Table 1 Comparison of structural units and their properties in models of amorphous chalcogens and ternary chalcogenides.

From: Hypervalency in amorphous chalcogenides

Model

Structural unit (CN, # LP)

Octet/hyperv.

Z* (e)

Bonding type

r (Ã…)

ELFb

χ (polarity index)

MLWFbond spread \({\Omega }^{1/2}\) (Ã…)

a-S

S(2,2)

Octet

−0.01 (0.14)

Covalent

2.07 (0.07)

0.8 (0.03)

0.50 (0.00)

1.08 (0.04)

a-Se

Se(2,2)

Octet

0.00 (0.38)

Covalent

2.39 (0.04)

0.73 (0.01)

0.50 (0.01)

1.31 (0.03)

a-Te

Te(2,2)

Octet

−0.15 (1.57)

Covalent

2.89 (0.07)

0.67 (0.05)

0.50 (0.06)

1.72 (0.10)

Te(3,1)

Octet

−0.62 (1.54)

Cov. + Hyp.

2.97 (0.10)

0.63 (0.06)

0.50 (0.10)

1.77 (0.10)

Te(3,2)

Hyperv.

1.44 (1.02)

Covalent

2.90 (0.07)

0.68 (0.04)

0.49 (0.06)

1.72 (0.09)

Hyperbond

3.05 (0.06)

0.57 (0.04)

0.64 (0.03)

1.84 (0.07)

a-GSS

Ge(3,1)

Octet

2.14 (0.34)

Covalent

2.47 (0.07)

0.68 (0.05)

0.69 (0.03)

1.30 (0.03)

Ge(4,0)

Octet

2.25 (0.39)

Covalent

2.31 (0.05)

0.81 (0.03)

0.62 (0.03)

1.26 (0.03)

Sb(3,1)

Octet

2.82 (0.70)

Covalent

2.52 (0.07)

0.71 (0.05)

0.65 (0.03)

1.31 (0.03)

Sb(4,1)

Hyperv.

3.13 (0.78)

Covalent

2.53 (0.07)

0.72 (0.05)

0.65 (0.03)

1.31 (0.02)

Hyperbond

2.77 (0.05)

0.54 (0.03)

0.74 (0.02)

1.37 (0.02)

a-GSSe

Ge(3,1)

Octet

2.13 (0.42)

Covalent

2.61 (0.07)

0.69 (0.05)

0.68 (0.03)

1.44 (0.04)

Ge(4,0)

Octet

2.22 (0.39)

Covalent

2.46 (0.05)

0.79 (0.03)

0.60 (0.03)

1.39 (0.03)

Sb(3,1)

Octet

2.74 (0.75)

Covalent

2.67 (0.07)

0.72 (0.04)

0.63 (0.03)

1.45 (0.04)

Sb(4,1)

Hyperv.

3.66 (0.55)

Covalent

2.68 (0.07)

0.73 (0.04)

0.63 (0.03)

1.45 (0.05)

Hyperbond

2.90 (0.06)

0.56 (0.04)

0.73 (0.02)

1.53 (0.03)

a-GST

Ge(3,1)

Octet

2.76 (0.85)

Covalent

2.82 (0.07)

0.69 (0.05)

0.65 (0.04)

1.74 (0.08)

Ge(4,0)

Octet

2.07 (0.80)

Covalent

2.73 (0.07)

0.75 (0.05)

0.59 (0.04)

1.68 (0.07)

Ge(4,1)

Hyperv.

3.60 (0.92)

Covalent

2.86 (0.08)

0.67 (0.07)

0.67 (0.04)

1.77 (0.10)

Hyperbond

2.98 (0.06)

0.56 (0.05)

0.73 (0.03)

1.86 (0.11)

Sb(3,1)

Octet

3.10 (1.63)

Covalent

2.92 (0.06)

0.71 (0.04)

0.60 (0.03)

1.73 (0.07)

Sb(4,1)

Hyperv.

4.56 (1.45)

Covalent

2.92 (0.06)

0.71 (0.04)

0.60 (0.03)

1.73 (0.08)

Hyperbond

3.10 (0.06)

0.57 (0.04)

0.70 (0.03)

1.88 (0.09)

Sb(5,1)

Hyperv.

5.24 (1.49)

Covalent

2.94 (0.05)

0.71 (0.04)

0.60 (0.03)

1.79 (0.07)

Hyperbond

3.09 (0.07)

0.58 (0.05)

0.70 (0.03)

1.89 (0.09)

  1. Structural units conforming to the octet rule (‘octet’) have four pairs of electrons in total, whilst more than four pairs are associated with hypervalent units (‘hyperv.’). The structural units for cations for ternary chalcogenides only are shown. The standard deviation for each observable is shown in parentheses. Z* indicates the Born effective charge, r the bond length and ELFb is the ELF value at a bond-critical point. The spread of MLWFbond corresponds to \({\Omega }^{1/2}\) (see text) for either covalent bonds or hyperbonds. \(\bar{\chi }\) denotes a polarity index, as defined in Lee and Elliott4, quantifying the ionicity of a bond; for instance, \(\bar{\chi }\) is supposed to be 0.5 for homopolar bonds, and a positive deviation from this value denotes the degree of charge transfer of bonding electrons to a ligand. For a proper comparison, we present chemical-bonding properties of chemically-correct bonds with only chalcogen ligands for each structural unit. The distributions of r, ELFb, χ and the spread of MLWFbond values for selected hypervalent units are shown in Supplementary Figs. 6–9.
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