Covalent 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(HH, 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.

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
LiBe BCNOFNe
34Radius (standard deviation) / pm 5678910
128(7)96(3) 84(3)sp3 76(1)
sp2 73(2)
sp  69(1)
71(1)66(2)57(3)58
NaMg AlSiPSClAr
1112 131415161718
166(9)141(7) 121(4)111(2)107(3)105(3)102(4)106(10)
KCa ScTiVCrMnFeCoNiCuZnGaGeAsSeBrKr
1920 21222324252627282930313233343536
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)
RbSr YZrNbMoTcRuRhPdAgCdInSnSbTeIXe
3738 39404142434445464748495051525354
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)
CsBa*LuHfTaWReOsIrPtAuHgTlPbBiPoAtRn
5556 71727374757677787980818283848586
244(11)215(11) 175(10)187(8)170(8)162(7)151(7)144(4)141(6)136(5)136(6)132(5)145(7)146(5)148(4)140(4)150150
FrRa**
8788
260221(2)
 
 *LaCePrNdPmSmEuGdTbDyHoErTmYb
 5758596061626364656667686970
 207(8)204(9)203(7)201(6)199198(8)198(6)196(6)194(5)192(7)192(7)189(6)190(10)187(8)
 **AcThPaUNpPuAmCm
 8990919293949596
 215206(6)200196(7)190(1)187(1)180(6)169(3)

Radii 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] and triple-bond[7] covalent radii, determined using typically
400 experimental or calculated primary distances, R, per set.
H   He
1 2
32
-
-
 46
-
-
LiBe BCNOFNe
34Radius / pm:5678910
133
124
-
102
90
85
single-bond

double-bond

triple-bond

85
78
73
75
67
60
71
60
54
63
57
53
64
59
53
67
96
-
NaMg AlSiPSClAr
1112 131415161718
155
160
-
139
132
127
 126
113
111
116
107
102
111
102
94
103
94
95
99
95
93
96
107
96
KCa ScTiVCrMnFeCoNiCuZnGaGeAsSeBrKr
1920 21222324252627282930313233343536
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
RbSr YZrNbMoTcRuRhPdAgCdInSnSbTeIXe
3738 39404142434445464748495051525354
210
202
-
185
157
139
 163
130
124
154
127
121
147
125
116
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
CsBa*LuHfTaWReOsIrPtAuHgTlPbBiPoAtRn
5556 71727374757677787980818283848586
232
209
-
196
161
149
 162
131
131
152
128
122
146
126
119
137
120
115
131
119
110
129
116
109
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
FrRa**Lr RfDbSgBhHsMtDsRgCnNhFlMcLvTsOg
8788 103104105106107108109110111112113114115116117118
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
-
-
 
 *LaCePrNdPmSmEuGdTbDyHoErTmYb
 5758596061626364656667686970
 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
-
 **AcThPaUNpPuAmCmBkCfEsFmMdNo
 8990919293949596979899100101102
 186
153
140
175
143
136
169
138
129
170
134
118
171
136
116
172
135
-
166
135
-
166
136
-
168
139
-
168
140
-
165
140
-
167
-
-
173
139
-
176
-
-

See also

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. 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. S2CID 244110.
  5. 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. 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. 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. Bibcode:2012PhRvB..85b4115P. doi:10.1103/PhysRevB.85.024115.
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