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<title>Covalent radius</title>

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Covalent radius

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</style><table class="sidebar nomobile nowraplinks" style="width:auto"><tbody><tr><th class="sidebar-title" style="border-bottom:2px solid; background:#d3d3d3">Types of radii</th></tr><tr><td class="sidebar-content">

<ul><li><a href="Atomic_radius" title="Atomic radius">Atomic radius</a></li>

<li><a href="Ionic_radius" title="Ionic radius">Ionic radius</a></li>

<li><a href="Metallic_radius" class="mw-redirect" title="Metallic radius">Metallic radius</a></li>

<li><a href="Van_der_Waals_radius" title="Van der Waals radius">Van der Waals radius</a></li></ul>

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The covalent radius, rcov, is a measure of the size of an <a href="Atom" title="Atom">atom</a> that forms part of one <a href="Covalent_bond" title="Covalent bond">covalent bond</a>. It is usually measured either in <a href="Picometre" title="Picometre">picometres</a> (pm) or <a href="Angstrom" title="Angstrom">angstroms</a> (Å), with 1 Å = 100 pm.

In principle, the sum of the two covalent radii should equal the covalent <a href="Bond_length" title="Bond length">bond length</a> 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 <a href="Heteroatom" title="Heteroatom">heteroatomic</a> A–B bonds, ionic terms may enter. Often the <a href="Polar_covalent_bond" class="mw-redirect" title="Polar covalent bond">polar covalent bonds</a> 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 <a href="Transferability_(chemistry)" title="Transferability (chemistry)">transferability</a> between different situations, which makes them useful.

The bond lengths R(AB) are measured by <a href="X-ray_diffraction" title="X-ray diffraction">X-ray diffraction</a> (more rarely, <a href="Neutron_diffraction" title="Neutron diffraction">neutron diffraction</a> on <a href="Molecular_crystal" class="mw-redirect" title="Molecular crystal">molecular crystals</a>). <a href="Rotational_spectroscopy" title="Rotational spectroscopy">Rotational spectroscopy</a> can also give extremely accurate values of bond lengths. For <a href="Homonuclear" class="mw-redirect" title="Homonuclear">homonuclear</a> A–A bonds, <a href="Linus_Pauling" title="Linus Pauling">Linus Pauling</a> 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,<a href="#cite_note-1">[1]</a> but the availability of large collections of bond lengths, which are more <a href="Transferability_(chemistry)" title="Transferability (chemistry)">transferable</a>, from the <a href="Cambridge_Crystallographic_Database" class="mw-redirect" title="Cambridge Crystallographic Database">Cambridge Crystallographic Database</a><a href="#cite_note-2">[2]</a><a href="#cite_note-3">[3]</a> has rendered covalent radii obsolete in many situations.

<div class="mw-heading mw-heading2"><h2 id="Average_radii">Average radii</h2></div>

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.<a href="#cite_note-CSD-4">[4]</a> For carbon, values are given for the different <a href="Orbital_hybridisation" title="Orbital hybridisation">hybridisations</a> of the orbitals.

<caption>Covalent radii in pm from analysis of the <a href="Cambridge_Structural_Database" title="Cambridge Structural Database">Cambridge Structural Database</a>, which contains about 1,030,000 crystal structures<a href="#cite_note-CSD-4">[4]</a>

</caption>

<td>H

</td>

</td>

<td>He

</td></tr>

<td>2

</td></tr>

<tr>

<td>28

</td></tr>

<td>Ne

</td></tr>

<td colspan="11" style="background: #ffffff;">Radius (<a href="Standard_deviation" title="Standard deviation">standard deviation</a>) / <a href="Picometre" title="Picometre">pm</a>

</td>

<td>10

</td></tr>

<td>58

</td></tr>

<td>Ar

</td></tr>

<td>18

</td></tr>

<tr>

<td>106(10)

</td></tr>

<td>Kr

</td></tr>

<td>36

</td></tr>

<td>116(4)

</td></tr>

<td>Xe

</td></tr>

<td>54

</td></tr>

<tr>

<td>140(9)

</td></tr>

<td>Rn

</td></tr>

<td>86

</td></tr>

<tr>

<td>150

</td></tr>

<td style="background: #ffffff;">**

</td></tr>

<td>88

</td></tr>

<tr>

<td>221(2)

</td></tr>

<tr>

<td>

</td></tr>

<td>Yb

</td></tr>

<td>70

</td></tr>

<tr>

<td>187(8)

</td></tr>

<td>Cm

</td></tr>

<td>96

</td></tr>

<tr>

<td>169(3)

</td></tr></tbody></table>

<div class="mw-heading mw-heading2"><h2 id="Radius_for_multiple_bonds">Radius for multiple bonds</h2></div>

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,<a href="#cite_note-Calc1-5">[5]</a>

double,<a href="#cite_note-Calc2-6">[6]</a>

and triple bonds<a href="#cite_note-Calc3-7">[7]</a>

up to superheavy elements. Both experimental and computational data were used.

The single-bond results are often similar to those of Cordero et al.<a href="#cite_note-CSD-4">[4]</a> When they are different, the <a href="Coordination_number" title="Coordination number">coordination numbers</a> 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 <a href="Atomic_number" title="Atomic number">atomic number</a> 118 (<a href="Oganesson" title="Oganesson">oganesson</a>) 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.<a href="#cite_note-Tet-8">[8]</a>

<caption>Single-,<a href="#cite_note-Calc1-5">[5]</a> double-,<a href="#cite_note-Calc2-6">[6]</a> and triple-bond<a href="#cite_note-Calc3-7">[7]</a> covalent radii, determined using typically 400 experimental or calculated primary distances, R, per set.

</caption>

<td>H

</td>

</td>

<td>He

</td></tr>

<td>2

</td></tr>

<tr>

<td>46 - -

</td></tr>

<td>Ne

</td></tr>

<td colspan="11" style="background: #ffffff;">Radius / <a href="Picometre" title="Picometre">pm</a>:</td>

<td>10

</td></tr>

<td colspan="11">single-bond

double-bond

triple-bond

</td>

<td>67 96 -

</td></tr>

<td>Ar

</td></tr>

<td>18

</td></tr>

<tr>

<td>96 107 96

</td></tr>

<td>Kr

</td></tr>

<td>36

</td></tr>

<td>148 116 114

</td>

<td>118 120 -

</td>

<td>117 121 108

</td></tr>

<td>Xe

</td></tr>

<td>54

</td></tr>

<tr>

<td>163 130 124

</td>

<td>136 144 -

</td>

<td>131 135 122

</td></tr>

<td>Rn

</td></tr>

<td>86

</td></tr>

<tr>

<td>162 131 131

</td>

<td>133 142 -

</td>

<td>142 145 133

</td></tr>

<td>Lr

</td>

<td>Og

</td></tr>

<td>118

</td></tr>

<tr>

<td>161 141 -

</td>

<td>157 - -

</td></tr>

<tr>

<td>

</td></tr>

<td>Yb

</td></tr>

<td>70

</td></tr>

<td>170 129 -

</td></tr>

<td>No

</td></tr>

<td>102

</td></tr>

<td>176 - -

</td></tr></tbody></table>

<ul><li><a href="Atomic_radii_of_the_elements_(data_page)" title="Atomic radii of the elements (data page)">Atomic radii of the elements (data page)</a></li>

<li><a href="Ionization_energy" title="Ionization energy">Ionization energy</a></li>

<li><a href="Electron_affinity" title="Electron affinity">Electron affinity</a></li>

<li><a href="Electron_configuration" title="Electron configuration">Electron configuration</a></li>

<li><a href="Periodic_table" title="Periodic table">Periodic table</a></li></ul>

<div class="mw-heading mw-heading2"><h2 id="References">References</h2></div>

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</style><cite id="CITEREFSanderson,_R._T.1983" class="citation journal cs1">Sanderson, R. T. (1983). "Electronegativity and Bond Energy". Journal of the American Chemical Society. 105 (8): 2259–2261. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1021%2Fja00346a026">10.1021/ja00346a026</a>.</cite>

</li>

<li id="cite_note-2"><a href="#cite_ref-2">^</a> <cite id="CITEREFAllen,_F._H.Kennard,_O.Watson,_D._G.Brammer,_L.1987" class="citation journal cs1">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. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1039%2FP298700000S1">10.1039/P298700000S1</a>.</cite>

</li>

<li id="cite_note-3"><a href="#cite_ref-3">^</a> <cite id="CITEREFOrpenBrammerAllenKennard1989" class="citation journal cs1">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. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1039%2FDT98900000S1">10.1039/DT98900000S1</a>.</cite>

</li>

<li id="cite_note-CSD-4">^ <a href="#cite_ref-CSD_4-0">a</a> <a href="#cite_ref-CSD_4-1">b</a> <a href="#cite_ref-CSD_4-2">c</a> <cite id="CITEREFBeatriz_CorderoVerónica_GómezAna_E._Platero-PratsMarc_Revés2008" class="citation journal cs1">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. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1039%2Fb801115j">10.1039/b801115j</a>. <a href="PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/18478144">18478144</a>. <a href="S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:244110">244110</a>.</cite>

</li>

<li id="cite_note-Calc1-5">^ <a href="#cite_ref-Calc1_5-0">a</a> <a href="#cite_ref-Calc1_5-1">b</a> <cite id="CITEREFP._PyykköM._Atsumi2009" class="citation journal cs1">P. Pyykkö; M. Atsumi (2009). "Molecular Single-Bond Covalent Radii for Elements 1-118". Chemistry: A European Journal. 15 (1): 186–197. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1002%2Fchem.200800987">10.1002/chem.200800987</a>. <a href="PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/19058281">19058281</a>.</cite>

</li>

<li id="cite_note-Calc2-6">^ <a href="#cite_ref-Calc2_6-0">a</a> <a href="#cite_ref-Calc2_6-1">b</a> <cite id="CITEREFP._PyykköM._Atsumi2009" class="citation journal cs1">P. Pyykkö; M. Atsumi (2009). "Molecular Double-Bond Covalent Radii for Elements Li–E112". Chemistry: A European Journal. 15 (46): 12770–12779. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1002%2Fchem.200901472">10.1002/chem.200901472</a>. <a href="PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/19856342">19856342</a>.</cite>. Figure 3 of this paper contains all radii of refs. [5-7]. The mean-square deviation of each set is 3 pm.

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<li id="cite_note-Calc3-7">^ <a href="#cite_ref-Calc3_7-0">a</a> <a href="#cite_ref-Calc3_7-1">b</a> <cite id="CITEREFP._PyykköS._RiedelM._Patzschke2005" class="citation journal cs1">P. Pyykkö; S. Riedel; M. Patzschke (2005). "Triple-Bond Covalent Radii". Chemistry: A European Journal. 11 (12): 3511–3520. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1002%2Fchem.200401299">10.1002/chem.200401299</a>. <a href="PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/15832398">15832398</a>.</cite>

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<li id="cite_note-Tet-8"><a href="#cite_ref-Tet_8-0">^</a> <cite id="CITEREFP._Pyykkö2012" class="citation journal cs1">P. Pyykkö (2012). "Refitted tetrahedral covalent radii for solids". Physical Review B. 85 (2): 024115, 7 p. <a href="Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2012PhRvB..85b4115P">2012PhRvB..85b4115P</a>. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1103%2FPhysRevB.85.024115">10.1103/PhysRevB.85.024115</a>.</cite>

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