Diagonalization of Kernels

The non condensed kernel can be computed and their eigenmodes analyzed.

For now, only the linear response function kernel has been implemented.

Linear Response Function Kernel

The linear response function kernel can be computed as :

\(\chi(r,r') = -2\sum_{k\neq0} \frac{\rho_0^k(r) \rho_0^k(r')}{E_k-E_0}\)

With \(\rho_0^k\) the transition density, and \(E_k\) the energy of the transition k.

Therefore, the linear response function kernel can be computed using the MO calculated from molden file combined with the extraction of the coefficients from a TD-DFT calculation.

If one wants to use Orca for the TD-DFT calculation, triplets states should not be included and the keyword TPRINT 0.00001 will allow more transitions to be printed.

The eigenmodes are sorted by eigenvalues. They can be selected using a slider. A script contaning all the examples can be found here.

Only the eigenmodes are computed using this method.

The following code is an example of the diagonalization of the linear response function kernel

import rgmol
import rgmol.examples

file = rgmol.examples.molden_H2CO
mol = rgmol.extract_molden.extract(file,do_order_bonds=1)
rgmol.extract_orca.extract_transition(rgmol.examples.orca_H2CO,mol=mol)
mol.plot_diagonalized_kernel(kernel="linear_response_function")

Softness Kernel

Using the Parr-Berkowitz relation, one can compute the softness kernel from the linear response, the fukui functions and the hardness of the molecule.

\(s(r,r') = -\chi(r,r') + \frac{f(r)f(r')}{\eta}\)

One needs to look at the computation of the linear response function, and the fukui function in order to know which arguments and calculations has to be made.

The following code is an example of the diagonalization of the softness kernel

import rgmol
import rgmol.examples

file = rgmol.examples.molden_H2CO
mol = rgmol.extract_molden.extract(file,do_order_bonds=1)
rgmol.extract_orca.extract_transition(rgmol.examples.orca_H2CO,mol=mol)

file_m = rgmol.examples.molden_H2CO_m
mol_m = rgmol.extract_molden.extract(file,do_order_bonds=1)

mol.plot_diagonalized_kernel(kernel="softness_kernel",mol_m=mol_m,fukui_type="f-")