The covalent radius, rcov, is a measure of the size of atom which forms part of a covalent bond. It is measured either in picometres (pm) or í¥ngstrí¶ms (í…), with 1 í… = 100 pm.
In principle, the sum of the two covalent radii should equal the covalent bond length between two atoms. This relationship does not hold exactly because the size of an atom is not constant but depends on its chemical environment. In particular, polar covalent bonds tend to be 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.
Covalent radii are measured by X-ray diffraction (more rarely, neutron diffraction on molecular crystals). Rotational spectroscopy can also give extremely accurate values of bond lengths. One method takes the covalent radius to be half the single bond length in the element, e.g. d(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] has rendered covalent radii obsolete in many situations.
[] Table of covalent radii
The values in this table are based on a statistical analysis of more than 228,000 experimental bond lengths from the Cambridge Structural Database.[3] The numbers in parentheses are the estimated standard deviations for the last digit.
| Z |
Symbol |
r (í…) |
| 1 |
H |
0.31(5) |
| 2 |
He |
0.28 |
| 3 |
Li |
1.28(7) |
| 4 |
Be |
0.96(3) |
| 5 |
B |
0.84(3) |
| 6 |
C (sp3) |
0.76(1) |
|
C (sp2) |
0.73(2) |
|
C (sp) |
0.69(1) |
| 7 |
N |
0.71(1) |
| 8 |
O |
0.66(2) |
| 9 |
F |
0.57(3) |
| 10 |
Ne |
0.58 |
| 11 |
Na |
1.66(9) |
| 12 |
Mg |
1.41(7) |
| 13 |
Al |
1.21(4) |
| 14 |
Si |
1.11(2) |
| 15 |
P |
1.07(3) |
| 16 |
S |
1.05(3) |
| 17 |
Cl |
1.02(4) |
| 18 |
Ar |
1.06(10) |
| 19 |
K |
2.03(12) |
| 20 |
Ca |
1.76(10) |
| 21 |
Sc |
1.70(7) |
| 22 |
Ti |
1.60(8) |
| 23 |
V |
1.53(8) |
| 24 |
Cr |
1.39(5) |
| 25 |
Mn (low spin) |
1.39(5) |
|
Mn (high spin) |
1.61(8) |
| 26 |
Fe (low spin) |
1.32(3) |
|
Fe (high spin) |
1.52(6) |
| 27 |
Co (low spin) |
1.26(3) |
|
Co (high spin) |
1.50(7) |
| 28 |
Ni |
1.24(4) |
| 29 |
Cu |
1.32(4) |
| 30 |
Zn |
1.22(4) |
| 31 |
Ga |
1.22(3) |
| 32 |
Ge |
1.20(4) |
| 33 |
As |
1.19(4) |
| 34 |
Se |
1.20(4) |
| 35 |
Br |
1.20(3) |
| 36 |
Kr |
1.16(4) |
| 37 |
Rb |
2.20(9) |
| 38 |
Sr |
1.95(10) |
| 39 |
Y |
1.90(7) |
| 40 |
Zr |
1.75(7) |
| 41 |
Nb |
1.64(6) |
| 42 |
Mo |
1.54(5) |
| 43 |
Tc |
1.47(7) |
| 44 |
Ru |
1.46(7) |
| 45 |
Rh |
1.42(7) |
| 46 |
Pd |
1.39(6) |
| 47 |
Ag |
1.45(5) |
| 48 |
Cd |
1.44(9) |
| 49 |
In |
1.42(5) |
| 50 |
Sn |
1.39(4) |
| 51 |
Sb |
1.39(5) |
| 52 |
Te |
1.38(4) |
| 53 |
I |
1.39(3) |
| 54 |
Xe |
1.40(9) |
| 55 |
Cs |
2.44(11) |
| 56 |
Ba |
2.15(11) |
| 57 |
La |
2.07(8) |
| 58 |
Ce |
2.04(9) |
| 59 |
Pr |
2.03(7) |
| 60 |
Nd |
2.01(6) |
| 61 |
Pm |
1.99 |
| 62 |
Sm |
1.98(8) |
| 63 |
Eu |
1.98(6) |
| 64 |
Gd |
1.96(6) |
| 65 |
Tb |
1.94(5) |
| 66 |
Dy |
1.92(7) |
| 67 |
Ho |
1.92(7) |
| 68 |
Er |
1.89(6) |
| 69 |
Tm |
1.90(10) |
| 70 |
Yb |
1.87(8) |
| 71 |
Lu |
1.87(8) |
| 72 |
Hf |
1.75(10) |
| 73 |
Ta |
1.70(8) |
| 74 |
W |
1.62(7) |
| 75 |
Re |
1.51(7) |
| 76 |
Os |
1.44(4) |
| 77 |
Ir |
1.41(6) |
| 78 |
Pt |
1.36(5) |
| 79 |
Au |
1.36(6) |
| 80 |
Hg |
1.32(5) |
| 81 |
Tl |
1.45(7) |
| 82 |
Pb |
1.46(5) |
| 83 |
Bi |
1.48(4) |
| 84 |
Po |
1.40(4) |
| 85 |
At |
1.50 |
| 86 |
Rn |
1.50 |
| 87 |
Fr |
2.60 |
| 88 |
Ra |
2.21(2) |
| 89 |
Ac |
2.15 |
| 90 |
Th |
2.06(6) |
| 91 |
Pa |
2.00 |
| 92 |
U |
1.96(7) |
| 93 |
Np |
1.90(1) |
| 94 |
Pu |
1.87(1) |
| 95 |
Am |
1.80(6) |
| 96 |
Cm |
1.69(3) |
[] References
- ^ Sanderson, R. T. (1983). "Electronegativity and Bond Energy." J. Am. Chem. Soc. 105:2259-61.
- ^ 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 S1-S19.
- ^ Beatriz Cordero, Verónica Gómez, Ana E. Platero-Prats, Marc Revés, Jorge Echeverría, Eduard Cremades, Flavia Barragán and Santiago Alvarez. Covalent radii revisited. Dalton Trans., 2008, 2832-2838, doi:10.1039/b801115j
The covalent radius, rcov, is a measure of the size of atom which forms part of a covalent bond. It is measured either in picometres (pm) or í¥ngstrí¶ms (í…), with 1 í… = 100 pm.
In principle, the sum of the two covalent radii should equal the covalent bond length between two atoms. This relationship does not hold exactly because the size of an atom is not constant but depends on its chemical environment. In particular, polar covalent bonds tend to be 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.
Covalent radii are measured by X-ray diffraction (more rarely, neutron diffraction on molecular crystals). Rotational spectroscopy can also give extremely accurate values of bond lengths. One method takes the covalent radius to be half the single bond length in the element, e.g. d(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] has rendered covalent radii obsolete in many situations.
[] Table of covalent radii
The values in this table are based on a statistical analysis of more than 228,000 experimental bond lengths from the Cambridge Structural Database.[3] The numbers in parentheses are the estimated standard deviations for the last digit.
| Z |
Symbol |
r (í…) |
| 1 |
H |
0.31(5) |
| 2 |
He |
0.28 |
| 3 |
Li |
1.28(7) |
| 4 |
Be |
0.96(3) |
| 5 |
B |
0.84(3) |
| 6 |
C (sp3) |
0.76(1) |
|
C (sp2) |
0.73(2) |
|
C (sp) |
0.69(1) |
| 7 |
N |
0.71(1) |
| 8 |
O |
0.66(2) |
| 9 |
F |
0.57(3) |
| 10 |
Ne |
0.58 |
| 11 |
Na |
1.66(9) |
| 12 |
Mg |
1.41(7) |
| 13 |
Al |
1.21(4) |
| 14 |
Si |
1.11(2) |
| 15 |
P |
1.07(3) |
| 16 |
S |
1.05(3) |
| 17 |
Cl |
1.02(4) |
| 18 |
Ar |
1.06(10) |
| 19 |
K |
2.03(12) |
| 20 |
Ca |
1.76(10) |
| 21 |
Sc |
1.70(7) |
| 22 |
Ti |
1.60(8) |
| 23 |
V |
1.53(8) |
| 24 |
Cr |
1.39(5) |
| 25 |
Mn (low spin) |
1.39(5) |
|
Mn (high spin) |
1.61(8) |
| 26 |
Fe (low spin) |
1.32(3) |
|
Fe (high spin) |
1.52(6) |
| 27 |
Co (low spin) |
1.26(3) |
|
Co (high spin) |
1.50(7) |
| 28 |
Ni |
1.24(4) |
| 29 |
Cu |
1.32(4) |
| 30 |
Zn |
1.22(4) |
| 31 |
Ga |
1.22(3) |
| 32 |
Ge |
1.20(4) |
| 33 |
As |
1.19(4) |
| 34 |
Se |
1.20(4) |
| 35 |
Br |
1.20(3) |
| 36 |
Kr |
1.16(4) |
| 37 |
Rb |
2.20(9) |
| 38 |
Sr |
1.95(10) |
| 39 |
Y |
1.90(7) |
| 40 |
Zr |
1.75(7) |
| 41 |
Nb |
1.64(6) |
| 42 |
Mo |
1.54(5) |
| 43 |
Tc |
1.47(7) |
| 44 |
Ru |
1.46(7) |
| 45 |
Rh |
1.42(7) |
| 46 |
Pd |
1.39(6) |
| 47 |
Ag |
1.45(5) |
| 48 |
Cd |
1.44(9) |
| 49 |
In |
1.42(5) |
| 50 |
Sn |
1.39(4) |
| 51 |
Sb |
1.39(5) |
| 52 |
Te |
1.38(4) |
| 53 |
I |
1.39(3) |
| 54 |
Xe |
1.40(9) |
| 55 |
Cs |
2.44(11) |
| 56 |
Ba |
2.15(11) |
| 57 |
La |
2.07(8) |
| 58 |
Ce |
2.04(9) |
| 59 |
Pr |
2.03(7) |
| 60 |
Nd |
2.01(6) |
| 61 |
Pm |
1.99 |
| 62 |
Sm |
1.98(8) |
| 63 |
Eu |
1.98(6) |
| 64 |
Gd |
1.96(6) |
| 65 |
Tb |
1.94(5) |
| 66 |
Dy |
1.92(7) |
| 67 |
Ho |
1.92(7) |
| 68 |
Er |
1.89(6) |
| 69 |
Tm |
1.90(10) |
| 70 |
Yb |
1.87(8) |
| 71 |
Lu |
1.87(8) |
| 72 |
Hf |
1.75(10) |
| 73 |
Ta |
1.70(8) |
| 74 |
W |
1.62(7) |
| 75 |
Re |
1.51(7) |
| 76 |
Os |
1.44(4) |
| 77 |
Ir |
1.41(6) |
| 78 |
Pt |
1.36(5) |
| 79 |
Au |
1.36(6) |
| 80 |
Hg |
1.32(5) |
| 81 |
Tl |
1.45(7) |
| 82 |
Pb |
1.46(5) |
| 83 |
Bi |
1.48(4) |
| 84 |
Po |
1.40(4) |
| 85 |
At |
1.50 |
| 86 |
Rn |
1.50 |
| 87 |
Fr |
2.60 |
| 88 |
Ra |
2.21(2) |
| 89 |
Ac |
2.15 |
| 90 |
Th |
2.06(6) |
| 91 |
Pa |
2.00 |
| 92 |
U |
1.96(7) |
| 93 |
Np |
1.90(1) |
| 94 |
Pu |
1.87(1) |
| 95 |
Am |
1.80(6) |
| 96 |
Cm |
1.69(3) |
[] References
- ^ Sanderson, R. T. (1983). "Electronegativity and Bond Energy." J. Am. Chem. Soc. 105:2259-61.
- ^ 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 S1-S19.
- ^ Beatriz Cordero, Verónica Gómez, Ana E. Platero-Prats, Marc Revés, Jorge Echeverría, Eduard Cremades, Flavia Barragán and Santiago Alvarez. Covalent radii revisited. Dalton Trans., 2008, 2832-2838, doi:10.1039/b801115j