update dynamical_matrix docs

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Axel Kohlmeyer
2020-02-03 09:01:31 -05:00
parent ecf30b47a0
commit 1827ce1d32
3 changed files with 20 additions and 16 deletions

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@ -40,42 +40,46 @@ Description
Calculate the dynamical matrix by finite difference of the selected group,
.. image:: JPG/dynamical_matrix_dynmat.jpg
:align: center
.. math::
where D is the dynamical matrix and Phi is the force constant matrix defined by
D = \frac{\Phi_{ij}^{\alpha\beta}}{\sqrt{M_i M_j}}
.. image:: JPG/dynamical_matrix_force_constant.jpg
:align: center
where D is the dynamical matrix and :math:`\Phi` is the force constant
matrix defined by
The output for the dynamical matrix is printed three elements at a time. The
three elements are the three beta elements for a respective i/alpha/j combination.
Each line is printed in order of j increasing first, alpha second, and i last.
.. math::
If the style eskm is selected, the dynamical matrix will be in units of inverse squared
femtoseconds. These units will then conveniently leave frequencies in THz, where
frequencies, represented as omega, can be calculated from
\Phi_{ij}^{\alpha\beta} = \frac{\partial^2 U}{\partial x_{i,\alpha} \partial x_{j,\beta}}
:c, image(Eqs/dynamical\_matrix\_phonons.jpg)
The output for the dynamical matrix is printed three elements at a time.
The three elements are the three :math:`\beta` elements for a respective
i/:math:`\alpha`/j combination. Each line is printed in order of j
increasing first, :math:`\alpha` second, and i last.
If the style eskm is selected, the dynamical matrix will be in units of
inverse squared femtoseconds. These units will then conveniently leave
frequencies in THz.
Restrictions
""""""""""""
The command collects an array of nine times the number of atoms in a group
on every single MPI rank, so the memory requirements can be very significant
for large systems.
This command is part of the USER-PHONON package. It is only enabled if
LAMMPS was built with that package. See the :doc:`Build package <Build_package>` doc page for more info.
LAMMPS was built with that package.
See the :doc:`Build package <Build_package>` doc page for more info.
Related commands
""""""""""""""""
:doc:`fix phonon <fix_phonon>`
:doc:`compute hma <compute_hma>` uses an analytic formulation of the hessian
provided by Pair's single\_hessian.
:doc:`compute hma <compute_hma>` uses an analytic formulation of the
Hessian provided by a pair_style's Pair::single\_hessian() funcion,
if implemented.
Default
"""""""