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)[source]

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)[source]

Utility function for unpickling numpy arrays

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

Computes the root mean squared difference between two geometries.

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

  • (np.array (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')[source]

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)[source]

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')[source]

Computes the dihedral angle between four points.

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

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)[source]

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)[source]

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)[source]

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)[source]

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)[source]

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)[source]

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)[source]

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)[source]

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)[source]

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)[source]

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)[source]

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)[source]

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)[source]

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)[source]

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)[source]

Utility function for pickling numpy arrays

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

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