stereochemistry module¶

Stereochemistry for connectivity and restraints.

Module author: Michael S. Chapman <chapmanms@missouri.edu>

Authors:

Michael S. Chapman <chapmami@missouri.edu>,

University of Missouri

Version:

1, Nov 26, 2024

Changed in version 08/10/20.

Changed in version 0.6.0: 08/19/20 Completed calculation of radii for functional groups.

Changed in version 1.0.0: 09/26/20 Python 2.7 –> 3.6

class stereochemistry.CovalentRadii¶

Bases: object

Approximation of Bond Lengths

For a covalent bond, the distance is approximated by the sum of radii for the two elements. The class supports look-up for single, double and triple bonds which are stored as lists of length 3 in picometers. Zero is used if undefined. Errors are estimated to be about 3 pm.

The following is lightly edited from the Wiki page from which the data were obtained: https://en.wikipedia.org/wiki/Covalent_radius

Radii form a self-consistent fit for all elements in a small set of molecules. This was done separately for single,[5] double,[6] and triple bonds[7] up to superheavy elements. Both experimental and computational data were used. The single-bond results are often similar to those of Cordero et al.[4] When they are different, the coordination numbers used can be different. This is notably the case for most (d and f) transition metals. Normally one expects that r1 > r2 > r3. Deviations may occur for weak multiple bonds, if the differences of the ligand are larger than the differences of R in the data used.

Note that elements up to atomic number 118 (oganesson) have now been experimentally produced and that there are chemical studies on an increasing number of them. The same, self-consistent approach was used to fit tetrahedral covalent radii for 30 elements in 48 crystals with subpicometer accuracy.[8]

Single-,[5] double-,[6] and triple-bond[7] covalent radii, determined using typically 400 experimental or calculated primary distances, R, per set.

P. Pyykko; M. Atsumi (2009). “Molecular Single-Bond Covalent Radii for Elements 1-118”. Chemistry: A European Journal. 15 (1): 186-197. doi:10.1002/chem.200800987. PMID 19058281.
P. Pyykko; M. Atsumi (2009). “Molecular Double-Bond Covalent Radii for Elements Li-E112”. Chemistry: A European Journal. 15 (46): 12770-12779. doi:10.1002/chem.200901472. PMID 19856342.. Figure 3 of this paper contains all radii of refs. [5-7]. The mean-square deviation of each set is 3 pm.
P. Pyykko; S. Riedel; M. Patzschke (2005). “Triple-Bond Covalent Radii”. Chemistry: A European Journal. 11 (12): 3511-3520. doi:10.1002/chem.200401299. PMID 15832398.
P. Pyykko (2012). “Refitted tetrahedral covalent radii for solids”. Physical Review B. 85 (2): 024115, 7 p. Bibcode:2012PhRvB..85b4115P. doi:10.1103/PhysRevB.85.024115.

bonds = ('single', 'double', 'triple')¶

checkRadii(verbose, exception, *bonds, **bonding)¶

Check that covalent radii are optimal with respect to target bonds.

Parameters:

verbose (bool) – document
exception (bool) – raise ValueError if any covalent radius is non-optimal
bonds (tuples) – (atom(str), atom(str), target-distance (float)) This can be the same as the argument to fitBondTypes.
bonding (dict) – keyed by every atom in bonds, 3-list of (str-element, float-single-bonding, float-double-bonding, bool-optimize). This will usually be the dict returned from fitBondTypes.

Returns:

optimal?

Return type:

bool

Raises:

ValueError if exception=True and any radius non-optimal

curated(element, residue=None, atom=None)¶

Single-bonded radius optionally superseded by residue/atom type.

Parameters:

element (str) – 1 or 2-character periodic table symbol
residue (str) – 3-character residue type, eg. “ALA”, “GLY”
atom (str) – atom name, eg. “CA”, “NH1”, required if residue!=None

Returns:

radius

Return type:

float

Unless residue and atom match one of the combinations below, radius will be set by element as single-bonded. The exceptions below are for protein atoms with mixed single/double bonding, resonance or tautomers. The hard-wired parameters come from prior fitting in self.protein() to the .cif geometry files of Coot.

Caution

Limitations based on nomenclature:

# Protein is recognized by residue matching one of the standard 20: as defined in translate.Dictionary.to1.keys().

# Atom names use .cif nomenclature.

Generalization should be possible, but of limited benefit, because problems are mostly avoided, because identification uses standard names “N”, “C”, “O”, “CA”, “CB”, “NE” (Lys), but otherwise infers from element.

For the C-terminus, an “O” will be treated as double-bonded, while “OXT” (most nomenclatures), “OT1” or “OT2” will be considered single-bonded. (Ideally, we would want resonance between the 2 oxygens, but no attempt is made to identify the “O” of the terminal residue.)

element = ['H', 'He', 'Li', 'Be', 'B', 'C', 'N', 'O', 'F', 'Ne', 'Na', 'Mg', 'Al', 'Si', 'P', 'S', 'Cl', 'Ar', 'K', 'Ca', 'Sc', 'Ti', 'V', 'Cr', 'Mn', 'Fe', 'Co', 'Ni', 'Cu', 'Zn', 'Ga', 'Ge', 'As', 'Se', 'Br', 'Kr', 'Rb', 'Sr', 'Y', 'Zr', 'Nb', 'Mo', 'Tc', 'Ru', 'Rh', 'Pd', 'Ag', 'Cd', 'In', 'Sn', 'Sb', 'Te', 'I', 'Xe', 'Cs', 'Ba', 'La', 'Ce', 'Pr', 'Nd', 'Pm', 'Sm', 'Eu', 'Gd', 'Tb', 'Dy', 'Ho', 'Er', 'Tm', 'Yb', 'Lu', 'Hf', 'Ta', 'W', 'Re', 'Os', 'Ir', 'Pt', 'Au', 'Hg', 'Tl', 'Pb', 'Bi', 'Po', 'At', 'Rn', 'Fr', 'Ra', 'Ac', 'Th', 'Pa', 'U', 'Np', 'Pu', 'Am', 'Cm', 'Bk', 'Cf', 'Es', 'Fm', 'Md', 'No', 'Lr', 'Rf', 'Db', 'Sg', 'Bh', 'Hs', 'Mt', 'Ds', 'Rg', 'Cn', 'Nh', 'Fl', 'Mc', 'Lv', 'Ts', 'Og']¶

Variables:: element – list of element abbreviations by atomic number

fitBondTypes(*bonds, **bonding)¶

Fit the single/double bond combinations of atoms to target bonds.

If connectivity or bond lengths are to be determined from atom-based attributes, what designation of single- or double-bonded for an atom best replicates its several bonds? This might be further complicated in the presence of resonance or tautomerism.

This routine optimizes the covalent radii to match optimally a set of bond lengths.

The algorithm is simplistic, 1-D searches through each atom-type, repeated with progressively smaller step size.

Note that this can be unstable / ill-posed particularly when the fitted atom-types is close to or exceeds the number of target bond lengths. See method protein() for examples that mitigate these problems.

Parameters:

bonds (tuples) – (atom(str), atom(str), target-distance (float))
bonding (dict) – keyed by every atom in bonds, 3-tuple of (str-element, float-single-bonding, float-double-bonding, bool-optimize).

Returns:

optimized bonding

Return type:

same as bonding, except the 3-tuples are 3-lists.

Nothing special is inferred from the atom names as the elements are explicitly defined in bonding. Thus, to find the best common parameters for several atoms types of the same element, choose a common atom pseudonym in both bonds and bonding. For example, one might use ‘CY’ as a common pseudonym for ‘CD1’, ‘CD2’, ‘CG1’, … to derive a single parameter set for the aromatic ring.

halfLength(atom, bond=1)¶

Parameters:

atom (int|str) – atomic number or element abbreviation
int|3-tuple|NoneType – 1, 2 or 3 for single, double or triple bond. Tuple for an average of bond-types, (i * single, j * double, k * triple)/(i+j+k). This might be slightly more appropriate for some atom types when search for possible bond connectivity before bonding type has been established.

Returns:

half bond length (Angstrom)

Return type:

float

number = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118]¶

Variables:: number – list of atomic numbers, for checking only

optimizeProteinAmide(bonding=None)¶

Find the single/double bond combinations that fit amide side chain.

Parameters:: bonding (dict|NoneType) – keyed by every atom in bonds, 3-tuple of (str-element, float-single-bonding, float-double-bonding, bool-optimize). If None will start with single-bonded defaults.
Returns:: updated bonding
Return type:: dict