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.
Average radii
editThe 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.
| 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
editA 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]
| 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-bond
double-bond triple-bond |
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 | * | 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 | ** | 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 |
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
editReferences
edit- ^ Sanderson, R. T. (1983). "Electronegativity and Bond Energy". Journal of the American Chemical Society. 105 (8): 2259–2261. doi:10.1021/ja00346a026.
- ^ 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.
- ^ 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.
- ^ a b c 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.
- ^ a b 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.
- ^ 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. PMID 19856342.. Figure 3 of this paper contains all radii of refs. [5-7]. The mean-square deviation of each set is 3 pm.
- ^ 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.
- ^ 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.