Source code for mchammer.ensembles.thermodynamic_integration_ensemble

from mchammer.free_energy_tools \
        import (_lambda_function_forward, _lambda_function_backward)

from ase import Atoms
from ase.units import kB
from typing import List

from .thermodynamic_base_ensemble import ThermodynamicBaseEnsemble
from ..calculators.base_calculator import BaseCalculator
from .. import DataContainer
from icet.input_output.logging_tools import logger

logger = logger.getChild('thermodynamic_integration_ensemble')

[docs] class ThermodynamicIntegrationEnsemble(ThermodynamicBaseEnsemble): r"""Instances of this class allow one to find the free energy of the system. To this end, we use the :class:`canonncal ensemble <mchammer.ensembles.CanonicalEnsemble>` with a modified Hamiltonian, .. math:: H(\lambda) = (1 - \lambda) H_{A} + \lambda H_{B} The Hamiltonian is then sampled continuously from :math:`\lambda=0` to :math:`\lambda=1`. :math:`H_{B}` is your cluster expansion and :math:`H_{A}=0`, is a completely disordered system, with free energy given by the ideal mixing entropy. The free energy, A, of system B is then given by: .. math:: A_{B} = A_{A} + \int_{0}^{1} \left\langle\frac{\mathrm{d}H(\lambda)} {\mathrm{d}\lambda}\right\rangle_{H} \mathrm{d}\lambda and since :math:`A_{A}` is known it is easy to compute :math:`A_{B}` :math:`\lambda` is parametrized as, .. math:: \lambda(x) = x^5(70x^4 - 315x^3 + 540x^2 - 420x + 126) where :math:`x = \mathrm{step} / (\mathrm{n\_steps} - 1)`. Parameters ---------- structure Atomic configuration to be used in the Monte Carlo simulation; also defines the initial occupation vector. calculator Calculator to be used for calculating the potential changes that enter the evaluation of the Metropolis criterion. temperature Temperature :math:`T` in appropriate units, commonly Kelvin. n_lambdas Number of :math:`\lambda` values to be sampled between 0 and 1. forward If this is set to ``True`` the simulation runs from :math:`H_A` to :math:`H_B`, otherwise it runs from :math:`H_B` to :math:`H_A`. :math:`H_B` is the cluster expansion and :math:`H_A = 0`, is the fully disordered system. boltzmann_constant Boltzmann constant :math:`k_B` in appropriate units, i.e., units that are consistent with the underlying cluster expansion and the temperature units. Default: eV/K. user_tag Human-readable tag for ensemble. Default: ``None``. random_seed Seed for the random number generator used in the Monte Carlo simulation. dc_filename Name of file the data container associated with the ensemble will be written to. If the file exists it will be read, the data container will be appended, and the file will be updated/overwritten. data_container_write_period Period in units of seconds at which the data container is written to file. Writing periodically to file provides both a way to examine the progress of the simulation and to back up the data. Default: 600 s. ensemble_data_write_interval Interval at which data is written to the data container. This includes for example the current value of the calculator (i.e., usually the energy) as well as ensembles specific fields such as temperature or the number of atoms of different species. Default: Number of sites in the :attr:`structure`. trajectory_write_interval Interval at which the current occupation vector of the atomic configuration is written to the data container. Default: Number of sites in the :attr:`structure`. sublattice_probabilities Probability for picking a sublattice when doing a random swap. This should be as long as the number of sublattices and should sum up to 1. Example ------- The following snippet illustrate how to carry out a simple thermodynamic integration. Here, the parameters of the cluster expansion are set to emulate a simple Ising model in order to obtain an example that can be run without modification. In practice, one should of course use a proper cluster expansion:: >>> from import bulk >>> from icet import ClusterExpansion, ClusterSpace >>> from mchammer.calculators import ClusterExpansionCalculator >>> # prepare cluster expansion >>> # the setup emulates a second nearest-neighbor (NN) Ising model >>> # (zerolet and singlet ECIs are zero; only first and second neighbor >>> # pairs are included) >>> prim = bulk('Au') >>> cs = ClusterSpace(prim, cutoffs=[4.3], chemical_symbols=['Ag', 'Au']) >>> ce = ClusterExpansion(cs, [0, 0, 0.1, -0.02]) >>> # prepare initial configuration >>> structure = prim.repeat(3) >>> for k in range(5): >>> structure[k].symbol = 'Ag' >>> # set up and run MC simulation >>> calc = ClusterExpansionCalculator(structure, ce) >>> mc = ThermodynamicIntegrationEnsemble(structure=structure, calculator=calc, ... temperature=600, ... n_steps=100000, ... forward=True, ... dc_filename='myrun_thermodynamic_integration.dc') >>> """ def __init__(self, structure: Atoms, calculator: BaseCalculator, temperature: float, n_steps: int, forward: bool, user_tag: str = None, boltzmann_constant: float = kB, random_seed: int = None, dc_filename: str = None, data_container: str = None, data_container_write_period: float = 600, ensemble_data_write_interval: int = None, trajectory_write_interval: int = None, sublattice_probabilities: List[float] = None, ) -> None: self._ensemble_parameters = dict(temperature=temperature, n_steps=n_steps) self._last_state = dict() super().__init__( structure=structure, calculator=calculator, user_tag=user_tag, random_seed=random_seed, data_container=data_container, dc_filename=dc_filename, data_container_class=DataContainer, data_container_write_period=data_container_write_period, ensemble_data_write_interval=ensemble_data_write_interval, trajectory_write_interval=trajectory_write_interval, boltzmann_constant=boltzmann_constant) if sublattice_probabilities is None: self._swap_sublattice_probabilities = \ self._get_swap_sublattice_probabilities() else: self._swap_sublattice_probabilities = sublattice_probabilities sublattices = [] for sl in self.sublattices: sublattices.append(sl.atomic_numbers) # add species count to ensemble parameters symbols = set([symbol for sub in calculator.sublattices for symbol in sub.chemical_symbols]) for symbol in symbols: key = 'n_atoms_{}'.format(symbol) count = structure.get_chemical_symbols().count(symbol) self._ensemble_parameters[key] = count self._n_steps = n_steps if forward: self._lambda_function = _lambda_function_forward self._lambda = 0 else: self._lambda_function = _lambda_function_backward self._lambda = 1 @property def temperature(self) -> float: """ Current temperature. """ return self._ensemble_parameters['temperature'] @property def n_steps(self) -> int: return self._n_steps def _do_trial_step(self): """ Carries out one Monte Carlo trial step. """ self._lambda = self._lambda_function(self.n_steps, self.step) sublattice_index = self.get_random_sublattice_index(self._swap_sublattice_probabilities) swap = self.do_thermodynamic_swap(sublattice_index=sublattice_index, lambda_val=self._lambda) return swap
[docs] def run(self): """ Runs the thermodynamic integration. """ if self.step >= self.n_steps: logger.warning('The simulation is already done') else: super().run(self.n_steps - self.step)
def _get_ensemble_data(self): data = super()._get_ensemble_data() data['lambda'] = self._lambda return data