I am trying to perform phonon band structure calculation. In the unit cell, the total number of atoms is 10. First, I optimized the structure using the GGA-PBE level of theory, with maximum force and stress criteria set at 0.001 eV/Å and 0.0001 eV/Å^3 respectively. The K-point and density mesh cutoffs are 12×12×2 and 120 Hartree (In the attached PDF file: 1_opt.py). Then we performed phonon band structure calculations (In the attached PDF file: 1_ph.py)

I have attached my input file and band structure here.

Here we have got small negative energy value for the bands 0, 1 and 2 around the gamma point.

# Band 0

# 1/Ang meV

0.000000e+00 -2.342471e-01

1.264492e-02 -3.318510e-01

2.528983e-02 8.371568e-01

3.793475e-02 2.223294e+00

5.057967e-02 3.981579e+00

# Band 1

# 1/Ang meV

0.000000e+00 -2.280458e-01

1.264492e-02 3.274673e+00

2.528983e-02 6.550177e+00

# Band 2

# 1/Ang meV

0.000000e+00 -1.967910e-01

1.264492e-02 5.028213e+00

2.528983e-02 1.003663e+01

Next, we increased the optimization criteria by raising the maximum force and stress criteria to 0.00001 eV/Å and 0.000001 eV/Å^3 respectively. We also adjusted the K-point and density mesh cutoffs to 17×17×2 and 120 Hartree. Additionally, we applied constraints: [FixStrain(x=False, y=False, z=True)] (In the attached PDF file: 2_opt.py). Then we performed phonon band structure calculations (In the attached PDF file: 2_ph.py).

This optimized geometry also give negative frequencies. I have attached my input file and band structure here.

Here we have got small negative energy value for the bands 0, 1 and 2 around the gamma point.

# Band 0

# 1/Ang meV

0.000000e+00 -2.321445e-02

1.401243e-02 3.107976e-01

2.802487e-02 1.152214e+00

4.203730e-02 2.450887e+00

# Band 1

# 1/Ang meV

0.000000e+00 -9.857491e-03

1.401243e-02 3.218123e+00

2.802487e-02 6.426866e+00

# Band 2

# 1/Ang meV

0.000000e+00 -2.934085e-03

1.401243e-02 4.968902e+00

2.802487e-02 9.909250e+00

Next, we repeated the unit cell of 2×2×1 and optimized the structure using the same level of theory (GGA-PBE) The maximum force and stress criteria are set to 0.00001 eV/Å and 0.000001 eV/Å^3 respectively and the K-point and density mesh cut off are adjusted to 17×17×2 and 120 Hartree. Additionally. Constrain are applied: constraints = [FixStrain(x=False, y=False, z=True)]) (Please see input file 3_opt_sup.py). Then we performed phonon band structure calculations (In the attached PDF file: 3_opt_sup.py).

I have attached my input file and band structure here.

And again, we have got the negative energy value for the bands 0 and 1 around Gamma point.

# Band 0

# 1/Ang meV

0.000000e+00 -2.189732e+00

1.340313e-02 -1.088189e+00

2.680625e-02 -8.431176e-01

4.020938e-02 -5.896596e-01

5.361251e-02 7.192593e-01

6.701563e-02 1.493273e+00

# Band 1

# 1/Ang meV

0.000000e+00 -9.583849e-01

1.340313e-02 7.469365e-01

2.680625e-02 3.028471e+00

After increasing the unit cell and force and stress tolerance also I could not able to get positive energy of phonon band structure. If we further increase the force and stress tolerance geometrical optimization not achieved. Increasing the unit cell and dynamical matrix repetition also now becomes very expensive computationally. So, how to proceed it?

## Same type results we have also seen in our others two structures here I have given the details of the calculations:

Second Structure: 2D Planar Structure

I am trying to perform phonon band structure calculation for 2D planar structure. In the unit cell, the total number of atoms is 8. First, I optimized the structure using the GGA-PBE level of theory, with maximum force and stress criteria set at 0.00001 eV/Å and 0.000001 eV/Å^3 respectively. The K-point and density mesh cutoffs are set to 14×14×1 and 180 Hartree. Additionally, we applied constraints: [FixStrain(x=False, y=False, z=True)] (In the attached PDF file: 4_opt.py). Then we performed phonon band structure calculations (In the attached PDF file: 4_ph.py ).

I have attached my input file and band structure here.

Here we have got small negative energy value for the bands 0, 1 and 2 around the gamma point.

# Band 0

# 1/Ang meV

0.000000e+00 -3.064599e-03

1.077417e-02 -1.969762e-01

2.154835e-02 -3.809684e-01

3.232252e-02 -5.376789e-01

4.309669e-02 -6.493431e-01

5.387086e-02 -6.898061e-01

6.464504e-02 -6.070034e-01

7.541921e-02 -4.573584e-02

8.619338e-02 8.558822e-01

9.696756e-02 1.397870e+00

# Band 1

# 1/Ang meV

0.000000e+00 -2.113916e-03

1.077417e-02 1.858280e+00

# Band 2

# 1/Ang meV

0.000000e+00 -1.334959e-03

1.077417e-02 3.584186e+00

2.154835e-02 7.161529e+00

Next, we calculated the phonon band structure using the same level of theory but adjusted the dynamical matrix by changing the repetition keyword from 'automatic' to 'custom' with the keyword 'repetitions=Custom' and specifying repetitions as (5, 7, 1) (In the attached PDF file: 5_ph.py).

I have attached my input file and band structure here

Here we have got negative energy value for the bands 0, 1 and 2 around the gamma point.

# Band 0

# 1/Ang meV

0.000000e+00 -3.101306e-03

1.077417e-02 2.789666e-02

# Band 1

# 1/Ang meV

0.000000e+00 -2.532241e-03

1.077417e-02 1.860980e+00

2.154835e-02 3.721967e+00

# Band 2

# 1/Ang meV

0.000000e+00 -2.314590e-03

1.077417e-02 3.532907e+00

2.154835e-02 7.065107e+00

Next, we increased the repetitions of the dynamical matrix to (7, 9, 1), (please see the phonon input file 6_ph.py). And we still got similar negative energy value for the first two bands (band 0 and band 1) around the gamma point. I have attached my input file and band structure here.

I have attached the bands with negative energy values.

# Band 0

# 1/Ang meV

0.000000e+00 -6.247893e-03

1.077417e-02 2.604093e-02

2.154835e-02 9.318862e-02

# Band 1

# 1/Ang meV

0.000000e+00 -2.470139e-03

1.077417e-02 1.861942e+00

2.154835e-02 3.723651e+00

After increasing the repetition of the dynamical matrix, I still cannot obtain positive energy values for the phonon band structure. How should I proceed?

Structure: 2D Planar BN-doped Naphyne:

I am trying to perform phonon band structure calculation for 2D planar structure. In the unit cell, the total number of atoms is 18. First, I optimized the structure using the GGA-PBE level of theory, with maximum force and stress criteria set at 0.001 eV/Å and 0.0001 eV/Å^3 respectively. The K-point and density mesh cutoffs are set to 8×8×1 and 120 Hartree (In the attached PDF file: file 7_opt.py). Then we performed phonon band structure calculations (In the attached PDF file: 7_ph.py).

I have attached my input file and phonon band structure here.

Here we have got negative energy value for the bands 0, 1 and 2 around the gamma point.

# Band 0

# 1/Ang meV

0.000000e+00 -1.777498e-01

2.104488e-02 -4.018820e-01

4.208975e-02 -4.065330e-01

6.313463e-02 -4.035637e-01

8.417951e-02 -3.789745e-01

1.052244e-01 -3.036235e-01

1.262693e-01 1.037179e-01

1.473141e-01 4.336711e-01

# Band 1

# 1/Ang meV

0.000000e+00 -1.147148e-01

2.104488e-02 1.238858e+00

4.208975e-02 2.518674e+00

# Band 2

# 1/Ang meV

0.000000e+00 -6.983817e-02

2.104488e-02 2.798706e+00

Next, we repeated the unit cell of 2×2×1 and calculated the phonon band structure (please see the phonon input file 8_ph.py) calculation using the same level of theory and we still got similar negative energy value around the gamma point.

I have attached my input file and phonon band structure here.

Here we have got negative energy value for the bands 0, 1 and 2 around the gamma point.

# Band 0

# 1/Ang meV

0.000000e+00 -3.476066e-01

1.759794e-02 -5.849682e-01

3.519588e-02 -5.877884e-01

5.279382e-02 -5.653690e-01

7.039176e-02 -5.301257e-01

8.798970e-02 -4.840881e-01

1.055876e-01 -4.272542e-01

1.231856e-01 -3.575770e-01

1.407835e-01 -2.677467e-01

1.583815e-01 -1.202378e-01

1.759794e-01 2.109239e-01

1.935773e-01 3.269962e-01

# Band 1

# 1/Ang meV

0.000000e+00 -3.416710e-01

1.759794e-02 6.020273e-01

3.519588e-02 1.276709e+00

# Band 2

# 1/Ang meV

0.000000e+00 -7.423587e-02

1.759794e-02 1.422069e+00

3.519588e-02 2.523704e+00

After increasing the unit cell, I still cannot obtain positive energy values for the phonon band structure. How should I proceed?