Dnamical matrix at a q-point is constructed by supercell force
constants and is written as,
![$\displaystyle D_{\alpha\beta}(j j',\mathbf{k}) = \frac{1}{(m_j m_{j'})^{1/2}} \...
...\ ll' \\ \end{pmatrix} \exp(i\mathbf{k}\cdot[\mathbf{r}(j'l')-\mathbf{r}(j0)]).$](img56.png) |
(3.9) |
An element of a dynamical matrix is calculated by the sum of force
constants multiplied by phase factor which is a vector product of the
q-point and a vector between focused atoms.
runs through all
unitcells contained in a supercell. In output of fropho, a column
(
) of a dynamical matrix corresponds to a displaced atom number and
a row (
) of that corresponds to an atom number where force is
affected. If an atom of a force constant is on a rim of the supercell,
the force constant is divided by the multiplicty which the atom is
shared by the neighboring supercells.
togo
2009-02-12