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Reference: Density Functional Theory: A Practical Introduction, David Sholl, Janice A. Steckel, Chapter 2, Page No. 46

  1. Hf is experimentally observed to be an hcp metal with c/a 1.58. Perform calculations to predict the lattice parameters for Hf and compare them with experimental observations.

[hf.vc-rlx.in]

 &CONTROL
                 calculation = 'vc-relax' ,
                restart_mode = 'from_scratch' ,
                      outdir = '../tmp' ,
                  pseudo_dir = '../pseudo' ,
                      prefix = 'hf' ,
 /
 &SYSTEM
                       ibrav = 4,
                   celldm(1) = 6.5,
                   celldm(3) = 1.58,
                         nat = 1,
                        ntyp = 1,
                     ecutwfc = 36 ,
                     degauss = 0.02 ,
                    smearing = 'methfessel-paxton' ,
 /
 &ELECTRONS
                    conv_thr = 1d-8 ,
                 mixing_mode = 'plain' ,
                 mixing_beta = 0.7 ,
 /
 &IONS
                ion_dynamics = 'bfgs' ,
 /
 &CELL
               cell_dynamics = 'bfgs' ,
                       press = 0 ,
              press_conv_thr = 0.5 ,
 /
ATOMIC_SPECIES
   Hf  178.49000  Hf.pbe-spdfn-rrkjus_psl.1.0.0.UPF 
ATOMIC_POSITIONS alat 
   Hf      0.000000000    0.000000000    0.000000000    
K_POINTS automatic 
  4 4 4   0 0 0

[hf.vc-rlx.out](limited)

 Final enthalpy           =   -1516.8783325778 Ry

     File ../tmp/hf.bfgs deleted, as requested
Begin final coordinates
     new unit-cell volume =     76.72443 a.u.^3 (    11.36939 Ang^3 )
     density =     26.06909 g/cm^3

CELL_PARAMETERS (alat=  6.50000000)
   0.631871376  -0.000000000  -0.000000000
  -0.315935688   0.547216664  -0.000000000
  -0.000000000  -0.000000000   0.807989338

ATOMIC_POSITIONS (alat)
Hf            0.0000000000        0.0000000000        0.0000000000
End final coordinates

[Results]
Lattice paramter of Hafnium is:

$$ a = 2.248600941 \, \mathrm{A}^\circ \tag{Without shape preserving} $$ $$ a = 3.818654808 \, \mathrm{A}^\circ \tag{with shape preserving} $$

But these values are incorrect, the experimental value is $3.19 \mathrm{A}^\circ$. I could not figure out where am I doing wrong.

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  • $\begingroup$ You are not doing something wrong, necessarily. It is well know that some functionals fail to predict the cell parameters and some electronic properties. $\endgroup$
    – Camps ♦
    Sep 28, 2021 at 13:07
  • $\begingroup$ @Camps They were able to predict the lattice parameter of Hafnium accurately, I used similar configuration as them. $\endgroup$
    – 147875
    Sep 28, 2021 at 13:24
  • $\begingroup$ Well, I will start checking all the parameters for the calculations be the same they used. $\endgroup$
    – Camps ♦
    Sep 28, 2021 at 13:33
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    $\begingroup$ why there is one atom in halfnium unit cell? There should be two atom in hcp unit cell @Camps $\endgroup$
    – Pranav kumar
    Sep 30, 2021 at 10:34
  • $\begingroup$ @pranavkumar I think you found the problem! $\endgroup$
    – Camps ♦
    Sep 30, 2021 at 13:02

1 Answer 1

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The source of mistake is assuming one atom in the primitive cell of the hexagonal system. Actually there are two atoms, the atomic positions are

ATOMIC_POSITIONS {alat}
   Hf    0.000000000    0.000000000    0.000000000
   Hf    0.666666667    0.333333333    0.790000000
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