Virtual crystal approximation (VCA)

A. Pseudo-Potential Mixinxg

Suppose we want to calculate an alloy, for example, $InSb_{x}As_{1-x}$.

We can generate a mixed pseudopotential of $Sb$ and $As$ in the following way:

$Sb_x + As_{1-x}$ norm-conserving pseudo-potential (ONCV case), follow the below instruction.

Keep ready the original pseudopotentials of $Sb$ and $As$.

mkdir mixed-pseudo
cd mixed-pseudo
git clone https://github.com/pipidog/ONCVPSP.git
cd ONCVPSP/sg15

[Optional] For the first time, go to the Quantum Espresso parent (installation) directory and execute
```
cd ./bin/
ln -s ../upflib/*.x ./
```

Run virtual_v2.x.

virtual_v2.x

 Input PP file #  1 in UPF format > Sb_ONCV_PBE_fr.upf
 Input PP file #  1 in UPF format > As_ONCV_PBE_fr.upf

(for example,)

 New Pseudo = x Sb_ONCV_PBE_fr.upf + (1-x) As_ONCV_PBE_fr.upf
 mixing parameter x [0<x<1] = 0.25

Rename the newly created mixed pseudopotential.

mv ./NewPseudo.UPF ./Sb25As75_ONCV_PBE_fr.upf

B. Example DFT Calculation

Generate mixed pseudopotential in Section A.

To relax the structure using vc-relax. Create the input file for vc-relax calculation as follow:

cat> OPT_VCRELAX.in <<EOF

&CONTROL 
    calculation  = 'vc-relax'
    restart_mode = 'from_scratch'
    pseudo_dir   = './pseudo_dir/'
    outdir       = './OUT_DIR/'
/
&SYSTEM 
    ibrav        = 2
    A            = 6.479
    ntyp         = 2
    nat          = 2
    ecutwfc      = 60.0
    occupations  = 'smearing'
    smearing     = 'gaussian'
    degauss      = 0.01
/
&ELECTRONS 
    conv_thr     = 1.0d-8
/
&IONS
/
&CELL
/
ATOMIC_SPECIES
    In  114.8180  In_ONCV_PBE_fr.upf
    Xx  100.0000  Sb25As75_ONCV_PBE_fr.upf
ATOMIC_POSITIONS (alat)
    In  0.00  0.00  0.00
    Xx  0.25  0.25  0.25
K_POINTS (automatic) 
    2 2 2   0 0 0

EOF

Run the variable cell relaxation calculation.

mpirun -np 4 pw.x < OPT_VCRELAX.in> OPT_VCRELAX.out

Re-run the vc-relax relaxation a couple of times more using the latest lattice parameters until lattice parameter stops to change below 1 decimal point.

Formula to use for optimized lattice parameter read from grep 'final coordinates' OPT_VCRELAX.out:
```
 alat_value[=celldm(1)] * 0.433080256 / 0.5 (unit is in $Bohr$)
```

Virtual crystal approximation (VCA)

VCA for alloys

Virtual crystal approximation (VCA)

A. Pseudo-Potential Mixinxg

B. Example DFT Calculation

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