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, but the availability of large collections of bond lengths, which are more transferable, from the Cambridge Crystallographic Database 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. 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 structuresH He1 231(5) 28LiBe BCNOFNe34Radius (standard deviation) / pm5678910128(7)96(3) 84(3)sp3 76(1)sp2 73(2)sp 69(1)71(1)66(2)57(3)58NaMg AlSiPSClAr1112 131415161718166(9)141(7) 121(4)111(2)107(3)105(3)102(4)106(10)KCa ScTiVCrMnFeCoNiCuZnGaGeAsSeBrKr1920 21222324252627282930313233343536203(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 YZrNbMoTcRuRhPdAgCdInSnSbTeIXe3738 39404142434445464748495051525354220(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*LuHfTaWReOsIrPtAuHgTlPbBiPoAtRn5556 71727374757677787980818283848586244(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)150150FrRa**8788260221(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)
Radius 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, double,. Figure 3 of this paper contains all radii of refs. [5-7]. The mean-square deviation of each set is 3 pm. and triple bonds up to superheavy elements. Both experimental and computational data were used. The single-bond results are often similar to those of Cordero et al. 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.
+ Single-, double-, triple-, and sixfold- bond covalent radii, determined using typically 400 experimental or calculated primary distances, R, per set.H He1 232-- 46--LiBe BCNOFNe34Radius / pm:5678910133124-1029085single-bond double-bond
triple-bond
sixfold-bond 8578737567607160546357536459536796-NaMg AlSiPSClAr1112 131415161718155160-139132127 1261131111161071021111029410394959995939610796KCa ScTiVCrMnFeCoNiCuZnGaGeAsSeBrKr1920 21222324252627282930313233343536196193-171147133 148116114136117108 89134112106 83122111103 82119105103 79116109102 8011110396110101101112115120118120-124117121121111114121114106116107107114109110117121108RbSr YZrNbMoTcRuRhPdAgCdInSnSbTeIXe3738 39404142434445464748495051525354210202-185157139 163130124154127121 108147125116 100138121113 97128120110 98125114103 99125110106120117112128139137136144-142136146140130132140133127136128121133129125131135122CsBa*LuHfTaWReOsIrPtAuHgTlPbBiPoAtRn5556 71727374757677787980818283848586232209-196161149 162131131152128122 109146126119 105137120115 102131119110 102129116109 103122115107123112110124121123133142-144142150144135137151141135145135129147138138142145133FrRa**LrRfDbSgBhHsMtDsRgCnNhFlMcLvTsOg8788 103104105106107108109110111112113114115116117118223218-201173159 161141-157140131149136126143128121141128119134125118129125113128116112121116118122137130136--143--162--175--165--157-- *LaCePrNdPmSmEuGdTbDyHoErTmYb 5758596061626364656667686970 180139139163137131176138128174137-173135-172134-168134-169135132168135-167133-166133-165133-164131-170129- **AcThPaUNpPuAmCmBkCfEsFmMdNo 8990919293949596979899100101102 186153140175143136 115169138129 105170134118 104171136116 99172135-166135-166136-168139-168140-165140-167--173139-176--
See also Atomic radii of the elements (data page) Ionization energy Electron affinity Electron configuration Periodic table References