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