Source code for MMTK.NormalModes.EnergeticModes

# Energetic normal mode calculations.
#
# Written by Konrad Hinsen
#

"""
Energetic normal modes
"""

__docformat__ = 'restructuredtext'

from MMTK import Features, Units, ParticleProperties
from MMTK.NormalModes import Core
from Scientific import N

#
# Class for a single mode
#
[docs]class EnergeticMode(Core.Mode): """ Single energetic normal mode Mode objects are created by indexing a :class:`MMTK.NormalModes.EnergeticModes.EnergeticModes` object. They contain the atomic displacements corresponding to a single mode. In addition, the force constant corresponding to the mode is stored in the attribute "force_constant". """ def __init__(self, universe, n, force_constant, mode): self.force_constant = force_constant Core.Mode.__init__(self, universe, n, mode) def __str__(self): return 'Mode ' + `self.number` + ' with force constant ' + \ `self.force_constant` __repr__ = __str__ # # Class for a full set of normal modes #
[docs]class EnergeticModes(Core.NormalModes): """ Energetic modes describe the principal axes of an harmonic approximation to the potential energy surface of a system. They are obtained by diagonalizing the force constant matrix without prior mass-weighting. In order to obtain physically reasonable normal modes, the configuration of the universe must correspond to a local minimum of the potential energy. Individual modes (see class :class:`~MMTK.NormalModes.EnergeticModes.EnergeticMode`) can be extracted by indexing with an integer. Looping over the modes is possible as well. """ features = [] def __init__(self, universe=None, temperature = 300*Units.K, subspace = None, delta = None, sparse = False): """ :param universe: the system for which the normal modes are calculated; it must have a force field which provides the second derivatives of the potential energy :type universe: :class:`~MMTK.Universe.Universe` :param temperature: the temperature for which the amplitudes of the atomic displacement vectors are calculated. A value of None can be specified to have no scaling at all. In that case the mass-weighted norm of each normal mode is one. :type temperature: float :param subspace: the basis for the subspace in which the normal modes are calculated (or, more precisely, a set of vectors spanning the subspace; it does not have to be orthogonal). This can either be a sequence of :class:`~MMTK.ParticleProperties.ParticleVector` objects or a tuple of two such sequences. In the second case, the subspace is defined by the space spanned by the second set of vectors projected on the complement of the space spanned by the first set of vectors. The first set thus defines directions that are excluded from the subspace. The default value of None indicates a standard normal mode calculation in the 3N-dimensional configuration space. :param delta: the rms step length for numerical differentiation. The default value of None indicates analytical differentiation. Numerical differentiation is available only when a subspace basis is used as well. Instead of calculating the full force constant matrix and then multiplying with the subspace basis, the subspace force constant matrix is obtained by numerical differentiation of the energy gradients along the basis vectors of the subspace. If the basis is much smaller than the full configuration space, this approach needs much less memory. :type delta: float :param sparse: a flag that indicates if a sparse representation of the force constant matrix is to be used. This is of interest when there are no long-range interactions and a subspace of smaller size then 3N is specified. In that case, the calculation will use much less memory with a sparse representation. :type sparse: bool """ if universe == None: return Features.checkFeatures(self, universe) Core.NormalModes.__init__(self, universe, subspace, delta, sparse, ['array', 'force_constants']) self.temperature = temperature self.weights = N.ones((1, 1), N.Float) self._forceConstantMatrix() ev = self._diagonalize() self.force_constants = ev self.sort_index = N.argsort(self.force_constants) self.array.shape = (self.nmodes, self.natoms, 3) self.cleanup() def __getitem__(self, item): index = self.sort_index[item] f = self.force_constants[index] #!! if self.temperature is None or item < 6: amplitude = 1. else: amplitude = N.sqrt(2.*self.temperature*Units.k_B / self.force_constants[index]) return EnergeticMode(self.universe, item, self.force_constants[index], amplitude*self.array[index])
[docs] def rawMode(self, item): """ :param item: the index of a normal mode :type item: int :returns: the unscaled mode vector :rtype: :class:`~MMTK.NormalModes.EnergeticModes.EnergeticMode` """ index = self.sort_index[item] f = self.force_constants[index] return EnergeticMode(self.universe, item, self.force_constants[index], self.array[index])
def fluctuations(self, first_mode=6): f = ParticleProperties.ParticleScalar(self.universe) for i in range(first_mode, self.nmodes): mode = self.rawMode(i) f += (mode*mode)/mode.force_constant if self.temperature is not None: f.array *= Units.k_B*self.temperature return f def anisotropicFluctuations(self, first_mode=6): f = ParticleProperties.ParticleTensor(self.universe) for i in range(first_mode, self.nmodes): mode = self.rawMode(i) array = mode.array f.array += (array[:, :, N.NewAxis]*array[:, N.NewAxis, :]) \ / mode.force_constant if self.temperature is not None: f.array *= Units.k_B*self.temperature return f