.. _user-section-potential: The Potential section ===================== The potential section specifies a single potential function to add to the force field. .. pyretis-input-example:: Potential .. code-block:: rst Potential --------- class = DoubleWell parameter a = 1.0 parameter b = 2.0 parameter c = 0.0 In order to add several potential functions to a force field, several Potential sections can be added: .. pyretis-input-example:: Potential .. code-block:: rst Potential --------- class = PairLennardJonesCutnp shift = True dim = 2 mixing = geometric parameter 0 = {'sigma': 1.0, 'epsilon': 1.0, 'factor': 1.12246205} parameter 1 = {'sigma': 1.0, 'epsilon': 1.0, 'factor': 1.12246205} Potential --------- class = DoubleWellWCA dim = 2 parameter rzero = 1.122462048309373 parameter height = 15.0 parameter width = 0.5 parameter types = [(1, 1)] As the different potentials typically require different settings, detailed information can be found below for specific potentials: .. contents:: :local: :depth: 3 .. _user-section-potential-doublewell: The DoubleWell potential ------------------------ This class defines a one-dimensional double well potential. The potential energy (:math:V_\text{pot}) is given by .. _user-doublewell-equation: .. math:: V_\text{pot} = a x^4 - b (x - c)^2 where :math:x is the position and :math:a, :math:b and :math:c are parameters for the potential. .. pyretis-input-example:: Potential :class-name: DoubleWell .. code-block:: rst Potential --------- class = DoubleWell parameter a = 1.0 parameter b = 2.0 parameter c = 0.0 Keywords for the DoubleWell potential ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ The following keywords can be specified for the DoubleWell potential: .. |dwell_class| replace:: :ref:class  .. |dwell_parameter| replace:: :ref:parameter  .. _table-keywords-doublewell: .. table:: Keywords for the DoubleWell potential. :class: table-striped table-hover +-------------------+------------------------------------------------------+ | Keyword | Description | +===================+======================================================+ | |dwell_class| | Selects the DoubleWell potential. | +-------------------+------------------------------------------------------+ | |dwell_parameter| | Sets the parameters for the potential. | +-------------------+------------------------------------------------------+ .. _user-section-doublewell-class: Keyword class ............. .. pyretis-keyword:: class DoubleWell :specific: yes This keyword selects the potential and should be set to: DoubleWell. .. _user-section-doublewell-parameter: Keyword parameter ................. For the DoubleWell potential, three parameters can be specified: .. pyretis-keyword:: parameter a float The a parameter in the potential energy :ref:function  given above. Default: The default is: parameter a = 1.0 .. pyretis-keyword:: parameter b float The b parameter in the potential energy :ref:function  given above. Default: The default is: parameter b = 1.0 .. pyretis-keyword:: parameter c float The c parameter in the potential energy :ref:function  given above. Default: The default is: parameter c = 0.0 .. _user-section-potential-rectangularwell: The RectangularWell potential ----------------------------- This class defines a one-dimensional rectangular well potential. The potential energy is zero within the potential well and infinite outside. The well is defined with a left and right boundary. .. pyretis-input-example:: Potential :class-name: RectangularWell .. code-block:: rst Potential --------- class = RectangularWell parameter left = -1.0 parameter right = 1.0 Keywords for the RectangularWell potential ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ The following keywords can be specified for the RectangularWell potential: .. |rwell_class| replace:: :ref:class  .. |rwell_parameter| replace:: :ref:parameter  .. _table-keywords-rectangularwell: .. table:: Keywords for the RectangularWell potential. :class: table-striped table-hover +-------------------+------------------------------------------------------+ | Keyword | Description | +===================+======================================================+ | |rwell_class| | Selects the RectangularWell potential. | +-------------------+------------------------------------------------------+ | |rwell_parameter| | Sets the parameters for the potential. | +-------------------+------------------------------------------------------+ .. _user-section-rectangularwell-class: Keyword class ............. .. pyretis-keyword:: class RectangularWell :specific: yes This keyword selects the potential and should be set to: RectangularWell. .. _user-section-rectangularwell-parameter: Keyword parameter ................. For the RectangularWell potential, two parameters can be set. .. pyretis-keyword:: parameter left float The left border for the potential well function. The potential energy is 0 for positions :math:x such that :math:\text{left} < x < \text{right}. Default: The default parameter is: parameter left = 0.0 .. pyretis-keyword:: parameter right float The right border for the potential well function. The potential energy is 0 for positions :math:x such that :math:\text{left} < x < \text{right}. Default: The default parameter is: parameter right = 1.0 .. _user-section-potential-pairlennardjonescutnp: The PairLennardJonesCutnp potential ----------------------------------- This class implements as simple Lennard-Jones 6-12 potential which employs a simple cut-off and can be shifted. The potential energy (:math:V_\text{pot}) is defined in the usual way for an interacting pair :math:(i,j) of particles a distance :math:r apart, .. math:: V_\text{pot} = 4 \varepsilon_{ij} \left( x^{12} - x^{6} \right), where :math:x = \sigma_{ij}/r and :math:\varepsilon_{ij} and :math:\sigma_{ij} are the potential parameters. .. pyretis-input-example:: Potential :class-name: PairLennardJonesCutnp Here is an example for defining parameters for a mixture of 3 particle types with geometric mixing. .. code-block:: rst Potential --------- class = PairLennardJonesCutnp shift = True dim = 3 mixing = geometric parameter 0 = {'sigma': 1.0, 'epsilon': 1.0, 'rcut': 2.5} parameter 1 = {'sigma': 1.2, 'epsilon': 1.1, 'rcut': 2.5} parameter 2 = {'sigma': 1.4, 'epsilon': 0.9, 'rcut': 2.5} Keywords for the PairLennardJonesCutnp potential ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ The following keywords can be specified for the PairLennardJonesCutnp potential: .. |ljnp_class| replace:: :ref:class  .. |ljnp_dim| replace:: :ref:dim  .. |ljnp_shift| replace:: :ref:shift  .. |ljnp_mixing| replace:: :ref:mixing  .. |ljnp_parameter| replace:: :ref:parameter  .. _table-pairljnp-keywords: .. table:: Keywords for the PairLennardJonesCutnp potential. :class: table-striped table-hover +------------------+-------------------------------------------------------+ | Keyword | Description | +==================+=======================================================+ | |ljnp_class| | Selects the potential. | +------------------+-------------------------------------------------------+ | |ljnp_dim| | Set the number of dimensions to consider. | +------------------+-------------------------------------------------------+ | |ljnp_shift| | Determines if the potential should be shifted. | +------------------+-------------------------------------------------------+ | |ljnp_mixing| | Selects the mixing rules for generating parameters | | | for cross interactions. | +------------------+-------------------------------------------------------+ | |ljnp_parameter| | Sets the parameters for the potential. | +------------------+-------------------------------------------------------+ .. _user-section-pairljnp-class: Keyword class ............. .. pyretis-keyword:: class PairLennardJonesCutnp :specific: yes This keyword selects the potential and should be set to: PairLennardJonesCutnp. .. _user-section-pairljnp-dim: Keyword dim ........... .. pyretis-keyword:: dim integer Sets the dimensionality for the potential. Should be 1, 2, or 3 for 1D, 2D or 3D, respectively. Default: The default value is dim = 3. .. _user-section-pairljnp-shift: Keyword shift ............. .. pyretis-keyword:: shift boolean Determines if the potential should be shifted or not. This should be either True (enables shifting) or False (disables shifting). If shifting is True, the following value will be added to the potential (for a given :math:(i, j) pair): .. math:: V_{\text{shift}} = 4 \varepsilon_{ij} \left( x_{\text{c}}^{12} - x_{\text{c}}^{6} \right), where :math:x_{\text{c}} = \sigma_{ij} / r_{\text{c}, ij} and :math:r_{\text{c}, ij} is the cut-off. Default: The default value is shift = True. .. _user-section-pairljnp-mixing: Keyword mixing .............. .. pyretis-keyword:: mixing string Determines how mixing parameters for the potential should be determined. The supported mixing rules are: * mixing = geometric: * :math:\epsilon_{ij} = \sqrt{\epsilon_{i} \times \epsilon_{j}} * :math:\sigma_{ij} = \sqrt{\sigma_{i} \times \sigma_{j}} * :math:r_{\text{c},ij} = \sqrt{r_{\text{c},i} \times r_{\text{c},j}} * mixing = arithmetic: * :math:\epsilon_{ij} = \sqrt{\epsilon_{i} \times \epsilon_{j}} * :math:\sigma_{ij} = \frac{\sigma_{i} \times \sigma_{j}}{2} * :math:r_{\text{c},ij} = \frac{r_{\text{c},i} \times r_{\text{c},j}}{2} * mixing = Sixthpower: * :math:\epsilon_{ij} = 2 \sqrt{\epsilon_{i} \times \epsilon_{j}} \frac{\sigma_i^3 \times \sigma_j^3}{\sigma_i^6 + \sigma_j^6} * :math:\sigma_{ij} = \left( \frac{\sigma_{i}^6 \times \sigma_{j}^6}{2} \right)^{1/6} * :math:r_{\text{c},ij} = \left(\frac{r_{\text{c},i}^6 \times r_{\text{c},j}^6}{2}\right)^{1/6} Default The default value is mixing = geometric. .. _user-section-pairljnp-parameter: Keyword parameter ................. The following parameters can be set for the PairLennardJonesCutnp potential: .. pyretis-keyword:: parameter i dictionary The parameters for the PairLennardJonesCutnp potentials are given for each particle type on the form: .. code-block:: rst parameter i = {'sigma': 1.0, 'epsilon': 1.0, 'rcut': 2.5} Where i is the particle type, identified as an integer. Here, sigma is :math:\sigma_i, epsilon is :math:\varepsilon_i and rcut is :math:r_{\text{c},i}. Note that several parameters can be given in this way and that they will be combined according to the selected :ref:mixing rule . .. _user-section-potential-doublewellwca: The DoubleWellWCA potential --------------------------- This class defines a n-dimensional Double Well potential. The potential energy (:math:V_\text{pot}) for a pair of particles separated by a distance :math:r is given by, .. _user-doublewellwca-equation: .. math:: V_\text{pot} = h (1 - (r - r_0 - w)^2/w^2)^2, where :math:h gives the 'height' of the potential, :math:r_0 the minimum and :math:w the width. .. pyretis-input-example:: Potential :class-name: DoubleWellWCA .. code-block:: rst Potential --------- class = DoubleWellWCA dim = 2 parameter rzero = 1.122462048309373 parameter height = 6.0 parameter width = 0.25 parameter types = [(1, 1)] Keywords for the DoubleWellWCA potential ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ The following keywords can be specified for the DoubleWellWCA potential: .. |dwca_class| replace:: :ref:class  .. |dwca_dim| replace:: :ref:dim  .. |dwca_parameter| replace:: :ref:parameter  .. _table-keywords-doublewellwca: .. table:: Keywords for the DoubleWellWCA potential :class: table-striped table-hover +------------------+-------------------------------------------------------+ | Keyword | Description | +==================+=======================================================+ | |dwca_class| | Selects the potential. | +------------------+-------------------------------------------------------+ | |dwca_dim| | Sets the number of dimensions to consider. | +------------------+-------------------------------------------------------+ | |dwca_parameter| | Sets the parameters for the potential. | +------------------+-------------------------------------------------------+ .. _user-section-dwwca-class: Keyword class ............. .. pyretis-keyword:: class DoubleWellWCA :specific: yes Selects the potential, should be set to: DoubleWellWCA. .. _user-section-dwwca-dim: Keyword dim ........... .. pyretis-keyword:: dim integer Sets the dimensionality for the potential. Should be 1, 2, or 3 for 1D, 2D or 3D, respectively. Default: The default value is dim = 3. .. _user-section-dwwca-parameter: Keyword parameter ................. The following parameters can be set for the DoubleWellWCA potential: .. pyretis-keyword:: parameter zero float This is the :math:r_0 parameter in the potential energy :ref:function  given above. Default The default is rzero = 0 .. pyretis-keyword:: parameter height float This is the :math:h parameter in the potential energy :ref:function  given above. Default The default is height = 0 .. pyretis-keyword:: parameter width float This is the :math:w parameter in the potential energy :ref:function  given above. Default The default is width = 0 .. pyretis-keyword:: parameter types list of tuples of integers This parameter determines for which pair of particles the interaction should act on. If this is not set, it will turn on the interaction for all particles. For example, if types = [(1,2)] the interaction will be turned on between particles of type 1 and type 2 only. (See the :ref:particle section  for a description about the particle type.) Note that several types can be specified at the same time: types = [(1, 2), (0, 1), (0, 2)]. Default The default is activated for all pairs. .. _user-section-potential-custom: User-defined potential functions -------------------------------- User-defined potential functions are selected as follows: .. pyretis-input-example:: Potential :class-name: a user-defined class .. code-block:: rst Potential --------- class = PotentialName module = potential.py keyword1 = value parameter p = 123. Here, the user can both define custom keywords and parameters. However, the class and the module **must** always be specified in this case. Keywords for user-defined potential functions ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ At least, the following keywords can be specified for user-defined potential functions: .. |user_class| replace:: :ref:class  .. |user_module| replace:: :ref:module  .. _table-keywords-user-potential: .. table:: Keywords for user.defined potential functions. :class: table-striped table-hover +---------------+----------------------------------------------------------+ | Keyword | Description | +===============+==========================================================+ | |user_class| | Selects the Python class which implements the potential. | +---------------+----------------------------------------------------------+ | |user_module| | Defines the file where the Python class with the | | | potential can be found. | +---------------+----------------------------------------------------------+ .. _user-section-potential-user-class: Keyword class ............. .. pyretis-keyword:: class string This keyword selects the potential function and it should be set to the class name of the custom potential function class defined in the given :ref:module . .. _user-section-potential-user-module: Keyword module .............. .. pyretis-keyword:: module string This keyword specified the location of the file containing the user-defined class for the potential function. This file must be accessible by |pyretis|. Default Not any. This keyword must be specified.