Editing Covalent radius

{{short description|Measure of the size of an atom that forms part of one covalent bond}}
{{Atomic radius}}
[[File:Radis_d'un_àtom.png | thumb | right]]
The '''covalent radius''', ''r''<sub>cov</sub>, is a measure of the size of an [[atom]] that forms part of one [[covalent bond]]. It is usually measured either in [[picometre]]s (pm) or [[angstrom]]s (Å), with 1&nbsp;Å&nbsp;= 100&nbsp;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 (r<sub>1</sub>, r<sub>2</sub> and r<sub>3</sub> 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 [[heteroatom]]ic A–B bonds, ionic terms may enter. Often the [[polar covalent bond]]s 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 (chemistry)|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 crystal]]s). [[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&ndash;H, in H<sub>2</sub>)&nbsp;= 74.14&nbsp;pm so ''r''<sub>cov</sub>(H)&nbsp;= 37.07&nbsp;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,<ref>{{ cite journal |doi=10.1021/ja00346a026 |author=Sanderson, R. T. |year=1983| title=Electronegativity and Bond Energy|journal=Journal of the American Chemical Society| volume=105|pages=2259–2261 |issue=8 }}</ref> but the availability of large collections of bond lengths, which are more [[Transferability (chemistry)|transferable]], from the [[Cambridge Crystallographic Database]]<ref>{{ cite journal|author1=Allen, F. H. |author2=Kennard, O. |author3=Watson, D. G. |author4=Brammer, L. |author5=Orpen, A. G. |author6=Taylor, R. |year=1987|title=Table of Bond Lengths Determined by X-Ray and Neutron Diffraction|journal=J. Chem. Soc., Perkin Trans. 2| doi=10.1039/P298700000S1|pages= S1–S19| issue=12}}</ref><ref>{{cite journal|last1=Orpen|first1=A. Guy|last2=Brammer|first2=Lee|last3=Allen|first3=Frank H.|last4=Kennard|first4=Olga|last5=Watson|first5=David G.|last6=Taylor|first6=Robin|title=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=Journal of the Chemical Society, Dalton Transactions|pages=S1|year=1989|doi=10.1039/DT98900000S1|issue=12}}</ref> 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.<ref name="CSD">{{cite journal|author1=Beatriz Cordero |author2=Verónica Gómez |author3=Ana E. Platero-Prats |author4=Marc Revés |author5=Jorge Echeverría |author6=Eduard Cremades |author7=Flavia Barragán |author8=Santiago Alvarez |s2cid=244110 |title=Covalent radii revisited | journal=Dalton Trans.|year=2008|pages=2832–2838|doi=10.1039/b801115j|issue=21|pmid=18478144 }}</ref> For carbon, values are given for the different [[Orbital hybridisation|hybridisations]] of the orbitals.

{| style="text-align: center; border: none; min-width:70em" cellpadding="2" cellspacing="0"
|+ '''Covalent radii in pm from analysis of the [[Cambridge Structural Database]], which contains about 1,030,000 crystal structures'''<ref name="CSD"/>
|- style="background: #7DF9FF;"
|H
|colspan="17" style="background: #ffffff;" |&nbsp;
|He
|- style="background: #efefef;"
|1||colspan="17" style="background: #ffffff;"|&nbsp;||2
|-
|31(5)||colspan="17" |&nbsp;||28
|- style="background: #7DF9FF;"
|Li||Be||colspan="11" style="background: #ffffff;"|&nbsp;||B||C||N||O||F||Ne
|- style="background: #efefef;"
|3||4||colspan="11" style="background: #ffffff;"|Radius ([[standard deviation]]) / [[Picometre|pm]]
|5||6||7||8||9||10
|- valign="top"
|128(7)||96(3)||colspan="11" |&nbsp;||84(3)||sp<sup>3</sup> 76(1)<br>sp<sup>2</sup> 73(2)<br>sp &nbsp;69(1)||71(1)||66(2)||57(3)||58
|- style="background: #7DF9FF;"
|Na||Mg||colspan="11" style="background: #ffffff;" |&nbsp;||Al||Si||P||S||Cl||Ar
|- style="background: #efefef;"
|11||12||colspan="11" style="background: #ffffff;" |&nbsp;||13||14||15||16||17||18
|-
|166(9)||141(7)|| colspan="11" |&nbsp;||121(4)||111(2)||107(3)||105(3)||102(4)||106(10)
|- style="background: #7DF9FF;"
|K||Ca||style="background: #ffffff;" |&nbsp;||Sc||Ti||V||Cr||Mn||Fe||Co||Ni||Cu||Zn||Ga||Ge||As||Se||Br||Kr
|- style="background: #efefef;"
|19||20||style="background: #ffffff;" |&nbsp;||21||22||23||24||25||26||27||28||29||30||31||32||33||34||35||36
|- valign="top"
|203(12)||176(10)||style="background: #ffffff;" |&nbsp;||170(7)||160(8)||153(8)||139(5)||l.s. 139(5)<br>h.s. 161(8)||l.s. 132(3)<br>h.s. 152(6)||l.s. 126(3)<br>h.s. 150(7)||124(4)||132(4)||122(4)||122(3)||120(4)||119(4)||120(4)||120(3)||116(4)
|-  style="background: #7DF9FF;"
|Rb||Sr||style="background: #ffffff;" |&nbsp;||Y||Zr||Nb||Mo||Tc||Ru||Rh||Pd||Ag||Cd||In||Sn||Sb||Te||I||Xe
|- style="background: #efefef;"
|37||38||style="background: #ffffff;" |&nbsp;||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)
|-  style="background: #7DF9FF;"
|Cs||Ba||style="background: #ffffff;" |*||Lu||Hf||Ta||W||Re||Os||Ir||Pt||Au||Hg||Tl||Pb||Bi||Po||At||Rn
|- style="background: #efefef;"
|55||56||style="background: #ffffff;" |&nbsp;||71||72||73||74||75||76||77||78||79||80||81||82||83||84||85||86
|-
|244(11)||215(11)||&nbsp;||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
|-  style="background: #7DF9FF;"
|Fr||Ra||style="background: #ffffff;"|**
|- style="background: #efefef;"
|87||88
|-
|260||221(2)
|-
|&nbsp;
|-  style="background: #7DF9FF;"
|colspan="2" style="background: #ffffff;"|&nbsp;||style="background: #ffffff;"|*||La||Ce||Pr||Nd||Pm||Sm||Eu||Gd||Tb||Dy||Ho||Er||Tm||Yb
|- style="background: #efefef;"
|colspan="3" style="background: #ffffff;"|&nbsp;||57||58||59||60||61||62||63||64||65||66||67||68||69||70
|-
|colspan="3" style="background: #ffffff;"|&nbsp;||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)
|-  style="background: #7DF9FF;"
|colspan="2" style="background: #ffffff;"|&nbsp;||style="background: #ffffff;"|**||Ac||Th||Pa||U||Np||Pu||Am||Cm
|- style="background: #efefef;"
|colspan="3" style="background: #ffffff;"|&nbsp;||89||90||91||92||93||94||95||96
|-
|colspan="3" style="background: #ffffff;"|&nbsp;||215||206(6)||200||196(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,<ref name="Calc1">{{cite journal|author1=P. Pyykkö|author2=M. Atsumi|year=2009|title=Molecular Single-Bond Covalent Radii for Elements 1-118|journal=Chemistry: A European Journal|volume=15|issue=1|pages=186–197|doi=10.1002/chem.200800987|pmid=19058281}}</ref>
double,<ref name="Calc2">{{cite journal|author1=P. Pyykkö|author2=M. Atsumi|year=2009|title=Molecular Double-Bond Covalent Radii for Elements Li–E112|journal=Chemistry: A European Journal|volume=15|issue=46|pages=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.</ref>
and triple bonds<ref name="Calc3">{{cite journal|author1=P. Pyykkö|author2=S. Riedel|author3=M. Patzschke|year=2005|title=Triple-Bond Covalent Radii|journal=Chemistry: A European Journal|volume=11|issue=12|pages=3511–3520|doi=10.1002/chem.200401299|pmid=15832398}}</ref>
up to superheavy elements. Both experimental and computational data were used. 
The single-bond results are often similar to those of Cordero et al.<ref name="CSD" /> When they are different, the [[coordination number]]s used can be different. This is notably the case for most (d and f) transition metals. Normally one expects that ''r''<sub>1</sub> > ''r''<sub>2</sub>  > ''r''<sub>3</sub>. 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.<ref name="Tet">{{cite journal|author1=P. Pyykkö|year=2012|title=Refitted tetrahedral covalent radii for solids|journal=Physical Review B|volume=85|issue=2|pages=024115, 7 p|bibcode=2012PhRvB..85b4115P|doi=10.1103/PhysRevB.85.024115}}</ref>

{| style="text-align: center; border: none; min-width:70em" cellpadding="2" cellspacing="0"
|+ '''Single-,<ref name="Calc1" /> double-,<ref name="Calc2" /> and triple-bond<ref name="Calc3" /> covalent radii,  determined using typically <br>400 experimental or calculated primary distances, ''R'', per set.'''
|- style="background: #7DF9FF;"
|H
| colspan="17" style="background: #ffffff;" |&nbsp;
|He
|- style="background: #efefef;"
|1|| colspan="17" style="background: #ffffff;" |&nbsp;||2
|-
|32<br>-<br>-|| colspan="17" |&nbsp;||46<br>-<br>-
|- style="background: #7DF9FF;"
|Li||Be|| colspan="11" style="background: #ffffff;" |&nbsp;||B||C||N||O||F||Ne
|- style="background: #efefef;"
|3||4|| colspan="11" style="background: #ffffff;" |Radius / [[Picometre|pm]]:||5||6||7||8||9||10
|- valign="top"
|133<br>124<br>-||102<br>90<br>85|| colspan="11" |single-bond
double-bond

triple-bond 
|85<br>78<br>73||75<br>67<br>60||71<br>60<br>54||63<br>57<br>53||64<br>59<br>53||67<br>96<br>-
|- style="background: #7DF9FF;"
|Na||Mg|| colspan="11" style="background: #ffffff;" |&nbsp;||Al||Si||P||S||Cl||Ar
|- style="background: #efefef;"
|11||12|| colspan="11" style="background: #ffffff;" |&nbsp;||13||14||15||16||17||18
|-
|155<br>160<br>-||139<br>132<br>127|| colspan="11" |&nbsp;||126<br>113<br>111||116<br>107<br>102||111<br>102<br>94||103<br>94<br>95||99<br>95<br>93||96<br>107<br>96
|- style="background: #7DF9FF;"
|K||Ca||style="background: #ffffff;" |&nbsp;||Sc||Ti||V||Cr||Mn||Fe||Co||Ni||Cu||Zn||Ga||Ge||As||Se||Br||Kr
|- style="background: #efefef;"
|19||20||style="background: #ffffff;" |&nbsp;||21||22||23||24||25||26||27||28||29||30||31||32||33||34||35||36
|- valign="top"
|196<br>193<br>-||171<br>147<br>133||style="background: #ffffff;" |&nbsp;||148<br>116<br>114
|136<br>117<br>108||134<br>112<br>106||122<br>111<br>103||119<br>105<br>103||116<br>109<br>102||111<br>103<br>96||110<br>101<br>101||112<br>115<br>120||118<br>120<br>-
|124<br>117<br>121||121<br>111<br>114||121<br>114<br>106||116<br>107<br>107||114<br>109<br>110||117<br>121<br>108
|- style="background: #7DF9FF;"
|Rb||Sr||style="background: #ffffff;" |&nbsp;||Y||Zr||Nb||Mo||Tc||Ru||Rh||Pd||Ag||Cd||In||Sn||Sb||Te||I||Xe
|- style="background: #efefef;"
|37||38||style="background: #ffffff;" |&nbsp;||39||40||41||42||43||44||45||46||47||48||49||50||51||52||53||54
|-
|210<br>202<br>-||185<br>157<br>139||style="background: #ffffff;" |&nbsp;||163<br>130<br>124
|154<br>127<br>121||147<br>125<br>116||138<br>121<br>113||128<br>120<br>110||125<br>114<br>103||125<br>110<br>106||120<br>117<br>112||128<br>139<br>137||136<br>144<br>-
|142<br>136<br>146||140<br>130<br>132||140<br>133<br>127||136<br>128<br>121||133<br>129<br>125||131<br>135<br>122
|- style="background: #7DF9FF;"
|Cs||Ba|| style="background: #ffffff;" |*||Lu||Hf||Ta||W||Re||Os||Ir||Pt||Au||Hg||Tl||Pb||Bi||Po||At||Rn
|- style="background: #efefef;"
|55||56|| style="background: #ffffff;" |&nbsp;||71||72||73||74||75||76||77||78||79||80||81||82||83||84||85||86
|-
|232<br>209<br>-||196<br>161<br>149||&nbsp;||162<br>131<br>131
|152<br>128<br>122||146<br>126<br>119||137<br>120<br>115||131<br>119<br>110||129<br>116<br>109||122<br>115<br>107||123<br>112<br>110||124<br>121<br>123||133<br>142<br>-
|144<br>142<br>150||144<br>135<br>137||151<br>141<br>135||145<br>135<br>129||147<br>138<br>138||142<br>145<br>133
|- style="background: #7DF9FF;"
|Fr||Ra|| style="background: #ffffff;" |**||Lr
||Rf||Db||Sg||Bh||Hs||Mt||Ds||Rg||Cn||Nh||Fl||Mc||Lv||Ts||Og
|- style="background: #efefef;"
|87||88|| style="background: #ffffff;" |&nbsp;||103||104||105||106||107||108||109||110||111||112||113||114||115||116||117||118
|-
|223<br>218<br>-||201<br>173<br>159||&nbsp;||161<br>141<br>-
|157<br>140<br>131||149<br>136<br>126||143<br>128<br>121||141<br>128<br>119||134<br>125<br>118||129<br>125<br>113||128<br>116<br>112||121<br>116<br>118||122<br>137<br>130||136<br>-<br>-||143<br>-<br>-||162<br>-<br>-||175<br>-<br>-||165<br>-<br>-||157<br>-<br>-
|-
|&nbsp;
|- style="background: #7DF9FF;"
| colspan="2" style="background: #ffffff;" |&nbsp;||style="background: #ffffff;" |*||La||Ce||Pr||Nd||Pm||Sm||Eu||Gd||Tb||Dy||Ho||Er||Tm||Yb
|- style="background: #efefef;"
| colspan="3" style="background: #ffffff;" |&nbsp;||57||58||59||60||61||62||63||64||65||66||67||68||69||70
|- valign="top"
| colspan="3" style="background: #ffffff;" |&nbsp;||180<br>139<br>139||163<br>137<br>131||176<br>138<br>128||174<br>137<br>-||173<br>135<br>-||172<br>134<br>-||168<br>134<br>-||169<br>135<br>132||168<br>135<br>-||167<br>133<br>-||166<br>133<br>-||165<br>133<br>-||164<br>131<br>-||170<br>129<br>-
|- style="background: #7DF9FF;"
| colspan="2" style="background: #ffffff;" |&nbsp;||style="background: #ffffff;" |**||Ac||Th||Pa||U||Np||Pu||Am||Cm||Bk||Cf||Es||Fm||Md||No
|- style="background: #efefef;"
| colspan="3" style="background: #ffffff;" |&nbsp;||89||90||91||92||93||94||95||96||97||98||99||100||101||102
|- valign="top"
| colspan="3" style="background: #ffffff;" |&nbsp;||186<br>153<br>140||175<br>143<br>136||169<br>138<br>129||170<br>134<br>118||171<br>136<br>116||172<br>135<br>-||166<br>135<br>-||166<br>136<br>-||168<br>139<br>-||168<br>140<br>-||165<br>140<br>-||167<br>-<br>-||173<br>139<br>-||176<br>-<br>-
|}

== See also ==
* [[Atomic radii of the elements (data page)]]
* [[Ionization energy]]
* [[Electron affinity]]
* [[Electron configuration]]
* [[Periodic table]]
== References ==
{{reflist}}

[[Category:Chemical properties]]
[[Category:Chemical bonding]]
[[Category:Atomic radius]]