Geometric functions

class nmrcryspy.geometric.Distance_Function(distance_measures: Optional[dict] = None)

Bases: object

Distance_Function class used to calculate the distance and gradients between atoms in the structure.

distance_measures

deviation of relevant bond distance types. Example: {‘SiO’:{‘mu’: 1.595, ‘sigma’: 0.011}}

Type:

Dictionary containing mean bond distance and standard

assemble_residual_and_grad(structure, data_dictionary)

Function to package the Jacobian matrix and residual vector for the Gauss_Newton_Solver class.

Parameters:

  • structure – pymatgen.Structure object used to calculate the residual and Jacobian.

  • data_dictionary – Dict of the data_dictionary attribute from the Gauss_Newton_Solver which contains the ML data.

Returns: np.ndarray, np.array

calculate_gradients(idx_1, idx_2, structure, structure_e, epsilon, bond_type, mic=True)

Function to calculate the gradient and residual for processing by the assemble_residual_and_grad function.

Parameters:

  • idx_1 – integer index of atom 1

  • idx_2 – integer index of atom 2

  • structure – pymatgen.Structure

  • structure_e – pymatgen.Structure perturbed by a translation to one of the coordinates by epsilon.

  • epsilon – float of the stepsize used for calculating numerical derivatives.

  • bond_type – string denoting the type of bond

Returns: np.array

calculate_residual(idx_1, idx_2, structure, bond_type, mic=True)

Function to calculate the gradient and residual for processing by the assemble_residual_and_grad function.

Parameters:

  • idx_1 – integer index of atom 1

  • idx_2 – integer index of atom 2

  • structure – pymatgen.Structure

  • bond_type – string denoting the type of bond

Returns: np.array

make_symmetry_dictionary(structure)

Given the structure, finds the mapping between the atoms in the complete cell and the base atoms. Returns a dictionary where each entry is an atom in the structure, its symmetry operation, and the original atom it is derived from.

Parameters:

structure – pymatgen.Structure object to derive symmetry dictionary from.

Returns: list

perturb_structure(initial_structure, sym_dict, x_prime, epsilon=1e-05)

Applies a translation to one of the atom sites for the calculation of numerical derivatives.

Parameters:

  • initial_structure – pymatgen.Structure object of the original structure

  • sym_dict – dictionary of symmetry operation mappings to the atoms in the structure

  • x_prime – np.ndarray for the perturbation vector.

  • epsilon – float of the scaling parameter for the perturbation vector.

Returns: pymatgen.Structure