Electrostatic interactions#
Second order#
Isotropic electrostatics#
The isotropic electrostatic in a shell-resolved formulation is given by the parametrized Coulomb interaction between shellwise partial charges
The interaction potential is parametrized by a Klopman–Ohno type potential in the xTB Hamiltonian or the γ-functional as used in the DFTB Hamiltonian.
Klopman–Ohno kernel#
The interaction kernel for the Klopman–Ohno electrostatic is given by
where η:sub:A/B are the chemical hardness parameters of the respective shells and g is the exponent to manipulate the potential shape.
γ-functional kernel#
The interaction kernel for the DFTB γ-functional is derived from the integral of two exponential densities
where τ:sub:A/B are scaled Hubbard parameters of the respective shells and R is the distance between the atomic sides.
Anisotropic electrostatics#
The anisotropic electrostatic in an atom-resolved formulation is given by the multipole interactions between the different moments:
Third order#
The isotropic third-order contributions are included as the trace of the on-site shell-resolved Hubbard derivatives.