Source code for chemtools.conceptual.exponential

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"""Conceptual Density Functional Theory (DFT) Reactivity Tools Based on Exponential Energy Model.

This module contains the global tool class corresponding to exponential energy models.

import math
import numpy as np

from chemtools.conceptual.base import BaseGlobalTool
from chemtools.conceptual.utils import check_dict_values, check_number_electrons
from chemtools.utils.utils import doc_inherit

__all__ = ["ExponentialGlobalTool"]

[docs]class ExponentialGlobalTool(BaseGlobalTool): r""" Class of global conceptual DFT reactivity descriptors based on the exponential energy model. The energy is approximated as a exponential function of the number of electrons, .. math:: E(N) = A \exp(-\gamma(N-N_0)) + B Given :math:`E(N_0 - 1)`, :math:`E(N_0)` and :math:`E(N_0 + 1)` values, the unknown parameters of the energy model are obtained by interpolation. The :math:`n^{\text{th}}`-order derivative of the rational energy model with respect to the number of electrons at fixed external potential is given by: .. math:: \left(\frac{\partial^n E}{\partial N^n}\right)_{v(\mathbf{r})} = A (-\gamma)^n \exp(-\gamma (N - N_0)) """ def __init__(self, dict_energy): r"""Initialize exponential energy model to compute global reactivity descriptors. Parameters ---------- dict_energy : dict Dictionary of number of electrons (keys) and corresponding energy (values). This model expects three energy values corresponding to three consecutive number of electrons differing by one, i.e. :math:`\{(N_0 - 1): E(N_0 - 1), N_0: E(N_0), (N_0 + 1): E(N_0 + 1)\}`. The :math:`N_0` value is considered as the reference number of electrons. """ # check number of electrons & energy values n_ref, energy_m, energy_0, energy_p = check_dict_values(dict_energy) # check energy values if not energy_m > energy_0 > energy_p: energies = [energy_m, energy_0, energy_p] raise ValueError("For exponential model, the energy values for consecutive number of " "electrons should be monotonic! E={0}".format(energies)) # calculate parameters A, B, gamma parameters of the exponential model param_a = (energy_m - energy_0) * (energy_0 - energy_p) param_a /= (energy_m - 2 * energy_0 + energy_p) param_b = energy_0 - param_a param_g = (energy_m - 2 * energy_0 + energy_p) / (energy_p - energy_0) param_g = math.log(1. - param_g) self._params = [param_a, param_g, param_b] # calculate N_max n_max = float("inf") super(ExponentialGlobalTool, self).__init__(n_ref, n_max) self.dict_energy = dict_energy @property def params(self): r"""Parameter :math:`A`, :math:`\gamma` and :math:`B` of energy model.""" return self._params
[docs] @doc_inherit(BaseGlobalTool) def energy(self, n_elec): # check n_elec argument check_number_electrons(n_elec, self._n0 - 1, self._n0 + 1) # evaluate energy if np.isinf(n_elec): # limit of E(N) as N goes to infinity equals B value = self._params[2] else: dn = n_elec - self._n0 value = self._params[0] * math.exp(- self._params[1] * dn) + self._params[2] return value
[docs] @doc_inherit(BaseGlobalTool) def energy_derivative(self, n_elec, order=1): # check n_elec argument check_number_electrons(n_elec, self._n0 - 1, self._n0 + 1) # check order if not (isinstance(order, int) and order > 0): raise ValueError("Argument order should be an integer greater than or equal to 1.") # evaluate derivative if np.isinf(n_elec): # limit of E(N) derivatives as N goes to infinity equals zero deriv = 0.0 else: dn = n_elec - self._n0 deriv = self._params[0] * (- self._params[1])**order * math.exp(- self._params[1] * dn) return deriv