[Pw_forum] Disagreement in vc-relax results between orthogonal and non-orthogonal cell

[Sungkwang Mun]

Hello Quantum Espresso users,

I have a question about the disagreement in vc-relax results between orthogonal and non-orthogonal cell. I am working on carbon structures to get the basic properties such as energy and lattice constant using 'C.pbe-rrkjus.UPF' pseudo potential (QE version 5.3 and 5.2.1). The diamond calculations using orthogonal (ibrav = 1) and non-orthogonal operations (ibrav = 2)  agree each other, but FCC, BCC and HCP do not.

For example, the input script of FCC variable cell relaxation using ibrav = 2 (non-orthogonal structure) are attached below.

*****************************************************************
&control
     pseudo_dir='../'
      calculation='vc-relax'
      tstress=.true.
/
&system
      ibrav=  2, celldm(1) = 6.04709, nat=  1, ntyp= 1,
      ecutwfc = 50,
      ecutrho = 400,
/
&electrons
/
&ions
/
&cell
/
ATOMIC_SPECIES
   C  12.0106  C.pbe-rrkjus.UPF
ATOMIC_POSITIONS crystal
   C 0 0 0
K_POINTS automatic
   7 7 7 1 1 1
*****************************************************************

  The results using the script is listed below. (Energy and lattice constant is converted to eV and Å, receptively.)

******** C (FCC-min) *********
Quantum espresso, C.pbe-rrkjus.UPF
k-point: 7, energy cutoff (Rad): 50

Total energy(eV); -148.951
Energy/atom(eV); -148.951
Pressure(Kbar): 0.75
lattice const(Å): 3.50449

Stress tensor(Kbar)
   0.750 -0.000 0.000
   -0.000 0.750 -0.000
   0.000 -0.000 0.750
********************************

Next input and output using ibrav = 1 (orthogonal structure) are attached below.

*****************************************************************
&control
     pseudo_dir='../'
      calculation='vc-relax'
      tstress=.true.
/
&system
      ibrav=  1, celldm(1) = 6.04709, nat=  4, ntyp= 1,
      ecutwfc = 50,
      ecutrho = 400,
/
&electrons
/
&ions
/
&cell
/
ATOMIC_SPECIES
   C  12.0106  C.pbe-rrkjus.UPF
ATOMIC_POSITIONS crystal
   C 0 0 0
   C 0.5 0.5 0
   C 0 0.5 0.5
   C 0.5 0 0.5
K_POINTS automatic
   7 7 7 1 1 1
*****************************************************************

******** C (FCC) *********
Quantum espresso, C.pbe-rrkjus.UPF
k-point: 7, energy cutoff (Rad): 50

Total energy(eV); -601.511
Energy/atom(eV); -150.378
Pressure(Kbar): -0.74
lattice const(Å): 3.09758

Stress tensor(Kbar)
   -0.740 0.000 0.000
   0.000 -0.740 0.000
   0.000 0.000 -0.740
***************************

As seen, the energy of orthogonal structure is 2 eV lower than the
non-orthogonal structure. Also, the difference of lattice constant is
~0.4 Å.

I checked the initial and final crystal structure using Xcrysden, and
both look fine.

Could you please tell me what I am missing here?

Thank you very much,

Sungkwang Mun
Postdoctoral Associate
Center for Advanced Vehicular Systems
Mississippi State University