Covalent radius

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 co 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, 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,[1] but the availability of large collections of bond lengths, which are more transferable, from the Cambridge Crystallographic Database[2][3] 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.[4] 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 426,000 crystal structures[4]
H   He
1   2
31(5)   28
Li Be   B C N O F Ne
3 4 Radius (standard deviation) / pm 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)

Radii 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,[5] double,[6] and triple bonds[7] up to superheavy elements. Both experimental and computational data were used. The single-bond results are often similar to those of Cordero et al.[4] 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.[8]

Single-,[5] double-,[6] and triple-bond[7] covalent radii, determined using typically
400 experimental or calculated primary distances, R, per set.
H   He
1   2
32
-
-
  46
-
-
Li Be   B C N O F Ne
3 4 Radius / pm: 5 6 7 8 9 10
133
124
-
102
90
85
single-bond

double-bond

triple-bond

85
78
73
75
67
60
71
60
54
63
57
53
64
59
53
67
96
-
Na Mg   Al Si P S Cl Ar
11 12   13 14 15 16 17 18
155
160
-
139
132
127
  126
113
111
116
107
102
111
102
94
103
94
95
99
95
93
96
107
96
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
196
193
-
171
147
133
148
116
114
136
117
108
134
112
106
122
111
103
119
105
103
116
109
102
111
103
96
110
101
101
112
115
120
118
120
-
124
117
121
121
111
114
121
114
106
116
107
107
114
109
110
117
121
108
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
210
202
-
185
157
139
163
130
124
154
127
121
147
125
116
138
121
113
128
120
110
125
114
103
125
110
106
120
117
112
128
139
137
136
144
-
142
136
146
140
130
132
140
133
127
136
128
121
133
129
125
131
135
122
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
232
209
-
196
161
149
  162
131
131
152
128
122
146
126
119
137
120
115
131
119
110
129
116
109
122
115
107
123
112
110
124
121
123
133
142
-
144
142
150
144
135
137
151
141
135
145
135
129
147
138
138
142
145
133
Fr Ra Ac-No Lr Rf Db Sg Bh Hs Mt Ds Rg Cn Nh Fl Mc Lv Ts Og
87 88   103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118
223
218
-
201
173
159
  161
141
-
157
140
131
149
136
126
143
128
121
141
128
119
134
125
118
129
125
113
128
116
112
121
116
118
122
137
130
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
  180
139
139
163
137
131
176
138
128
174
137
173
135
172
134
168
134
169
135
132
168
135
167
133
166
133
165
133
164
131
170
129
  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
  186
153
140
175
143
136
169
138
129
170
134
118
171
136
116
172
135
166
135
166
136
168
139
168
140
165
140
167 173
139
176

See also

References

  1. ^ Sanderson, R. T. (1983). "Electronegativity and Bond Energy". Journal of the American Chemical Society. 105 (8): 2259–2261. doi:10.1021/ja00346a026.
  2. ^ 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. doi:10.1039/P298700000S1.
  3. ^ 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. doi:10.1039/DT98900000S1.
  4. ^ a b c 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. doi:10.1039/b801115j.
  5. ^ a b P. Pyykkö; M. Atsumi (2009). "Molecular Single-Bond Covalent Radii for Elements 1-118". Chemistry: A European Journal. 15: 186–197. doi:10.1002/chem.200800987.
  6. ^ a b P. Pyykkö; M. Atsumi (2009). "Molecular Double-Bond Covalent Radii for Elements Li–E112". Chemistry: A European Journal. 15 (46): 12770–12779. doi:10.1002/chem.200901472.. Figure 3 of this paper contains all radii of refs. [5-7]. The mean-square deviation of each set is 3 pm.
  7. ^ a b P. Pyykkö; S. Riedel; M. Patzschke (2005). "Triple-Bond Covalent Radii". Chemistry: A European Journal. 11 (12): 3511–3520. doi:10.1002/chem.200401299. PMID 15832398.
  8. ^ P. Pyykkö (2012). "Refitted tetrahedral covalent radii for solids". Physical Review B. 85 (2): 024115, 7 p. Bibcode:2012PhRvB..85b4115P. doi:10.1103/PhysRevB.85.024115.
Atomic radii of the elements (data page)

The atomic radius of a chemical element is the distance from the centre of the nucleus to the outermost shell of the electron. Since the boundary is not a well-defined physical entity, there are various non-equivalent definitions of atomic radius. Depending on the definition, the term may apply only to isolated atoms, or also to atoms in condensed matter, covalently bound in molecules, or in ionized and excited states; and its value may be obtained through experimental measurements, or computed from theoretical models. Under some definitions, the value of the radius may depend on the atom's state and context.Atomic radii vary in a predictable and explicable manner across the periodic table. For instance, the radii generally decrease rightward along each period (row) of the table, from the alkali metals to the noble gases; and increase down each group (column). The radius increases sharply between the noble gas at the end of each period and the alkali metal at the beginning of the next period. These trends of the atomic radii (and of various other chemical and physical properties of the elements) can be explained by the electron shell theory of the atom; they provided important evidence for the development and confirmation of quantum theory.

Atomic radius

The atomic radius of a chemical element is a measure of the size of its atoms, usually the mean or typical distance from the center of the nucleus to the boundary of the surrounding cloud of electrons. Since the boundary is not a well-defined physical entity, there are various non-equivalent definitions of atomic radius. Three widely used definitions of atomic radius are: Van der Waals radius, ionic radius, and covalent radius.

Depending on the definition, the term may apply only to isolated atoms, or also to atoms in condensed matter, covalently bound in molecules, or in ionized and excited states; and its value may be obtained through experimental measurements, or computed from theoretical models. The value of the radius may depend on the atom's state and context.Electrons do not have definite orbits, or sharply defined ranges. Rather, their positions must be described as probability distributions that taper off gradually as one moves away from the nucleus, without a sharp cutoff. Moreover, in condensed matter and molecules, the electron clouds of the atoms usually overlap to some extent, and some of the electrons may roam over a large region encompassing two or more atoms.

Under most definitions the radii of isolated neutral atoms range between 30 and 300 pm (trillionths of a meter), or between 0.3 and 3 ångströms. Therefore, the radius of an atom is more than 10,000 times the radius of its nucleus (1–10 fm), and less than 1/1000 of the wavelength of visible light (400–700 nm).

For many purposes, atoms can be modeled as spheres. This is only a crude approximation, but it can provide quantitative explanations and predictions for many phenomena, such as the density of liquids and solids, the diffusion of fluids through molecular sieves, the arrangement of atoms and ions in crystals, and the size and shape of molecules.Atomic radii vary in a predictable and explicable manner across the periodic table. For instance, the radii generally decrease along each period (row) of the table, from the alkali metals to the noble gases; and increase down each group (column). The radius increases sharply between the noble gas at the end of each period and the alkali metal at the beginning of the next period. These trends of the atomic radii (and of various other chemical and physical properties of the elements) can be explained by the electron shell theory of the atom; they provided important evidence for the development and confirmation of quantum theory. The atomic radii decrease across the Periodic Table because as the atomic number increases, the number of protons increases across the period, but the extra electrons are only added to the same quantum shell. Therefore, the effective nuclear charge towards the outermost electrons increases, drawing the outermost electrons closer. As a result, the electron cloud contracts and the atomic radius decreases.

Bond energy

In chemistry, bond energy (E) or bond enthalpy (H) is the measure of bond strength in a chemical bond. IUPAC defines bond energy as the average value of the gas-phase bond dissociation energies (usually at a temperature of 298 K) for all bonds of the same type within the same chemical species. For example, the carbon–hydrogen bond energy in methane H(C–H) is the enthalpy change involved with breaking up one molecule of methane into a carbon atom and four hydrogen radicals, divided by 4. Tabulated bond energies are generally values of bond energies averaged over a number of selected typical chemical species containing that type of bond. Bond energy (E) or bond enthalpy (H) should not be confused with bond-dissociation energy. Bond energy is the average of all the bond-dissociation energies in a molecule, and will show a different value for a given bond than the bond-dissociation energy would. This is because the energy required to break a single bond in a specific molecule differs for each bond in that molecule. For example, methane has four C–H bonds and the bond-dissociation energies are 435 kJ/mol for D(CH3–H), 444 kJ/mol for D(CH2–H), 444 kJ/mol for D(CH–H) and 339 kJ/mol for D(C–H). Their average, and hence the bond energy, is 414 kJ/mol, even though not a single bond required specifically 414 kJ/mol to be broken.

Bond length

In molecular geometry, bond length or bond distance is the average distance between nuclei of two bonded atoms in a molecule. It is a transferable property of a bond between atoms of fixed types, relatively independent of the rest of the molecule.

Carbon–fluorine bond

The carbon–fluorine bond is a polar covalent bond between carbon and fluorine that is a component of all organofluorine compounds. It is the fourth strongest single bond in organic chemistry—behind the B-F single bond, Si-F single bond and the H-F single bond, and relatively short—due to its partial ionic character. The bond also strengthens and shortens as more fluorines are added to the same carbon on a chemical compound. As such, fluoroalkanes like tetrafluoromethane (carbon tetrafluoride) are some of the most unreactive organic compounds.

Covalent (disambiguation)

Covalent may refer to:

Covalent bond, a type of chemical bond

Covalent radius, half the distance between two covalently bonded atoms

Covalent modulation, the alteration of protein structure by covalent bonding

Covalent radius of fluorine

The covalent radius of fluorine is a measure of the size of a fluorine atom; it is approximated at about 60 picometres.

Since fluorine is a relatively small atom with a large electronegativity, its covalent radius is difficult to evaluate. The covalent radius is defined as half the bond lengths between two neutral atoms of the same kind connected with a single bond. By this definition, the covalent radius of F is 71 pm. However, the F-F bond in F2 is abnormally weak and long. Besides, almost all bonds to fluorine are highly polar because of its large electronegativity, so the use of a covalent radius to predict the length of such a bond is inadequate and the bond lengths calculated from these radii are almost always longer than the experimental values.

Bonds to fluorine have considerable ionic character, a result of its small atomic radius and large electronegativity. Therefore, the bond length of F is influenced by its ionic radius, the size of ions in an ionic crystal, which is about 133 pm for fluoride ions. The ionic radius of fluoride is much larger than its covalent radius. When F becomes F−, it gains one electron but has the same number of protons, meaning the attraction of the protons to the electrons is weaker, and the radius is larger.

Ionic radius

Ionic radius, rion, is the radius of an atom's ion in ionic crystals structure. Although neither atoms nor ions have sharp boundaries, they are sometimes treated as if they were hard spheres with radii such that the sum of ionic radii of the cation and anion gives the distance between the ions in a crystal lattice. Ionic radii are typically given in units of either picometers (pm) or angstroms (Å), with 1 Å = 100 pm. Typical values range from 30 pm (0.3 Å) to over 200 pm (2 Å).

The concept can be extended to solvated ions in liquid solutions taking into consideration the solvation shell.

List of data references for chemical elements

Values for many properties of the elements, together with various references, are collected on these data pages.

List of examples of lengths

This is a list of examples of lengths, in metres in order to give an understanding of lengths.

Molar ionization energies of the elements

These tables list values of molar ionization energies, measured in kJ mol−1. This is the energy per mole necessary to remove electrons from gaseous atoms or atomic ions. The first molar ionization energy applies to the neutral atoms. The second, third, etc., molar ionization energy applies to the further removal of an electron from a singly, doubly, etc., charged ion. For ionization energies measured in the unit eV, see Ionization energies of the elements (data page). All data from rutherfordium onwards is predicted.

Periodic trends

Periodic trends are specific patterns in the properties of chemical elements that are revealed in the periodic table of elements. Major periodic trends include electronegativity, ionization energy, electron affinity, atomic radius, ionic radius, metallic character, and chemical reactivity.

Periodic trends arise from the changes in the atomic structure of the chemical elements within their respective periods (horizontal rows) and groups in the periodic table. These trends enable the chemical elements to be organized in the periodic table based on their atomic structures and properties.

Some exceptions to these trends exist, such as that of ionization energy in Groups 3 and 6.

Ronald Gillespie

Ronald James Gillespie, (born August 21, 1924 in London), a chemistry professor at McMaster University, specializes in the field of Molecular Geometry in Chemistry. In 2007 he was awarded the Order of Canada.He was educated at the University of London obtaining a B.Sc in 1945, a Ph.D in 1949 and a D.Sc in 1957. He was Assistant Lecturer and then Lecturer in the Department of Chemistry at University College London in England from 1950 to 1958. He moved to McMaster University, Hamilton, Ontario, Canada in 1958 and is now emeritus professor. He was elected as a Fellow of the Royal Society of Canada in 1965 and a Fellow of the Royal Society of London in 1977.

Gillespie has done extensive work on expanding the idea of the Valence Shell Electron Pair Repulsion (VSEPR) model of Molecular Geometry, which he developed with Ronald Nyholm (and thus is also known as the Gillespie-Nyholm theory), and setting the rules for assigning numbers. He has written several books on this VSEPR topic in chemistry. With other workers he developed LCP theory, (ligand close packing theory), which for some molecules allows geometry to be predicted on the basis of ligand-ligand repulsions. Gillespie has also done extensive work on interpreting the covalent radius of fluorine. The covalent radius of most atoms is found by taking half the length of a single bond between two similar atoms in a neutral molecule. Calculating the covalent radius for fluorine is more difficult because of its high electronegativity compared to its small atomic radius size. Ronald Gillespie’s work on the bond length of fluorine focuses on theoretically determining the covalent radius of fluorine by examining its covalent radius when it is attached to several different atoms.

Speeds of sound of the elements

The speed of sound in any chemical element in the fluid phase has one temperature-dependent value. In the solid phase, different types of sound wave may be propagated, each with its own speed: among these types of wave are longitudinal (as in fluids), transversal, and (along a surface or plate) extensional.

Thiopyrylium

Thiopyrylium is a cation with the chemical formula C5H5S+. It is analogous to the pyrylium cation with the oxygen atom replaced by a sulfur atom.

Thiopyrylium salts are less reactive than the analogous pyrylium salts due to the lower electronegativity of the sulfur atom. Among the chalcogenic 6-membered unsaturated heterocycles, thiopyrylium is the most aromatic, due to sulfur having the same Pauling electronegativity as carbon and only a slightly higher covalent radius.Thiopyrylium salts can be synthesized by hydrogen abstraction from thiopyran by a hydride ion acceptor, such as trityl perchlorate.The thiopyrylium analogue of 2,4,6-trisubstituted pyrylium salts can be synthesized by treatment with sodium sulfide followed by precipitation with acid. This reaction causes the oxygen atom in the pyrylium cation to be substituted with sulfur.

Ångström

The ångström (,ANG-strəm; ANG-strum Swedish: [²ɔŋːstrœm]) or angstrom is a unit of length equal to 10−10 m (one ten-billionth of a metre) or 0.1 nanometre. Its symbol is Å, a letter in the Swedish alphabet.

The natural sciences and technology often use ångström to express sizes of atoms, molecules, microscopic biological structures, and lengths of chemical bonds, arrangement of atoms in crystals, wavelengths of electromagnetic radiation, and dimensions of integrated circuit parts. Atoms of phosphorus, sulfur, and chlorine are about an ångström in covalent radius, while a hydrogen atom is about half an ångström; see atomic radius. Visible light has wavelengths in the range of 4000–7000 Å.

The unit is named after the Swedish physicist Anders Jonas Ångström (1814–1874). The symbol is always written with the Swedish alphabet letter 'Å'. Though it appears to be of the Latin alphabet 'A' with a ring diacritic, it is not. The unit's name is often written in English with the Latin alphabet 'A', but the official definition is the Swedish letter 'Å'. It is not a part of the SI system of units, but it can be considered part of the metric system.

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