# chemtools.conceptual.mixed.MixedLocalTool¶

class chemtools.conceptual.mixed.MixedLocalTool(dict_energy, dict_density)[source]

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

Initialize to compute mixed local 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_density (dict) – Dictionary of number of electrons (keys) and corresponding density array (values). This model expects three energy values corresponding to three consecutive number of electrons differing by one, i.e. $$\{(N_0 - 1): \rho_{N_0 - 1}\left(\mathbf{ r}\right), N_0: \rho_{N_0}\left(\mathbf{r}\right), (N_0 + 1): \rho_{N_0 + 1}\left( \mathbf{r}\right)\}$$. The $$N_0$$ value is considered as the reference number of electrons.
softness_yp

Local softness of Yang and Parr.

Equation [18] of Proc. Natl. Acad. Sci. USA (1985) 82, 6723-6726:

$\begin{split}s^+(\mathbf{r}) &= S f^+(\mathbf{r}) \\ s^0(\mathbf{r}) &= S f^0(\mathbf{r}) \\ s^-(\mathbf{r}) &= S f^-(\mathbf{r})\end{split}$

where $$f^{+,0,-}(\mathbf{r})$$ is 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) – Local softness from above measuring nucleophilic attack, $$s^+(\mathbf{r})$$. softness_0 (ndarray) – Local softness (centered) measuring radical attack, $$s^0(\mathbf{r})$$. softness_m (ndarray) – Local softness from below measuring electrophilic attack, $$s^-(\mathbf{r})$$.
philicity_mgvgc

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

Equation [46], [15] & [47] of Phys. Chem. Chem. Phys. (2014) 16, 26832-26842:

$\begin{split}\omega^+(\mathbf{r}) &= -(\frac{\mu^+}{\eta}) f^+(\mathbf{r}) + \frac{1}{2} \left(\frac{\mu^+}{\eta}\right)^2 f^{(2)}(\mathbf{r}) \\ \omega^0(\mathbf{r}) &= -(\frac{\mu^0}{\eta}) f^0(\mathbf{r}) + \frac{1}{2} \left(\frac{\mu^0}{\eta}\right)^2 f^{(2)}(\mathbf{r}) \\ \omega^-(\mathbf{r}) &= +(\frac{\mu^-}{\eta}) f^-(\mathbf{r}) + \frac{1}{2} \left(\frac{\mu^-}{\eta}\right)^2 f^{(2)}(\mathbf{r})\end{split}$

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

Returns: omega_p (ndarray) – Local philicity index from above measuring nucleophilic attack, $$\omega^+(\mathbf{r})$$. omega_0 (ndarray) – Local philicity index (centered) measuring radical attack, $$\omega^0(\mathbf{r})$$. omega_m (ndarray) – Local philicity index from below measuring electrophilic attack, $$\omega^-(\mathbf{r})$$.
philicity_cms

Local philicity index of Chattaraj, Maiti & Sarkar.

Equation [12] of J. Phys. Chem. A (2003) 107, 4973–4975:

$\begin{split}\omega^+(\mathbf{r}) &= \omega \text{ } f^+(\mathbf{r}) \\ \omega^0(\mathbf{r}) &= \omega \text{ } f^0(\mathbf{r}) \\ \omega^-(\mathbf{r}) &= \omega \text{ } f^-(\mathbf{r})\end{split}$

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

Returns: omega_p (ndarray) – Local philicity index from above measuring nucleophilic attack, $$\omega^+(\mathbf{r})$$. omega_0 (ndarray) – Local philicity index (centered) measuring radical attack, $$\omega^0(\mathbf{r})$$. omega_m (ndarray) – Local philicity index from below measuring electrophilic attack, $$\omega^-(\mathbf{r})$$.