gidx

Computes the geometry indices of a four-, five-, six- or eight-coordinate centre. The indices that apply are chosen from the number of ligands: τ4 and τ4′ for four, τ5 for five, τ6 and its complement τ6′ for six, and τ8 and τ8′ for eight.

cosmochlore gidx <NAME> [OPTIONS]

Important

gidx needs a centred structure with exactly one central atom and four, five, six or eight ligands (5, 6, 7 or 9 atoms in the .xyz file).

Options

Flag	Value	Description
-c, --center	<POSITION>	1-based position of the atom in the .xyz table that is the centre of the structure. Defaults to the first atom (position 1) when omitted.
-t, --table		Write the output table to a .csv file.

Examples

Five-coordinate copper centre (τ5)

Given the following ML5.xyz file, a five-coordinate copper centre halfway between a trigonal bipyramid and a square pyramid:

ML5.xyz

6
Distorted five-coordinate copper centre (halfway between trigonal bipyramidal and square pyramidal)
Cu    0.00000    0.00000    0.00000
N1    0.35000    0.05000    2.00000
N2   -0.30000   -0.10000   -2.05000
N3    2.10000    0.00000    0.10000
N4   -1.78000    1.02000   -0.05000
N5   -0.56000   -2.08000    0.00000

cosmochlore gidx ML5.xyz -t

Will output:

Input file: ML5.xyz
==================================
Geometry indices (CN = 5)
----------------------------------
Alpha                150.18  deg
Beta                 177.91  deg
----------------------------------
Tau5                  0.462
==================================
Writing output table to ML5_gidx_table.csv...

Four-coordinate copper centre (τ4 and τ4′)

ML4.xyz

5
Distorted four-coordinate copper centre (between tetrahedral and seesaw)
Cu    0.00000    0.00000    0.00000
N1    1.92000    0.31000   -0.60000
N2   -1.83000   -0.28000   -0.62000
N3    0.20000    1.62000    1.18000
N4   -0.10000   -1.55000    1.35000

cosmochlore gidx ML4.xyz

Will output:

Input file: ML4.xyz
==================================
Geometry indices (CN = 4)
----------------------------------
Alpha                113.23  deg
Beta                 144.34  deg
----------------------------------
Tau4                  0.726
Tau4'                 0.630
==================================
Program finished in 339.4µs

Both indices fall between the seesaw and the tetrahedron. The two values differ because τ4′ also accounts for the difference between the two largest angles.

Six-coordinate iron centre (τ6 and τ6′)

Using the FeHS.xyz structure from the `cshm` example:

cosmochlore gidx FeHS.xyz

Will output:

Input file: FeHS.xyz
==================================
Geometry indices (CN = 6)
----------------------------------
Alpha 1              162.81  deg
Alpha 2              161.60  deg
Alpha 3              161.17  deg
Gamma 1               73.14  deg
Gamma 2               73.62  deg
Gamma 3               88.05  deg
Gamma 4               88.11  deg
Gamma 5               88.12  deg
----------------------------------
Tau6                  0.302
Tau6'                 0.433
==================================
Program finished in 377.4µs

Eight-coordinate tantalum centre (τ8 and τ8′)

A $D_{2d}$ dodecahedral TaCl₄(PH₃)₄ complex, with only the donor atoms kept:

TaCl4_PH3_4_D2d.xyz

9
TaCl4(PH3)4 (D2d), B3LYP/aVTZ optimised geometry, donor atoms only (Turnbull, Wetmore, Gerken, Chem. Eur. J. 2021, SI section 4.2)
Ta       0.000000      0.000000      0.000000
Cl1      0.000000      2.388165      0.831610
Cl2     -2.388165      0.000000     -0.831610
Cl3      0.000000     -2.388165      0.831610
Cl4      2.388165      0.000000     -0.831610
P1       1.719643      0.000000      2.060737
P2      -1.719643      0.000000      2.060737
P3       0.000000      1.719643     -2.060737
P4       0.000000     -1.719643     -2.060737

cosmochlore gidx TaCl4_PH3_4_D2d.xyz

Will output:

Input file: TaCl4_PH3_4_D2d.xyz
==================================
Geometry indices (CN = 8)
----------------------------------
Theta 1              126.12  deg
Phi 1                 96.21  deg
Theta 2              126.12  deg
Phi 2                 96.21  deg
Dihedral A            90.00  deg
Dihedral B            90.00  deg
----------------------------------
Tau8 (face 1)         0.913
Tau8 (face 2)         0.913
Tau8'                 1.000
Tau8'-Tau8            0.087
==================================
Program finished in 364.3µs

The two faces give the same τ8, as expected from the $D_{2d}$ symmetry of the complex.

Passing the -t/--table flag writes the angles and the indices to a <NAME>_gidx_table.csv. The columns depend on the number of ligands:

Ligands	Columns
4	alpha,beta,tau4,tau4_prime
5	alpha,beta,tau5
6	alpha1,alpha2,alpha3,tau6,gamma1,gamma2,gamma3,gamma4,gamma5,tau6_prime
8	theta1,phi1,tau8_1,theta2,phi2,tau8_2,dihedral_a,dihedral_b,tau8_prime,cube_delta