The dynamical matrix for the thermal transmission coefficient calculation is written as follows: $$D_{I\alpha,J\beta}(\overrightarrow{q})=\frac{1}{\sqrt{M_{I}M_{J}}}\sum_{b}K_{I\alpha,J\beta}(a,b)e^{i\cdot\overrightarrow{q}(\vec{R}_{b}-\vec{R}_{a})}\tag{1}$$ ,where $M_{I}$ and $M_{J}$ are atomic weight; $\vec{R}_{a}$ and $\vec{R}_{b}$ are the original lattice constant.
$K_{I\alpha,J\beta}$ is the force constant matrix and it is given as follows: $$K_{I\alpha,J\beta}(R-R^{'})=\frac{\partial^{2}E_{tot}}{\partial{\mu_{I\alpha}}(R)\partial{\mu_{J\beta}(R^{'})}}=-\frac{\partial{F_{I\alpha}}}{\partial{\mu_{J\beta}(R^{'})}}\tag{2}$$
- Compute the force constant matrix for the unit cell and this force constant matrix is $3n\times3n$ matrix; for example, if there are three atoms in the unit cell; then, this force constant matrix is a $9\times9$ matrix.
- Compute the dynamical matrix through summing all the neighbour cell of the central unit cell
- Symmterize the dynamical matrix and make sure the upper and lower triangle blocks in this dynamical matrix are hermitian conjugate to each other.
Is my understanding correct or not?
