sk_builder.slater_koster_onsite

Implementation of Slater-Koster on-site matrices.

This module provides implementations for on-site Slater-Koster matrix elements., i.e., the part of the Hamiltonian describing atomic energy levels on a single atom and local crystal field corrections due to neighboring atoms.

@private

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def get_orbital_energies_diagonal(sk_params: dict, species: str) -> numpy.ndarray:

Return orbital energies for given species.

Arguments:
  • sk_params (dict): Dictionary containing Slater-Koster parameters.
  • species (str): String indicating the species of the atom.
Returns:

np.ndarray: (Diagonal) entries for orbital energies of atom.

def get_e0(sk_params: dict, species: str, orb: str) -> float:

Returns onsite energy.

Arguments:
  • sk_params (dict): Dictionary containing Slater-Koster parameters.
  • species (str): String denoting the atomic species.
  • orb (str): String labeling the atomic orbital.
Raises:
  • ValueError: If atom species is not supported.
Returns:

float: Onsite energy of atomic orbital

def get_coupling_matrix( displacement: numpy.ndarray, bond_type: str, sk_params: dict) -> numpy.ndarray:

Return "on site" coupling matrix due to single neigbor.

Arguments:
  • displacement (np.ndarray): Displacement vector to neigboring atoms.
  • bond_type (str): Atomic species connected by the bond as string, e.g., "Si-Ge".
  • sk_params (dict): Dictionary containing Slater-Koster parameters.
Returns:

np.ndarray: 10x10 matrix of "on site" coupling elements.

def get_s_s_block( displacement: numpy.ndarray, bond_type: str, sk_params: dict) -> numpy.ndarray:

Return s-s block of Slater-Koster "on site" matrix.

Arguments:
  • displacement (np.ndarray): Displacement vector between the two atoms.
  • bond_type (str): Atomic species connected by the bond as string, e.g., "Si-Ge".
  • sk_params (dict): Dictionary containing Slater-Koster parameters.
Returns:

np.ndarray: 2x2 matrix of "on site" couplings between s orbitals.

def get_s_p_block( displacement: numpy.ndarray, bond_type: str, sk_params: dict) -> numpy.ndarray:

Return s-p block of Slater-Koster "on site" matrix.

Arguments:
  • displacement (np.ndarray): Displacement vector between the two atoms.
  • bond_type (str): Atomic species connected by the bond as string, e.g., "Si-Ge".
  • sk_params (dict): Dictionary containing Slater-Koster parameters.
Returns:

np.ndarray: 2x3 matrix of "on site" couplings between s and p orbitals.

def get_s_d_block( displacement: numpy.ndarray, bond_type: str, sk_params: dict) -> numpy.ndarray:

Return s-d block of Slater-Koster "on site" matrix.

Arguments:
  • displacement (np.ndarray): Displacement vector between the two atoms.
  • bond_type (str): Atomic species connected by the bond as string, e.g., "Si-Ge".
  • sk_params (dict): Dictionary containing Slater-Koster parameters.
Returns:

np.ndarray: 2x5 matrix of "on site" couplings between s and d orbitals.

def get_p_p_block( displacement: numpy.ndarray, bond_type: str, sk_params: dict) -> numpy.ndarray:

Return p-p block of Slater-Koster "on site" matrix.

Arguments:
  • displacement (np.ndarray): Displacement vector between the two atoms.
  • bond_type (str): Atomic species connected by the bond as string, e.g., "Si-Ge".
  • sk_params (dict): Dictionary containing Slater-Koster parameters.
Returns:

np.ndarray: 3x3 matrix of "on site" couplings between p orbitals.

def get_p_d_block( displacement: numpy.ndarray, bond_type: str, sk_params: dict) -> numpy.ndarray:

Return p-d block of Slater-Koster "on site" matrix.

Arguments:
  • displacement (np.ndarray): Displacement vector between the two atoms.
  • bond_type (str): Atomic species connected by the bond as string, e.g., "Si-Ge".
  • sk_params (dict): Dictionary containing Slater-Koster parameters.
Returns:

np.ndarray: 3x5 matrix of "on site" couplings between p and d orbitals.

def get_d_d_block( displacement: numpy.ndarray, bond_type: str, sk_params: dict) -> numpy.ndarray:

Return d-d block of Slater-Koster "on site" matrix.

Arguments:
  • displacement (np.ndarray): Displacement vector between the two atoms.
  • bond_type (str): Atomic species connected by the bond as string, e.g., "Si-Ge".
  • sk_params (dict): Dictionary containing Slater-Koster parameters.
Returns:

np.ndarray: 5x5 matrix of "on site" couplings between d orbitals.