molecule.calculate_softness_kernel_eigenmodes#

molecule.calculate_softness_kernel_eigenmodes(fukui_type='0', mol_p=None, mol_m=None)#

Calculates the softness kernel from the transition densities and the fukui function using the Parr-Berkowitz relation. For that, a calculation adding (mol_p) or removing an electron (mol_m) needs to be done with the same geometry. This method does not calculate directly the softness kernel, but only the eigenmodes. The mathematics behind this function will soon be available somewhere…

Parameters:

  • mol_p (molecule, optional) – The molecule with an electron added. Needed for calculating the softness kernel with a fukui_type of “0” or “+”

  • mol_n (molecule, optional) – The molecule with an electron removed. Needed for calculating the softness kernel with a fukui_type of “0” or “-”

  • fukui_type (molecule, optional) – The type of fukui function used to calculate the softness kernel. The available types are “0”, “+” or “-”

Returns:

  • linear_response_eigenvalues – the eigenvalues of the linear response function

  • linear_response_eigenvectors – the eigenvectors of the linear response function

Notes

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 molecule needs the transition properties that can be extracted from a TD-DFT calculation, and the MO extracted from a molden file. More details can be found here.