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.

Types of radii

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.

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		167173
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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