One of the most important characteristics of the chemical elements involved in the formation of a chemical bond is the size of an atom (ion): with its increase, the strength of interatomic bonds decreases. The size of an atom (ion) is usually determined by the value of its radius or diameter. Since an atom (ion) does not have clear boundaries, the concept of "atomic (ionic) radius" implies that 90–98% of the electron density of an atom (ion) is contained in the sphere of this radius. Knowing the values ​​of atomic (ionic) radii makes it possible to estimate internuclear distances in crystals (that is, the structure of these crystals), since for many problems the shortest distances between the nuclei of atoms (ions) can be considered the sum of their atomic (ionic) radii, although such additivity is approximate and is satisfied not in all cases.

Under atomic radius chemical element (about the ionic radius, see below), involved in the formation of a chemical bond, in the general case, agreed to understand half the equilibrium internuclear distance between the nearest atoms in the crystal lattice of the element. This concept, which is quite simple if we consider atoms (ions) as rigid spheres, actually turns out to be complex and often ambiguous. The atomic (ionic) radius of a chemical element is not a constant value, but varies depending on a number of factors, the most important of which are the type of chemical bond

and coordination number.

If the same atom (ion) in different crystals forms different types of chemical bonds, then it will have several radii - covalent in a crystal with a covalent bond; ionic in a crystal with an ionic bond; metallic in metal; van der Waals in a molecular crystal. The influence of the type of chemical bond can be seen in the following example. In diamond, all four chemical bonds are covalent and are formed sp 3-hybrids, so all four neighbors of a given atom are on the same and

the same distance from it d= 1.54 A˚) and the covalent radius of carbon in diamond will be

is equal to 0.77 A˚. In an arsenic crystal, the distance between atoms bound by covalent bonds ( d 1 = 2.52 A˚), much less than between atoms bound by van der Waals forces ( d 2 = 3.12 A˚), so As will have a covalent radius of 1.26 A˚ and van der Waals of 1.56 A˚ .

The atomic (ionic) radius also changes very sharply with a change in the coordination number (this can be observed during polymorphic transformations of elements). The smaller the coordination number, the lower the degree of space filling with atoms (ions) and the smaller the internuclear distances. An increase in the coordination number is always accompanied by an increase in internuclear distances.

It follows from the foregoing that the atomic (ionic) radii of different elements involved in the formation of a chemical bond can only be compared when they form crystals in which the same type of chemical bond is realized, and these elements in the formed crystals have the same coordination numbers .

Let us consider the main features of atomic and ionic radii in more detail.

Under covalent radii of elements It is customary to understand half of the equilibrium internuclear distance between the nearest atoms connected by a covalent bond.

A feature of covalent radii is their constancy in different "covalent structures" with the same coordination number Z j. In addition, covalent radii, as a rule, are additively bonded to each other, that is, the A–B distance is half the sum of the A–A and B–B distances in the presence of covalent bonds and the same coordination numbers in all three structures.

There are normal, tetrahedral, octahedral, quadratic and linear covalent radii.

The normal covalent radius of an atom corresponds to the case when an atom forms as many covalent bonds as it corresponds to its place in the periodic table: for carbon - 2, for nitrogen - 3, etc. This results in different values ​​of normal radii depending on the multiplicity (order) bonds (single bond, double, triple). If the bond is formed when the hybrid electron clouds overlap, then they speak of tetrahedral

(Z k = 4, sp 3-hybrid orbitals), octahedral ( Z k = 6, d 2sp 3-hybrid orbitals), quadratic ( Z k = 4, dsp 2-hybrid orbitals), linear ( Z k = 2, sp-hybrid orbitals) covalent radii.

It is useful to know the following about covalent radii (the values ​​\u200b\u200bof covalent radii for a number of elements are given in).

1. Covalent radii, unlike ionic ones, cannot be interpreted as the radii of atoms that have a spherical shape. Covalent radii are used only to calculate the internuclear distances between atoms united by covalent bonds, and do not say anything about the distances between atoms of the same type that are not covalently bonded.

2. The value of the covalent radius is determined by the multiplicity of the covalent bond. A triple bond is shorter than a double bond, which in turn is shorter than a single bond, so the covalent radius of a triple bond is smaller than the covalent radius of a double bond, which is smaller

single. It should be borne in mind that the order of the multiplicity of the relationship does not have to be an integer. It can also be fractional if the bond is resonant (benzene molecule, Mg2 Sn compound, see below). In this case, the covalent radius has an intermediate value between the values ​​corresponding to integer orders of the bond multiplicity.

3. If the bond is of a mixed covalent-ionic nature, but with a high degree of the covalent component of the bond, then the concept of the covalent radius can be introduced, but the influence of the ionic component of the bond on its value cannot be neglected. In some cases, this effect can lead to a significant decrease in the covalent radius, sometimes down to 0.1 A˚. Unfortunately, attempts to predict the magnitude of this effect in various

cases have not yet been successful.

4. The value of the covalent radius depends on the type of hybrid orbitals that take part in the formation of a covalent bond.

Ionic radii, of course, cannot be defined as half the sum of the distances between the nuclei of the nearest ions, since, as a rule, the sizes of cations and anions differ sharply. In addition, the symmetry of the ions may differ somewhat from spherical. Nevertheless, for real ionic crystals under ionic radius It is customary to understand the radius of the ball, which approximates the ion.

Ionic radii are used for approximate estimates of internuclear distances in ionic crystals. It is assumed that the distance between the nearest cation and anion is equal to the sum of their ionic radii. The typical error in determining internuclear distances in terms of ionic radii in such crystals is ≈0.01 A˚.

There are several systems of ionic radii that differ in the values ​​of the ionic radii of individual ions, but lead to approximately the same internuclear distances. The first work on the determination of ionic radii was carried out by V. M. Goldshmit in the 1920s. In it, the author used, on the one hand, the internuclear distances in ionic crystals measured by X-ray structural analysis, and, on the other hand, the values ​​of the ionic radii F– and O2– determined by

refractometry method. Most other systems also rely on the internuclear distances in crystals determined by diffraction methods and on some "reference" values ​​of the ionic radius of a particular ion. In the most widely known system

Pauling, this reference value is the ionic radius of the O2− peroxide ion, equal to

1.40A˚. This value for O2– agrees well with theoretical calculations. In the system of G. B. Bokiya and N. V. Belov, which is considered one of the most reliable, the ionic radius O2– is taken equal to 1.36 A˚.

In the 1970s and 1980s, attempts were made to directly determine the radii of ions by measuring the electron density using X-ray structural analysis, provided that the minimum of the electron density on the line connecting the nuclei is taken as the boundary of the ions. It turned out that this direct method leads to overestimated values ​​of the ionic radii of cations and to underestimated values ​​of the ionic radii of anions. In addition, it turned out that the values ​​of ionic radii determined by a direct method cannot be transferred from one compound to another, and the deviations from additivity are too large. Therefore, such ionic radii are not used to predict internuclear distances.

It is useful to know the following about ionic radii (in the tables below, the values ​​\u200b\u200bof ionic radii according to Bokiy and Belov are given).

1. The ionic radius for ions of the same element varies depending on its charge, and for the same ion it depends on the coordination number. Depending on the coordination number, tetrahedral and octahedral ionic radii are distinguished.

2. Inside one vertical row, more precisely, inside one group, periodic

system, the radii of ions with the same charge increase with an increase in the atomic number of the element, since the number of shells occupied by electrons increases, and hence the size of the ion.

3. For positively charged ions of atoms from the same period, the ionic radii rapidly decrease with increasing charge. The rapid decrease is explained by the action of two main factors in one direction: the strong attraction of “own” electrons by the cation, the charge of which increases with increasing atomic number; an increase in the strength of interaction between the cation and the anions surrounding it with an increase in the charge of the cation.

4. For negatively charged ions of atoms from the same period, the ionic radii increase with increasing negative charge. The two factors discussed in the previous paragraph in this case act in opposite directions, and the first factor prevails (an increase in the negative charge of the anion is accompanied by an increase in its ionic radius), therefore, an increase in ionic radii with an increase in the negative charge occurs much more slowly than a decrease in the previous case.

5. For the same element, that is, with the same initial electronic configuration, the radius of the cation is less than that of the anion. This is due to a decrease in the attraction of external "additional" electrons to the anion nucleus and an increase in the screening effect due to internal electrons (the cation has a lack of electrons, while the anion has an excess).

6. The sizes of ions with the same charge follow the periodicity of the periodic table. However, the value of the ionic radius is not proportional to the charge of the nucleus Z, which is due to the strong attraction of electrons by the nucleus. In addition, the lanthanides and actinides, in whose series the radii of atoms and ions with the same charge do not increase, but decrease with increasing atomic number (the so-called lanthanide contraction and actinide contraction), are an exception to the periodic dependence.11

11 Lanthanide contraction and actinide contraction are due to the fact that in lanthanides and actinides, electrons added with an increase in atomic number fill internal d And f-shells with a principal quantum number less than the principal quantum number of a given period. At the same time, according to quantum mechanical calculations in d and especially in f states, the electron is much closer to the nucleus than in s And p states of a given period with a large quantum number, therefore d And f-electrons are located in the inner regions of the atom, although the filling of these states with electrons (we are talking about electronic levels in the energy space) occurs differently.

metal radii are considered equal to half the shortest distance between the nuclei of atoms in the crystallizing structure of a metal element. They depend on the coordination number. If we take the metallic radius of any element at Z k \u003d 12 per unit, then when Z k = 8, 6 and 4 the metallic radii of the same element will be 0.98 respectively; 0.96; 0.88. Metallic radii have the property of additivity. Knowing their values ​​makes it possible to approximately predict the parameters of the crystal lattices of intermetallic compounds.

The atomic radii of metals are characterized by the following features (data on the values ​​of the atomic radii of metals can be found in).

1. The metallic atomic radii of transition metals are generally smaller than the metallic atomic radii of non-transition metals, reflecting the greater bond strength in transition metals. This feature is due to the fact that the metals of transition groups and the metals closest to them in the periodic system have electronic d-shells, and electrons in d-states can take part in the formation of a chemical bond. Strengthening of the bond may be due partly to the appearance of a covalent component of the bond and partly to the van der Waals interaction of the ionic cores. In crystals of iron and tungsten, for example, electrons in d-states make a significant contribution to the binding energy.

2. Within one vertical group, as we move from top to bottom, the atomic radii of metals increase, which is due to a sequential increase in the number of electrons (the number of shells occupied by electrons increases).

3. Within one period, more precisely, starting from the alkali metal to the middle of the transition metal group, in the direction from left to right, the atomic metal radii decrease. In the same sequence, the electric charge of the atomic nucleus increases and the number of electrons in the valence shell increases. With an increase in the number of binding electrons per atom, the metallic bond is strengthened, and at the same time, due to an increase in the charge of the nucleus, the attraction of core (inner) electrons by the nucleus increases, so the value of the metallic atomic radius decreases.

4. Transition metals of groups VII and VIII from the same period in the first approximation have almost the same metal radii. Apparently, when it comes to elements that have 5 or more d-electrons, an increase in the nuclear charge and the associated effects of attraction of core electrons, leading to a decrease in the atomic metallic radius, are compensated by the effects caused by the increasing number of electrons in the atom (ion) that do not participate in the formation of a metallic bond, and leading to an increase in the metallic radius (increasing the number of states occupied by electrons).

5. The increase in radii (see paragraph 2) for transition elements, which occurs during the transition from the fourth to the fifth period, is not observed for transition elements at

transition from the fifth to the sixth period; the metallic atomic radii of the corresponding (vertical comparison) elements in these last two periods are almost the same. Apparently, this is due to the fact that the elements located between them are completed with a relatively deep f-shell, so the increase in the charge of the nucleus and the associated attraction effects turn out to be more significant than the effects associated with an increasing number of electrons (lanthanide contraction).

6. Usually, metallic radii are much larger than ionic radii, but they do not differ so significantly from the covalent radii of the same elements, although without exception they are all larger than covalent ones. The large difference in the values ​​of the metallic atomic and ionic radii of the same elements is explained by the fact that the bond, which owes its origin to almost free conduction electrons, is not strong (hence the observed relatively large interatomic distances in the metal lattice). A significantly smaller difference in the values ​​of the metallic and covalent radii of the same elements can be explained if we consider the metallic bond as some special "resonant" covalent bond.

Under van der Waals radius It is customary to understand half of the equilibrium internuclear distance between the nearest atoms connected by a van der Waals bond. Van der Waals radii determine the effective sizes of noble gas atoms. In addition, as follows from the definition, the van der Waals atomic radius can be considered to be half the internuclear distance between the nearest atoms of the same name, connected by a van der Waals bond and belonging to different molecules (for example, in molecular crystals). When atoms approach each other at a distance less than the sum of their van der Waals radii, a strong interatomic repulsion occurs. Therefore, van der Waals atomic radii characterize the minimum allowable contacts of atoms belonging to different molecules. Data on the values ​​of van der Waals atomic radii for some atoms can be found in).

Knowing the van der Waals atomic radii makes it possible to determine the shape of molecules and their packing in molecular crystals. The van der Waals radii are much larger than all the radii of the same elements listed above, which is explained by the weakness of the van der Waals forces.

Ionic radius- value in Å characterizing the size of ion-cations and ion-anions; characteristic size of spherical ions, used to calculate interatomic distances in ionic compounds. The concept of ionic radius is based on the assumption that the size of ions does not depend on the composition of the molecules in which they are included. It is affected by the number of electron shells and the packing density of atoms and ions in the crystal lattice.

The size of an ion depends on many factors. With a constant charge of the ion, with an increase in the serial number (and, consequently, the charge of the nucleus), the ionic radius decreases. This is especially noticeable in the lanthanide series, where the ionic radii change monotonically from 117 pm for (La3+) to 100 pm (Lu3+) at a coordination number of 6. This effect is called lanthanide contraction.

In groups of elements, ionic radii generally increase with increasing atomic number. However, for d-elements of the fourth and fifth periods, due to lanthanide contraction, even a decrease in the ionic radius can occur (for example, from 73 pm for Zr4+ to 72 pm for Hf4+ at a coordination number of 4).

In the period, there is a noticeable decrease in the ionic radius, associated with an increase in the attraction of electrons to the nucleus with a simultaneous increase in the charge of the nucleus and the charge of the ion itself: 116 pm for Na+, 86 pm for Mg2+, 68 pm for Al3+ (coordination number 6). For the same reason, an increase in the ion charge leads to a decrease in the ionic radius for one element: Fe2+ 77 pm, Fe3+ 63 pm, Fe6+ 39 pm (coordination number 4).

Comparison of ionic radii can only be done at the same coordination number, since it affects the size of the ion due to the repulsive forces between the counterions. This is clearly seen in the example of the Ag+ ion; its ionic radius is 81, 114, and 129 pm for coordination numbers 2, 4, and 6, respectively.
The structure of an ideal ionic compound, due to the maximum attraction between unlike ions and the minimum repulsion of like ions, is largely determined by the ratio of the ionic radii of cations and anions. This can be shown by simple geometric constructions.

The ionic radius depends on many factors, such as the charge and size of the nucleus, the number of electrons in the electron shell, its density due to the Coulomb interaction. Since 1923, this concept has been understood as effective ionic radii. Goldschmidt, Ahrens, Bokiy and others created systems of ionic radii, but all of them are qualitatively identical, namely, cations in them, as a rule, are much smaller than anions (with the exception of Rb + , Cs + , Ba 2+ and Ra 2+ in relation to O 2- and F-). For the initial radius in most systems, the size of the radius K + = 1.33 Å was taken, all the rest were calculated from the interatomic distances in heteroatomic compounds, which were considered ionic according to the chemical type. connections. In 1965 in the USA (Waber, Grower) and in 1966 in the USSR (Brattsev) the results of quantum-mechanical calculations of the sizes of ions were published, which showed that cations, indeed, have a smaller size than the corresponding atoms, and anions practically do not differ in size from the corresponding atoms. This result is consistent with the laws of the structure of electron shells and shows the erroneousness of the initial positions adopted in calculating the effective ionic radii. Orbital ionic radii are unsuitable for estimating interatomic distances; the latter are calculated on the basis of a system of ionic-atomic radii.

The problem of ion radii is one of the central ones in theoretical chemistry, and the terms themselves "ionic radius" And " crystal radius”, characterizing the corresponding dimensions, are a consequence of the ion-covalent model of the structure. The problem of radii develops primarily within the framework of structural chemistry (crystal chemistry).

This concept found experimental confirmation after the discovery of X-ray diffraction by M. Laue (1912). The description of the diffraction effect almost coincided with the beginning of the development of the ionic model in the works of R. Kossel and M. Born. Subsequently, the diffraction of electrons, neutrons and other elementary particles was discovered, which served as the basis for the development of a number of modern methods of structural analysis (X-ray, neutron, electron diffraction, etc.). The concept of radii played a decisive role in the formation of the concept of lattice energy, the theory of closest packings, contributed to the emergence of the Magnus-Goldschmidt rules, the Goldschmidt-Fersman isomorphism rules, etc.

Back in the early 1920s. two axioms were accepted: on the portability (transferability) of ions from one structure to another and on the constancy of their sizes. It seemed quite logical to take half of the shortest internuclear distances in metals as radii (Bragg, 1920). Somewhat later (Huggins, Slater) a correlation was found between the atomic radii and distances to the maxima of the electron density of the valence electrons of the corresponding atoms.

Problem ionic radii (g yup) is somewhat more difficult. In ionic and covalent crystals, according to X-ray diffraction analysis, the following are observed: (1) some shift in the overlap density to a more electronegative atom, as well as (2) a minimum electron density on the bond line (the electron shells of ions at close distances should repel each other). This minimum can be considered as the area of ​​contact between individual ions, from which the radii can be counted. However, from the structural data for internuclear distances it is impossible to find a way to determine the contribution of individual ions and, accordingly, a way to calculate the ionic radii. To do this, it is necessary to specify at least the radius of one ion or the ratio of ion radii. Therefore, already in the 1920s. a number of criteria for such a definition were proposed (Lande, Pauling, Goldschmidt, etc.) and various systems of ionic and atomic radii were created (Arens, Goldschmidt, Boky, Zakhariazen, Pauling) (in domestic sources, the problem is described in detail by V.I. Lebedev, V.S. Urusov and B. K. Vainshtein).

Currently, the system of ionic radii of Shannon and Pruitt is considered the most reliable, in which the ionic radius F “(r f0W F "= 1.19 A) and O 2_ (r f0W О 2- = 1.26 A) (in monographs by B. K. Vainshtein, these are called physical.) A set of radii values ​​for all elements of the periodic system, for various oxidation states and cn, as well as for transition metal ions and for various spin states (the values ​​of the ionic radii of transition elements for cn 6 are given in Table 3.1) This system provides an accuracy of about 0.01 A in the calculation of internuclear distances in the most ionic compounds (fluorides and oxygen salts) and allows reasonable estimates of the radii of ions for which there are no structural data. Pruitt in 1988 calculated the then unknown radii for ions d- transition metals in high oxidation states, consistent with subsequent experimental data.

Table 3.1

Some ionic radii r (according to Shannon and Pruitt) of transition elements (CH 6)

The end of the table. 3.1

th CC 4 ; b CC 2; LS- low spin state; HS- high-spin state.

An important property of ionic radii is that they differ by about 20% when the cn changes by two units. Approximately the same change occurs when their oxidation state changes by two units. Spin "crossover"

conditional characteristics of ions used for an approximate estimate of internuclear distances in ionic crystals (See Ionic radii). Values ​​I. r. are naturally related to the position of the elements in the periodic system of Mendeleev. I. r. are widely used in crystal chemistry (see. Crystal chemistry), making it possible to reveal patterns in the structure of crystals of various compounds, in geochemistry (see. Geochemistry) in the study of the phenomenon of substitution of ions in geochemical processes, etc.

Several systems of values ​​of I. are offered. These systems are usually based on the following observation: the difference between the internuclear distances A - X and B - X in ionic crystals of the composition AX and BX, where A and B are a metal, X is a non-metal, practically does not change when X is replaced by another non-metal similar to it ( for example, when replacing chlorine with bromine), if the coordination numbers of similar ions in the compared salts are the same. It follows from this that I. p. possess the property of additivity, i.e., that the experimentally determined internuclear distances can be considered as the sum of the corresponding "radii" of the ions. The division of this sum into terms is always based on more or less arbitrary assumptions. I. R. systems proposed by different authors differ mainly in the use of various initial assumptions.

The tables give I. p., corresponding to different values ​​​​of the oxidizing number (see. Valence). With its values ​​​​other than +1, the oxidation number does not correspond to the actual degree of ionization of atoms, and I. p. acquire an even more conventional meaning, since the bond can be largely covalent in nature. Values ​​I. r. (in Å) for some elements (according to N.V. Belov and G.B. Bokiy): F - 1.33, Cl - 1.81, Br - 1.96, I - 2.20, O 2- 1 .36, Li + 0.68, Na - 0.98, K + 1.33, Rb + 1.49, Cs + 1.65, Be 2+ 0.34, Mg 2+ 0.74, Ca 2+ 1.04, Sr 2+ 1.20, Ba 2+ 1.38, Sc 3+ 0.83, Y 3+ 0.97, La 3+ 1.04.

V. L. Kireev.

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