[QE-users] Relaxation of MoN/MoP2 heterostructure stops before force convergence despite SCF convergence

[BINOY CHANDRA DEY]

Dear Quantum ESPRESSO Community,

I am currently performing a geometry optimization of a MoN/MoP₂
heterostructure and would appreciate your guidance regarding the
convergence behavior I am observing.

*System construction:*
The heterostructure was built by cutting bulk MoN and MoP₂ into slabs using
experimentally suggested Miller indices. The two slabs were stacked
vertically along the z direction, with ~20 Å of vacuum added to avoid
spurious interactions. The initial interlayer distance between the slabs
was set to ~5 Å. All atoms were allowed to relax.

*Calculation details:*

   -

   calculation = 'relax'
   -

   Ionic dynamics: BFGS
   -

   Dispersion correction: DFT-D3
   -

   Fixed cell (no vc-relax)
   -

   nstep = 50

*Problem description:*
Although the SCF convergence is achieved smoothly at every ionic step
(estimated SCF accuracy ~10⁻⁸ Ry), the geometry optimization does not
converge within the specified number of BFGS steps. The run stops after
reaching nstep = 50, without printing final relaxed coordinates.

At the last few ionic steps, the total energy continues to decrease
monotonically; however, the total force remains relatively large (~0.063
Ry/Bohr), indicating that the structure is still far from force convergence.

Below I include excerpts from the last iterations for reference.
------------------------------

*Penultimate BFGS step:*

total energy              =  -3822.65535130 Ry
estimated scf accuracy    <      0.00000009 Ry

convergence has been achieved in 32 iterations
number of scf cycles      = 49
number of bfgs steps      = 48

energy old = -3822.65309557 Ry
energy new = -3822.65535130 Ry

CASE: energy_new < energy_old

new trust radius          = 0.5692417702 bohr
new conv_thr              = 0.0000001320 Ry

Total force = 0.063444

*Final BFGS step (terminated due to nstep limit):*

total energy              =  -3822.65857840 Ry
estimated scf accuracy    <      0.00000010 Ry

convergence has been achieved in 40 iterations
number of scf cycles      = 50
number of bfgs steps      = 49

energy old = -3822.65535130 Ry
energy new = -3822.65857840 Ry

CASE: energy_new < energy_old

new trust radius          = 0.4868398914 bohr
new conv_thr              = 0.0000002314 Ry

Total force = 0.063444

The stress tensor is also printed, but since the calculation is a slab
geometry with large vacuum and a fixed cell, I have not interpreted the
stress as a convergence criterion.

*My questions are:*

   1.

   Is it physically reasonable to use the final BFGS geometry as the
   relaxed structure, even though the force convergence threshold has not been
   met?
   2.

   Would simply increasing nstep and restarting the relaxation from the
   last configuration be sufficient, or is it strongly recommended to use
   selective dynamics (e.g., freezing bottom layers of the slabs) for such
   heterostructure systems?
   3.

   Are there any best-practice strategies or parameter adjustments (e.g.,
   force thresholds, trust radius, relaxation protocol) that you would
   recommend for improving convergence in slab-based heterostructure
   relaxations with large vacuum?

Best regards,
Binoy Chandra Dey
Ph.D. Scholar
IIT Bhubaneswar

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