this matter in a serious
> book, your ability to understand my "sloppy arguments" will be a check
> of your actual understanding of the serious arguments expounded in the
> book.
>
> Hope this helps, a bit
> Stefano
>
> On Aug 11, 2008, at 6:36 PM, Hande Ustunel wrote:
>
> > Dear Wenmei,
> >
> > I usually look at the output of the all-electron calculation and
> > choose an
> > energy close to the ae orbital energy. Once I manage to generate the
> > pseudopotential I go as far away as possible from that reference
> > without
> > upsetting the code.
> >
> > Hope this helps...
> > Hande
> >
> > On Tue, 12 Aug 2008, [gb2312] 明文美 wrote:
> >
> >>
> >> Dear all:
> >>
> >>      I want to generate my own RRKJ type ultrasoft pseudopotential
> >> with atomic code in PWSCF,
> >> I encountered a very confusing situation:
> >>
> >>  when I chose -0.20Ry as the second energy used to pseudize the 5s
> >> orbit, the ld1.x always complains :
> >> =================================================
> >>    from gener_pseudo : error #         1     too many nodes
> >> =================================================
> >>   however if I change the energy to be -0.50Ry, the corresponding
> >> complain disappeared.
> >>
> >> How should I choose these energy parameters to generate a good
> >> pseudopotential and how should I have a
> >> correct understanding of these parameters?
> >>
> >> Thanks very much .
> >>
> >> Wenmei
> >>
> >> My &inputp file is also listed as :
> >>
> >> 64D  3  2   10   0.00  1.00   2.004D  3  2   0    -0.20 1.00
> >> 2.005S  1  0   2    0.00  2.00   2.505S  1  0   0    -0.50  2.00
> >> 2.505P  2  1   3    0.00  2.66   2.985P  2  1   0    -0.20  2.66
> >> 2.98
> >>
> >>
> >>
> >>
> >>
> >> _________________________________________________________________
> >> 快来看看这些猫咪有多逗，爆笑！
> >> http://cnweb.search.live.com/video/results.aspx?q=%E5%8F%AF%E7%88%B1%E7%8C%AB%E5%92%AA&Form=MEVHAA
> >
> > --
> > Hande Toffoli
> > Department of Physics
> > Office 439
> > Middle East Technical University
> > Ankara 06531, Turkey
> > Tel : +90 312 210 3264
> > http://www.physics.metu.edu.tr/~hande
> >
> > _______________________________________________
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> > Pw_forum at pwscf.org
> > http://www.democritos.it/mailman/listinfo/pw_forum
>
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>
> -- 
> PRASENJIT GHOSH,
> POST-DOC,
> ROOM NO: 265, MAIN BUILDING,
> CM SECTION, ICTP,
> STRADA COSTERIA 11,
> TRIESTE, 34104,
> ITALY
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---
Stefano Baroni - SISSA  &  DEMOCRITOS National Simulation Center -  
Trieste
http://www.sissa.it/~baroni / [+39] 040 3787 406 (tel) -528 (fax) /  
stefanobaroni (skype)

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