[Pw_forum] GGA underestimate the lattice constant of BaTiO3

[Axel Kohlmeyer]

On Sat, 19 Jul 2008, ruizhi zhang wrote:

RZ> Dear all

dear ruizhi,

please note that when trying to optimize a lattice constant from a
variable cell calculation, you have to make sure that your stress tensor
is fully converged with respect to both the wavefunction and the density 
cutoff and shows no signs of pulay stress, i.e. changes in the stress 
tensor due to the fact that you are not running at constant cutoff, but
with a constant number of plane waves, so that with a change of volume
your effective cutoff changes (this effect can be reduced using the 
constant cutoff scheme, see input_pp description and the respective 
papers). in most cases, it is highly advantageous to do a series of 
single point calculations and then fit the resulting energy vs. volume
graph to an equation of state.

as it has been discussed here many times, for ultra-soft 
pseudopotentials, you usually have to use a much higher density
cutoff than the default of 4x the wavefunction cutoff. check out
the mailing list archives. a factor of 10 seems to be more common.
one recommended strategy was to first keep the 1:4 ratio and increase
the wavefunction cutoff until sufficient convergence is achieved and
then keep the resulting density cutoff value fixed and reduce the 
wavefunction cutoff until the error on the stress tensor becomes
larger again. for variable cell, you'll still have to use an increased
cutoff. how much increased depends on whether you use the constant 
cutoff scheme (correctly) or not.

hope that helps,
    axel.

RZ> I calculated the lattice constant of BaTiO3 using GGA. However, the calculated lattice constant ( 3.980 angstrom) is SMALLER than experimental results (4.012 angstrom). So is this result reasonable?
RZ>  
RZ> The GGA results of SrTiO3 is ok, 3.928 angstrom vs expermental result  3.905. As SrTiO3 and BaTiO3 both contain Ti and O, I calculated lattice constant of bulk metal Ba as a test, and the GGA results (5.014 angstrom for bcc cell) is also smaller than experimental one (5.019).
RZ>  

RZ> So is there something wrong with my calculation? Or GGA does 
RZ> underestimate the lattice constant of some metals, such as reported 
RZ> in Computer Coupling of Phase Diagrams and Thermochemistry 
RZ> 28(2004)79-90 ?



RZ>  
RZ> The input file is attached below. Thank you very much for your help 
RZ> Ruizhi 
RZ> 
RZ> ===========input file of BaTiO3===============
RZ> &control
RZ>     calculation  = 'vc-relax'
RZ>     restart_mode = 'from_scratch'
RZ>     prefix = 'bto'
RZ>     pseudo_dir   = '~/pseudo/'
RZ>     outdir       = './tmp/'
RZ>  /
RZ>  &system
RZ>     ibrav=1
RZ>     celldm(1)=7.584
RZ>     nat=5
RZ>     ntyp=3
RZ>     ecutwfc=30.0
RZ>     occupations = 'smearing'
RZ>     degauss=0.01
RZ>  /
RZ>  &electrons
RZ>     conv_thr = 1e-8
RZ>     mixing_beta=0.3
RZ>  /
RZ> &IONS
RZ>   ion_dynamics = 'damp',
RZ>  /
RZ>  &CELL
RZ>   cell_dynamics ='damp-pr'
RZ>  
RZ>  /
RZ> ATOMIC_SPECIES
RZ>   Ba    137.33  Ba.pbe-nsp-van.UPF 
RZ>   Ti    47.90   Ti.pbe-sp-van_ak.UPF
RZ>   O     15.99   O.pbe-van_ak.UPF
RZ> ATOMIC_POSITIONS (crystal)
RZ>   Ba    0.000    0.000    0.000
RZ>   Ti    0.500    0.500    0.500
RZ>   O     0.000    0.500    0.500
RZ>   O     0.500    0.500    0.000
RZ>   O     0.500    0.000    0.500
RZ> K_POINTS {automatic}
RZ>   8 8 8 1 1 1
RZ> =============end input file=============
RZ> 
RZ> ========================
RZ> Ruizhi Zhang, PhD
RZ> School of Physics,Shandong University
RZ> Jinan, Peopel's Republic of China




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Axel Kohlmeyer   akohlmey at cmm.chem.upenn.edu   http://www.cmm.upenn.edu
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