[CPMD-list] about the Lanczos method

[Ari.P.Seitsonen at iki.fi]

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.

  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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