Covalent radius
Encyclopedia
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 picometre
s (pm) or angstrom
s (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 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, that 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.
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,
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 number
s 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 E118 have now been experimentally produced and that there are chemical studies on an increasing number of them.
Atom
The atom is a basic unit of matter that consists of a dense central nucleus surrounded by a cloud of negatively charged electrons. The atomic nucleus contains a mix of positively charged protons and electrically neutral neutrons...
that forms part of one covalent bond
Covalent bond
A covalent bond is a form of chemical bonding that is characterized by the sharing of pairs of electrons between atoms. The stable balance of attractive and repulsive forces between atoms when they share electrons is known as covalent bonding....
. It is usually measured either in picometre
Picometre
A picometre is a unit of length in the metric system, equal to one trillionth, i.e. of a metre, which is the current SI base unit of length...
s (pm) or angstrom
Ångström
The angstrom or ångström, is a unit of length equal to 1/10,000,000,000 of a meter . Its symbol is the Swedish letter Å....
s (Å), with 1 Å = 100 pm.
In principle, the sum of the two covalent radii should equal the covalent bond length
Bond length
- Explanation :Bond length is related to bond order, when more electrons participate in bond formation the bond will get shorter. Bond length is also inversely related to bond strength and the bond dissociation energy, as a stronger bond will be shorter...
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
Heteroatom
In organic chemistry, a heteroatom is any atom that is not carbon or hydrogen. Usually, the term is used to indicate that non-carbon atoms have replaced carbon in the backbone of the molecular structure...
A–B bonds, ionic terms may enter. Often the polar covalent bonds are 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
Transferability
This page is about transferability in chemistry. Transferability in economics also exists.Transferability, in chemistry, is the assumption that a chemical property that is associated with an atom or a functional group in a molecule will have a similar value in a variety of different circumstances...
between different situations, that makes them useful.
The bond lengths R(AB) are measured by X-ray diffraction (more rarely, neutron diffraction
Neutron diffraction
Neutron diffraction or elastic neutron scattering is the application of neutron scattering to the determination of the atomic and/or magnetic structure of a material: A sample to be examined is placed in a beam of thermal or cold neutrons to obtain a diffraction pattern that provides information of...
on molecular crystals). Rotational spectroscopy
Rotational spectroscopy
Rotational spectroscopy or microwave spectroscopy studies the absorption and emission of electromagnetic radiation by molecules associated with a corresponding change in the rotational quantum number of the molecule...
can also give extremely accurate values of bond lengths. For homonuclear A–A bonds, Linus Pauling
Linus Pauling
Linus Carl Pauling was an American chemist, biochemist, peace activist, author, and educator. He was one of the most influential chemists in history and ranks among the most important scientists of the 20th century...
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
Transferability
This page is about transferability in chemistry. Transferability in economics also exists.Transferability, in chemistry, is the assumption that a chemical property that is associated with an atom or a functional group in a molecule will have a similar value in a variety of different circumstances...
, from the Cambridge Crystallographic Database has rendered covalent radii obsolete in many situations.
Table of covalent 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. The numbers in parentheses are the estimated standard deviations for the last digit. This fit pre-fixes the radii for C, N and O.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,
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 number
Coordination number
In chemistry and crystallography, the coordination number of a central atom in a molecule or crystal is the number of its nearest neighbours. This number is determined somewhat differently for molecules and for crystals....
s 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 E118 have now been experimentally produced and that there are chemical studies on an increasing number of them.
| H | He | |||||||||||||||||
| 1 | 2 | |||||||||||||||||
| 31(5) | 28 | |||||||||||||||||
| Li | Be | B | C | N | O | F | Ne | |||||||||||
| 3 | 4 | 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 | La | 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 | Ac | ||||||||||||||||
| 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) | |||||||||||
| H | He | |||||||||||||||||
| 1 | 2 | |||||||||||||||||
| 32-- | 46-- | |||||||||||||||||
| Li | Be | B | C | N | O | F | Ne | |||||||||||
| 3 | 4 | Radius / pm: | 5 | 6 | 7 | 8 | 9 | 10 | ||||||||||
| 133124- | 1029085 | single double triple | 857873 | 756760 | 716054 | 635753 | 645953 | 6796- | ||||||||||
| Na | Mg | Al | Si | P | S | Cl | Ar | |||||||||||
| 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | |||||||||||
| 155160- | 139132127 | 126113111 | 116107102 | 11110294 | 1039495 | 999593 | 9610796 | |||||||||||
| 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 | |
| 196193- | 171147133 | 148116114 | 136117108 | 134112106 | 122111103 | 119105103 | 116109102 | 11110396 | 110101101 | 112115120 | 118120- | 124117121 | 121111114 | 121114106 | 116107107 | 114109110 | 117121108 | |
| 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 | |
| 210202- | 185157139 | 163130124 | 154127121 | 147125116 | 138121113 | 128120110 | 125114103 | 125110106 | 120117112 | 128139137 | 136144- | 142136146 | 140130132 | 140133127 | 136128121 | 133129125 | 131135122 | |
| Cs | Ba | La-Yb | 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 | |
| 232209- | 196161149 | 162131131 | 152128122 | 146126119 | 137120115 | 131119110 | 129116109 | 122115107 | 123112110 | 124121123 | 133142- | 144142150 | 144135137 | 151141135 | 145135129 | 147138138 | 142145133 | |
| Fr | Ra | Ac-No | Lr | Rf | Db | Sg | Bh | Hs | Mt | Ds | Rg | Cn | Uut | Uuq | Uup | Uuh | Uus | Uuo |
| 87 | 88 | 103 | 104 | 105 | 106 | 107 | 108 | 109 | 110 | 111 | 112 | 113 | 114 | 115 | 116 | 117 | 118 | |
| 223218- | 201173159 | 161141- | 157140131 | 149136126 | 143128121 | 141128119 | 134125118 | 129125113 | 128116112 | 121116118 | 122137130 | 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 | |||||
| 180139139 | 163137131 | 176138128 | 174137 | 173135 | 172134 | 168134 | 169135132 | 168135 | 167133 | 166133 | 165133 | 164131 | 170129 | |||||
| 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 | |||||
| 186153140 | 175143136 | 169138129 | 170134118 | 171136116 | 172135 | 166135 | 166136 | 168139 | 168140 | 165140 | 167 | 173139 | 176 | |||||