A Python3 script that calculates the geometry indices τ4 and τ5 of selected atoms from crystallographic information file (CIF). The script saves you the tedious checking of the two largest angles and the calculation of the τ-values.
If you use the τ4 or τ5 index to describe the coordination geometry of your compounds, please cite one or more of the following articles:
τ4:
"Structural variation in copper(i) complexes with pyridylmethylamide ligands: structural analysis with a new four-coordinate geometry index, τ4"
Lei Yang, Douglas R. Powell, Robert P. Houser, Dalton Trans. 2007, 955-964.
τ4' (τ4 improved):
"Coordination polymers and molecular structures among complexes of mercury(II) halides with selected 1-benzoylthioureas"
Andrzej Okuniewski, Damian Rosiak, Jarosław Chojnacki, Barbara Becker, Polyhedron 2015, 90, 47–57.
τ5:
"Synthesis, structure, and spectroscopic properties of copper(II) compounds containing nitrogen–sulphur donor ligands; the crystal and molecular structure of aqua[1,7-bis(N-methylbenzimidazol-2′-yl)-2,6-dithiaheptane]copper(II) perchlorate"
Anthony W. Addison, T. Nageswara Rao, Jan Reedijk, Jacobus van Rijn, Gerrit C. Verschoor, J. Chem. Soc., Dalton Trans. 1984, 1349-1356.
The script uses the Gemmi library for CIF processing:
https://gemmi.readthedocs.io/en/latest/
https://github.com/project-gemmi/gemmi
The geometry indices τ4 and τ5 help you in assigning a coordination geometry for four-coordinated (tetrahedral, trigonal pyramidal, square planar or seesaw geometry) or five-coordinates compounds (square pyramidal or trigonal bipyramidal geometry). Only the two largest angles enclosing the central atom are needed for the assignment. Please check the concise Wikipedia article or the papers above for more information.
re, gemmi
Start the script with:
python3 tau-calc.py filename.cif atomThe input is case sensitive.
The following output will be printed:
atom binds to:
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atom1-atom2 distance Å site symmetry
...
The predicted coordination number for atom is x.
atom angles are:
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atom2-atom1-atom3 angle° site symmetry site symmetry
...
The two largest angles are beta = angle° and alpha = angle°.
atom geometry indices:
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tau_4 = value
tau_4' = value
tau_5 = value <--
Table of typical geometries and their corresponding tau_x values
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...
The suggested τ parameter is marked with an arrow (<--).
filename, required: the CIF (crystallographic information file)atom_name, required: the central atom, input is case sensitive, e.g.Co1calculates τ for Co1-eatom(s), optional: exclude atoms, e.g.-e N1 N3excludes bonds and angles to N1 and N3 from calculation-dN, optional: excludes atoms outsided = N Åfrom calculation, e.g.-d 2.1excludes atoms with bond lengths larger than 2.1 Å from the central atom from calculation
- If the predicted coordination number is larger than 2, τ will be calculated independently of the real coordination geometry.
- The suggestion τ4 or τ5 (<--) is based on the number of angles (6 for τ4, 10 for τ5).
- The script is not very well tested with symmetry generated atom positions. However, this is rarely the case with small molecule structures.
- All flavors of τ are calculated as soon as two angles are present. So you have to check if it makes sense.
- The script can only remove atoms from the coordination sphere, not add atoms. Therefore, make sure that the connectivity list is appropriate.
python3 tau-calc.py test.cif Cu1Cu1 binds to:
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Cu1-O1 1.907(2) Å .
Cu1-N1 1.911(3) Å .
Cu1-N3 2.154(3) Å .
Cu1-N5 2.170(3) Å .
Cu1-N4 2.187(3) Å .
The predicted coordination number for Cu1 is 5.
Cu1 angles are:
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O1-Cu1-N1 98.68(12)° . .
O1-Cu1-N3 171.94(12)° . .
N1-Cu1-N3 80.09(13)° . .
O1-Cu1-N5 103.92(12)° . .
N1-Cu1-N5 137.78(13)° . .
N3-Cu1-N5 81.87(12)° . .
O1-Cu1-N4 91.77(11)° . .
N1-Cu1-N4 130.58(13)° . .
N3-Cu1-N4 83.17(12)° . .
N5-Cu1-N4 84.14(13)° . .
The two largest angles are beta = 171.94° and alpha = 137.78°.
Cu1 geometry indices:
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tau_4 = 0.36
tau_4' = 0.25
tau_5 = 0.57 <--
Table of typical geometries and their corresponding tau_x values
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Coordination number 4:
Tetrahedral : tau_4 = 1.00 tau_4' = 1.00
Trigonal pyramidal : tau_4 = 0.85 tau_4' = 0.85
Seesaw : tau_4 = 0.43 tau_4' = 0.24
Square planar : tau_4 = 0.00 tau_4' = 0.00
Coordination number 5:
Trigonal bipyramidal : tau_5 = 1.00
Square pyramidal : tau_5 = 0.00
python3 tau-calc.py test2.cif Co1 -e N12 -d 2.0Excluded atoms: ['N12']
Excluded atoms (distance larger than 2.0 Å): ['N11']
Co1 binds to:
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Co1-N7 1.8860(15) Å .
Co1-N8 1.8900(15) Å 3_666
Co1-N14 1.9404(15) Å .
Co1-N13 1.9502(15) Å .
The predicted coordination number for Co1 is 4.
Co1 angles are:
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N7-Co1-N8 92.29(6)° . 3_666
N7-Co1-N14 91.55(6)° . .
N8-Co1-N14 87.16(6)° 3_666 .
N7-Co1-N13 85.35(6)° . .
N8-Co1-N13 92.05(6)° 3_666 .
N14-Co1-N13 176.77(6)° . .
The two largest angles are beta = 176.77° and alpha = 92.29°.
Co1 geometry indices:
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tau_4 = 0.64 <--
tau_4' = 0.38 <--
tau_5 = 1.41
Table of typical geometries and their corresponding tau_x values
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Coordination number 4:
Tetrahedral : tau_4 = 1.00 tau_4' = 1.00
Trigonal pyramidal : tau_4 = 0.85 tau_4' = 0.85
Seesaw : tau_4 = 0.43 tau_4' = 0.24
Square planar : tau_4 = 0.00 tau_4' = 0.00
Coordination number 5:
Trigonal bipyramidal : tau_5 = 1.00
Square pyramidal : tau_5 = 0.00