Covalent radius

Short description: Measure of the size of an atom that forms part of one covalent bond

Template:Atomic radius

The covalent radius, rcov, is a measure of the size of an atom that forms part of one covalent bond. It is usually measured either in picometres (pm) or angstroms (Å), with 1 Å = 100 pm.

In principle, the sum of the two covalent radii should equal the covalent bond length between two atoms, R(AB) = r(A) + r(B). Moreover, different radii can be introduced for single, double and triple bonds (r1, r2 and r3 below), in a purely operational sense. These relationships are certainly not exact because the size of an atom is not constant but depends on its chemical environment. For heteroatomic A–B bonds, ionic terms may enter. Often the polar covalent bonds are shorter than would be expected based on the sum of covalent radii. Tabulated values of covalent radii are either average or idealized values, which nevertheless show a certain transferability between different situations, which makes them useful.

The bond lengths R(AB) are measured by X-ray diffraction (more rarely, neutron diffraction on molecular crystals). Rotational spectroscopy can also give extremely accurate values of bond lengths. For homonuclear A–A bonds, Linus Pauling took the covalent radius to be half the single-bond length in the element, e.g. R(H-H, in H2) = 74.14 pm so rcov(H) = 37.07 pm: in practice, it is usual to obtain an average value from a variety of covalent compounds, although the difference is usually small. Sanderson has published a recent set of non-polar covalent radii for the main-group elements,[1] but the availability of large collections of bond lengths, which are more transferable, from the Cambridge Crystallographic Database[2][3] has rendered covalent radii obsolete in many situations.

## Contents

* 1 Average radii
* 2 Radius for multiple bonds
* 3 See also
* 4 References

## Average radii

The values in the table below are based on a statistical analysis of more than 228,000 experimental bond lengths from the Cambridge Structural Database.[4] For carbon, values are given for the different hybridisations of the orbitals.

Covalent radii in pm from analysis of the Cambridge Structural Database, which contains about 1,030,000 crystal structures[4] H  |  | He

|
|

1 |  | 2
31(5) |  | 28
Li | Be |  | B | C | N | O | F | Ne
3 | 4 | Radius (standard deviation) / pm | 5 | 6 | 7 | 8 | 9 | 10
128(7) | 96(3) |  | 84(3) | sp3 76(1)
sp2 73(2)
sp  69(1) | 71(1) | 66(2) | 57(3) | 58
Na | Mg |  | Al | Si | P | S | Cl | Ar
11 | 12 |  | 13 | 14 | 15 | 16 | 17 | 18
166(9) | 141(7) |  | 121(4) | 111(2) | 107(3) | 105(3) | 102(4) | 106(10)
K | Ca |  | Sc | Ti | V | Cr | Mn | Fe | Co | Ni | Cu | Zn | Ga | Ge | As | Se | Br | Kr
19 | 20 |  | 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 | 31 | 32 | 33 | 34 | 35 | 36
203(12) | 176(10) |  | 170(7) | 160(8) | 153(8) | 139(5) | l.s. 139(5)
h.s. 161(8) | l.s. 132(3)
h.s. 152(6) | l.s. 126(3)
h.s. 150(7) | 124(4) | 132(4) | 122(4) | 122(3) | 120(4) | 119(4) | 120(4) | 120(3) | 116(4)
Rb | Sr |  | Y | Zr | Nb | Mo | Tc | Ru | Rh | Pd | Ag | Cd | In | Sn | Sb | Te | I | Xe
37 | 38 |  | 39 | 40 | 41 | 42 | 43 | 44 | 45 | 46 | 47 | 48 | 49 | 50 | 51 | 52 | 53 | 54
220(9) | 195(10) |  | 190(7) | 175(7) | 164(6) | 154(5) | 147(7) | 146(7) | 142(7) | 139(6) | 145(5) | 144(9) | 142(5) | 139(4) | 139(5) | 138(4) | 139(3) | 140(9)
Cs | Ba | * | Lu | Hf | Ta | W | Re | Os | Ir | Pt | Au | Hg | Tl | Pb | Bi | Po | At | Rn
55 | 56 |  | 71 | 72 | 73 | 74 | 75 | 76 | 77 | 78 | 79 | 80 | 81 | 82 | 83 | 84 | 85 | 86
244(11) | 215(11) |  | 187(8) | 175(10) | 170(8) | 162(7) | 151(7) | 144(4) | 141(6) | 136(5) | 136(6) | 132(5) | 145(7) | 146(5) | 148(4) | 140(4) | 150 | 150
Fr | Ra | **
87 | 88
260 | 221(2)
| * | La | Ce | Pr | Nd | Pm | Sm | Eu | Gd | Tb | Dy | Ho | Er | Tm | Yb
| 57 | 58 | 59 | 60 | 61 | 62 | 63 | 64 | 65 | 66 | 67 | 68 | 69 | 70
| 207(8) | 204(9) | 203(7) | 201(6) | 199 | 198(8) | 198(6) | 196(6) | 194(5) | 192(7) | 192(7) | 189(6) | 190(10) | 187(8)
| ** | Ac | Th | Pa | U | Np | Pu | Am | Cm
| 89 | 90 | 91 | 92 | 93 | 94 | 95 | 96
| 215 | 206(6) | 200 | 196(7) | 190(1) | 187(1) | 180(6) | 169(3)

## Radius for multiple bonds

A different approach is to make a self-consistent fit for all elements in a smaller 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] triple-, [7] and sixfold- bond[9] covalent radii, determined using typically
400 experimental or calculated primary distances, R, per set. H  |  | He

|
|

1 |  | 2

- |  | 46

Li | Be |  | B | C | N | O | F | Ne
3 | 4 | Radius / pm: | 5 | 6 | 7 | 8 | 9 | 10
133
124
- | 102

85 | single-bond

double-bond

triple-bond

sixfold-bond

| 85

73 | 75

60 | 71

54 | 63

53 | 64

53 | 67

Na | Mg |  | Al | Si | P | S | Cl | Ar
11 | 12 |  | 13 | 14 | 15 | 16 | 17 | 18
155
160
- | 139
132
127 |  | 126
113
111 | 116
107
102 | 111
102
94 | 103

95 | 99

93 | 96
107

K | Ca |  | Sc | Ti | V | Cr | Mn | Fe | Co | Ni | Cu | Zn | Ga | Ge | As | Se | Br | Kr
19 | 20 |  | 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 | 31 | 32 | 33 | 34 | 35 | 36
196
193
- | 171
147
133 |  | 148
116
114  | 136
117
108

| 134
112
106

| 122
111
103

| 119
105
103

| 116
109
102

| 111
103
96 | 110
101
101 | 112
115
120 | 118
120
\-  | 124
117
121 | 121
111
114 | 121
114
106 | 116
107
107 | 114
109
110 | 117
121
108
Rb | Sr |  | Y | Zr | Nb | Mo | Tc | Ru | Rh | Pd | Ag | Cd | In | Sn | Sb | Te | I | Xe
37 | 38 |  | 39 | 40 | 41 | 42 | 43 | 44 | 45 | 46 | 47 | 48 | 49 | 50 | 51 | 52 | 53 | 54
210
202
- | 185
157
139 |  | 163
130
124  | 154
127
121

108

| 147
125
116

100

| 138
121
113

| 128
120
110

| 125
114
103

| 125
110
106 | 120
117
112 | 128
139
137 | 136
144
\-  | 142
136
146 | 140
130
132 | 140
133
127 | 136
128
121 | 133
129
125 | 131
135
122
Cs | Ba | * | Lu | Hf | Ta | W | Re | Os | Ir | Pt | Au | Hg | Tl | Pb | Bi | Po | At | Rn
55 | 56 |  | 71 | 72 | 73 | 74 | 75 | 76 | 77 | 78 | 79 | 80 | 81 | 82 | 83 | 84 | 85 | 86
232
209
- | 196
161
149 |  | 162
131
131  | 152
128
122

109

| 146
126
119

105

| 137
120
115

102

| 131
119
110

102

| 129
116
109

103

| 122
115
107 | 123
112
110 | 124
121
123 | 133
142
\-  | 144
142
150 | 144
135
137 | 151
141
135 | 145
135
129 | 147
138
138 | 142
145
133
Fr | Ra | ** | Lr  | Rf | Db | Sg | Bh | Hs | Mt | Ds | Rg | Cn | Nh | Fl | Mc | Lv | Ts | Og
87 | 88 |  | 103 | 104 | 105 | 106 | 107 | 108 | 109 | 110 | 111 | 112 | 113 | 114 | 115 | 116 | 117 | 118
223
218
- | 201
173
159 |  | 161
141
\-  | 157
140
131 | 149
136
126 | 143
128
121 | 141
128
119 | 134
125
118 | 129
125
113 | 128
116
112 | 121
116
118 | 122
137
130 | 136

- | 143

- | 162

- | 175

- | 165

- | 157

| * | La | Ce | Pr | Nd | Pm | Sm | Eu | Gd | Tb | Dy | Ho | Er | Tm | Yb
| 57 | 58 | 59 | 60 | 61 | 62 | 63 | 64 | 65 | 66 | 67 | 68 | 69 | 70
| 180
139
139 | 163
137
131 | 176
138
128 | 174
137
- | 173
135
- | 172
134
- | 168
134
- | 169
135
132 | 168
135
- | 167
133
- | 166
133
- | 165
133
- | 164
131
- | 170
129

| ** | Ac | Th | Pa | U | Np | Pu | Am | Cm | Bk | Cf | Es | Fm | Md | No
| 89 | 90 | 91 | 92 | 93 | 94 | 95 | 96 | 97 | 98 | 99 | 100 | 101 | 102
| 186
153
140 | 175
143
136

115

| 169
138
129

105

| 170
134
118

104

| 171
136
116

| 172
135
- | 166
135
- | 166
136
- | 168
139
- | 168
140
- | 165
140
- | 167

- | 173
139
- | 176

## See also

* Atomic radii of the elements (data page)
* Ionization energy
* Electron affinity
* Electron configuration
* Periodic table

## References

1. ↑ Sanderson, R. T. (1983). "Electronegativity and Bond Energy". Journal of the American Chemical Society 105 (8): 2259–2261. doi:10.1021/ja00346a026.
2. ↑ Allen, F. H.; Kennard, O.; Watson, D. G.; Brammer, L.; Orpen, A. G.; Taylor, R. (1987). "Table of Bond Lengths Determined by X-Ray and Neutron Diffraction". J. Chem. Soc., Perkin Trans. 2 (12): S1–S19. doi:10.1039/P298700000S1.
3. ↑ Orpen, A. Guy; Brammer, Lee; Allen, Frank H.; Kennard, Olga; Watson, David G.; Taylor, Robin (1989). "Supplement. Tables of bond lengths determined by X-ray and neutron diffraction. Part 2. Organometallic compounds and co-ordination complexes of the d- and f-block metals". Journal of the Chemical Society, Dalton Transactions (12): S1. doi:10.1039/DT98900000S1.
4. ↑ 4.0 4.1 4.2 Beatriz Cordero; Verónica Gómez; Ana E. Platero-Prats; Marc Revés; Jorge Echeverría; Eduard Cremades; Flavia Barragán; Santiago Alvarez (2008). "Covalent radii revisited". Dalton Trans. (21): 2832–2838. doi:10.1039/b801115j. PMID 18478144.
5. ↑ 5.0 5.1 P. Pyykkö; 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.
6. ↑ 6.0 6.1 P. Pyykkö; 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.
7. ↑ 7.0 7.1 P. Pyykkö; S. Riedel; M. Patzschke (2005). "Triple-Bond Covalent Radii". Chemistry: A European Journal 11 (12): 3511–3520. doi:10.1002/chem.200401299. PMID 15832398.
8. ↑ P. Pyykkö (2012). "Refitted tetrahedral covalent radii for solids". Physical Review B 85 (2): 024115, 7 p. doi:10.1103/PhysRevB.85.024115. Bibcode: 2012PhRvB..85b4115P.
9. ↑ Pyykkö, Pekka; Atsumi, Michiko. "Approaching Sixfold Chemical Bonding: Metal Dimers MM' Involving Group 4–8 Transition Metals and the Actinides Th–Np. Additive Covalent Radii r6". https://chemistry-europe.onlinelibrary.wiley.com/doi/10.1002/chem.70818.

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