Source code for chemtools.conceptual.cubic

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

This module contains the global and local tool classes corresponding to cubic energy models.
"""


import numpy as np

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


__all__ = ["CubicGlobalTool"]


[docs]class CubicGlobalTool(BaseGlobalTool): r""" Class of global conceptual DFT reactivity descriptors based on the cubic energy model. The energy is approximated as a quadratic function of the number of electrons, .. math:: E(N) = a + b N + c N^2 + d N^3 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. First, second and higher order derivatives of the cubic energy model with respect to the number of electrons at fixed external potential are given by: .. math:: \left(\frac{\partial E}{\partial N}\right)_{v(\mathbf{r})} &= b + 2 c N + 3 d N^2\\ \left(\frac{\partial^2 E}{\partial N^2}\right)_{v(\mathbf{r})} &= 2 c + 6 d N\\ \left(\frac{\partial^3 E}{\partial N^3}\right)_{v(\mathbf{r})} &= 6 d \\ \left(\frac{\partial^n E}{\partial N^n}\right)_{v(\mathbf{r})} &= 0 \quad \text{for} \quad n \geq 3 """ def __init__(self, dict_energy, omega=0.5): r"""Initialize cubic 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. omega : float Value of omega parameter in the energy model. """ # check number of electrons & energy values n_ref, energy_m, energy_0, energy_p = check_dict_values(dict_energy) # compute parameters of energy model param_a = energy_0 param_b = -omega * energy_m + 2. * omega * energy_0 - omega * energy_p param_b += energy_p - energy_0 param_c = (energy_m - 2. * energy_0 + energy_p) / 2. param_d = (2. * omega - 1.) * (energy_m - 2. * energy_0 + energy_p) / 2. self._omega = omega self._params = np.array([param_a, param_b, param_c, param_d]) super(CubicGlobalTool, self).__init__(n_ref, None) self.dict_energy = dict_energy @property def omega(self): r"""Parameter :math:`\omega` in the energy model.""" return self._omega @property def params(self): r"""Parameters :math:`a`, :math:`b`, :math:`c`, and :math:`d` 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) # compute the change in the number of electrons w.r.t. N0 delta_n = n_elec - self._n0 # compute energy result = self._params[0] + self._params[1] * delta_n + self._params[2] * delta_n ** 2 result += self._params[3] * delta_n ** 3. return result
[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.") # compute the change in the number of electrons w.r.t. N0 delta_n = n_elec - self._n0 # compute derivative of energy if order == 1: result = self._params[1] + 2. * self._params[2] * delta_n + \ 3. * self._params[3] * delta_n ** 2. elif order == 2: result = 2. * self._params[2] + 6. * self._params[3] * delta_n elif order == 3: result = 6. * self._params[3] else: result = 0 return result