Persistent SCF non-convergence for 2D monolayer with Quantum ESPRESSO 7.4.1 + Environ 3.1.1

[Darshil Chodvadiya]

Dear Environ developers and users,

I am performing implicit-solvent calculations for a 2D h-AlN monolayer containing a substitutional C defect using Quantum ESPRESSO 7.4.1 with Environ 3.1.1. The corresponding vacuum calculations converge normally. However, I have not been able to achieve SCF convergence in any of the Environ calculations tested so far, despite trying different Environ models, environ_thr values, and electronic mixing parameters.

The system is a neutral 4×4 h-AlN monolayer containing 32 atoms, with a cell height of approximately 20 Å along the non-periodic direction. I use a 4×4×1 k-point mesh, ecutwfc = 80 Ry, ecutrho = 640 Ry, and a target electronic convergence threshold of conv_thr = 1.0d-6.

For the 2D electrostatics, I have been using:

&ELECTROSTATIC pbc_correction = 'parabolic', pbc_dim = 2, pbc_axis = 3, tol = 1.d-10, /

I have performed the following convergence tests.

Test 1 – Full water model

environ_type = 'water' environ_thr = 1.d0 solvent_mode = 'full' mixing_beta = 0.7

The SCF became strongly unstable and did not converge. The calculation eventually terminated with:

Error in routine c_bands (1): too many bands are not converged

Test 2 – Full water model with more conservative electronic mixing

environ_type = 'water' environ_thr = 20.d0 solvent_mode = 'full' mixing_mode = 'local-TF' mixing_beta = 0.10

The SCF behavior improved compared with Test 1. However, the requested SCF convergence was still not achieved, and the calculation eventually encountered the c_bands error.

Test 3 – Simplified dielectric/electrostatic model

environ_type = 'input' environ_thr = 20.d0 env_static_permittivity = 78.3 solvent_mode = 'full' mixing_mode = 'local-TF' mixing_beta = 0.10

This calculation showed the best numerical behavior among the tested cases. However, it also failed to reach SCF convergence. The calculation ran for the maximum 500 electronic iterations and reached SCF accuracies of approximately – Ry, but ultimately reported:

convergence NOT achieved after 500 iterations

Therefore, although this setup was numerically more stable than the other tested configurations, its total energy cannot be considered electronically converged.

Test 4 – Reduced environ_thr and electronic mixing

environ_type = 'input' environ_thr = 1.d0 env_static_permittivity = 78.3 solvent_mode = 'full' mixing_mode = 'local-TF' mixing_beta = 0.05

In this case, Environ was introduced after the first few SCF iterations. However, SCF convergence was again not achieved. The calculation developed band-convergence problems and eventually terminated with the c_bands error. Thus, reducing mixing_beta from 0.10 to 0.05 did not resolve the convergence problem.

In summary, none of the four Environ calculations has reached the requested SCF convergence criterion of conv_thr = 1.0d-6. Among the tested settings, the dielectric-only calculation using environ_thr = 20 and mixing_beta = 0.10 showed the best numerical behavior, but even this calculation remained unconverged after 500 electronic iterations.

I would therefore be very grateful for your advice on the following points:

1. Is the combination pbc_correction = 'parabolic', pbc_dim = 2, and pbc_axis = 3 appropriate for this neutral 2D monolayer geometry?
2. Would you recommend further adjustment of environ_thr, or does the observed behavior suggest that this parameter is not the primary source of the convergence problem?
3. Could tightening the Environ polarization tolerance from tol = 1.d-10 to 1.d-12 or lower help achieve SCF convergence?
4. Would increasing the cell height/vacuum along the direction be advisable even when the parabolic PBC correction is used?
5. Could the convergence difficulty originate from the solvent cavity/interface? If so, would you recommend examining or modifying parameters such as solvent_radius or filling_threshold for this type of 2D material?
6. Are there any other Environ or Quantum ESPRESSO SCF/mixing settings that you would recommend for obtaining reliable convergence for this system?

I have attached representative scf.in, scf.out, environ.in, and environ.debug files from these calculations. I would be happy to provide the complete outputs, additional test cases, or any other diagnostic files if needed.

Thank you very much for your time and assistance.

Best regards,
Darshil