Covalent radius

Covalent radius
Types of radii
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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

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.


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
400 experimental radii, and calculated radii
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 Uuq Uup Uuh 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

  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. 

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