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Tutorial for Thermalized Drude oscillators in LAMMPS
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====================================================
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This tutorial explains how to use Drude oscillators in LAMMPS to
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simulate polarizable systems using the USER-DRUDE package. As an
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illustration, the input files for a simulation of 250 phenol molecules
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are documented. First of all, LAMMPS has to be compiled with the
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USER-DRUDE package activated. Then, the data file and input scripts
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have to be modified to include the Drude dipoles and how to handle
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them.
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----------
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**Overview of Drude induced dipoles**
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Polarizable atoms acquire an induced electric dipole moment under the
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strategies, as in the following examples of polarizable force
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fields:
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#. :ref:`Lamoureux and Roux <Lamoureux>` suggest adopting a global half-stiffness, :math:`K_D` = 500 kcal/(mol Ang :math:`{}^2`) - which corresponds to a force constant :math:`k_D` = 4184 kJ/(mol Ang :math:`{}^2`) - for all types of core-Drude bond, a global mass :math:`m_D` = 0.4 g/mol (or u) for all types of Drude particles, and to calculate the Drude charges for individual atom types from the atom polarizabilities using equation (1). This choice is followed in the polarizable CHARMM force field.
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#. Alternately :ref:`Schroeder and Steinhauser <Schroeder>` suggest adopting a global charge :math:`q_D` = -1.0e and a global mass :math:`m_D` = 0.1 g/mol (or u) for all Drude particles, and to calculate the force constant for each type of core-Drude bond from equation (1). The timesteps used by these authors are between 0.5 and 2 fs, with the degrees of freedom of the Drude oscillators kept cold at 1 K.
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#. In both these force fields hydrogen atoms are treated as non-polarizable.
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* :ref:`Lamoureux and Roux <Lamoureux>` suggest adopting a global half-stiffness, :math:`K_D` = 500 kcal/(mol Ang :math:`{}^2`) - which corresponds to a force constant :math:`k_D` = 4184 kJ/(mol Ang :math:`{}^2`) - for all types of core-Drude bond, a global mass :math:`m_D` = 0.4 g/mol (or u) for all types of Drude particles, and to calculate the Drude charges for individual atom types from the atom polarizabilities using equation (1). This choice is followed in the polarizable CHARMM force field.
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* Alternately :ref:`Schroeder and Steinhauser <Schroeder>` suggest adopting a global charge :math:`q_D` = -1.0e and a global mass :math:`m_D` = 0.1 g/mol (or u) for all Drude particles, and to calculate the force constant for each type of core-Drude bond from equation (1). The timesteps used by these authors are between 0.5 and 2 fs, with the degrees of freedom of the Drude oscillators kept cold at 1 K.
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* In both these force fields hydrogen atoms are treated as non-polarizable.
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The motion of of the Drude particles can be calculated by minimizing
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the energy of the induced dipoles at each timestep, by an interative,
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self-consistent procedure. The Drude particles can be massless and
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#. The possibility to thermostat the additional degrees of freedom associated with the induced dipoles at very low temperature, in terms of the reduced coordinates of the Drude particles with respect to their cores. This makes the trajectory close to that of relaxed induced dipoles.
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#. The Drude dipoles on covalently bonded atoms interact too strongly due to the short distances, so an atom may capture the Drude particle (shell) of a neighbor, or the induced dipoles within the same molecule may align too much. To avoid this, damping at short of the interactions between the point charges composing the induced dipole can be done by :ref:`Thole <Thole>` functions.
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----------
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