Re: Dynamical Matrix for the Thermal Property ( No.1 ) 
 Date: 2024/02/13 13:35
 Name: Naoya Yamaguchi
 Hi,
As mentioned in https://www.openmxsquare.org/openmx_man3.9/node224.html , there is "ALAMODE": https://alamode.readthedocs.io/en/latest/tutorial.html .
Regards, Naoya Yamaguchi

Re: Dynamical Matrix for the Thermal Property ( No.2 ) 
 Date: 2024/02/13 20:03
 Name: Kieran <skn_neu@hotmail.co.uk>
 Dear Naoya,
Thank you for the reply.
I referred to ALAMODE code and found that it only ouputs the force constant matrix; not the dynamical matrix.
I can use the force constant matrix to construct the dynamical matrix.
On the other hand, I also heard that the dynamical matrix needs to be symmetrized so that the upper and lower triangle block in the dynamical matrix are hermitian conjugate to each other.
Would you please tell me how to symmetrize the dynamical matrix, which is built with the force constant matrix?
Thank you.
Kind regards,
Kieran

Re: Dynamical Matrix for the Thermal Property ( No.3 ) 
 Date: 2024/02/13 20:38
 Name: Masanobu Miyata <mmiyata@jaist.ac.jp>
 Hi．
This is Miyata. In general case, the offdiagonal part of dynamical matrix can be negleted, because this contribution is very small except for the materials including large anharmonic phonon. For conventional lattice thermal conductivity calculations in ALAMODE, the offdiagonal part of dynamical matrix is ignored. Of course, we can also treat the offdiagonal part with specified keyword of ALAMODE. However, the calculaiton cost is very expensive. Please see the sessions of "Coherent component of lattice thermal conductivity" or "Selfconsistent phonon (SCPH) calculation" in official HP( https://alamode.readthedocs.io/en/latest/anphondir/formalism_anphon.html.) I'm not a specialist of theorerical lattice dynamical calculation. I recommend to discussion for technical forum of ALAMODE. (https://github.com/ttadano/alamode/discussions)
Best regards, Miyata,

Re: Dynamical Matrix for the Thermal Property ( No.4 ) 
 Date: 2024/02/13 22:23
 Name: Kieran <skn_neu@hotmail.co.uk>
 Dear Miyata,
Thank you for your suggestion.
I will refer to the ALAMODE forum.
Kind regards,
Kieran

Re: Dynamical Matrix for the Thermal Property ( No.5 ) 
 Date: 2024/02/15 19:35
 Name: YungTing Lee
 Dear Kieran,
Regarding "the sum rules" in the matrix of force constants, one may check Eq. (2)(4) in the section 2 and 3 in the paper [1].
(A) Due to the fact that the force constants corresponds to the second derivative of energy or the first derivative of force with respect to r, the force constants usually are estimated by the first derivative of forces (numerical differentiation).
One can notice that the offdiagonal terms of the force constants exhibit a tiny difference, e.g. FC_{i,j} ~= FC_{j.i}. Therefore, one have to apply Eq. (2) to make force constants symmetry.
(B) Eq. (3) is Newton’s third law.
Once applying Eq. (2) and Eq. (3), Eq. (4) is satisfied automatically. Therefore, the 3 lowest phonon dispersion (close to the Gamma point) should be close to zero.
Furthermore, in my opinion, there is an advanced approach for constructing phonon bands (close to Gamma point) with accurate forces in a supercell, one may check a great article [2] by ChiCheng Lee et. al..
................................................................ Reference: [1] G. J. Ackland et. al., J. Phys.: Condens. Matter 9, 7861 (1997). [2] ChiCheng Lee et. al., J. Phys.: Condens. Matter 33, 055902 (2020). ................................................................
Best regards, YungTing Lee

Re: Dynamical Matrix for the Thermal Property ( No.6 ) 
 Date: 2024/02/20 00:49
 Name: Kieran <skn_neu@hotmail.co.uk>
 Dear Dr. Lee,
Thank you very much for the answer with so many details.
I will read these two reference paper.
Kind regards,
Kieran

