The influence of cell expansion on the calculation about anharmonic phonon

[LHDphy]

Dear all,

I start the anharmonic calculation of my system within a nq=331 harmonic phonon, as shown in Fig. 1.

Here, several things have to be highlighted in Fig. 1, which presents nq= 331, 661, and 12121 harmonic phonon spectra:
(1) The maximum values of imaginary frequency at the high-symmetry point $M$ are almost equal;
(2) There is no imaginary frequency around the path from $Gamma$ and 1/2$Gamma$$M$ in 661, and 12121 harmonic phonon spectra; however, imaginary frequency exists around the path from $Gamma$ and 1/2$Gamma$$M$ in 331 harmonic phonon spectrum.

Next, I create 1000 configurations within a nq=331 harmonic phonon at 0K in one population, and calculate 5 populations to reach convergence. Then, I create 3000 configurations from population5 and produce population6 to verify the convergence further. Finally, I got the Hessian phonon spectrum in Fig. 2.

Similarly, there are also several things to be highlighted in Fig. 2.
(3) A distinct difference between the 3th-order and 4th-order SSCHA FC term to calculate the Hessian;
(4) The Hessian phonon spetrum calculated with 4th-order SSCHA FC term around the path from $Gamma$ and 1/2$Gamma$$M$ is still imaginary.

Consequently, as for results (3) and (4) calculated by me, I have two questions that need help.
[1] As for (3), since the phonon spectra calculated by the 3rd-order and 4th-order SSCHA FC term to calculate the Hessian differ significantly, will the spectra calculated by the 5th-order SSCHA FC term eliminate the imaginary frequencies? Does a 5th-order switch exist?

[2] As for (4), I doubt that the imaginary frequency around the path from $Gamma$ and 1/2$Gamma$$M$ comes from the way of 331 [Fig. 1, detail in (2)]. If I use the 661 expansion method to calculate SSCHA, is it possible to avoid this problem?

Actually, I have implemented the SSCHA calculations of 661, but it is too expensive and will take a long time.

Best wishes,
HD Liu

[mesonepigreco]

Hi.
To reply to your points:

• there is no 5th-order in the sscha, as the 4th order already accounts for the complete (infinite-order) anharmonicity within the RPA approximation.
• The convergence with the supercell can be tricky. For the 3rd order we have a way to interpolate the result you get from the 3x3x1 in an arbitrary large supercell (explained in this tutorial ), but we do not have implemente the same yet for the 4th order.

In this case, you can probably try to interpolate the difference between the4th order and harmonic dynamical matrices obtained in a 3x3x1 into the 12x12x1 and then add back the harmonic one, to see the results in a bigger supercell. This is automatically done by the method Interpolate of the phonon Class. You can check the guide from the API document here (page 50, method Interpolate).

Brifely, it is used as follows:

# [...] Load the dynamical matrices harm_331, harm_12121, and hessianv4_331 
hessianv4_12121 = hessianv4_331.Interpolate((3,3,1), (12,12,1), support_dyn_coarse=harm_331, support_dyn_fine=harm_12121)
hessianv4_12121.save_qe("hessian_12121_")

[LHDphy]

Hi,

First, thanks for your reply!

I wrote a script based on your answer before (github.com/orgs/SSCHAcode/discussions/129):

import cellconstructor as CC, cellconstructor.Phonons

v2025.08.11 Debug to phyhdliu@163.com

fine = 12 # Here the number of nq=12x12x1
coarse = 3 # Here the number of nq=3x3x1

nqirr_fine = 19 # Here the number of irreducible q points for the 12x12
nqirr_coarse = 3 # Here the number of irreducible q points for the 3x3

dyn_harmonic_fine = CC.Phonons.Phonons(f"harm_dyn_{fine}", nqirr_fine)
dyn_harmonic_coarse = CC.Phonons.Phonons(f"harm_dyn{coarse}_", nqirr_coarse)

dyn_sscha_coarse = CC.Phonons.Phonons(f"sscha_dyn_{coarse}_", nqirr_coarse)

anharmonic_dyn_fine = dyn_sscha_coarse.Interpolate(
(coarse, coarse, 1),
(fine, fine, 1),
support_dyn_coarse=dyn_harmonic_coarse,
support_dyn_fine=dyn_harmonic_fine
)

anharmonic_dyn_fine.save_qe(f"sscha_dyn_{fine}_")

Can this script be used for HessianV4?

Best wishes,
HD Liu