chemtools.toolbox.interactions.LOL

class chemtools.toolbox.interactions.LOL(dens, grad, ked, grid=None, trans='inverse_rational', trans_k=1, trans_a=1, denscut=0.0005)

Localized Orbital Locator (LOL) introduced by Becke and Schmider.

The LOL ratio is defined as:

$$\zeta_\text{LOL}(\mathbf{r}) = \frac{\tau_\text{TF}(\mathbf{r})}{\tau_\text{PD}(\mathbf{r})}$$

where $\tau_\text{TF}(\mathbf{r})$ and $\tau_\text{PD}(\mathbf{r})$ are Thomas-Fermi and positive-definite (Lagrangian) kinetic energy densities defined in chemtools.toolbox.kinetic.KED.

The LOL is computed by transforming the ratio:

$$\text{LOL}(\mathbf{r}) = f\left(\zeta_\text{LOL}(\mathbf{r})\right)$$

where the transformation $f$ can be:

$$\begin{split}\text{inverse_rational : } \, f(\zeta, k, a) &= 1 - \frac{1}{1 + a \, \zeta^k} \\ \text{inverse_hyperbolic: } \, f(\zeta, k, a) &= \tfrac{1}{2} \left(1 + \tanh\left(-a \left(\zeta^{-k} - \zeta^{k}\right)\right)\right)\end{split}$$

Traditionally, the ‘inverse_rational’ transformation with $k=1$ and $a=1$ is used.

Initialize class from arrays.

Parameters:

• dens (np.ndarray) – Electron density of grid points, $\rho(\mathbf{r})$.
• grad (np.ndarray) – Gradient of electron density of grid points, $\nabla \rho(\mathbf{r})$.
• ked (np.ndarray) – Positive-definite or Lagrangian kinetic energy density of grid points; $\tau_\text{PD} (\mathbf{r})$ or $G(\mathbf{r})$.
• grid (instance of Grid, optional) – Grid used for computation of LOL. Only if this a CubeGrid one can generate the scripts.
• trans (str, optional) – Type of transformation applied to LOL ratio; options are ‘inverse_rational’ or ‘inverse_hyperbolic’.
• trans_k (float, optional) – Parameter $k$ of transformation.
• trans_a (float, optional) – Parameter $a$ of transformation.
• denscut (float, optional) – Value of density cut. LOL value of points with density < denscut is set to zero.

classmethod from_molecule(molecule, spin='ab', index=None, grid=None, trans='inverse_rational', trans_k=1, trans_a=1, denscut=0.0005)

Initialize class from molecule.

Parameters:

• molecule (instance of Molecule class.) – Instance of Molecular class.
• spin (str, optional) – Type of occupied spin orbitals; options are ‘a’, ‘b’ & ‘ab’.
• index (int or sequence of int, optional) – Sequence of spin orbital indices to use. If None, all occupied spin orbitals are used.
• grid (instance of Grid, optional) – Grid used for computation of LOL. Only if this a CubeGrid one can generate the scripts. If None, a cubic grid is constructed from molecule with spacing=0.1 & extension=2.0.
• trans (str, optional) – Type of transformation applied to ELF ratio; options are ‘inverse_rational’ or ‘inverse_hyperbolic’.
• trans_k (float, optional) – Parameter $k$ of transformation.
• trans_a (float, optional) – Parameter $a$ of transformation.
• denscut (float, optional) – Value of density cut. LOL value of points with density < denscut is set to zero.

classmethod from_file(fname, spin='ab', index=None, grid=None, trans='inverse_rational', trans_k=1, trans_a=1, denscut=0.0005)

Initialize class from wave-function file.

Parameters:

• fname (str) – Path to a molecule’s file.
• spin (str, optional) – Type of occupied spin orbitals; options are ‘a’, ‘b’ & ‘ab’.
• index (int or sequence of int, optional) – Sequence of spin orbital indices to use. If None, all occupied spin orbitals are used.
• grid (instance of Grid, optional) – Grid used for computation of LOL. Only if this a CubeGrid one can generate the scripts. If None, a cubic grid is constructed from molecule with spacing=0.1 & extension=2.0.
• trans (str, optional) – Type of transformation applied to LOL ratio; options are ‘inverse_rational’ or ‘inverse_hyperbolic’.
• trans_k (float, optional) – Parameter $k$ of transformation.
• trans_a (float, optional) – Parameter $a$ of transformation.
• denscut (float, optional) – Value of density cut. LOL value of points with density < denscut is set to zero.

ratio

The LOL ratio evaluated on the grid points.

value

The $\text{LOL}(\mathbf{r})$ evaluated on grid points.

generate_scripts(fname, isosurf=0.5)

Generate VMD scripts & cube file to visualize LOL iso-surface.

Parameters:

• fname (str) – A string representing the path to a fname of generated files. The VMD script and cube file will be named fname.vmd and fname-lol.cube, respectively.
• isosurf (float) – Value of LOL iso-surface used in VMD script.