Source code for MDAnalysis.analysis.dielectric

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Dielectric --- :mod:`MDAnalysis.analysis.dielectric`

:Authors: Mattia Felice Palermo, Philip Loche
:Year: 2022
:Copyright: GNU Public License v3

import numpy as np

from MDAnalysis.units import constants, convert
from MDAnalysis.analysis.base import AnalysisBase
from MDAnalysis.due import due, Doi
from MDAnalysis.exceptions import NoDataError

         description="Dielectric analysis",
del Doi

[docs]class DielectricConstant(AnalysisBase): r""" Computes the average dipole moment .. math:: \boldsymbol M = \sum_i q_i \boldsymbol r_i where :math:`q_i` is the charge and :math:`\boldsymbol r_i` the position of atom :math:`i` in the given :class:`MDAnalysis.core.groups.AtomGroup`. Also, the static dielectric constant .. math:: \varepsilon = 1 + \frac{\langle M^2 \rangle - \langle M \rangle^2} {3 \varepsilon_ 0 V k_B T} is calculated for a system in tin foil boundary conditions, which is the usual case if electrostatics are handled with a Ewald summation technique. See [Neumann1983]_ for details on the derivation. Parameters ---------- atomgroup : MDAnalysis.core.groups.AtomGroup Atomgroup on which the analysis is executed temperature : float Temperature (Kelvin) at which the system has been simulated make_whole : bool Make molecules whole; If the input already contains whole molecules this can be disabled to gain speedup verbose : bool Show detailed progress of the calculation Attributes ---------- results.M : numpy.ndarray Directional dependant dipole moment :math:`\langle \boldsymbol M \rangle` in :math:`eÅ`. results.M2 : numpy.ndarray Directional dependant squared dipole moment :math:`\langle \boldsymbol M^2 \rangle` in :math:`(eÅ)^2` results.fluct : float Directional dependant dipole moment fluctuation :math:`\langle \boldsymbol M^2 \rangle - \langle \boldsymbol M \rangle^2` in :math:`(eÅ)^2` results.eps : numpy.ndarray Directional dependant static dielectric constant results.eps_mean : float Static dielectric constant Example ------- Create a :class:`DielectricConstant` instance by supplying an :class:`~MDAnalysis.core.groups.AtomGroup`, then use the :meth:`run` method:: import MDAnalysis as mda from MDAnalysis.analysis.dielectric import DielectricConstant from MDAnalysisTests.datafiles import PSF_TRICLINIC, DCD_TRICLINIC # Load a pure water system universe = mda.Universe(PSF_TRICLINIC, DCD_TRICLINIC) diel = DielectricConstant(universe.atoms) print(diel.results) The static dielectric constant of the provided atomgroup is saved within the :class:`~MDAnalysis.analysis.base.Results` attribute. .. versionadded:: 2.1.0 """ def __init__(self, atomgroup, temperature=300, make_whole=True, **kwargs): super(DielectricConstant, self).__init__(atomgroup.universe.trajectory, **kwargs) self.atomgroup = atomgroup self.temperature = temperature self.make_whole = make_whole def _prepare(self): if not hasattr(self.atomgroup, "charges"): raise NoDataError("No charges defined given atomgroup.") if not np.allclose(self.atomgroup.total_charge(compound='fragments'), 0.0, atol=1E-5): raise NotImplementedError("Analysis for non-neutral systems or" " systems with free charges are not" " available.") self.volume = 0 self.results.M = np.zeros(3) self.results.M2 = np.zeros(3) self.results.fluct = np.zeros(3) self.results.eps = np.zeros(3) self.results.eps_mean = 0 def _single_frame(self): if self.make_whole: self.atomgroup.unwrap() self.volume += self.atomgroup.universe.trajectory.ts.volume M =, self.atomgroup.positions) self.results.M += M self.results.M2 += M * M def _conclude(self): self.results.M /= self.n_frames self.results.M2 /= self.n_frames self.volume /= self.n_frames self.results.fluct = self.results.M2 - self.results.M * self.results.M self.results.eps = self.results.fluct / ( convert(constants["Boltzman_constant"], "kJ/mol", "eV") * self.temperature * self.volume * constants["electric_constant"]) self.results.eps_mean = self.results.eps.mean() self.results.eps += 1 self.results.eps_mean += 1