cctk.helper_functions

Miscellaneous helper functions.

Functions

align_matrices(P_partial, P_full, Q_partial)	Rotates one set of points onto another using the Kabsch algorithm.
bytes_to_numpy(arr_bytes)	Utility function for unpickling numpy arrays
compute_RMSD(geometry1, geometry2[, checks])	Computes the root mean squared difference between two geometries.
compute_angle_between(v1, v2[, unit])	Computes the angle between two vectors.
compute_chirality(v1, v2, v3, v4)	Given 4 bond vectors, returns 1 or -1 based on chirality.
compute_dihedral_between(p0, p1, p2, p3[, unit])	Computes the dihedral angle between four points.
compute_distance_between(v1, v2[, _norm])	Computes the L2 distance between two vectors.
compute_mass_spectrum(formula_dict, **kwargs)	Computes the expected low-res mass spec ions for a given formula.
compute_rotation_matrix(axis, theta)	Return the rotation matrix for rotation around axis by theta degrees.
compute_unit_vector(vector)	Normalizes a vector, returning a unit vector pointing in the same direction.
draw_isotopologue(z)	For an element with number z, return a weighted random atomic mass (so will return 12 99% of the time and 13 1% of the time for carbon).
formula_dict_from_string(formula_string)	Eugene challenged me to code golf, this isn't my fault.
get_avg_mass(z)	For an element with number z, return average mass of that element.
get_corrected_free_energy(free_energy, ...)	Computes the free energy by moving all positive frequencies below frequency_cutoff to the cutoff.
get_covalent_radius(atomic_number)	Gets the covalent radius for a given element.
get_entropy(frequencies, temperature)	Computes the total entropy of a given set of frequencies.
get_isotopic_distribution(z)	For an element with number z, returns two np.ndarray objects containing that element's weights and relative abundances.
get_number(atomic_symbol)	Gets atomic number from a given element symbol (converted to titlecase using string.title()).
get_symbol(atomic_number)	Gets element symbol from a given atomic number.
get_vdw_radius(atomic_number)	Gets the van der Waals radius for a given element.
get_z_from_mass(desired_mass[, tolerance])	For an element with atomic mass desired_mass, return the element's atomic number.
numpy_to_bytes(arr)	Utility function for pickling numpy arrays
scale_nmr_shifts(ensemble[, ...])	Apply linear scaling to isotropic shieldings to get chemical shifts.

cctk.helper_functions.align_matrices(P_partial, P_full, Q_partial, return_matrix=False)

Rotates one set of points onto another using the Kabsch algorithm. The rotation that best aligns P_partial into Q_partial will be found and then applied to P_full.

Parameters:

• P_partial (matrix) – atoms of P that correspond to Q

• P_full (matrix) – full matrix to rotate

• Q (matrix) – matrix to align to

Returns:

rotated P matrix

cctk.helper_functions.bytes_to_numpy(arr_bytes)

Utility function for unpickling numpy arrays

cctk.helper_functions.compute_RMSD(geometry1, geometry2, checks=True)

Computes the root mean squared difference between two geometries.

Parameters:

• (dimensions (geometry2 (np.array) – n atoms x 3): geometry

• (dimensions – n atoms x 3): geometry

• checks (bool) – whether to check that the inputs make sense (True by default)

Returns:

the root-mean-square distance between the two geometries

cctk.helper_functions.compute_angle_between(v1, v2, unit='degree')

Computes the angle between two vectors.

Parameters:

• v1 (ndarray) – first vector

• v2 (ndarray) – second vector

• unit (str) – ‘degree’ or ‘radian’

Returns:

the angle between the two vectors

cctk.helper_functions.compute_chirality(v1, v2, v3, v4)

Given 4 bond vectors, returns 1 or -1 based on chirality. For proper Cahn–Ingold–Prelog results, vectors should be passed from highest to lowest priority; however, any predictable order will give meaningful results.

Parameters:

• v1 (np.ndarray) – 3D bond vector

• v2 (np.ndarray) – 3D bond vector

• v3 (np.ndarray) – 3D bond vector

• v4 (np.ndarray) – 3D bond vector

Returns:

value of 1 (R by CIP) or -1 (S by CIP)

cctk.helper_functions.compute_dihedral_between(p0, p1, p2, p3, unit='degree')

Computes the dihedral angle between four points.

cctk.helper_functions.compute_distance_between(v1, v2, _norm=<function norm>)

Computes the L2 distance between two vectors.

(preloading _norm speeds repeated calls, since Python doesn’t have to look up the function every time)

cctk.helper_functions.compute_mass_spectrum(formula_dict, **kwargs)

Computes the expected low-res mass spec ions for a given formula.

Parameters:

dict (formula) – e.g. {“C”: 6, “H”: 6}

Returns:

list of m/z ions list of relative weights (out of 1 total)

cctk.helper_functions.compute_rotation_matrix(axis, theta)

Return the rotation matrix for rotation around axis by theta degrees.. Adapted from user “unutbu” on StackExchange.

Parameters:

• axis (np.ndarray) – the vector to rotate about

• theta (float) – how much to rotate (in degrees)

Returns:

the 3x3 rotation matrix

cctk.helper_functions.compute_unit_vector(vector)

Normalizes a vector, returning a unit vector pointing in the same direction. Returns the zero vector if the zero vector is given.

cctk.helper_functions.draw_isotopologue(z)

For an element with number z, return a weighted random atomic mass (so will return 12 99% of the time and 13 1% of the time for carbon).

cctk.helper_functions.formula_dict_from_string(formula_string)

Eugene challenged me to code golf, this isn’t my fault.

Parameters:

formula_string (str) – the formula as a string, e.g. C10H12N2O1. you need the “1” explicitly

Returns:

e.g. {‘C’: 10, ‘H’: 12, ‘N’: 2, ‘O’: 1}

Return type:

formula_dict (dict)

cctk.helper_functions.get_avg_mass(z)

For an element with number z, return average mass of that element.

cctk.helper_functions.get_corrected_free_energy(free_energy, frequencies, frequency_cutoff=100.0, temperature=298.15)

Computes the free energy by moving all positive frequencies below frequency_cutoff to the cutoff. See Cramer/Truhlar, J. Phys. Chem. B, 2011, 115, 14556.

Parameters:

• free_energy (float) – in hartree

• frequencies (list) – in cm-1

• frequency_cutoff (float) – in cm-1

• temperature (float) – in K

Returns:

in hartree

Return type:

corrected_free_energy (float)

cctk.helper_functions.get_covalent_radius(atomic_number)

Gets the covalent radius for a given element.

Parameters:

atomic_number (int) – the number of the given element

Returns:

the covalent radius in Angstroms (float)

cctk.helper_functions.get_entropy(frequencies, temperature)

Computes the total entropy of a given set of frequencies.

Parameters:

• frequencies (list) – in cm-1

• temperature (float) – in K

Returns:

in hartree

Return type:

entropy (float)

cctk.helper_functions.get_isotopic_distribution(z)

For an element with number z, returns two np.ndarray objects containing that element’s weights and relative abundances.

Parameters:

z (int) – atomic number

Returns:

list of isotope masses weights (np.ndarray): list of weights (relative to 1.00 for largest)

Return type:

masses (np.ndarray)

cctk.helper_functions.get_number(atomic_symbol)

Gets atomic number from a given element symbol (converted to titlecase using string.title()).

Parameters:

atomic_symbol (str) – the two-character symbol

Returns:

the atomic number

cctk.helper_functions.get_symbol(atomic_number)

Gets element symbol from a given atomic number.

Parameters:

atomic_number (int) – the number of the given element

Returns:

the two-character atomic symbol string

cctk.helper_functions.get_vdw_radius(atomic_number)

Gets the van der Waals radius for a given element.

Parameters:

atomic_number (int) – the number of the given element

Returns:

the van der Waals radius in Angstroms (float)

cctk.helper_functions.get_z_from_mass(desired_mass, tolerance=0.001)

For an element with atomic mass desired_mass, return the element’s atomic number.

Returns None if no mass within tolerance is found.

cctk.helper_functions.numpy_to_bytes(arr)

Utility function for pickling numpy arrays

cctk.helper_functions.scale_nmr_shifts(ensemble, symmetrical_atom_numbers=None, scaling_factors='default', property_name='isotropic_shielding')

Apply linear scaling to isotropic shieldings to get chemical shifts. Shifts are calculated as (intercept-shielding)/slope. If there are no shifts available for a structure, None will be placed in both return lists.

Parameters:

• ensemble – an Ensemble with calculated nmr shifts

• symmetrical_atom_numbers – None to perform no symmetry-averaging, a list of lists of 1-indexed atom numbers (e.g. [ [2,4,5], [7,8] ]) for a ConformationalEnsemble, or triply-nested lists for an Ensemble, where the outer index refers to the index of the Ensemble.

• scaling_factors – “default” to use DEFAULT_NMR_SCALING_FACTORS or a dict (atomic symbol –> (slope,intercept)). Elements for which scaling factors are not provided will be ignored.

• property_name – the key in properties_dict to use to locate the predicted isotropic shieldings (default=”isotropic_shielding”)

Returns:

np.array (matching the shape of the original shieldings minus symmetry averaging) shift_labels: np.array (also matches shape)

Return type:

scaled_shifts