Bond length and effective radii of atoms and ions. Atomic radius: what is it and how to determine In connection with the atomic radius

The division of the chemical bond into types is conditional.

For a metallic bond, due to the attraction of electrons and metal ions, some signs of a covalent bond are characteristic, if we take into account the overlap of the atomic orbitals of atoms. In the formation of a hydrogen bond, in addition to the electrostatic interaction, the donor-acceptor nature of the interaction plays an important role.

It is also impossible to draw a sharp boundary between ionic and covalent polar bonds. It is impossible to attribute any metal-nonmetal bond to the ionic type. It is customary to consider an ionic bond between atoms whose electronegativity difference is greater than or equal to 2 (on the Pauling scale). For example, in sodium oxide, the Na 2 O bond (3.44 - 0.93 = 2.51) is an ionic bond, and in magnesium bromide MgBr it is a covalent polar bond (2.96 - 1.31 = 1.65).

In real substances, all types of chemical bonds are not found in pure form. For most compounds, the bond type is intermediate. This is possible, since the nature of the chemical bond is the same - it is the electrostatic interaction of electrons and nuclei inside and between atoms that are close at a distance, when an effective overlap of electron shells occurs.

Therefore, a continuous transition between all limiting cases is possible: ionic, covalent, metallic and residual bond. Visually, the transition can be represented as a tetrahedron, at the vertices of which there are extreme representatives, along the edges there are transitions between two types, and on the faces and inside the volume of the tetrahedron there are complex mixed types of bonds.

Effective radii of atoms and ions

Under effective radii of atoms and ions understand the radii of the spheres of atoms or ions, that is, the minimum distances at which the centers of the spheres of atoms or ions can approach the surface of neighboring atoms.

To determine the effective radius of an atom or ion, the crystal structure is represented as contiguous balls, the distance between which is equal to the sum of their radii. Depending on the type of chemical bond between the structural units of the crystal, there are: metallic radii, ionic radii, covalent radii and van der Waals radii.

metal radii
Defined as half the distance between neighboring atoms, obtained as a result of X-ray diffraction analysis:

Ionic radii
To calculate the radii of ions, it is assumed that with a sufficiently large difference in the sizes of cations and anions, large anions will touch each other, and smaller cations will be located in the voids between the anions, then the radius of the anion will be:

the radius of the cation is: .

covalent radii
Covalent radii are defined as half of the interatomic distance (bond length): .

In addition, when calculating the covalent radius, the ability of some elements to form multiple bonds, which reduce the distance between atoms and the type of hybridization of the central atom, is taken into account.

Van der Waals radii are calculated for atoms that are connected to each other only by intermolecular forces. Calculated as half the distance between the centers of atoms: .

Since the methods for calculating atomic and ionic radii are different, there are a large number of tables of radii.

Ionic crystals

The combination of cations and anions into a crystal is carried out due to the Coulomb attraction of electric charges. In a molecule, charges interact with a force. Value R is the distance between two ions. If this distance is infinitely far, then the force is zero. At a finite distance, the interaction force of two oppositely charged ions is negative, which corresponds to attraction, the ions tend to approach the minimum allowable distance, which corresponds to a stable bound state. The interaction force of two identically charged ions is positive, which corresponds to repulsion. Ions tend to scatter and do not form a stable connection at any distance. Thus, the crystal formation energy must be negative. This condition is realized during the formation of an ionic crystal.

There are no molecules in ionic crystals, so there are no boundaries between structural units. Ions can be thought of as charged spheres whose force fields are uniformly distributed in all directions in space. Therefore, each ion can attract ions of the opposite sign to itself in any direction, therefore the ionic bond has no direction.

The interaction of two ions of opposite sign cannot lead to complete mutual compensation of their force fields. Because of this, they retain the ability to attract ions of the opposite sign in other directions. Therefore, the ionic bond is not saturated.

Cations tend to surround themselves with as many anions as possible so that the Coulomb repulsion of ions of the same sign from each other is compensated by the mutual Coulomb attraction of cations and anions. Therefore, structures with an ionic type of chemical bond are characterized by high coordination numbers and densest spherical packings. The symmetry of ionic crystals is usually high.

Crystalline substances with an ionic type of chemical bond are characterized by dielectric properties, brittleness, average values ​​of hardness and density, low thermal and electrical conductivity.

Atomic ions; have the meaning of the radii of the spheres representing these atoms or ions in molecules or crystals. Atomic radii make it possible to approximate internuclear (interatomic) distances in molecules and crystals.

The electron density of an isolated atom decreases rapidly as the distance to the nucleus increases, so that the radius of an atom could be defined as the radius of the sphere in which the main part (for example, 99%) of the electron density is concentrated. However, to estimate the internuclear distances, it turned out to be more convenient to interpret the atomic radii in a different way. This led to various definitions and systems of atomic radii.

The covalent radius of an X atom is defined as half the length of a simple X-X chemical bond. So, for halogens, covalent radii are calculated from the equilibrium internuclear distance in the X 2 molecule, for sulfur and selenium - in S 8 and Se 8 molecules, for carbon - in a diamond crystal. The exception is the hydrogen atom, for which the covalent atomic radius is assumed to be 30 pm, while half the internuclear distance in the H 2 molecule is 37 pm. For compounds with a covalent bond, as a rule, the additivity principle is satisfied (the X–Y bond length is approximately equal to the sum of the atomic radii of the X and Y atoms), which makes it possible to predict the bond lengths in polyatomic molecules.

Ionic radii are defined as the values ​​whose sum for a pair of ions (for example, X + and Y -) is equal to the shortest internuclear distance in the corresponding ionic crystals. There are several systems of ionic radii; systems differ in numerical values ​​for individual ions, depending on which radius and which ion is taken as the basis for calculating the radii of other ions. For example, according to Pauling, this is the radius of the O 2- ion, taken equal to 140 pm; according to Shannon - the radius of the same ion, taken equal to 121 pm. Despite these differences, different systems for calculating internuclear distances in ionic crystals lead to approximately the same results.

Metallic radii are defined as half the shortest distance between atoms in the crystal lattice of a metal. For metal structures that differ in the type of packing, these radii are different. The closeness of the values ​​of the atomic radii of various metals often serves as an indication of the possibility of the formation of solid solutions by these metals. The additivity of the radii makes it possible to predict the parameters of the crystal lattices of intermetallic compounds.

Van der Waals radii are defined as quantities whose sum is equal to the distance that two chemically unrelated atoms of different molecules or different groups of atoms of the same molecule can approach. On average, van der Waals radii are about 80 pm larger than covalent radii. Van der Waals radii are used to interpret and predict the stability of molecular conformations and the structural ordering of molecules in crystals.

Lit .: Housecroft K., Constable E. Modern course of general chemistry. M., 2002. T. 1.

EFFECTIVE ATOMIC RADIUS - see. atomic radius.

Geological dictionary: in 2 volumes. - M.: Nedra. Edited by K. N. Paffengolts et al.. 1978 .

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The effective radius of an atom or ion is understood as the radius of the sphere of its action, and the atom (ion) is considered to be an incompressible ball. Using the planetary model of the atom, it is represented as a nucleus around which electrons revolve in orbits. The sequence of elements in the Periodic system of Mendeleev corresponds to the sequence of filling the electron shells. The effective radius of an ion depends on the occupancy of the electron shells, but it is not equal to the radius of the outer orbit. To determine the effective radius, the atoms (ions) in the crystal structure are represented as contacting rigid balls, so that the distance between their centers is equal to the sum of the radii. Atomic and ionic radii were determined experimentally from X-ray measurements of interatomic distances and calculated theoretically on the basis of quantum mechanical concepts.

The sizes of ionic radii obey the following laws:

1. Within one vertical row of the periodic system, the radii of ions with the same charge increase with increasing atomic number, since the number of electron shells increases, and hence the size of the atom.

2. For the same element, the ionic radius increases with increasing negative charge and decreases with increasing positive charge. The radius of the anion is greater than the radius of the cation, since the anion has an excess of electrons, while the cation has a deficiency. For example, for Fe, Fe 2+, Fe 3+, the effective radius is 0.126, 0.080 and 0.067 nm, respectively, for Si 4-, Si, Si 4+, the effective radius is 0.198, 0.118 and 0.040 nm.

3. The sizes of atoms and ions follow the periodicity of the Mendeleev system; exceptions are elements from No. 57 (lanthanum) to No. 71 (lutetium), where the atomic radii do not increase, but decrease uniformly (the so-called lanthanide contraction), and elements from No. 89 (actinium) and beyond (the so-called actinoid contraction).

The atomic radius of a chemical element depends on the coordination number. An increase in the coordination number is always accompanied by an increase in interatomic distances. In this case, the relative difference between the values ​​of atomic radii corresponding to two different coordination numbers does not depend on the type of chemical bond (provided that the type of bond in structures with compared coordination numbers is the same). A change in atomic radii with a change in the coordination number significantly affects the magnitude of volumetric changes during polymorphic transformations. For example, when iron is cooled, its transformation from a face-centered cubic modification to a body-centered cubic modification occurring at 906 ° C should be accompanied by an increase in volume by 9%, in fact, an increase in volume is 0.8%. This is due to the fact that due to a change in the coordination number from 12 to 8, the atomic radius of iron decreases by 3%. That is, the change in atomic radii during polymorphic transformations largely compensates for the volumetric changes that would have to occur if the atomic radius did not change in this case. The atomic radii of elements can only be compared with the same coordination number.

Atomic (ionic) radii also depend on the type of chemical bond.

In crystals with a metallic bond, the atomic radius is defined as half the interatomic distance between the nearest atoms. In the case of solid solutions, metallic atomic radii vary in a complex way.

Under the covalent radii of elements with a covalent bond is understood half of the interatomic distance between the nearest atoms connected by a single covalent bond. A feature of covalent radii is their constancy in different covalent structures with the same coordination numbers. So, the distances in single C-C bonds in diamond and saturated hydrocarbons are the same and equal to 0.154 nm.

Ionic radii in substances with an ionic bond cannot be defined as half the sum of the distances between the nearest ions. As a rule, the sizes of cations and anions differ sharply. In addition, the symmetry of the ions differs from spherical. There are several approaches to estimating the value of ionic radii. Based on these approaches, the ionic radii of the elements are estimated, and then the ionic radii of other elements are determined from the experimentally determined interatomic distances.

Van der Waals radii determine the effective sizes of noble gas atoms. In addition, van der Waals atomic radii are considered to be half of the internuclear distance between the nearest identical atoms that are not chemically bonded, i.e. belonging to different molecules (for example, in molecular crystals).

When using the values ​​of atomic (ionic) radii in calculations and constructions, their values ​​should be taken from tables built according to one system.

An important characteristic of an atom is its size, i.e., atomic radius. The size of an individual atom is not determined, since its outer boundary is blurred due to the probabilistic presence of electrons at various points in the circumnuclear space. Because of this, depending on the type of bond between atoms, metallic, covalent, van der Waals, ionic, and other atomic radii are distinguished.

"Metal" radii (r me) are found by dividing in half the shortest interatomic distances in the crystal structures of simple substances with a coordination number of 12. At other values ​​of c.h. necessary correction is taken into account.

Values covalent radii (r cov) calculated as half the length of a homoatomic bond. If it is not possible to determine the length of a single homoatomic bond, the r cov value of an atom of element A is obtained by subtracting the covalent radius of an atom of element B from the length of the heteroatomic bond A-B. Covalent radii depend mainly on the size of the inner electron shell.

Radii of valence-unbound atoms - van der Waals radii (r w) determine the effective sizes of atoms due to the repulsive forces of the filled energy levels.

Electron energy values ​​determined by Slater's rules. made it possible to estimate the relative value - the apparent size of the atom - r cmp (empirical radius).

The bond length is given in angstroms (1 Å = 0.1 nm = 100 pm).

Element	r me	r cov	rw	r cmp
H	0.46	0.37	1.20	0.25
He	1.22	0.32	1.40	-
Li	1.55	1.34	1.82	1.45
Be	1.13	0.90	-	1.05
B	0.91	0.82	-	0.85
C	0.77	0.77	1.70	0.70
N	0.71	0.75	1.55	0.65
O	-	0.73	1.52	0.60
F	-	0.71	1.47	0.50
Ne	1.60	0.69	1.54	-
Na	1.89	1.54	2.27	1.80
mg	1.60	1.30	1.73	1.50
Al	1.43	1.18	-	1.25
Si	1.34	1.11	2.10	1.10
P	1.30	1.06	1.80	1.00
S	-	1.02	1.80	1.00
Cl	-	0.9	1.75	1.00
Ar	1.92	0.97	1.88	-
K	2.36	1.96	2.75	2.20
Ca	1.97	1.74	-	1.80
sc	1.64	1.44	-	1.60
Ti	1.46	1.36	-	1.40
V	1.34	1.25	-	1.35
Cr	1.27	1.27	-	1.40
Mn	1.30	1.39	-	1.40
Fe	1.26	1.25	-	1.40
co	1.25	1.26	-	1.35
Ni	1.24	1.21	1.63	1.35
Cu	1.28	1.38	1.40	1.35
Zn	1.39	1.31	1.39	1.35
Ga	1.39	1.26	1.87	1.30
Ge	1.39	1.22	-	1.25
As	1.48	1.19	1.85	1.15
Se	1.60	1.16	1.90	1.15
Br	-	1.14	1.85	1.15
kr	1.98	1.10	2.02	-
Rb	2.48	2.11	-	2.35
Sr	2.15	1.92	-	2.00
Y	1.81	1.62	-	1.80
Zr	1.60	1.48	-	1.55
Nb	1.45	1.37	-	1.45
Mo	1.39	1.45	-	1.45
Tc	1.36	1.56	-	1.35
Ru	1.34	1.26	-	1.30
Rh	1.34	1.35	-	1.35
Pd	1.37	1.31	1.63	1.40
Ag	1.44	1.53	1.72	1.60
CD	1.56	1.48	1.58	1.55
In	1.66	1.44	1.93	1.55
sn	1.58	1.41	2.17	1.45
Te	1.70	1.35	2.06	1.40
I	-	1.33	1.98	1.40
Xe	2.18	1.30	2.16	-
Cs	2.68	2.25	-	2.60
Ba	2.21	1.98	-	2.15
La	1.87	1.69	-	1.95
Ce	1.83	-	-	1.85
Pr	1.82	-	-	1.85
Nd	1.82	-	-	1.85
Pm	-	-	-	1.85
sm	1.81	-	-	1.85
Eu	2.02	-	-	1.80
Gd	1.79	-	-	1.80
Tb	1.77	-	-	1.75
Dy	1.77	-	-	1.75
Ho	1.76	-	-	1.75
Er	1.75	-	-	1.75
Tm	1.74	-	-	1.75
Yb	1.93	-	-	1.75
Lu	1.74	1.60	-	1.75
hf	1.59	1.50	-	1.55
Ta	1.46	1.38	-	1.45
W	1.40	1.46	-	1.35
Re	1.37	1.59	-	1.35
Os	1.35	1.28	-	1.30
Ir	1.35	1.37	-	1.35
Pt	1.38	1.28	1.75	1.35
Au	1.44	1.44	1.66	1.35
hg	1.60	1.49	1.55	1.50
Tl	1.71	1.48	1.96	1.90
Pb	1.75	1.47	2.02	1.80
Bi	1.82	1.46	-	1.60
Po	-	-	-	1.90
At	-	-	-	-
Rn	-	1.45	-	-
Fr	2.80	-	-	-
Ra	2.35	-	-	2.15
AC	2.03	-	-	1.95
Th	180	-	-	1.80
Pa	1.62	-	-	1.80
U	1.53	-	1.86	1.75
Np	1.50	-	-	1.75
Pu	1.62	-	-	1.75
Am	-	-	-	1.75

The general trend of atomic radii is as follows. In groups, atomic radii increase, since with an increase in the number of energy levels, the sizes of atomic orbitals with a large value of the principal quantum number increase. For d-elements, in whose atoms the orbitals of the previous energy level are filled, this tendency does not have a distinct character during the transition from the elements of the fifth period to the elements of the sixth period.

In small periods, the radii of atoms generally decrease, since an increase in the charge of the nucleus during the transition to each next element causes the attraction of external electrons with increasing force; the number of energy levels at the same time remains constant.

The change in the atomic radius in periods for d-elements is more complex.

The value of the atomic radius is quite closely related to such an important characteristic of the atom as the ionization energy. An atom can lose one or more electrons, turning into a positively charged ion - a cation. This ability is quantified by the ionization energy.

List of used literature

1. Popkov V. A., Puzakov S. A. General chemistry: textbook. - M.: GEOTAR-Media, 2010. - 976 p.: ISBN 978-5-9704-1570-2. [with. 27-28]
2. Volkov, A.I., Zharsky, I.M. Big chemical reference book / A.I. Volkov, I.M. Zharsky. - Minsk: Modern school, 2005. - 608 with ISBN 985-6751-04-7.