Crystal field theory replaced theory valence bonds in the 40s of the XX century. In its pure form it is not used now, since it cannot explain the formation covalent bonds in complex compounds and does not take into account the true state of the ligands (for example, their actual sizes) even in the case of interactions close to purely electrostatic.

Already in the mid-50s, the simplified crystal field theory was replaced by an improved ligand field theory, taking into account the covalent nature of the chemical bonds between the complexing agent and the ligand.

However, the most general approach to explaining the formation of complex compounds is given by theory molecular orbitals (MO), which currently prevails over all others. The molecular orbital method provides for both purely electrostatic interaction in the absence of overlapping atomic orbitals, and the entire set of intermediate degrees of overlap.

Let's look at the basic concepts crystal field theory, which, like the theory of valence bonds, still retains its importance for the qualitative description of chemical bonds in complex compounds due to its great simplicity and clarity.

In crystal field theory chemical bond complexing agent – ​​ligand is considered electrostatic. According to this theory, the ligands are located around the complexing agent at the vertices regular polyhedra (polyhedra) as point charges. The theory does not take into account the actual volume of the ligand.

Ligands, like point charges, create around the complexing agent electrostatic field(“crystal field”, if we consider a crystal of a complex compound, or ligand field), in which the energy levels of the complexing agent and, above all, d-sublevels are splitting, and their energy changes. The nature of the splitting, the energy of new energy levels depends on symmetry arrangement of ligands (octahedral, tetrahedral or other crystal field). When molecules H 2 O, NH 3 , CO and others are coordinated as ligands, they are considered as dipoles, oriented with a negative charge towards the complexing agent.

Consider the case of an octahedral arrangement of ligands (for example, -3 or 3+). In the center of the octahedron there is a complexing ion M(+ n) with electrons on d-atomic orbitals, and at its vertices there are ligands in the form of point negative charges (for example, F - ions or polar molecules like NH 3). In a conventional ion M(+ n), not associated with ligands, the energies of all five d-AO are the same (i.e. atomic orbitals degenerate).

However, in the octahedral field of ligands d-AOs of the complexing agent fall into unequal position. Atomic orbitals d(z 2) and d(x 2 -y 2), elongated along the coordinate axes, come closest to the ligands. Between these orbitals and the ligands located at the vertices of the octahedron, significant differences arise repulsive forces, leading to an increase in orbital energy. In other words, these atomic orbitals are subject to maximum exposure to the ligand field. A strongly compressed spring can serve as a physical model of such interaction.
Other three d-AO – d(xy), d(xz) And d(yz), located between the coordinate axes and between the ligands, are at a greater distance from them. The interaction of such d-AO with ligands is minimal, and therefore energy d(xy), d(xz) And d(yz)-AO decreases compared to the original one.
Thus, fivefold degenerate d-AO complexing agent, getting into octahedral ligand field, exposed splitting into two groups of new orbitals – triply degenerate orbitals with lower energy, d(xy), d(xz) And d(yz), And doubly degenerate orbitals with higher energy d(z 2) and d(x 2 -y 2). These new groups d-orbitals with lower And higher energy denote dε and dγ:

d(z 2) and d(x 2 -y 2)

d(xy), d(xz),d(yz)

Energy difference two new sublevels dε and dγ was named splitting parameter Δ 0:

E 2 – E 1 = Δ 0 ≈ 0

Location of two new energy sublevels dε and dγ relative to the original ( d-AO) on the energy diagram asymmetrical:

(E 2 – E 0) > (E 0 – E 1).

Quantum mechanical theory requires that when new energy levels are completely populated with electrons, the total energy remains unchanged, i.e. she should stay equal to E 0 .
In other words, the equality must be satisfied

4(E 2 – E 0) = 6(E 0 – E 1),

where 4 and 6 – maximum number of electrons per dγ- and dε-AO. From this equality it follows that

(E 2 – E 0) / (E 0 – E 1) = 3/2 and
(E 2 – E 1) / (E 0 – E 1) = 5/2, or

Δ 0 / ( E 0 – E 1) = 5/2, whence ( E 0 – E 1) = 2/5Δ 0 .

Placing each electron out of the maximum six possible on dε orbitals cause decrease (winnings) energy by 2/5 Δ 0 .

On the contrary, the placement of each electron out of four possible on dγ orbitals cause increase (cost) energy by 3/5 Δ 0 .

If populated with electrons dε- and dγ-orbitals completely, then no winning energy will not(just as it won't additional energy consumption).

But if the original d-AO is populated only partially and contains from 1 to 6 electrons, and these electrons are placed only on dε-AO, then we get significant energy gain.
Energy gain due to priority settlement electrons dε-atomic orbitals are called energy of stabilization of the complex by the ligand field.

The specificity of each of the ligands affects the field that this ligand creates - strong or weak. How stronger field ligands than more meaning splitting parameter Δ 0 .

The study of the splitting parameter is usually based on spectroscopic research. Wavelengths absorption bands complexes in crystalline state or in solution, due to the transfer of electrons from dε- on dγ-AO, associated with splitting parameterΔ 0 as follows:

λ = c / ν; Δ 0 = E 2 – E 1 = h ν = h · ( c / λ),

where is Planck's constant h equal to 6.6260693 ∙ 10 -34 J s;
speed of light With = 3 · 10 10 cm/s.
UnitΔ 0 is the same as the wave number: cm -1, which approximately corresponds to 12 J/mol. Splitting parameter, in addition to the type of ligand, depends on the degree of oxidation And nature complexing agent.
In complex compounds that include complexing agents of the same period and in the same oxidation state, with the same ligands, the cleavage parameter is approximately the same. With increasing degree of oxidation of the complexing agent, the value Δ 0 increases. Thus, for aqua complexes 2+ and 2+ the value of the splitting parameter is 7800 and 10400 cm -1, and for 3+ and +3 13700 and 21000 cm -1, respectively. At increasing nuclear charge of the complex-forming atom Δ 0 also increases. Cations of hexaammine cobalt(III) 3+, hexaammine rhodium(III) 3+, hexaammine ridium(III) 3+ ( Z= 27, 45 and 77) are characterized by splitting parameters equal to 22900, 34100 and 41000 cm -1.

The dependence of Δ 0 on the nature of the ligands is more diverse. As a result of the study of numerous complex compounds, it was found that in terms of their ability to increase the cleavage parameter of complexing metals located in their usual oxidation states, the most common ligands can be arranged in the following spectrochemical series, along which the value Δ 0 monotonically increases:
I > Br > Cl > NCS - ≈ NO 3 - > F - > OH - > H 2 O > H - > NH 3 > NO 2 - > CN - > NO > CO.

Thus, the strongest electrostatic field around the complexing agent and the strongest cleavage d-AO is caused by the ligands CN-, NO and CO. Let us consider the distribution of electrons over dε- and dγ-orbitals in the octahedral field of ligands. Check-in dε- and dγ-orbitals occurs in full accordance with Hund's rule And Pauli principle. In this case, regardless of the value of the splitting parameter, the first three electrons are occupied by quantum cells dε-sublevel:

dε

If the number of electrons per d- there are more than three sublevels of the complexing agent; there are two possibilities for placing them on split sublevels. At a low value of the splitting parameter (weak field of the ligands), electrons overcome the energy barrier separating dε- and dγ-orbitals; the fourth and then the fifth electrons populate quantum cells dγ-sublevel.

dε

With a strong ligand field and a high value of Δ 0, the population of the fourth and fifth electrons dγ-sublevel is excluded; filling in progress dε-orbitals.

dε

At weak field ligands populating quantum cells with 4 or 5 electrons parallel spins, so the resulting complex turns out to be strongly paramagnetic. In a strong ligand field one and then two electron pairs are formed on dε-sublevel, so paramagnetism the complex turns out to be much weaker. The sixth, seventh and eighth electrons in the case of a weak field end up back on dγ-sublevel, complementing the configurations to electron pairs (one in the case d 6, two – d 7 and three - d 8):

dε

In the case of a strong ligand field, the sixth electron populates dε-AO, leading to diamagnetism complex, after which the seventh and eighth electrons go to dγ-sublevel:

dε

Obviously, with an eight-electron configuration differences in structure between complexes with ligands weak And strong fields disappear. The occupation of orbitals by the ninth and tenth electron also does not differ for complexes of both types:

dε

Let us return to the consideration of the electronic structure of the octahedral complex ions 3+ and -3. According to the location in spectrochemical series, ammonia NH 3 is one of the ligands strong field, and fluoride ion F - – weak field. In the -3 anion, the F - ligands create a weak crystal field (Δ 0 = 13000 cm -1), and all electrons of the original 3 d 6 -JSC are located on dε- and dγ orbitals without any pairing. A complex ion is high-spin and contains four unpaired electrons, so it paramagnetic:

In the 3+ ion, NH 3 ligands create a strong crystal field (Δ 0 = 22900 cm -1), all 3 d 6 -electrons are placed on a more energetically favorable dε-orbitals. Transfer of electrons from dε- on dγ orbitals impossible because too high energy barrier. Therefore, this complex cation is low spin, it does not contain unpaired electrons and diamagnetic:

In a similar way, schemes for the distribution of electrons over orbitals in an octahedral field for 2+ and -4 ions can be presented:

H 2 O ligands create a weak field; exchange of electrons between dε- and dγ-orbitals does not cause any difficulties and therefore the number of unpaired electrons in the complex ion is the same as in the conventional ion Fe + II. The resulting aqua complex is high-spin, paramagnetic.
Conversely, CN - ligands cause significant cleavage d-AO, amounting to 33000 cm -1. This means that there is a strong tendency to allocate all electrons on dε-orbitals. Energy Gain, obtained with such a population of orbitals, is much greater than the energy costs due to electron pairing.

From the perspective of the valence bond method, the hybridization of valence orbitals that form a bond in the aqua complex involves d-AO external sublevel (4 sp 3 d 2), and in low-spin - d-JSC internal sublevel (3 d 2 4sp 3).

Thus, in high-spin complexes with weak-field ligands, hybridization occurs with the participation of d-AO of the outer sublevel, and low-spin with high-field ligands - d- JSC of the internal sublevel. The number of unpaired electrons in the complex can be determined by electron paramagnetic resonance (EPR). Using instruments this method, called EPR spectrometers, study paramagnetic substances.

The crystal field theory makes it possible to explain the appearance of one color or another in complex compounds. Among complex compounds, a significant amount is in the crystalline state and aqueous solution are distinguished by their bright colors. Thus, an aqueous solution containing 2+ cations is colored intensely blue, 3+ cations give the solution a purple color, and 2+ cations give it a red color. If light is passed through a solution or crystalline sample of a substance visible part of the spectrum, then, in principle, three options for the physical behavior of the sample are possible: no light absorption any wavelength (substance sample colorless, although it may have absorption bands in the ultraviolet region of the spectrum); complete light absorption over the entire wavelength range (the sample will appear black); finally, light absorption only certain wavelength(then the sample will have color complementary to that absorbed narrow part of the spectrum).

Thus, the color of the solution or crystals is determined frequency of absorption bands visible light. The absorption of light quanta by complexes (for example, those with an octahedral structure) is explained by the interaction of light with electrons located on dε-sublevel, accompanied by their transition to vacant orbitals dγ-sublevel. For example, when passing light through an aqueous solution containing hexaaquatitanium(III) 3+ cations, a light absorption band is detected in the yellow-green region of the spectrum (20300 cm -1, λ=500 nm). This is due to the transition of the single electron of the complexing agent from dε-AO on dγ-sublevel:

Therefore, a solution containing 3+ acquires a violet color (in addition to the absorbed yellow-green). A solution of vanadium salt Cl 3 is green. This is also due to the corresponding transitions of electrons when they absorb part of the energy of the light beam. In the ground state, with the electronic configuration of vanadium(III) 3 d 2, two unpaired electrons are occupied dε-sublevel:

There is only two options for the transition of two electrons on dγ-sublevel: either both electrons are occupied dγ-AO, or only one of them. Any other electron transitions associated with a decrease in the total spin are prohibited.
The indicated transitions of electrons that have received excess energy correspond to absorption band about 400 nm in the absorption spectrum of a solution of hexaaquavanadium(III) chloride. Absorption of the purple-violet region of the spectrum gives an additional color to the solution - bright green. If the complexing agent has an electronic configuration d 0 or d 10 then electron transitions With dε- on dγ-sublevel or vice versa impossible either because absence of electrons, either because absence of vacant orbitals. Therefore, solutions of complexes with complexing agents such as Sc(III) (3 d 0), Cu(I) (3 d 10), Zn(II) (3 d 10), Cd(II) (4 d 10), etc., do not absorb energy in the visible part of the spectrum and appear colorless. The selectivity of light absorption depends not only on complexing agent And its oxidation state, but also from type of ligands. When replacing ligands on the left side of the spectrochemical series in a complex compound with ligands that create strong electrostatic field observed increase the fraction of energy absorbed by electrons from transmitted light and, as a consequence, decrease wavelength of the corresponding absorption band. Thus, an aqueous solution containing tetraaquacopper(II) 2+ cations is blue, and a solution of tetraamminecopper(II) 2+ sulfate is intensely blue.

Related information.

According to the degree of increase in the splitting parameter Δ, the ligands are arranged in a series called spectrochemical (Fig. 2.9).

Rice. 2.9. Spectrochemical series of ligands

When the high-field ligand interacts with the CA, splitting occurs d- orbitals. In this case, the distribution of electrons according to Hund’s rule becomes impossible, since for electrons to transfer from more low-level for more high level requires energy expenditure, which is energetically unfavorable ( great importance splitting parameter Δ). Therefore, electrons first completely fill the -level, and then only the -level is filled. If you are on d- orbitals of 6 electrons, under the influence of a strong field ligand, the - level is filled with electron pairing. This creates low-spin diamagnetic complex. And in the case of a weak field ligand, when the splitting parameter Δ takes a lower value, a uniform distribution of electrons according to Hund’s rule becomes possible. In this case, pairing of all electrons does not occur; high-spin paramagnetic complex.

The sequence of arrangement of ligands in the spectrochemical series within the framework of MO theory can be explained as follows. The greater the degree of overlap of the original orbitals, the greater the energy difference between the bonding and antibonding orbitals and the greater the Δ. In other words, the value of Δ increases with increasing σ- metal-ligand binding. In addition, the Δ value is significantly influenced by π-binding between CA and ligands.

If the ligands have orbitals (empty or filled) that, due to symmetry conditions, are capable of overlapping with d xy -, d xz - And d yz - orbitals of the Central Asia, then the MO diagram of the complex becomes significantly more complicated. In this case, to MO σ- And σ * - type molecular orbitals π are added - and π* - type. Ligand orbitals capable of π - overlap - this is, for example, p- And d- atomic orbitals or molecular π - and π* - orbitals of binuclear molecules. In Fig. Figure 2.10 shows combinations of ligand orbitals and dxz- orbital CA, which, according to symmetry conditions, can be combined to form molecular π - orbitals.

Rice. 2.10. dxz- Orbital CA (a) and combinations corresponding to its symmetry p –(b) and π * – (c) ligand orbitals leading to the formation of MOs of the octahedral complex

Rice. 2.11. Influence of π - binding by the amount Δ

Participation d xy -, d xz - And d yz - orbitals in the construction of π - orbitals leads to a change in Δ. Depending on the ratio of the energy levels of the CA orbitals and the ligand orbitals combined with them, the value of Δ can increase or decrease (Fig. 2.11).

When π is formed - orbitals of the complex, part of the electron density of the CA is transferred to the ligands. Such π - the interaction is called dative. When π is formed * - orbitals of the complex, some part of the electron density from the ligands is transferred to the CA. In this case π - the interaction is called donor-acceptor.

Ligands that are π - acceptors cause greater splitting d- level; ligands that are π - donors, on the contrary, cause little cleavage d- level. The nature σ- And π- Interaction ligands can be divided into the following groups.

Crystal Field Theory (CFT)

• 4.2.1 Introduction. This is a simplified theory of the electronic structure of d-element cations. The word “crystalline” in the name is unfortunate. The theory has nothing to do with crystallography and is even better applicable to isolated groups in solution or in a gas than to crystals. But it's too late to change the name. The theory describes structures with partially filled d-sublevel, but for comparison we will constantly involve two extreme cases - d 0 and d 10, that is, a total of 11 options.
• 4.2.2 Basic provisions of the TCH.
• 1. The connection of a d-element cation with its neighbors - ligands - is considered as a purely electrostatic attraction, and ligands are considered as point negative charges - anions or negative ends of polar molecules. The electronic structure of the ligands is not considered. This is a very rough approximation, but surprisingly effective. Of course, the bond is largely covalent in nature, and the structure of the ligands is very important. But it is taken into account in an implicit form.
• 2. Under the influence electrostatic field ligands, the d-sublevel is cleaved. The five d-orbitals have the same energy in the absence of an external field or in a spherically symmetric field, but in the field of the ligands they become unequal, the energy of some of them decreases, the energy of others increases, but their center of gravity on the energy scale remains the same, that is average the energy of the orbitals remains at the same level. Scheme splitting (which orbitals lowered the energy and which increased) depends only on the shape of the environment, but does not depend on the nature of the cation and ligands, because the angular parts of the wave functions are the same for all elements. A magnitude splitting (energy difference) depends on the nature of the cation and ligands.
• 3. The population of the split sublevel with electrons is subject to three general principles- Pauli's exclusion, the desire for a minimum of orbital energy and Hund's rule - the desire for maximum total spin. But in many cases, the last two principles come into conflict, and the result depends on the relationship between the splitting parameter and the pairing energy. Pairing energy P is the energy that must be expended to overcome interelectron repulsion when transferring an unpaired electron to an orbital where there is already another electron:

If< P, то энергетически выгоднее заселение по правилу Хунда, даже если при этом приходится переводить электрон на более высокий подуровень. Если >P, then it is energetically more favorable to populate the lower sublevel, even if this requires pairing electrons. Thus, for some cations two different states are possible: high-spin (HS), or a state in a weak field (< P), и низкоспиновое (НС), или состояние в сильном поле (>R). They differ in magnetic properties, ionic radii and bond strength (see below). A high-spin state corresponds to a larger magnetic moment; ions in this state are paramagnetic (the substance is drawn into the magnetic field). In a low-spin state, the magnetic moment decreases, and if all electrons are paired, then the magnetic moment is zero, and the substance is diamagnetic (pushed out of the magnetic field).

4.2.3 Splitting of the d-sublevel in different environments. To understand the reason for the splitting, you need to consider the shape electron clouds in space, but the drawings are not given here; they are in all textbooks. Let us first consider the octahedral environment - the simplest and most important case. Six identical ligands are located around the cation along three mutually perpendicular coordinate axes: left, right, front, back, top, bottom. The five d orbitals are then split into two groups. d-orbitals (d z 2 and d x 2 -y 2) are extended directly towards the ligands, repel from them, and their energy increases, and d-orbitals (d xy, d xz, d yz) are extended past the ligands - along the bisectors of coordinate angles, they repel little, and their energy decreases. To keep the average energy unchanged, three d-orbitals are lowered by 2/5, and two d-orbitals are raised by 3/5.

In a tetrahedral environment, on the contrary, d-orbitals have increased energy and d-orbitals have decreased energy. This can be understood if we combine a tetrahedron with an octahedron so that their axes of symmetry coincide. Then the vertices of the tetrahedron appear in the place of the faces of the octahedron, i.e. removed from the axes along which the d-orbitals are elongated.

On rice. 3 The splitting schemes for several of the simplest highly symmetrical coordinations with identical ligands are given. If the symmetry is low (for example, if all the ligands are different), then all five d orbitals will have different energies. For a square bipyramid (stretched octahedron) and a square pyramid, the levels are not plotted, because their position depends on the amount of stretching of the octahedron. The limiting case of stretching an octahedron is a flat square. By connecting the same orbitals of the octahedral and square complexes with straight lines, we obtain any intermediate stages of the transformation of the octahedron into a square when two vertices are removed.

Figure 3. Splitting of the d-sublevel in a field of different symmetries

4.2.4 Factors influencing the amount of splitting. TKP does not allow you to calculate the values ​​of and P, but it allows you to find from experimental measurements...

Exposure cannot be measured directly, but can be estimated by comparing thermochemical data different substances. For example, the heats of hydration of doubly charged cations of 3d elements vary in zigzags over the period with maxima at V 2+ and Ni 2+. Comparison with the ESC table (see above) shows that this corresponds well to the change in ESC in a weak octahedral field. Hence the conclusion: doubly charged cations of d-elements of the fourth period form, with excess water, high-spin complexes with coordination number 6 of an octahedral shape. Knowing the spin state, one can calculate the magnetic moment of the ion, choose the correct ionic radius, and predict metal-ligand distances. By measuring the deviation of the thermal effect from the smooth line Ca 2+ - Mn 2+ - Zn 2+ and taking it as the ESCO, we can find the splitting parameter and use it to predict the absorption spectrum. On the contrary, from the absorption spectrum one can determine coordination, spin state, ESC, etc. Thus, TCH established a relationship between such heterogeneous and seemingly unrelated characteristics as the thermal effects of reactions, structure geometry, optical and magnetic properties without using complex quantum chemical calculations.

4.2.7 Preferred coordinations of d-element cations (Table 9). Only for three electronic configurations(d 0, BC d 5 and d 10) ESP is equal to zero in any environment, and For most configurations, the stabilization energy in the octahedral field is greater than in the tetrahedral one. Let's calculate their difference (energy of preference for octahedral coordination) using the example of configuration d 3 (or d 8): 6 o /5 - 4 t /5 = 6 o /5 - (4/9)*(4/5) o = 38 o /45 = 0.84 o . This value, on the order of hundreds of kJ/mol, is a very serious contribution to the binding energy. Therefore, for ions with the d 3 configuration, octahedral coordination is especially characteristic, and tetrahedral coordination almost never occurs. Octahedral coordination is also characteristic of most other electronic configurations, especially since it usually corresponds to the maximum possible coordination number, taking into account the ratio of the radii of the cation and ligands. For configurations d 0 , BC d 5 and d 10 TCH does not predict a preference for any coordination, so tetrahedral coordination is somewhat more common in them, but still it is not preferred (except for cases where a higher coordination number is not possible due to dimensional restrictions or according to the condition of coordination balance). High CNs (7-12) due to geometric obstacles are rare in cations of d-elements: only in the largest of them with small ligands. They are almost not considered here, because... their analysis is more complex and the results less meaningful. In these cases, simple “ionic” representations are usually sufficient to predict coordination.

At the same time, TCH allows anticipate the appearance in certain cases coordinations that contradict the ionic model, that is, not providing maximin angles for a given CN: square pyramid, square, triangular prism. These coordinations arise due to directed covalent bonds, but in the language of SSP this is described in terms of ESCO.

Consider a cation with four d electrons in a weak octahedral field. It has the expected configuration d 3 d 1 . Thus, of the two d-orbitals, one is populated. But these two orbitals interact with different ligands: z 2 -orbital most strongly repels two ligands located along the z axis, and x 2 -y 2 -orbital, on the contrary, repels four ligands in the xoy plane. Consequently, the ligands are divided into two groups, differing in the repulsive force, and therefore in the bond length, and octahedron cannot be regular. This conclusion is a special case of quantum mechanical Jahn-Teller theorems, which in a simplified formulation says: if in a nonlinear structure the orbitals of one sublevel are unevenly populated, such a structure is unstable and is distorted so that the sublevel splits. There are no instructions here what does it feel like there must be distortion, but in a particular case it is not difficult to foresee. Of the two methods of distorting the octahedron: compression (2 short bonds + 4 long) and stretching (4 short + 2 long), the second is preferable, because gives a higher CN. This is what occurs most often. Stretching the octahedron along the z axis can lead to the following coordination options: square bipyramid (CN 4+2 or 4+1+1); square pyramid (CN 4+1); flat square (CC 4). When distorted, additional splitting of the d-sublevel occurs (see. rice. 3): the x 2 -y 2 orbital is repelled from the remaining ligands especially strongly and increases the energy, but the z 2 orbital sharply lowers its energy, because those ligands that interacted with it have left. The electron occupies a lower sublevel, and the stabilization energy by the crystal field compensates for the weakening of the ionic bond due to the removal of two ligands.

Will the Jahn-Teller effect be observed if the orbitals are unevenly populated? lower sublevel (for example, with configurations d 1 or d 2 in the octahedral field)? Theoretically - yes. In practice, these orbitals interact weakly with ligands and are weakly split, so the distortion is small and is often masked by thermal vibrations. The same applies to distortions of tetrahedral structures. To suppress vibrations, you can cool the substance. But then it crystallizes, and distortions in the crystal can arise for other reasons - due to packing conditions with neighboring ions or molecules. That's why The Jahn-Teller effect is most important where d-orbitals are unevenly occupied in the octahedral environment, that is, only for three configurations: BC d 4, HC d 7 and d 9. Ions with such configurations are often called Jahn-Teller ions. As an exercise, list such ions (in oxidation states 2+ and 3+) and determine at which electronic configurations the Jahn-Teller effect will be especially noticeable in tetrahedral coordination.

For the d 8 configuration in a weak octahedral field, such a distortion is unfavorable, because Of the two electrons occupying the d-sublevel, only one lowers the energy, and the other increases it. But with strong splitting (in a strong ligand field and with complete removal of two neighbors), electrons can pair at a lower z 2 sublevel, and then square coordination becomes advantageous for the d 8 configuration.

From the splitting schemes shown in rice. 3, the largest decrease in the energy of the lower sublevel is observed in a triangular prism. But the gain in ESKP compared to octahedral coordination is small, but the loss due to the convergence of like ions is significant. Therefore, triangular-prismatic coordination is rare. In order for it to become more stable than the octahedral one, the following conditions are simultaneously needed:

Table 9. Coordination preferences of cations of d-elements (if the size and conditions of coordination balance and compatibility of coordination groups allow). Cases in which this coordination is particularly preferable are highlighted in bold. Large cations may have a CN>6, but this is not taken into account in the table.

Electronic	Preferred coordination
d 1, d 2, d 3, NS d 4, NS d 5,NS d 6, sun d 6, BC d 7, VS d 8
BC d4, HC d7, d9	Stretched square (di)pyramid, sometimes square: CN 4+2, 4+1(+1), 4
5d 2, 4d 2, sometimes 5d 1, 4d 1	Triangular prism (with low electronegativity of ligands), square antiprism
	Any highly symmetrical coordination: octahedron, tetrahedron...
	The same, but due to the increased electronegativity of such ions (low ionicity of the bond) and the small number of free AOs, there is a preference for low CNs, slightly higher than the oxidation state: 4, 3, 2.
	The same as for BC d5, but with increased EO of the cation with -donor type ligands, distortions of octahedra are characteristic, especially CN 1+4(+1), 2+2+2, 3+3, with short bonds in the cis position (cm. clause 4.2)

• - a very large splitting value (therefore, such coordination is observed only in 4d and 5d elements, but not in 3d elements);
• - the presence of a small number of electrons on the d-sublevel, preferably two (with a different number of electrons there is no significant gain in ESCP compared to the octahedron);
• - small effective charges of ligands and long bond lengths (to reduce mutual repulsion of nearby ligands).

Typical examples where all these conditions are met are molybdenum sulfide (4+) 2 and its dithiolate complexes, for example, 2-. If you replace molybdenum with an element of the 4th period, or sulfur with oxygen, or change the oxidation state of molybdenum, triangular prisms will not work. In the same oxidation state with small ligands creating a strong field, molybdenum sometimes has coordination in the form of a square antiprism: 4-, but this form is also predicted by the ionic model without taking into account the electronic structure.

IN last years reliable data appeared on the existence of triangular-prismatic structures and highest degree oxidation of a d-element, for example, 2-. Within the framework of TCH and MBC, this is inexplicable. The explanation is provided by molecular orbital theory, but it is beyond the scope of this course.

• 4.2 Coordination chemistry of full-valent cations of d-elements
• 4.2.1 general characteristics. In the highest oxidation state, cations of d-elements have an 8-electron shell of an inert gas, i.e. are spherically symmetric, and it would seem that they should not have any peculiarities in coordination chemistry - a highly symmetric environment and the maximum possible coordination number depending on the size are expected. Indeed, the smallest of them, such as Cr(6+) and Mn(7+), are exclusively characterized by tetrahedral coordination, the largest with small ligands (zirconium fluoro complexes) - CN 7-9, and the majority - octahedral coordination. But the presence of nine empty AOs at the outer level makes them in the octahedral complex not only -acceptors (due to s, p and two d-orbitals), but also -acceptors (due to three d-orbitals), and this leads to the features discussed below.
• 4.2.2 Asymmetry of -binding in octahedral complexes. In an octahedral complex of a d0 cation with donor-type ligands, 6 (or even 12) electron pairs of ligands claim three empty d orbitals. All of them, according to the Pauli principle, cannot be transferred to these three orbitals. From these 12 orbitals, three symmetrical “group orbitals” can be combined. But usually it is energetically more favorable to choose one, two or three out of 6 neighbors and form short strong + bonds with them.

Rice. 4.

From rice. 4 it can be seen that the overlap of orbitals with one of the neighbors and the transfer of electron density from this oxygen atom to the d-orbital prevents, according to the Pauli principle, communication with the opposite neighbor. The stronger and shorter the connection with one of the neighbors, the weaker and longer the connection with the opposite (trans-) partner. Thus, short strong bonds should be located next to each other (in cis positions relative to each other), and long weak ones should be located against them. Note that the approach of atoms due to the formation one-connections facilitate education the second - connections with the same neighbor, in perpendicular to the plane. This is not necessarily a triple bond (+ two), the order of each of the three bonds may be less than one, but, in any case, the total bond order is quite large.

This leads to a displacement of the cation from the center of the octahedron to one, two or three vertices, and its CN is 1 + 4 (+1), 2 + 2 + 2 or 3+3, respectively. For small displacement external the outline of the octahedron may remain almost correct, but with a strong displacement the sixth vertex is lost, and a square pyramid is obtained.

Conditions for the occurrence of such distortion of octahedra:

• - ligand - -donor (oxygen, fluorine, nitride ion, but not ammonia or amine);
• - metal - - acceptor (electronic configuration d 0 or d 1, that is, the oxidation state is higher or 1 less);
• - significant covalency of the bond, that is, not a very large difference in electronegativity, therefore for oxygen compounds this is more typical than for fluorides, and for vanadium, molybdenum - more typical than for tungsten, niobium, titanium, and even more so tantalum, zirconium, hafnium.
• 4.2.3 Influence of -bonding in octahedra on the coordination of anions and the connectivity of structures

The existence of vanadyl and similar groups

Vanadium (+4), having one electron on the d-sublevel and, therefore, having two empty d-orbitals, can participate in two -bonds. It is most advantageous to form both -bonds with the same oxygen atom. This results in a very strong group O=V 2+ - vanadyl, where the bond order is almost equal to 2, capable of passing unchanged from one substance to another. In an acidic aqueous solution, it is not protonated, because the oxygen atom is valence saturated. Typical forms of vanadium (+4) in acidic solutions and crystalline hydrates are 2+ and 2+. In hydroxide, instead of water molecules, there are bridging hydroxyls: 1, and in alkaline solution- probably 2- .

Asymmetry - binding and connectivity of structures

The oxygen anion participating in the double bond with the d0 cation is valence-saturated and does not need to combine with the second cation, that is, to be a bridging one. There the structure breaks down and its connectivity is reduced. For example, in V 2 O 5 one of the oxygen atoms has a distance to the vanadium atoms of 1.56 A (very strong, almost double bond) and 2.84 A - almost complete absence of a bond. Therefore, vanadium oxide (5) is layered. This results in its relatively low melting point and high reactivity compared to niobium oxide (5): for example, V 2 O 5 dissolves more easily in both acids and alkalis. If you do not know the peculiarities of the coordination chemistry of vanadium and molybdenum, then it is difficult to predict these results. Assuming the CN of cations is 5 or 6, one would expect that all anions have a CN of 2 (or even more), the structure is cross-linked in three dimensions, the substance is refractory, nonvolatile, and inactive. In fact, 2 is only average The CN of oxygen, while the real ones are 1, 2 and 3, and the connectivity is therefore reduced.

4.2.4 Bonding asymmetry and special electrical and optical properties. If in the structure there are infinite linear chains -О-М-О-М-О-М- (octahedra MO 6 are connected by vertices), where M is a d 0 cation prone to asymmetric bonding, then the displacement of one of the cations to one of neighbors (for example, to the left) will cause, in order to maintain a local valency balance, a displacement of neighboring cations in the same direction. Short and long bonds will alternate in the chain, the center of gravity of positive charges will no longer coincide with the center of gravity of negative ones, the structure will become polar (plus on the left, minus on the right). If such a displacement is small, then by imposing an external electric field the same polarity can cause a displacement of ions in the opposite side. Then, if the field is removed, the reverse shift will not occur, because a shift of cations to the right is no worse than a shift to the left. This phenomenon - the existence of its own polarity, the direction of which can be reoriented by an external electric field - is called ferroelectricity, and the material itself - ferroelectric. Intrinsic polarization usually exists only at low temperatures, and heating promotes a transition to a more symmetrical non-polar structure without displacements (or with the replacement of constant displacements by intense thermal vibrations). Ferroelectrics have many practical applications based on the conversion of electrical signals into mechanical ones and vice versa (microphones, telephones, hydrophones, ultrasound emitters, pressure and acceleration sensors), electro-optical effects (control of a laser beam using an electric field), memory effect, etc. So that displacements exist, but are small, needed some, not too much and not too little, degree of bond ionicity. Perfectly suits this titanates and niobates. In the oxygen compounds of vanadium and molybdenum, the displacements of cations and distortions of the octahedra are usually so great (see above) that they cannot be reversed by an external field (one vertex of the octahedron is often completely lost, and the result is a quadrangular pyramid). On the contrary, when replacing oxygen with fluorine, or niobium with tantalum, or titanium with zirconium, the ionicity of the bond increases, covalent effects weaken, and the arrangement of ions becomes non-polar even at low temperatures. Partial substitution (formation of solid solutions) allows smooth adjustment of properties. The most important ferroelectrics: BaTiO 3, Pb(Ti 1-x Zr x)O 3, KNbO 3, LiNbO 3, PbNb 2 O 6.

Project assignment

As directed by the teacher, find structural information about a specific substance on the Internet, download the publication (or better yet, a cif crystallographic information file), analyze the structure using the Diamond program and give its written description according to the following scheme: formula, crystallographic data, research method (single crystal or powder, radiography or neutron diffraction), coordination of each component (not just the CN, but a detailed characterization taking into account the disparity of bonds, bond angles, fractional populations, if any), calculation of bond valences and checking the local valence balance, characterization of connectivity and the method of its implementation ( connection of polyhedra by vertices, edges or faces), personal assessment of the reliability of the data, degree of consistency with the principles set out in this manual, bibliographic reference. Recommendations for working with such materials are in the manuals.

Search recommendations. Specialized scientific search engines www.scopus.com and scholar.google.com. The first is available only through the SFU proxy server and provides free access to the full texts of many Elsevier journals. In addition, the SFU proxy server is available full texts from the Journals of the American Chemical (pubs.acs.org) and Physical Societies, the Royal Society of Chemistry of London (www.rsc.org). The journals of the International Union of Crystallography (www.iucr.org) do not provide free access to most articles, but cif are always available. Opening cif Diamond is incomparably easier than entering digital data from the article using the keyboard. A demo version of Diamond is available at the department.

Milestone control test No. 4

The test contains 6 tasks, which take 3 minutes to complete. Choose the answer option that is most correct, in your opinion, and mark it with any icon on the answer form.

1. Which pair of analogue elements has the greatest difference in radii?
2. Ionic radii of cations of d-elements in the same oxidation state over the period with increasing atomic number
	monotonically decrease		increase monotonically
	have local extrema with a general decreasing tendency		have local extrema with a general tendency to increase
3. The crystal field splitting parameter increases
	by subgroup from top to bottom		during the transition from ligands - - acceptors to ligands - - donors
	with increasing cation radius		with decreasing CN
4. If you need to indicate only one most important factor that determines the differences in the coordination of Mn(2+) and Mn(7+) (although everything is important!), it is
	number of free joint-stock companies
	ionic radius		magnetic moment
5. If you need to indicate only one most important factor that determines the differences in the coordination of Mn(2+), Mn(3+) and Mn(4+) (although everything is important!), it is
	number of free joint-stock companies		crystal stabilization energy. field
	ionic radius		magnetic moment
6. Displacement from the center of the oxygen octahedron (up to its transformation into a square pyramid) is most typical for

Answer form

Evaluation criterion: Each task is worth 5 points. The test is considered passed if you receive 25 points.

Weak field strong field

Middle field

Frac34;¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾® Δo

Weak field ligands with elements of the 3d series form high-spin complexes, and strong-field ligands form low-spin complexes. The difference between them affects the electronic structure of the complexes only for configurations d 4 – d 7:

3+ d 5 3– d 5

high-spin complex low-spin complex

H 2 O – weak field ligand CN – – strong field ligand

Low-spin complexes are always more stable than high-spin complexes. Medium-field ligands, depending on conditions (charge and nature of the central atom), can form both high-spin and low-spin complexes.

Example. Based on TCP, make an assumption about the electronic structure of hexaammine cobalt(II) (Δo = 21600 cm –1, P = 21000 cm –1) and hexaammine cobalt(III) ions (Δo = 9500 cm –1, P = 22500 cm –1).

Ammonia is a medium-field ligand and, depending on the degree of oxidation of the metal, can form both high-spin and low-spin complexes. Let us find out which complexes will be energetically more stable for cobalt(II) and cobalt(III). To do this, compare the ESC of each of the ions in a strong and weak field:

(a) 3+, d 6

strong field weak field

ESKP (strong field) = –6´(2/5)Δo + 2P = –6´(2/5) ´21600 + 2´21000 = –9840 cm –1

ESKP (weak field) = –4´(2/5)Δo + 2´(3/5)Δo = –4´(2/5) ´21600 + 2´(3/5) ´21600 = –8640 cm – 1

The energy gain is greater in the case of a low-spin complex.

(b) 2+ , d 7

strong field weak field

ESKP (strong field) = –6´(2/5)Δo + 1´(3/5)Δo + P = –6´(2/5)´9500 + 1´(3/5) ´9500 + 22500 = 7900 cm–1

ESKP (weak field) = –5´(2/5)Δo + 2´(3/5)Δo = –5´(2/5) ´9500 + 2´(3/5) ´9500 = –7600 cm – 1

The energy gain is greater in the case of a high-spin complex.

Thus, the 3+ ion is low spin and the 2+ ion is high spin.

The ESC increases with increasing Δo, however, it is different for high-spin and low-spin states (Fig. 1.28. The dependence of the ESC for high-spin and low-spin complexes with configuration d 6 on the value Δo = 10Dq. The region in which the existence of both states is possible is shaded). The region near the intersection point of these two lines corresponds to complexes that can exist in both high-spin and low-spin states.

An example is the iron(II) thiocyanate complex with 1,10-phenanthroline, which is high-spin (paramagnetic) at low temperatures, and low-spin (diamagnetic) at elevated temperatures (M. Marchivie, P. Guionneau, J. A. K. Howard, G. Chastanet, J.-F. Letard, A. E. Goeta, J. Am. Soc., 2002, p. The change in multiplicity is accompanied by a change in interatomic distances and the geometry of the coordination environment: the low-spin complex is a regular octahedron, and the high-spin complex is a distorted one. The reverse transition to the high-spin state is possible under the influence of high pressures or radiation. Currently, several dozen such systems are known.

Speaking about the σ-donor and π-acceptor properties of the ligand, we went beyond the TCP, using the approaches of the molecular orbital method in relation to complex compounds(volume 1). Recall that the d-orbital splitting pattern is a fragment general scheme molecular orbitals in an octahedral complex, where t 2g orbitals are considered as nonbonding, and e g as antibonding (Fig. Volume 1).

The formation of bonds in an octahedral complex without π-bonding involves the s-, p- and d-orbitals of the metal and one orbital from each ligand. From 15 atomic orbitals, 15 molecular orbitals are formed, six of them (a 1 g, t 1 u, e g (footnote: the letter in the designation of orbitals indicates the degree of their degeneracy: t - thrice-degenerate, e - doubly degenerate, a - non-degenerate, and the presence of a center of symmetry: g - symmetrical, u - asymmetrical)) σ-bonding, three (t 2 g) - non-bonding, and six (e g *, t 1 u *, a 1 g *) σ-loosening. Bonding orbitals are closer in energy to the ligand orbitals, while nonbonding orbitals are localized predominantly on the metal atom. The energy d xy , d xz , d yz (t 2 g) of the metal orbitals practically does not change during the formation of the complex.

The presence of a low-energy vacant orbital in the ligand, similar in symmetry to the metal orbitals, leads to a decrease in the energy of t 2g orbitals, practically without affecting eg, thereby increasing Δо (Fig. 1.29. Fragments of the MO diagram for the cobalt(III) complex with σ-donor ligand (a) and σ-donor, π-acceptor ligand (b)).

Jahn-Teller effect. In 1937, Yang and Teller proved the theorem according to which any nonlinear molecule in a degenerate electronic state is unstable and spontaneously undergoes a distortion that lowers its symmetry and leads to the removal of degeneracy. The theorem predicts only the very fact of removing degeneracy, but does not indicate how it will be removed. Based on this theorem, the distortion of the octahedral geometry of a number of complexes was explained, and the very fact of the presence of such a distortion was called the Jahn-Teller effect. Let's look at an example. Copper(II) complexes with the d9 configuration, as a rule, do not represent a regular octahedron, but are elongated or compressed along one of the axes (Fig. 1.30. Distortion of octahedral geometry in copper(II) complexes). Let us consider the case of a prolate octahedron. Removal of ligands located along the z axis causes the removal of degeneracy due to a change in the energies of the orbitals. Orbitals directed along the z axis (d xz, d yz, d z 2) interact weaker with the orbitals of the ligands compared to orbitals that do not have a z component (d xy, d x 2 -y 2), and therefore lower their energy. A pair of orbitals of the same symmetry, having a z-component (d xz, d yz), remains degenerate and acquires increased energy. (Fig. 1.31. Change in the energies of d-orbitals when the octahedron is distorted). The Jahn-Teller effect manifests itself most strongly in complexes with unequally filled e g orbitals, that is, with configurations t 2g 3 e g 1 (corresponding to the d 4 ion in a weak field: CrCl 2, K 3 MnF 6) and t 2g 6 e g 3 ( corresponds to the d 9 ion: almost all copper(II) complexes) and t 2g 6 e g 1 (corresponds to the d 7 ion in a strong field, rare, K 3 NiF 6),. An insignificant Jahn-Teller effect is typical for complexes with unequally filled t 2g orbitals, that is, for electronic configurations t 2g 1 (d 1), t 2g 2 (d 2), t 2g 4 (d 4 in a strong field), t 2g 5 (d 5 in a strong field), t 2g 5 e g 1 (d 6 in a weak field), t 2g 5 e g 2 (d 7 in a weak field). Ions with configurations d 3 and d 5 in a weak field, d 3 and d 6 in a strong field, d 8 and d 10 are under no circumstances Jahn-Teller.

The Jahn-Teller effect manifests itself in the inequality of bond lengths in many copper(II) and manganese(III) complexes and in a nonmonotonic change in the stepwise stability constants of the complexes. For example, in anhydrous copper(II) chloride, the copper atom is surrounded by six chlorine atoms, four of which are located at a distance of 0.230 nm, and the other two are located at a distance of 0.295 nm from it.

Copper(II) complexes (Cl 2, (C 6 H 5 SO 3) 2, etc.) are known, consisting of several crystallographically nonequivalent Jahn-Teller ions, each with its own type of distortion, which transform into each other, changing the metal-ligand distance so fast that overall all metal-ligand distances appear to be the same. This case was called dynamic or pulsating Jahn-Teller effect(P. E. M. Wijnands, J. S. Wood, J. Redijk, W. J. A. Maaskant, Inorg. Chem., 1986, 35, 1214) .

The Jahn-Teller effect, however, is not a universal law. Currently known complex ions with a Jahn-Teller configuration, representing undistorted octahedra: 4–, 3+.

Splitting in fields with symmetry other than octahedral.

In addition to octahedral ones, there are many known complexes with a different geometry - square-plane, tetrahedral, trigonal-pyramidal, square-pyramidal, linear, etc. The splitting in each of these fields is different than in the octahedron; it is determined by the symmetry of the coordination polyhedron.

Square-planar complexes can be considered as an extreme case of tetragonal distortion of the octahedral geometry, when the ligands located along one of the coordinate axes are removed to infinity (Fig. 1.27b). The designations of the orbitals are shown in the figure. Planar-square complexes are most typical for ions with the electronic configuration d 8 – Ni 2+, Pd 2+, Pt 2+, Au 3+. Their stability increases sharply with increasing Δ, that is, when moving from elements of the 3d series to heavy transition elements. So, for example, if palladium, platinum and gold have almost all complexes with a coordination number of four square, then nickel forms planar-square complexes only with high-field ligands: 2–, Ni(dmg) 2. Nickel(II) complexes with low-field ligands, such as halogens, have a tetrahedral geometry.

Some planar-square complexes transition metals in solid form they form chains with bridging ligands, for example, Pt-CN-Pt in K 2 Br 0.3, where the platinum atoms are partially in the +4 oxidation state. The high penetrating ability of 5d orbitals ensures their overlap with the formation of a single energy band, and, consequently, metallic conductivity in the direction of the chain. Such molecular complexes are capable of conducting electricity, and are currently being intensively studied.

In a field of tetrahedral symmetry, the orbitals d xy , d yz , d xz have the maximum energy, they are called t 2 -orbitals, and the minimum energy is the orbitals d x 2 –y 2 and d z 2, they are denoted e. Due to the presence of a smaller number of ligands and their different arrangement, the tetrahedral field (Fig. 1.32. Comparison of splittings in the tetrahedral and octahedral fields) turns out to be 2.25 times weaker than the octahedral one: .

Most tetrahedral complexes are high-spin. (Footnote - Several examples of low-spin tetrahedral complexes are known, for example, Cr(N(Si(CH 3) 3) 2 ) 3 NO (chromium(II), d 4 ; D. C. Bradley, Chem. Ber., 1979 , 11, 393); CoL 4, where L is 1-norbornyl (cobalt(IV), d 5; E. K: Brune, D. S. Richeson, K. H. Theopold, Chem. Commun., 1986, 1491)). Maximum stabilization of the tetrahedral environment by the crystalline field is achieved with configurations d 2 (FeO 4 2–, MnO 4 3–) and d 7 (2–). Due to the relatively low stabilization energy, tetrahedral complexes are more often formed by ions with configurations d 0 (TiCl 4, MnO 4 –, CrO 4 2–), d 5 in a weak field (FeCl 4 –) and d 10 (ZnCl 4 2–) with zero ESKP, as well as non-transition metal ions (AlCl 4 –). The formation of tetrahedral complexes compared to octahedral ones is often favored by the steric factor, for example, the ion is more stable than 3–.

Using TCP to explain the stability of complexes. Irving-Williams series. The crystal field theory makes it possible to explain the non-monotonic nature of changes in the energies of the crystal lattice of oxides and halides, the stability constants of complexes, etc. The order of change in the hydration energies of doubly charged cations of 3d metals generally coincides with the nature of changes in the ESC in high-spin complexes (Fig. 1.33. Change in the hydration energy of doubly charged cations metals of the 3d series (a) and the change in ESC in high-spin complexes (b)), the stronger the stabilization by the crystal field, the greater the hydration. It is known that the constants of substitution of a water molecule by a weak-field ligand L

2+ + L x– = (2-x)+ + H 2 O

obey the Irving-Williams series: Mn 2+< Fe 2+ < Co 2+ < Ni 2+ < Cu 2+ < Zn 2+ (Рис. 1.34. Зависимость первой константы устойчивости комплекса от природы 3d-металла). Согласно этому ряду, наибольшей устойчивостью обладают комплексы меди(II) и никеля(II). The simplest option ESKP predicts the greatest stability of nickel complexes. It should be taken into account that copper(II) complexes have a highly distorted octahedral geometry, which makes a significant contribution to the value of the stability constant.

Nepheloauxetic effect. It was discovered that the mutual repulsion of d-electrons weakens when the atom is placed in the field of ligands. This effect of the ligand on the d-electrons of the metal atom is called the nepheloauxetic effect. Greek wordsνεφελη – cloud and αυξανω – increase. The series of ligands, arranged in order of increasing their influence on the metal orbitals, almost completely corresponds to the spectrochemical series. The reason for the nepheloaxetic effect is the overlap of the d-orbitals of the metal with the orbitals of the ligands, due to which the d-cloud expands in space. The presence of this effect clearly demonstrates the limitations of the simplest electrostatic model - the crystalline field theory, which assumes that lignades are point negative charges.

Ligand field theory. Crystal field theory was developed by Bethe in 1929. Currently, it is widely used in a modified form with corrections for some covalency of the metal-ligand bond. This theory is called ligand field theory. The presence of a covalent contribution changes the energy of the metal orbitals compared to that calculated by TCP. The proportion of covalency is taken into account by introducing correction factors that make it possible to equate the experimental values ​​with the calculated ones.

Coloring of complexes.

The color of d-transition element complexes is associated with electron transitions from one d-orbital to another. This is clearly illustrated by the example of the Ti 3+ ion, discussed in the first volume of the textbook. By absorbing energy corresponding to the blue and green parts of the visible spectrum, the only d-electron in the Ti 3+ ion moves to the e g orbital (Fig. 1.35. Spectrum of the 3+ ion). The color of the ion is due to additional colors - red and violet. (Footnote - The attentive reader will notice some asymmetry of the absorption band. It is a consequence of a slight splitting of the t 2g level caused by the Jahn-Teller effect). A diagram showing complementary colors and which is well known to every artist is presented on the second flyleaf of the textbook. The transition energy, expressed in reciprocal centimeters (1000 cm –1 = 12 kJ), corresponds to the splitting parameter Δο - it is most often determined from electronic spectra. Wavelength is inversely proportional to energy:

.

In the case of complexes with a large number of electrons, the spectrum picture becomes more complicated, and additional bands appear in it. This is due to the fact that the excited state t 2g 1 e g 1 can be realized in several ways, depending on which two d-orbitals the electrons are in. For example, a state in which electrons occupy d xy and d x 2 –y 2 orbitals will be higher in energy than a d xy 1 d z 2 1 state due to the greater repulsion of electrons along the x axis. The energy corresponding to the band with the lowest energy is equal to the splitting parameter Δo.

To describe electronic spectra in more detail, it is necessary to introduce some concepts. Let us call any arrangement of electrons at a sublevel a microstate. The number of microstates N, in which n electrons occupy x orbitals, is equal to

Each microstate is characterized by its own values ​​of spin and angular momentum. A set of microstates with identical energies is called term, for example, 3 P, 5 D, 1 S. The digital index indicates multiplicity, which is calculated as:

multiplicity = number of unpaired electrons in the ground state + 1.

The names of the terms are read with an indication of multiplicity: “triplet P”, “quintet D”, “singlet S”. The letter denotes the total angular momentum L of an atom or ion, which is equal to the maximum value of the sum of the angular momenta m l of individual orbitals occupied by electrons. For example, the Ti 3+ ion contains one d-electron, the number of microstates is N = (2´5)!/1!(2´5 – 1)! = 10, L = 2(D) (since for the d-orbital m l = –2, –1, 0, 1, 2, the number of electrons is 1, therefore, the maximum sum m l is equal to the largest value of m l), multiplicity 1 + 1 = 2. Therefore, the ground state term (with the lowest energy) is 2 D. In the case of an ion with an electronic configuration d 2 N = (2´5)!/2!(2´5 – 2)! = 45, L = 3(F) (since for the d-orbital m l = –2, –1, 0, 1, 2, the number of electrons is 2, therefore, the maximum sum of two highest values is equal to m l), multiplicity 2 + 1 = 3. Consequently, the term of the ground microstate is 3 F. With a different arrangement of two electrons on the d-sublevel, states described by other terms are achieved - 3 P, 1 G, 1 D, 1 S, etc. . The relationship between the numerical values ​​of L and the alphabetic symbols is given below:

L = 0 1 2 3 4 5 6 7

Similarly, we can derive the terms of the ground and excited states for other ions of d-elements (Table 1.5.). Please note that the terms for ions with configuration d n and d 10-n are the same.

Table. 1.5.

Terms of the ground and nearest excited states for various configurations of d-electrons.

The terms are split in the octahedral field like orbitals, denoted by similar letters. D terms are split into T 2 g and E g components, like d-orbitals, F terms - into T 1 g, T 2 g and A 2 g, like f-orbitals. The S and P terms are not split at all. The possibilities for electron transitions between different states are limited by selection rules. Thus, in complexes only transitions between states with the same multiplicity are allowed. Each such transition corresponds to a band in the absorption spectrum. As an example, consider the electronic spectrum of complex 3+ (Fig. 1.36. Electronic spectrum of complex 3+). The three bands are due to three electronic transitions: 4 A 2 g ® 4 T 2 g, 4 A 2 g ® 4 T 1 g, 4 A 2 g ® 4 T 1 g (P). The transition with the lowest energy corresponds to the value of the splitting parameter: Δo = 17400 cm–1. The complex absorbs light in the red (17400 cm–1) and blue (23000 cm–1) parts of the visible spectrum and in the near ultraviolet (37800 cm–1), therefore, it has a violet color.

According to Laporte's rule, transitions between states with the same parity, which include s-s, p-p, d-d, f-f transitions, are unlikely, or, in the language of spectroscopy, they are prohibited in octahedral complexes. Forbidden transitions are possible, but occur with low intensity. This is why transition metal salts have a noticeable color only in concentrated solutions. It is many times weaker than the color of permanganate or dichromate, the ions of which do not contain d-electrons.

Laporte's rule is applicable only in the case of complexes that have a center of symmetry. When the octahedron is distorted, the center of symmetry disappears, the Laporte prohibition is lifted, and color appears. For example, the 3+ ion is colorless, but solutions of iron(III) salts are often yellow-orange due to hydrolysis leading to the formation of asymmetric particles with a distorted octahedral environment.

Coloring of complexes, in addition to d-d transitions from one metal d-orbital to another (from t 2g to e g in octahedral complexes), two more factors are responsible: transitions from ligand orbitals to metal orbitals (they are called charge transfer) and transitions within ligand orbitals. These transitions do not fall under Laporte's rule and, therefore, have high intensity.

The charge transfer band is present in the electronic spectrum of any compound, however, in some cases it is in the ultraviolet part of the spectrum and is not perceived by us as color. If the difference between the energies of the ligand orbitals and the metal orbitals is reduced, the charge transfer band falls into the visible part of the spectrum. It is charge transfer that explains the intense color of permanganate, dichromate, mercury sulfide, titanium(IV) peroxo complexes and many other compounds with empty d-orbitals. In some cases, under the influence of light, charge transfer from the orbitals of the ligand to the orbitals of the metal occurs irreversibly, that is, it is accompanied by a chemical process. An example is the photochemical decomposition of silver halides, which is the basis of black and white photography: Ag + Br – ¾® Ag 0 + Br 0 .

In the electronic spectrum of potassium permanganate, four bands are observed, corresponding to transitions of electrons from nonbonding orbitals localized predominantly on the ligand (a 1, t 2 σ orbitals and e, t 1, t 2 π orbitals) to e*, t2'' antibonding orbitals orbitals localized on the metal atom ((Fig. 1.37. Energy diagram of the tetrahedral ion MnO 4 - with π-bonding. Electron transitions are shown by arrows):

ν 1 , Mn(e*) ¾ O(t 1) 17700 cm –1

ν 2 , Mn(t 2 '') ¾ O(t 1) 29500 cm –1

ν 3 , Mn(e*) ¾ O(t 2) 30300 cm –1

ν 4 , Mn(t 2 '') ¾ O(t 2) 44400 cm –1

The band with the lowest energy falls in the visible part of the spectrum (λ = 107/17700 = 565 nm), which corresponds to the absorption of green light and the transmission of crimson-red light.

3. Mechanisms of reactions involving complex compounds.

Overwhelming majority chemical processes proceeds as a sequential chain of some elementary stages, and the reaction equation carries only information about the main final products of the reaction. This sequence of elementary transformations on the way from starting substances to products is called a mechanism. Intermediate, usually unstable compounds through which the path from reactants to products runs are called intermediates. Any intermediate has a certain lifetime, usually extremely short, up to 10 -14 s. On the energy profile of the reaction it corresponds to a minimum (Fig. a) (Fig. 1.38. Energy profiles of a reaction proceeding through: (a) intermediate, (b) transition state.). As a rule, intermediates can be detected in a reaction mixture by spectral methods, and only in rare cases can they be isolated in individual form. Therefore, the main information about the reaction mechanism is usually obtained through studying its kinetics - determining rate constants and calculating activation parameters (enthalpy, entropy, volume). In this case, the mechanism is a model that is in accordance with the kinetic data, a model that can be improved, modified, revised.

In some reactions, intermediates are not formed, and the transition from reactants to products occurs sequentially - one of the atoms is gradually removed, and the other approaches. In this case, the reaction is said to proceed through transition state or activated complex. It corresponds to a maximum in the energy profile of the reaction (Fig. B).

Addition: Labile and inert complexes

The thermodynamic stability of a particle is determined by the change in the Gibbs energy for the reaction of its dissociation, or by the value of the stability constant of this process. Kinetic stability shows how quickly a given particle interacts with other particles or undergoes decay. A chemical particle is considered inert, if it reacts with a half-life of more than 1 minute. Particles that react at a higher rate are called labile. It must be remembered that kinetic and thermodynamic stability do not depend on one another, that is, the same substance can have a high stability constant and at the same time be inert, or, conversely, labile. Some such examples are given in Table 1.6.

Table 1.6. Stability constants and rates of ligand substitution in cyano-complexes of some metals.

Henry Taube showed the connection between the kinetic stability of octahedral complexes and the electronic configuration of the central ion in the octahedral field. According to Taube, the following complexes are labile:

· possessing at least one vacant t 2g orbital - they can use it in reactions according to the associative (A, I a) mechanism, or

· having at least one electron in the e g orbital - this promotes the reaction by the dissociative (D, I d) mechanism, because Removing an electron from the e g orbital lowers the energy of the transition state.

Thus, octahedral complexes of chromium(III) (t 2g 3), low-spin complexes of iron(II) (t 2g 6) and iron(III) (t 2g 5), as well as complexes of 4d-, 5d-transition elements are classified as inert with the number of d-electrons more than two.

END OF ADDENDUM

A unified classification of inorganic reactions has not yet been developed. Conventionally, we can propose the following scheme (Fig. 1.39. Scheme illustrating the classification of inorganic reactions):

1) Reactions of substitution, addition or elimination of ligands affect a change in the coordination sphere of the metal,

2) Redox reactions are associated with a change in the electronic configuration of the metal, but do not affect its coordination environment,

3) Reactions of coordinated ligands involve a change in the ligand without changing the coordination sphere of the complex.

Substitution reactions. In a broad sense, substitution reactions mean the processes of replacing some ligands in the coordination sphere of a metal with others. Such reactions can occur either with or without a change in the oxidation state. Following the above classification, we will use this term only in relation to reactions that occur without a change in oxidation states.

Classification of substitution reactions in inorganic chemistry was developed by Langford and Gray. It is based on the definition of the so-called limiting mechanism, and not on the description of a specific mechanism. First, the stoichiometric mechanism is determined, and then the internal one. Stoichiometric mechanism is a sequence of elementary stages in the transition from starting substances to products. It can be dissociative (D), associative (A) and exchange (reciprocal exchange, I). Dissociative and associative processes represent, as it were, two limiting cases, directly opposite to one another. Both processes occur in two stages through the formation of an intermediate.

Dissociative (D)

The process is two-stage, in the limiting case it proceeds through an intermediate with a reduced concentration:

ML 6 + L, + Y ¾® ML 5 Y

Associative (A)

The process is two-stage, characterized by the formation of an intermediate with an increased concentration:

ML 6 + Y, ¾® ML 5 Y + L

Mutual exchange (I)

Most exchange reactions proceed through this mechanism. The process is one-stage and is not accompanied by the formation of an intermediate. In the transition state, the reactant and leaving group are bound to reaction center, enter its closest coordination sphere, and during the reaction one group is displaced by another, an exchange of two ligands occurs:

ML 6 + Y ML 5 Y + L.

The transition state is either an outer-sphere complex or, in the case of charged ligands, an ion pair MX 5 L + Y - .

Internal mechanism (a or d) characterizes the process of ligand substitution at the molecular level. It shows which of the two processes - the formation or rupture of a bond in the transition state - is limiting. If the reaction rate is determined by the formation of a bond between the reaction center and the reagent, we speak of associative activation. Otherwise, when the limiting factor is the rupture of the connection between the reaction center and the leaving group, the process proceeds with dissociative activation. Turning to the stoichiometric mechanism, it is easy to notice that the dissociative process always corresponds to dissociative activation, and the associative process always corresponds to associative activation, that is, the concept of an internal mechanism turns out to be informative only in the case of a mutual exchange mechanism - it can occur with both dissociative (I d) and associative (I a) activation. In the case of the reciprocal exchange mechanism with associative activation (Ia), the reaction rate depends on the nature of Y. In the transition state, the metal atom is tightly bound to both the leaving group and the attacking nucleophile. An example is the process of replacing a chlorine atom with bromine and iodine in a platinum complex with diethylenetriamine (dien):

Y - ¾¾® + + Cl -

Y = Br, I velocities vary greatly.

In the case of the reciprocal exchange mechanism with dissociative activation (I d), the reaction rate does not depend on the nature of the reagent Y. The attacking and leaving groups in the transition state are weakly bound to the central ion. This mechanism is used to replace water with amine in aqua complexes of many transition metals, for example, nickel:

2+ + Y ¾¾® 2+ + H 2 O

Y = NH 3 , py velocities are close.

The study of the mechanisms of substitution reactions in complexes of many metals is only in the initial stage. Comprehensive information has been obtained only for square-planar complexes of platinum and octahedral complexes of chromium(III) and cobalt(III). It can be considered firmly established that in platinum(II) complexes substitution occurs via the associative mechanism (A, Ia) through an intermediate or transition state in the form of a trigonal bipyramid. Octahedral cobalt(III) complexes react dissociatively (D, I d mechanisms). Specific examples of such reactions will be considered when describing the chemistry of these elements.

Redox reactions. Most redox processes are a complex combination of individual elementary stages, each of which involves the transfer of one or, much less frequently, two electrons. Simultaneous transfer of a larger number of electrons in solutions is impossible.

Single-electron transfer can occur through one of two mechanisms: outer-sphere, that is, by tunneling, or inner-sphere, through a bridging ligand. The intrasphere mechanism is realized in complexes containing halides, hydroxide ions, and carboxyl groups that can act as bridges between metals. An example is the reaction between pentammine chlorocobalt(III) and hexaaquachrome(II) ions. The process can be roughly divided into three stages: the formation of a heterometallic complex with a bridging chloride ion, electron transfer and decomposition of the bridging complex. The resulting 2+ ion, being labile, instantly turns into an aqua complex, and the inert [(H 2 O) 5 CrCl] 2+ does not interact with water:

If there are no particles in the system that could act as bridges, the process proceeds in the outer sphere:

2+ + 3+ = 3+ + 2+ .

It is especially necessary to highlight the reactions of oxidative addition and reductive elimination, discussed in Chapter 6.

Reactions of coordinated ligands. This group of reactions includes modification processes of ligands coordinated by a metal ion. For example, diketonate complexes, like free diketones, can be nitrated, acylated, or halogenated. The most interesting and unusual example of reactions of coordinated ligands is template synthesis– a unique method of “assembling” a ligand on a metal ion. An example is the synthesis of phthalocyanines from phthalic acid nitrile, which occurs in the presence of copper(II) ions, and the synthesis of a macrocyclic Schiff base from 2-aminobenzaldehyde, which occurs in the presence of nickel(II) ions:

In the absence of metal, the process proceeds along a different path, and the desired product is present in only a small amount in the reaction mixture. The metal ion acts in template synthesis as a matrix (“template”), stabilizing one of the products that are in equilibrium with each other, and shifting the equilibrium towards its formation. For example, in the reaction X + Y ¾® a mixture of products A and B is formed, in which B, which has a lower energy, predominates. In the presence of a metal ion, substance A predominates in the reaction products in the form of a complex with M (Fig. 1.40. Energy diagram of the interaction of X and Y in the absence of a metal ion (left) and in its presence (b)).

Questions and tasks

1. Which of the following compounds has a perovskite structure? BaTiO 3, LiNbO 3, LaCrO 3, FeTiO 3, Na 2 WO 4, CuLa 2 O 4, La 2 MgRuO 6. The table of ionic radii is given in the Appendix. Keep in mind that in complex oxide phases, the B positions may contain cations of two different metals.

2. Using the TCP, determine whether the following spinels will be straight or inverted: ZnFe 2 O 4, CoFe 2 O 4, Co 3 O 4, Mn 3 O 4, CuRh 2 O 4.

3. Thiocyanate ion SCN - has two donor centers - hard and soft. Predict what structure the thiocyanate complexes of calcium and copper(I) will have. Why is it not possible to obtain copper(II) thiocyanate?

4. The spectrum of the Cr 2+ aqua ion (ground state term 5 D) has two bands (Fig. 1.41. Spectrum of the Cr 2+ aqua ion), although among the terms of the nearest excited states there is not one with the same multiplicity. What explains this? What color does this ion have?

5. Using the Δο values ​​below, calculate the ESC for the following complexes in kJ/mol:

(a) 2–, Δο = 15000 cm–1,

(b) 2+, Δο = 13000 cm–1,

(c) 2–, Δο (for 4–)= 21000 cm–1,

Take the pairing energy equal to 19000 cm –1, 1 kJ/mol = 83 cm –1. Calculate their magnetic moments (spin component).

6. Using TCP, explain why the CN – ion reacts with hexaaquanickel(III) ion to form hexacyanoferrate(II), and with hexaaquanickel(II) ion to form tetracyanonickelate(II).

7. Below are the reaction constants for the sequential replacement of water in the copper(II) aqua complex with ammonia: K 1 = 2´10 4 , K 2 = 4´10 3 , K 3 = 1´10 3 , K 4 = 2´10 2 , K5 = 3´10 –1, K6<< 1. Чем объясняется трудность вхождения пятой и шестой молекул аммиака в координационную сферу меди?

8. How does the rigidity of cations change when moving along a 3d row? Is this consistent with the order of change in the stability constants of the complexes (Irving-Williams series, Fig. 1.34).

9. Explain why the hexaquatic iron (III) ion is colorless, and solutions of iron (III) salts are colored.

10. Suggest a mechanism for the reaction 3– + 3– = 4– + 2–, if it is known that the introduction of thiocyanate ion into the solution leads to a change in the reaction rate, and the rate is practically independent of the presence of ammonia. Offer an explanation for these facts.

The concept of changes in the electronic structure of transition metal ions under the action of the electric field of charged particles surrounding them was proposed by Becquerel and further developed by H.A. Bethe and J. Van Vleck at the beginning XX V. These concepts were applied to the description of the electronic structure and properties of complex compounds only in the middle XX century by H. Hartmann and the model was called “crystal field theory” (CFT).

Basic provisions of TCH for transition complexes d metals Fig. 24):

1. - The complex exists and is stable due to the electrostatic interaction of the complexing agent with the ligands.

2. - Ligands are considered without taking into account their electronic structure as point charges or dipoles.

3. - Under the influence of the electric field of the ligands, valence fivefold degenerate ( n -1) d orbitals are split depending on the symmetry of the ligand environment.

4. - Distribution of metal valence electrons among split ( n -1) d orbitals depends on the ratio of the spin-pairing energy and the splitting energy.

Consider, for example, the change in the energy of fivefold degenerate ( n -1) d orbitals of the central metal ion M n+ , located at the center of coordinates, under the influence of the octahedral field of negatively charged ligands [ ML 6] z , located on the coordinate axes (Fig. 25). As a result of the repulsion of the valence electrons of the metal from negatively charged ligands with a uniform distribution of negative charge around the metal (spherically symmetrical electric field), the energy of all five d orbitals will increase by the amount E 0 compared to free M n+ ion. Because the d orbitals have different spatial orientations, then with the concentration of negative charges on ligands located on the coordinate axes, the increase in their energy differs. Energy Boost d z 2 and d x 2- y 2 orbitals directed towards the ligands on the coordinate axes have a greater energy increase dxy, dxz and dyz orbitals directed between coordinate axes.

Energy of fissionfivefold degenerate ( n -1) orbitals into doubly degenerate d x 2- y 2, z 2 orbitals and triply degenerate d xy, xz, yz orbitals are called (Fig. 26) crystal field splitting parameter. Since the energy of the split d orbitals in the octahedral field of the ligands does not change compared to the spherically symmetric electric field, then the increase in the energy of two d x 2- y 2, z 2 orbitals occurs at 0.6D 0 and a decrease in the energy of three d xy , xz , yz orbitals by 0.4 D 0 .

To indicate the degree of degeneracy and symmetry of metal orbitals split under the influence of the electric field of ligands, special symbols are used. Triple degenerate and symmetric with respect to the center of symmetry and rotation around the coordinate axes d xy , xz , yz t 2 g ", while doubly degenerate and also symmetric with respect to the center of symmetry d x 2- y 2, z 2 orbitals are designated by the symbol " e g " Thus, under the influence of the octahedral electric field of the ligands, fivefold degenerate ( n -1) d the orbitals of the complexing agent are split into triply and doubly degenerate ones of different energies t 2 g and e g orbitals.

A similar consideration of the change in energy of fivefold degenerate ( n -1) d orbitals of a free metal ion in a tetrahedral environment of ligands in [ ML 4 ] z complexes shows (Fig. 27) their splitting also into twofold (e) and threefold ( t ) degenerate orbitals, however, with the opposite energy position. Subscript " g " when designated "e" and " t » orbitals are not indicated since the tetrahedral complex does not have a center of symmetry. A decrease in the number of ligands of a tetrahedral complex compared to an octahedral complex leads to a natural decrease in the crystal field splitting parameter:D T = 4/9 D ABOUT .

Reducing the symmetry of the ligand environment of the metal, for example, tetragonal distortion of octahedral [ ML 6] z complexes associated with the extension of metal-ligand bonds with axial ligands [ ML 4 X 2 ] z and the formation in the limiting case of plane-square [ ML 4 ] z complexes, leads (Fig. 28) to additional splitting of valence ( n -1) d metal orbitals.

Filling of split ( n -1) d metal orbitals occurs in accordance with the Pauli principles and minimum energy. For octahedral complexes with d 1 , d 2 and d 3 electronic configuration of the metal, valence electrons, in accordance with Hund’s rule, populate t 2 g orbitals with parallel spins, leading to t 2 g 1 , t 2 g 2 and t 2 g 3 electronic structure of complexes.

For metals with d 4 electronic configuration, three electrons also populate t 2 g orbitals with parallel spins. The population of the fourth electron depends on the energy costs for the value of the spin pairing energy (E sp.-sp.) during the population t 2 g orbitals with antiparallel spin and violation of Hund's rule, or overcoming the energy of splitting by the crystal fieldD o upon check-in e g orbitals with parallel spin in accordance with Hund's rule. In the first case, a complex is formed with t 2 g 4 electronic structure and reduced spin multiplicity compared to free metal 2 S +1 = 3 (S - total spin), called low-spin. When Hund's rule is fulfilled and the fourth electron is populated on e g orbitals, a complex is formed with t 2 g 3 e g 1 electronic structure and free metal-like spin multiplet 2 S +1 = 5. Such complexes are called high-spin.

Similarly, when distributing valence d5, d6 and d7 metal electrons t 2 g and e g orbitals of octadric complexes depending on the ratio E sp.-sp. AndD O The formation of two types of complexes is possible:

At E sp.-sp. > D O high-spin complexes with the electronic structure of the metal are formed t 2 g 3 e g 2 , t 2 g 4 e g 2 , t 2 g 5 e g 2 according to Hund's rule and free metal-like spin multiplicity - 2 S +1 = 6, 5, 4;

E sp.-sp.< D O low-spin complexes with the electronic structure of the metal are formed t 2 g 5 e g 0 , t 2 g 6 e g 0 , t 2 g 6 e g 1 and lower spin multiplicity compared to free metal 2 S +1 = 2, 1, 2.

Metal complexes with d 8, d 9 and d 10 electronic configuration are characterized by one type of electron distribution - t 2 g 6 e g 2 , t 2 g 6 e g 3 , t 2 g 6 e g 4 with spin multiplicity similar to free metal: 2 S +1 = 3, 2 and 0.

So the parameterD, characterizing the splitting ( n -1) d metal orbitals under the influence of the electric field of the ligands is one of the main characteristics of changes in the properties of complexes compared to a free metal ion. It is the parameter valueDdetermines for a number of electronic configurations of the metal determines the possibility of the formation of high- or low-spin complexes with different distributions of electrons over split orbitals and different properties.

The value of the crystal field splitting parameterDdepends on the nature of the metal of the complexing agent, the ligands surrounding it and their spatial position around the complexing agent:

1. Ligands in order of increasing parameterDfor complexes of the same metal and similar geometric structure are located in the so-called spectrochemical series: I -< Br - < Cl - < F - < OH - < C 2 O 4 2- ~ H 2 O < NCS - < NH 3 ~ En < NO 2 - < CN - < CO . At the beginning of the row there are “weak field” ligands - halide ions, hydroxide and oxalate ions, water, which form predominantly high-spin complexes. The ligands on the right side of the series: carbon monoxide, cyanide and nitrite ions are called “high field” ligands and are typically characterized by the formation of low-spin complexes. For ligands in the middle of the series - thiocyanate ion, ammonia, ethylenediamine, depending on the nature of the metal, high- or low-spin complexes are formed.

2. Increasing the efficiency of the electric field of ligands on d metal orbitals with increasing their size in row 3 d<< 4 d < 5 d , as well as an increase in the degree of oxidation of the metal leads to an increase in the parameterD in the series: Mn(II)< Ni (II ) < Co (II ) < Fe (II ) < V (II ) < Fe (III ) < Co (III ) < Mn (IV ) < Mo (III ) < Rh (III ) < Ru (III ) < Pd (IV ) < Ir (III ) < Pt (IV ).

3. Parameter Dfor tetrahedral complexes is only 4/9 of the parameterDoctahedral complexes.

“Heavy” complexes 4 d and 5 d metals, almost regardless of the nature of the ligands, form predominantly low-spin complexes, while the formation of low- or high-spin complexes is “light” 3 d metals is mainly determined by the strength of the ligand field.

In contrast to the MMS, the crystal field theory to justify the difference in the magnetic properties of complexes of the same metal ion with different ligand environments, for example, diamagnetic [ Fe(CN ) 6 ] 4- and paramagnetic [ Fe(H2O ) 6 ] 2+ does not use the hypothesis of their intraorbital ( d 2 sp 3 hybridization) and outer-orbital ( sp 3 d 2 hybridization) structure. The difference in magnetic properties is determined by the low- and high-spin nature of the distribution of 6-valent electrons Fe(II ) by split t 2 g and e g orbitals (Fig. 29). Being strong and weak field ligands, cyanide ions and water molecules form Fe(II ) low- and high-spin complexes with t 2 g 6 e g 0 and t 2 g 4 e g 2 distribution of electrons, which determines diamagnetism [ Fe(CN ) 6 ] 4- and paramagnetism [ Fe(H2O ) 6 ] 2+ complexes.

Splitting of fivefold degenerate ( n -1) d metal orbitals in complexes and parameter changesDdepending on the nature of the ligands, it determines the characteristic color of the complexes both in the solid state and in solutions. When the complex absorbs electromagnetic radiation in the visible region of the spectrum (400-750) nm, the energy of the quanta of which is E equal to the value D, electron transfer occurs from t 2 g on e g orbitals. It is the unabsorbed electromagnetic radiation of the visible region of the spectrum that determines the color of the complex in accordance with the “Newton’s color circle” (Fig. 30), showing the primary and secondary colors of visible radiation.

Aquacomplex titanium( III) [Ti (H 2 O) 6] 3+ c t 2 g 1 e g 0 electronic distribution as a result of photoexcitation, corresponding to the transition of the electron to higher energy e g orbitals:

3+ (t 2g 1 e g 0) + hn= * 3+ (t 2g 0 e g 1)

absorbs light quanta in the yellow region of the spectrum, which leads to its violet color. A change in the ligand environment of the metal ion in accordance with the position of the ligand in the spectrochemical series leads to a change in the parameterDand, as a consequence of this, to a change in the energy and wavelength of quanta absorbed by the complex and to the characteristic color of the complex - for example, in the series [ CuCl 4 ] 2- , [ Cu (H 2 O ) 4 ] 2+ , [ Cu (NH 3 ) 4 ] 2+ the color of the complexes changes from green to blue and violet.

Along with the crystal field splitting energyD, also plays an important role in TCH crystal field stabilization energy(ESKP) - gain in energy when distributing electrons among those split in the complex ( n -1) d metal orbitals compared to the energy of fivefold degenerate ones ( n -1) d metal orbitals in an equivalent spherical electric field (Fig. 31, 32).

ESCP of octadral and tetrahedral complexes.

Mn+	Octahedral complexes		Tetrahedral complexes
	Low spin	High spin	High spin
	0.4 D o		0.6 D T
	0.8 D o		1.2 D T
	1.2 D o		0.8 D T
d 4	1.6 D o	0.6 D o	0.4 D T
d 5	2.0 D o	0 D o	0 D T
d 6	2.4 D o	0.4 D o	0.6 D T
d 7	1.8 D o	0.8 D o	1.2 D T
d 8	1.2 D o		0.8 D T
d 9	0.6 D o		0.4 D T
d 10	0 D o

An estimate of the ESP value of the complex is obtained on the basis of splitting diagrams ( n -1) d metal orbitals in the electric field of ligands, showing a decrease or increase in the energy of the system compared to a spherical electric field when electrons populate split ( n -1) d orbitals. For octahedral [ ML 6] z complexes (Fig. 32) population of each electron t 2 g orbitals leads to a gain in system energy by 0.4D oh, check-in e g requires energy expenditure 0.6D O . For tetrahedral [ ML 4 ] z complexes with opposite energy positions e and t metal orbitals - occupation of each electron by split e and t orbitals is accompanied by a decrease and increase in the energy of the system by 0.6D t and 0.4 D T .

Being a reflection of the thermodynamic stability of the complexes, estimates of their ESCR values ​​are consistent with experimental data on changes in the energy of the crystal lattice for high-spin hexafluoride complexes 3 d metals (Fig. 33).

The ESC values ​​allow us to determine the most preferred coordination isomer (Fig. 34), for example [ Cu (NH 3 ) 6 ][ NiCl 4 ] or [ Ni (NH 3 ) 6 ][ CuCl 4 ]. To do this, calculate the difference in ESC for the complex cation and anion of the isomers. ESCR value [ Cu (NH 3 ) 6 ] 2+ and [NiCl 4 ] 2- is 0.6 D o and 0.8 D T respectively. Considering thatD t = 4/9 D o , the difference between the ESCP values ​​[ Cu (NH 3 ) 6 ] 2+ and [NiCl 4 ] 2- will be 19/45D o . Similarly, the values ​​of ESKP [ Ni (NH 3 ) 6 ] 2+ and [CuCl 4 ] 2- is 1.2 D o and 0.4 D T , and the difference between them is 28/45D o . Big difference ESCP complex cation [ Ni (NH 3 ) 6 ] 2+ and the anion [CuCl 4 ] 2- compared to [ Cu (NH 3 ) 6 ] 2+ and [NiCl 4 ] 2- shows a more preferable formation of the isomer of composition [ Ni (NH 3 ) 6 ][ CuCl 4 ].

Along with the magnetic and optical properties of the influence of the electronic structure of the metal on the thermodynamic stability of the complexes, TKP predicts a distortion of the geometric structure of the complexes with an uneven distribution of electrons over split ( n -1) d metal orbitals (Fig. 35). In contrast to the regular octahedral structure [ Co (CN) 6 ] 3- s t 2 g 6 e g 0 electronic distribution, tetragonal distortion of a similar complex [ Cu (CN) 6 ] 4- s t 2 g 6 e g 3 electronic distribution containing 3 electrons on 2-fold degenerate e g orbitals, leads to the effective transformation of the octahedral into a square-planar complex:

4- = 2- + 2CN - .

All of the above shows that the relative simplicity and broad capabilities of TCT for explaining and predicting the physicochemical properties of complexes determine the great popularity of this model for describing chemical bonds in complex compounds. At the same time, focusing on changes in the electronic structure of the metal during complex formation, TCP does not take into account the electronic structure of the ligands, considering them as point negative charges or dipoles. This leads to a number of limitations of TCP when describing the electronic structure of complexes. For example, within the framework of TCP it is difficult to explain the position of a number of ligands and metals in spectrochemical series, which is associated with a certain degree of covalency and the possibility of the formation of multiple metal-ligand bonds. These limitations are eliminated when considering the electronic structure of complex compounds using the more complex and less visual method of molecular orbitals.