End rst doc files with transition
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@ -127,9 +127,9 @@ fitted potentials. When fitting the same functional form on *Q* different data s
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obtain *Q* different optimized potentials, :math:`E(\boldsymbol R,\boldsymbol Z, \boldsymbol \eta, \boldsymbol \mu_q^*), 1 \le q \le Q`.
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Consequently, there exist many different sets of optimized parameters for empirical interatomic potentials.
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Instead of optimizing the potential parameters, inspired by the reduced basis method
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:ref:`(Thompson) <Thompson20141>` for parametrized partial differential equations,
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we view the parametrized PES as a parametric manifold of potential energies
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Instead of optimizing the potential parameters, inspired by the reduced basis method for
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parametrized partial differential equations, we view the parametrized PES as a parametric manifold
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of potential energies.
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.. math::
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@ -151,8 +151,7 @@ Proper Orthogonal Descriptors
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Proper orthogonal descriptors are finger prints characterizing the
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radial and angular distribution of a system of atoms. The detailed
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mathematical definition is given in the paper by Nguyen et
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al. :ref:`(Thompson) <Thompson20141>`
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mathematical definition is given in :ref:`(Nguyen) <Nguyen2022>`
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The descriptors for the one-body interaction are used to captured energy of isolated elements and defined as follows
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@ -660,18 +659,6 @@ The keyword defaults are also given in the description of the input files.
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----------
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.. _Thompson20142:
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.. _Nguyen2022:
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**(Thompson)** Thompson, Swiler, Trott, Foiles, Tucker, J Comp Phys, 285, 316 (2015).
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.. _Bartok20102:
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**(Bartok2010)** Bartok, Payne, Kondor, Csanyi, Phys Rev Lett, 104, 136403 (2010).
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.. _Wood20182:
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**(Wood)** Wood and Thompson, J Chem Phys, 148, 241721, (2018)
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.. _Cusentino20202:
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**(Cusentino)** Cusentino, Wood, and Thompson, J Phys Chem A, xxx, xxxxx, (2020)
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**(Nguyen)** Ngueyn, et. al., arxiv (2022).
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@ -21,10 +21,10 @@ Examples
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Description
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"""""""""""
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Pair style *pod* defines the proper orthogonal descriptor (POD) potential,
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:ref:`(Thompson) <Thompson20142>`. The mathematical definition of the POD potential
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is described from :doc:`compute podfit <compute_podfit>`, which is used to fit the POD
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potential to *ab initio* energy and force data.
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Pair style *pod* defines the proper orthogonal descriptor (POD) potential. The mathematical
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definition of the POD potential is described from :doc:`compute podfit <compute_podfit>`, which is
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used to fit the POD potential to *ab initio* energy and force data. More details on the POD potential
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are given in :ref:`(Nguyen) <Nguyen2022>`
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Only a single pair_coeff command is used with the *pod* style which
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specifies a POD parameter file followed by a coefficient file.
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@ -64,18 +64,6 @@ none
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----------
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.. _Thompson20142:
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.. _Nguyen2022:
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**(Thompson)** Thompson, Swiler, Trott, Foiles, Tucker, J Comp Phys, 285, 316 (2015).
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.. _Bartok20102:
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**(Bartok2010)** Bartok, Payne, Kondor, Csanyi, Phys Rev Lett, 104, 136403 (2010).
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.. _Wood20182:
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**(Wood)** Wood and Thompson, J Chem Phys, 148, 241721, (2018)
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.. _Cusentino20202:
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**(Cusentino)** Cusentino, Wood, and Thompson, J Phys Chem A, xxx, xxxxx, (2020)
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**(Nguyen)** Ngueyn, et. al., arxiv (2022).
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