Covalent radius

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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 on the basis of 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, that 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.

Table of covalent radii[edit]

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] The numbers in parentheses are the estimated standard deviations for the last digit. This fit pre-fixes the radii for C, N and O.

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 E118 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]

Covalent radii in pm from analysis of the Cambridge Structural Database,
which contains about 426,000 crystal structures[4]
H   He
1   2
31(5)   28
Li Be   B C N O F Ne
3 4   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 La 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 Ac
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)
Single-,[5] double-,[6] and triple-bond[7] covalent radii (in pm), determined using typically
400 experimental or calculated primary distances, R, per set.
H   He
1   2
32
-
-
  46
-
-
Li Be   B C N O F Ne
3 4                       Radius / pm: 5 6 7 8 9 10
133
124
-
102
90
85
                      single
                      double
                      triple
85
78
73
75
67
60
71
60
54
63
57
53
64
59
53
67
96
-
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
94
95
99
95
93
96
107
96
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
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
Cs Ba La-Yb 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
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
Fr Ra Ac-No Lr Rf Db Sg Bh Hs Mt Ds Rg Cn Uut Fl Uup Lv Uus Uuo
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
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

References[edit]

  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. ^ a b c Beatriz Cordero, Verónica Gómez, Ana E. Platero-Prats, Marc Revés, Jorge Echeverría, Eduard Cremades, Flavia Barragán and Santiago Alvarez (2008). "Covalent radii revisited". Dalton Trans. (21): 2832–2838. doi:10.1039/b801115j. 
  5. ^ a b P. Pyykkö, M. Atsumi (2009). "Molecular Single-Bond Covalent Radii for Elements 1-118". Chemistry: A European Journal 15: 186–197. doi:10.1002/chem.200800987. 
  6. ^ a b 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. . Figure 3 of this paper contains all radii of refs. [5-7]. The mean-square deviation of each set is 3 pm.
  7. ^ a b 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.