[CPMD-list] about the Lanczos method

[Francesco Filippone]

On Tue, 27 Aug 2002 Ari.P.Seitsonen at iki.fi wrote:

Dear all,

> 
> Dear Imre,
> 
> > I tried to optimize the cell parameter of Palladium using differenet
> > functional.
> > I used the following input
> > &CPMD
> > WAVEFUNCTION OPTIMIZATION
> > SPLINE POINTS
> >   5000
> > nothing or the following two line
> > LANCZOS DIAGONALISATION
> > ANDERSON MIXING
> >  0.2
> > &END
> > &DFT
> > FUNCTIONAL PBE
> > &END
> >  &SYSTEM
> >    SYMMETRY
> >     2
> >    CELL
> >     7.062  1.0    1.0   0.0 0.0 0.0
> >    CUTOFF
> >    36.
> > TESR
> >   4 4 4
> > SCALED
> > POINT GROUP
> >   AUTO
> > &END
> > &ATOMS
> > *46-PdPBE.pp KLEINMAN-BYLANDER
> >   LMAX=D  LOC=S
> >    1
> >            .00000      .00000      .00000
> >  &END
> 
> 
> First of all, the cutoff is most likely too low (you are using pseudos
> a'la Troullier-Martins, I presume?), so that the basis set is not
> nearly complete and the energy changes discontinuously with the
> lattice constant. You ought to increase the cutoff (and/or test the
> convergence) and maybe include the Francis/Payne (or what was the
> other name for this?) correction for the incomplete basis. Sorry, I
> don't have the reference at hand, now quite some years old article(s)
> in Journal of Physics: Condensed Matter.

The correct reference is; J. Phys.: Condens. Matter 2, 4395-4404 (1990)
A subsequent work on the same argument with a critical discussion of the 
F-P approach is;
G. -M. Rignanese et al., PRB 52, 8160-8178 (1995)

In my personal experience the approach of Rignanese (Gonze) works better.

ciao,
f.



> 
>   However the bigger problem is that you are dealing with a metal, you
> HAVE to allow different occupations at different k points!! So in CPMD
> you probably would like to use the keyword 'FREE ENERGY FUNCTIONAL'
> and use an appropriate "temperature" for the occupation numbers (you
> could start trying with 0.1 eV, but please test this value!), and you
> also have to take into account the extrapolation to zero temperature
> (Gillan: also an old article in Journal of Physics: Condensed Matter,
> volume 1 or 2).
> 
> > I got the following results.
> > First case.  ELECTRONIC GRADIENT:
> >     MAX. COMPONENT =    0.42507E-05         NORM =    0.25111E-06
> >  NUCLEAR GRADIENT:
> >     MAX. COMPONENT =    0.00000E+00         NORM =    0.00000E+00
> > 
> > 
> >  TOTAL INTEGRATED ELECTRONIC DENSITY
> >     IN G-SPACE =                                        10.000000
> >     IN R-SPACE =                                        10.000000
> > 
> >  (K+E+L+N+X)         TOTAL ENERGY =             -28.47799365 A.U.
> >  (K)               KINETIC ENERGY =              27.90230418 A.U.
> >  (E=A-S+R)   ELECTROSTATIC ENERGY =             -32.79364868 A.U.
> >  (S)         ESELF                =              33.24518871 A.U.
> >  (R)         ESR                  =               0.00165652 A.U.
> >  (L) LOCAL PSEUDOPOTENTIAL ENERGY =              14.97342034 A.U.
> >  (N)   N-L PSEUDOPOTENTIAL ENERGY =             -33.27787919 A.U.
> >  (X)  EXCHANGE-CORRELATION ENERGY =              -5.28219030 A.U.
> >        GRADIENT CORRECTION ENERGY =              -0.10149011 A.U.
> > 
> > 
> > 
> > Second case (Using lanczos method)
> >  ELECTRONIC GRADIENT:
> >     MAX. COMPONENT =    0.88452E-03         NORM =    0.86514E-03
> >  NUCLEAR GRADIENT:
> >     MAX. COMPONENT =    0.00000E+00         NORM =    0.00000E+00
> > 
> > 
> >  TOTAL INTEGRATED ELECTRONIC DENSITY
> >     IN G-SPACE =                                        10.000000
> >     IN R-SPACE =                                        10.000000
> > 
> >  (B+E+X-V)           TOTAL ENERGY =             -29.05367185 A.U.
> >  (B)                  BAND ENERGY =              -4.56088319 A.U.
> >  (E=I-H-S+R) ELECTROSTATIC ENERGY =             -25.98640781 A.U.
> >  (S)         ESELF                =              33.24518871 A.U.
> >  (R)         ESR                  =               0.00380195 A.U.
> >  (X)  EXCHANGE-CORRELATION ENERGY =              -4.95568472 A.U.
> >  (V)  EXCHANGE-CORRELATION POTEN. =              -6.44930386 A.U.
> >        GRADIENT CORRECTION ENERGY =              -0.06196058 A.U.
> > 
> > This two results somehow very strange. Can you explain me why I see so
> > large difference between the two results.
> 
> It might be that the different algorithms have converged to different
> minima (please see above on the occupation numbers). Or are you sure
> that the lattice constant is the same (the contribution 'ESR' is not
> the same, that's why I wonder).
> 
>     Greetings,
> 
>        apsi
> 
> 

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