chemtools.conceptual.mixed.MixedCondensedTool

class chemtools.conceptual.mixed.MixedCondensedTool(dict_energy, dict_population)[source]

Class of condensed conceptual DFT reactivity descriptors based on mixed energy models.

Initialize to compute mixed condensed 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. \(\{(N_0 - 1): E(N_0 - 1), N_0: E(N_0), (N_0 + 1): E(N_0 + 1)\}\). The \(N_0\) value is considered as the reference number of electrons.
  • dict_population (dict) – Dictionary of number of electrons (keys) and corresponding atomic population array (values). This model expects three atomic populations corresponding to three consecutive number of electrons differing by one, i.e. \(\{(N_0 - 1): \{p^{(N_0 - 1)}_A\}, N_0: \{p^{(N_0)}_A\}, N_0 + 1: \{p^{(N_0 + 1)}_A\}\}\). The \(N_0\) value is considered as the reference number of electrons.
softness_yp

Condensed softness of Yang and Parr.

Atom-condensed implementation of local MixedLocalTool.softness_yp:

\[\begin{split}s^+_A &= S \text{ } f^+_A \\ s^0_A &= S \text{ } f^0_A \\ s^-_A &= S \text{ } f^-_A\end{split}\]

where \(f^{+,0,-}_A\) is condensed Fukui function from the linear energy model, and \(S={}^1/_{\eta}\) is global chemical softness (inverse of global chemical hardness) from the quadratic energy model.

Returns:
  • softness_p (ndarray) – Condensed softness from above measuring nucleophilic attack, \(\{s^+_A\}_{A=1}^{N_{\text{atoms}}}\).
  • softness_0 (ndarray) – Condensed softness (centered) measuring radical attack, \(\{s^0_A\}_{A=1}^{N_{\text{atoms}}}\).
  • softness_m (ndarray) – Condensed softness from below measuring electrophilic attack, \(\{s^-_A\}_{A=1}^{N_{\text{atoms}}}\).
philicity_mgvgc

Condensed philicity measure of Morell, Gazquez, Vela, Guegana & Chermette.

Atom-condensed implementation of local MixedLocalTool.philicity_mgvgc:

\[\begin{split}\omega^+_A &= -\left(\frac{\mu^+}{\eta}\right) f^+_A + \frac{1}{2} \left(\frac{\mu^+}{\eta}\right)^2 f^{(2)}_A \\ \omega^0_A &= -\left(\frac{\mu^0}{\eta}\right) f^0_A + \frac{1}{2} \left(\frac{\mu^0}{\eta}\right)^2 f^{(2)}_A \\ \omega^-_A &= +\left(\frac{\mu^-}{\eta}\right) f^-_A + \frac{1}{2} \left(\frac{\mu^-}{\eta}\right)^2 f^{(2)}_A\end{split}\]

where \(\mu^{+,0,-}\) is global chemical potential from the linear energy model, \(\eta\) is global chemical hardness from the quadratic energy model, \(f^{+,0,-}_A\) is condensed Fukui function from the linear energy model, and \(f^{(2)}_A\) is condensed dual descriptor from the quadratic energy model.

Returns:
  • omega_p (ndarray) – Local philicity index from above measuring nucleophilic attack, \(\{\omega^+_A\}_{A=1}^{N_{\text{atoms}}}\).
  • omega_0 (ndarray) – Local philicity index (centered) measuring radical attack, \(\{\omega^0_A\}_{A=1}^{N_{\text{atoms}}}\).
  • omega_m (ndarray) – Local philicity index from below measuring electrophilic attack, \(\{\omega^-_A\}_{A=1}^{N_{\text{atoms}}}\).
philicity_cms

Condensed philicity index of Chattaraj, Maiti & Sarkar.

Atom-condensed implementation of local MixedLocalTool.philicity_cms:

\[\begin{split}\omega^+_A &= \omega \text{ } f^+_A \\ \omega^0_A &= \omega \text{ } f^0_A \\ \omega^-_A &= \omega \text{ } f^-_A\end{split}\]

where \(f^{+,0,-}_A\) is condensed Fukui function from linear energy model, and \(\omega\) is global electrophilicity from quadratic energy model.

Returns:
  • omega_p (ndarray) – Condensed philicity index from above measuring nucleophilic attack, \(\{\omega^+_A\}_{A=1}^{N_{\text{atoms}}}\).
  • omega_0 (ndarray) – Condensed philicity index (centered) measuring radical attack, \(\{\omega^0_A\}_{A=1}^{N_{\text{atoms}}}\).
  • omega_m (ndarray) – Condensed philicity index from below measuring electrophilic attack, \(\{\omega^-_A\}_{A=1}^{N_{\text{atoms}}}\).
philicity_rkgp

Relative electrophilicity & nucleophilicity of Roy, Krishnamurti, Geerlings & Pal.

Based on J. Phys. Chem. A (1998), 102, 3746–3755:

\[\begin{split}\epsilon_{\text{electrophilicity}, A} &= \frac{s^+_A}{s^-_A} = \frac{f^+_A}{f^-_A} \\ \epsilon_{\text{nucleophilicity}, A} &= \frac{s^-_A}{s^+_A} = \frac{f^-_A}{f^+_A}\end{split}\]
Returns:
  • epsilon_e (ndarray) – Condensed relative electrophilicity, \(\epsilon_{\text{electrophilicity},A}\).
  • epsilon_n (ndarray) – Condensed relative nucleophilicity, \(\epsilon_{\text{nucleophilicity},A}\).