Hcl molecular orbital method. Molecular orbital method (MMO). Questions for self-study

The shortcomings of the MVS considered above contributed to the development of another quantum mechanical method for describing the chemical bond, which was called molecular orbital method (MMO). The basic principles of this method were laid down by Lenard-Jones, Gund and Mulliken. It is based on the idea of ​​a polyatomic particle as a single system of nuclei and electrons. Each electron in such a system experiences attraction from all nuclei and repulsion from all other electrons. Such a system can be conveniently described using molecular orbitals, which are formal analogues of atomic orbitals. The difference between atomic and molecular orbitals is that some describe the state of an electron in the field of a single nucleus, while others describe the state of an electron in the field of several nuclei. Given the similarity of the approach to describing atomic and molecular systems, we can conclude that the orbitals of an n-atomic molecule must have the following properties:

a) the state of each electron in the molecule is described by the wave function ψ, and the value ψ 2 expresses the probability of finding an electron in any unit volume of a polyatomic system; these wave functions are called molecular orbitals (MO) and, by definition, are multicenter, i.e. describe the motion of an electron in the field of all nuclei (the probability of being at any point in space);

b) each molecular orbital is characterized by a certain energy;

c) each electron in the molecule has a certain value of the spin quantum number, the Pauli principle in the molecule is fulfilled;

d) molecular orbitals are constructed from atomic orbitals by a linear combination of the latter: ∑c n ψ n (if the total number of wave functions used in the summation is k, then n takes values ​​from 1 to k), c n are coefficients;

e) the MO energy minimum is reached at the maximum AO overlap;

f) the closer in energy are the initial ARs, the lower is the energy of MOs formed on their basis.

From the latter position, we can conclude that the inner orbitals of atoms, which have a very low energy, will practically not participate in the formation of MOs, and their contribution to the energy of these orbitals can be neglected.

Taking into account the properties of MOs described above, let us consider their construction for a diatomic molecule of a simple substance, for example, for an H 2 molecule. Each of the atoms that make up the molecule (H A and H B) have one electron per 1s orbital, then MO can be represented as:

Ψ MO = c A ψ A (1s) + c B ψ B (1s)

Since in the case under consideration the atoms that form the molecule are identical, the normalizing factors (c), showing the share of AO participation in the construction of the MO, are equal in absolute value and, therefore, two options are possible Ψ MO at c A \u003d c B and c A \u003d - c B:

Ψ MO(1) = c A ψ A (1s) + c B ψ B (1s) and

Ψ MO(2) = c A ψ A (1s) - c B ψ B (1s)

molecular orbital Ψ MO(1) corresponds to a state with a higher electron density between atoms compared to isolated atomic orbitals, and electrons located on it and having opposite spins in accordance with the Pauli principle have a lower energy compared to their energy in an atom. Such an orbital in the MMO LCAO is called linking.

At the same time, the molecular orbital Ψ MO(2) is the difference between the wave functions of the initial AO, i.e. characterizes the state of the system with reduced electron density in the internuclear space. The energy of such an orbital is higher than that of the initial AO, and the presence of electrons on it leads to an increase in the energy of the system. Such orbitals are called loosening. Figure 29.3 shows the formation of bonding and antibonding orbitals in the hydrogen molecule.

Fig.29.3. Formation of σ - bonding and σ-loosening orbitals in a hydrogen molecule.

Ψ MO(1) and Ψ MO(2) have cylindrical symmetry with respect to the axis passing through the centers of the nuclei. Orbitals of this type are called σ - symmetrical and are written: bonding - σ1s, loosening - σ ٭ 1s. Thus, the configuration σ1s 2 corresponds to the hydrogen molecule in the ground state, and the configuration of the He 2 + ion, which is formed in the electric discharge, in the ground state can be written as σ1s 2 σ ٭ 1s (Fig. 30.3).

Rice. 30.3. Energy diagram of the formation of bonding and antibonding orbitals and the electronic structure of molecules and ions of elements of the first period.

In the H 2 molecule, both electrons occupy a bonding orbital, which leads to a decrease in the energy of the system compared to the initial one (two isolated hydrogen atoms). As already noted, the binding energy in this molecule is 435 kJ/mol, and the bond length is 74 pm. The removal of an electron from the bonding orbital increases the energy of the system (reduces the stability of the reaction product compared to the precursor): the binding energy in H 2 + is 256 kJ/mol, and the bond length increases to 106 pm. In the H 2 - particle, the number of electrons increases to three, so one of them is located in a loosening orbital, which leads to destabilization of the system compared to the previously described: E (H 2 -) = 14.5 kJ / mol. Consequently, the appearance of an electron in an antibonding orbital affects the chemical bond energy to a greater extent than the removal of an electron from the bonding orbital. The above data indicate that the total binding energy is determined by the difference between the number of electrons in the bonding and loosening orbitals. For binary particles, this difference, divided in half, is called the bond order:

PS \u003d (ē St - ē Not St.) / 2

If PS is zero, then no chemical bond is formed (He 2 molecule, Figure 30.3). If the number of electrons in the antibonding orbitals is the same in several systems, then the particle with the maximum PS value has the greatest stability. At the same time, at the same PS value, a particle with a smaller number of electrons in antibonding orbitals (for example, H 2 + and H 2 - ions) is more stable. Another conclusion follows from Figure 30.3: a helium atom can form a chemical bond with an H + ion. Despite the fact that the energy of the He 1s orbital is very low (-2373 kJ/mol), its linear combination with the 1s orbital of the hydrogen atom (E = -1312 kJ/mol) leads to the formation of a bonding orbital whose energy is lower than that of helium AO. Since there are no electrons on the loosening orbitals of the HeH + particle, it is more stable than the system formed by helium atoms and hydrogen ions.

Similar considerations apply to linear combinations of atomic p-orbitals. If the z-axis coincides with the axis passing through the centers of the nuclei, as shown in Figure 31.3, then the bonding and antibonding orbitals are described by the equations:

Ψ MO(1) = c A ψ A (2p z) + c B ψ B (2p z) and Ψ MO (2) \u003d c A ψ A (2p z) - c B ψ B (2p z)

When MOs are constructed from p-orbitals whose axes are perpendicular to the line connecting the atomic nuclei, then the formation of π-bonding and π-loosening molecular orbitals (Fig. 32.3) occurs. The molecular π at 2p and π at ٭ 2p orbitals are similar to those shown in Fig. 32.3, but rotated relative to the first by 90 about. Thus the π2p and π ٭ 2p orbitals are doubly degenerate.

It should be noted that a linear combination can be built not from any AO, but only from those that have a fairly close energy and whose overlap is possible from a geometric point of view. Pairs of such orbitals suitable for the formation of σ-bonding σ-loosening orbitals can be s - s, s - p z, s - d z 2, p z - p z, p z - d z 2, d z 2 - d z 2, while with a linear combination p x - p x , p y – p y , p x – d xz , p y – d yz , molecular π-bonding and π-loosening molecular orbitals are formed.

If you build an MO from AO of the type d x 2- y 2 - d x 2- y 2 or d xy - d xy, then δ-MOs are formed. Thus, as noted above, the division of MO into σ, π and δ is predetermined by their symmetry with respect to the line connecting the atomic nuclei. Thus, for a σ-MO, the number of nodal planes is zero, a π-MO has one such plane, and a δ-MO has two.

To describe homoatomic molecules of the second period within the framework of the MMO LCAO, it is necessary to take into account that a linear combination of atomic orbitals is possible only when the AO orbitals are close in energy and have the same symmetry.

Fig.31.3. Formation of σ-bonding σ-antibonding orbitals from atomic p-orbitals

Fig.32.3. Formation of π-bonding and π-antibonding molecular orbitals from atomic p-orbitals.

Of the orbitals of the second period, the 2s and 2p z orbitals have the same symmetry about the z axis. The difference in their energies for Li, Be, B, and C atoms is relatively small, so the wave functions 2s and 2p can mix in this case. For O and F atoms, the differences in energy 2s and 2p are much larger, so their mixing does not occur (Table 4.3)

Table 4.3.

∆E energies between 2s and 2p orbitals of various elements

According to the data of Table 4.3, as well as the calculations performed, it is shown that the relative energy of MO is different for Li 2 - N 2 molecules on the one hand and for O 2 - F 2 molecules on the other. For molecules of the first group, the order of increase in the MO energy can be represented as a series:

σ2sσ ٭ 2sπ2p x π2p y σ2p z π٭2p x π ٭ 2p y σ ٭ 2p z , and for O 2 and F 2 molecules in the form:

σ2sσ ٭ 2sσ2p z π2p x π2p y π٭2p x π ٭ 2p y σ ٭ 2p z (Figure 33.3).

Orbitals of type 1s, which have a very low energy compared to the orbitals of the second energy level, pass into the molecule unchanged, that is, they remain atomic and are not indicated on the energy diagram of the molecule.

Based on the energy diagrams of molecules and molecular ions, one can draw conclusions about the stability of particles and their magnetic properties. Thus, the stability of molecules, the MOs of which are constructed from the same AO, can be roughly judged by the value of the bond order, and the magnetic properties - by the number of unpaired electrons per MO (Fig. 34.3).

It should be noted that AO orbitals of non-valence, internal levels, from the point of view of the MMO of LCAO, do not take part in the formation of MO, but have a noticeable effect on the binding energy. For example, when passing from H 2 to Li 2, the binding energy decreases by more than four times (from 432 kJ/mol to 99 kJ/mol).

Fig.33.3 Energy distribution of MO in molecules (a) O 2 and F 2 and (b) Li 2 - N 2.

Fig.34.3 Energy diagrams of binary molecules of elements of the second period.

Detachment of an electron from an H 2 molecule reduces the binding energy in the system to 256 kJ/mol, which is caused by a decrease in the number of electrons in the bonding orbital and a decrease in PS from 1 to 0.5. In the case of detachment of an electron from the Li 2 molecule, the binding energy increases from 100 to 135.1 kJ / mol, although, as can be seen from Figure 6.9, the electron, as in the previous case, is removed from the bonding orbital and PS decreases to 0.5. The reason for this is that when an electron is removed from the Li 2 molecule, the repulsion between the electrons located on the bonding MO and the electrons occupying the inner 1s orbital decreases. This pattern is observed for the molecules of all elements of the main subgroup of the first group of the Periodic system.

As the nuclear charge increases, the effect of the 1s orbital electrons on the energy of the MO decreases, therefore, in the B 2, C 2 and N 2 molecules, the detachment of an electron will increase the energy of the system (decrease in the PS value, decrease in the total bond energy) due to the fact that the electron is removed from the bonding orbitals. In the case of O 2 , F 2 and Ne 2 molecules, the removal of an electron occurs from the loosening orbital, which leads to an increase in PS and the total binding energy in the system, for example, the binding energy in the F 2 molecule is 154.8 kJ / mol, and in the ion F 2 + is almost twice as high (322.1 kJ / mol). The above reasoning is valid for any molecules, regardless of their qualitative and quantitative composition. We recommend that the reader conduct a comparative analysis of the stability of binary molecules and their negatively charged molecular ions, i.e. estimate the change in the energy of the system in process A 2 + ē = A 2 - .

It also follows from Figure 34.3 that only the B 2 and O 2 molecules, which have unpaired electrons, are paramagnetic, while the rest of the binary molecules of the elements of the second period are diomagnetic particles.

Proof of the fairness of the IMO, i.e. evidence of the real existence of energy levels in molecules is the difference in the values ​​of the ionization potentials of atoms and molecules formed from them (table 5.3).

Table 5.3.

Ionization potentials of atoms and molecules

The data presented in the table indicate that some molecules have higher ionization potentials than the atoms from which they are formed, while others have lower ionization potentials. This fact is inexplicable from the point of view of the MVS. Analysis of the data in Figure 34.3 leads to the conclusion that the potential of the molecule is greater than that of the atom in the case when the electron is removed from the bonding orbital (molecules H 2, N 2, C 2). If the electron is removed from the loosening MO (O 2 and F 2 molecules), then this potential will be less compared to the atomic one.

Turning to the consideration of heteroatomic binary molecules within the framework of the MMO LCAO, it is necessary to recall that the orbitals of atoms of various elements that have the same values ​​of the main and side quantum numbers differ in their energy. The higher the effective charge of the atomic nucleus with respect to the considered orbitals, the lower their energy. Figure 35.3 shows the MO energy diagram for heteroatomic molecules of type AB, in which the B atom is more electronegative. The orbitals of this atom are lower in energy than the similar orbitals of atom A. In this regard, the contribution of the orbitals of atom B to bonding MOs will be greater than to loosening ones. On the contrary, the main contribution to the antibonding MO will be made by the AO of the A atom. The energy of the inner orbitals of both atoms during the formation of the molecule remains practically unchanged, for example, in the hydrogen fluoride molecule, the orbitals 1s and 2s of the fluorine atom are concentrated near its nucleus, which, in particular, determines the polarity of this molecule (µ = 5.8 ∙ 10 -30). Consider, using Figure 34, the description of the NO molecule. The energy of oxygen AO is lower than that of nitrogen, the contribution of the former is higher to the bonding orbitals, and the latter to the loosening orbitals. The 1s and 2s orbitals of both atoms do not change their energy (σ2s and σ ٭ 2s are occupied by electron pairs, σ1s and σ ٭ 1s are not shown in the figure). The 2p orbitals of oxygen and nitrogen atoms, respectively, have four and three electrons. The total number of these electrons is 7, and there are three bonding orbitals formed due to 2p orbitals. After they are filled with six electrons, it becomes obvious that the seventh electron in the molecule is located on one of the antibonding π-orbitals and, therefore, is localized near the nitrogen atom. PS in the molecule: (8 - 3) / 2 = 2.5 i.e. the total binding energy in the molecule is high. However, an electron located in an antibonding orbital has a high energy, and its removal from the system will lead to its stabilization. This conclusion makes it possible to predict that the activation energy of NO oxidation processes will be low; these processes can proceed even at s.u..

At the same time, the thermal stability of these molecules will be high, the NO + ion will be close to nitrogen and CO molecules in terms of total binding energy, and NO will dimerize at low temperatures.

The analysis of the NO molecule within the framework of this method leads to another important conclusion - the most stable will be binary heteroatomic molecules, which include atoms with a total number of electrons in the valence s and p orbitals equal to 10. In this case, PS = 3. An increase in or a decrease in this number will lead to a decrease in the value of PS, i.e. to the destabilization of the particle.

Polyatomic molecules in MMO LCAO are considered based on the same principles as described above for duatomic particles. Molecular orbitals in this case are formed by a linear combination of AO of all atoms that make up the molecule. Consequently, MOs in such particles are multicenter, delocalized, and describe the chemical bond in the system as a whole. The equilibrium distances between the centers of atoms in a molecule correspond to the minimum potential energy of the system.

Fig.35.3. Energy diagram of MO of binary heteroatomic molecules

(Atom B has a high electronegativity).

Fig.36.3. Energy diagrams of molecules of various types in

within the MMO. (the p x axis of the orbital coincides with the bond axis)

Figure 36.3 shows the MOs of various types of molecules. We will consider the principle of their construction using the example of the BeH 2 molecule (Fig. 37.3). The formation of three-center MOs in this particle involves the 1s orbitals of two hydrogen atoms, as well as the 2s and 2p orbitals of the Be atom (the 1s orbital of this atom does not participate in the formation of the MO and is localized near its nucleus). Let us assume that the p-axis of the Be z-orbital coincides with the communication line in the particle under consideration. A linear combination of s orbitals of hydrogen and beryllium atoms leads to the formation of σ s and σ s ٭ , and the same operation with the participation of s orbitals of hydrogen atoms and p z -orbitals of Be leads to the formation of a bonding and loosening MO σ z and σ z ٭ , respectively.

Fig.37.3. MO in the Ven 2 molecule

Valence electrons are located in the molecule in bonding orbitals, i.e. its electronic formula can be represented as (σ s) 2 (σ z) 2 . The energy of these bonding orbitals is lower than the energy of the orbitals of the H atom, which ensures the relative stability of the molecule under consideration.

In the case when all systems of atoms have p-orbitals suitable for a linear combination, along with σ-MO, multicenter bonding, non-bonding, and loosening π-MOs are formed. Consider such particles on the example of a CO 2 molecule (Fig. 38.3 and 39.3).

Fig.38.3 CO 2 molecules binding and loosening σ-MO

Fig.39.3. Energy diagram of MO in a CO 2 molecule.

In this molecule, σ-MOs are formed by combining 2s and 2p x orbitals of a carbon atom with 2p x orbitals of oxygen atoms. Delocalized π-MOs are formed due to the linear combination of p y and p z orbitals of all atoms,

included in the molecule. As a result, three pairs of π-MOs are formed with different energies: binding - π y c in π z sv, non-bonding - π y π z (corresponding in energy to the p-orbitals of oxygen atoms), and loosening - π y res π z res.

When considering molecules within the framework of the MMO LCAO, abbreviated schemes for describing particles are often used (Fig. 40.3). When forming an MO, for example, in the BCI 3 molecule, it is sufficient to indicate only those AOs that actually participate in the linear combination (the figure does not show one of the AO p-orbitals of boron and 6 of the 9 p-orbitals of chlorine atoms, the linear combination of which gives non-bonding MO)

Fig.40.3. MO in the BCI 3 molecule

The energy diagram of MO in the CH 4 molecule is shown in Fig. 41.3. An analysis of the electronic structure of the carbon atom shows that due to the different directions of its 2p orbitals, the formation of five-center MOs in the CH 4 molecule with the participation of these AOs is impossible for geometric reasons. At the same time, the 2s orbital of carbon is equally capable of overlapping with the 1s orbitals of hydrogen atoms, resulting in the formation of five-center σ s and σ s ٭ MO. In the case of combinations of 2p and 1s orbitals, the number of atomic functions in a linear combination is only three, i.e. the energy of σ-MO in this case will be higher than that of the corresponding σ s and σ s ٭ .

Fig.41.3 .. Energy diagram of the MO of the CH 4 molecule.

The different energies of the five-center and three-center bonding orbitals are confirmed by experimental data on ionization potentials, which are different for electrons moving away from σ s and from σ x (σ y . σ z).

Molecular orbital method based on the assumption that electrons in a molecule are located in molecular orbitals, similar to atomic orbitals in an isolated atom. Each molecular orbital corresponds to a certain set of molecular quantum numbers. For molecular orbitals, the Pauli principle remains valid, i.e. Each molecular orbital can contain no more than two electrons with antiparallel spins.

In the general case, in a polyatomic molecule, the electron cloud belongs simultaneously to all atoms, i.e. participates in the formation of a multicenter chemical bond. In this way, all electrons in a molecule belong simultaneously to the whole molecule, and are not the property of two bonded atoms. Consequently, the molecule is viewed as a whole, and not as a collection of individual atoms.

In a molecule, as in any system of nuclei and electrons, the state of an electron in molecular orbitals must be described by the corresponding wave function. In the most common version of the molecular orbital method, the wave functions of electrons are found by representing molecular orbital as a linear combination of atomic orbitals(the variant itself received the abbreviated name "MOLCAO").

In the MOLCAO method, it is assumed that the wave function y , corresponding to the molecular orbital, can be represented as a sum:

y = c 1 y 1 + c 2 y 2 + ¼ + c n y n

where y i are wave functions characterizing the orbitals of interacting atoms;

c i are numerical coefficients, the introduction of which is necessary because the contribution of different atomic orbitals to the total molecular orbital can be different.

Since the square of the wave function reflects the probability of finding an electron at some point in space between interacting atoms, it is of interest to find out what form the molecular wave function should have. The easiest way to solve this problem is in the case of a combination of wave functions of 1s-orbitals of two identical atoms:

y = c 1 y 1 + c 2 y 2

Since for identical atoms with 1 \u003d c 2 \u003d c, one should consider the sum

y = c 1 (y 1 + y 2)

Constant With affects only the value of the amplitude of the function, therefore, to find the shape of the orbital, it is enough to find out what the sum will be y 1 and y2 .

Having located the nuclei of two interacting atoms at a distance equal to the bond length, and having depicted the wave functions of 1s-orbitals, we will add them. It turns out that, depending on the signs of the wave functions, their addition gives different results. In the case of adding functions with the same signs (Fig. 4.15, a), the values y in the internuclear space is greater than the values y 1 and y2 . In the opposite case (Fig. 4.15, b), the total molecular orbital is characterized by a decrease in the absolute value of the wave function in the internuclear space compared to the wave functions of the original atoms.

Rice. 4.15. Scheme of addition of atomic orbitals during formation

binding (a) and loosening (b) MO

Since the square of the wave function characterizes the probability of finding an electron in the corresponding region of space, i.e. the density of the electron cloud, which means that in the first version of the addition of wave functions, the density of the electron cloud in the internuclear space increases, and in the second it decreases.

Thus, the addition of wave functions with the same signs leads to the appearance of attractive forces of positively charged nuclei to the negatively charged internuclear region and the formation of a chemical bond. This molecular orbital is called binding , and the electrons located on it - bonding electrons .

In the case of the addition of wave functions of different signs, the attraction of each nucleus in the direction of the internuclear region weakens, and repulsive forces prevail - the chemical bond is not strengthened, and the resulting molecular orbital is called loosening (electrons located on it - loosening electrons ).

Similar to atomic s-, p-, d-, f-orbitals, MO denote s- , p- , d- , j orbitals . Molecular orbitals arising from the interaction of two 1s-orbitals denote: s-linking and s (with an asterisk) - loosening . When two atomic orbitals interact, two molecular orbitals are always formed - a bonding and a loosening.

The transition of an electron from the atomic 1s-orbital to the s-orbital, leading to the formation of a chemical bond, is accompanied by the release of energy. The transition of an electron from the 1s orbital to the s orbital requires energy. Consequently, the energy of the s-bonding orbital is lower, and the s-opening orbital is higher than the energy of the original atomic 1s-orbitals, which is usually depicted in the form of corresponding diagrams (Fig. 4.16).

JSC MO JSC

Rice. 4.16. Energy diagram of the formation of the MO of the hydrogen molecule

Along with the energy diagrams of the formation of molecular orbitals, the appearance of molecular clouds obtained by overlapping or repulsing the orbitals of interacting atoms is of interest.

Here it should be taken into account that not any orbitals can interact, but only those satisfying certain requirements.

1. The energies of the initial atomic orbitals should not differ greatly from each other - they should be comparable in magnitude.

2. Atomic orbitals must have the same symmetry properties about the axis of the molecule.

The last requirement leads to the fact that they can combine with each other, for example, s - s (Fig. 4.17, a), s - p x (Fig. 4.17, b), p x - p x, but they cannot s - p y, s - p z (Fig. 4.17, c), because in the first three cases, both orbitals do not change when rotating around the internuclear axis (Fig. 3.17 a, b), and in the last cases they change sign (Fig. 4.17, c). This leads, in the latter cases, to the mutual subtraction of the formed areas of overlap, and it does not occur.

3. Electron clouds of interacting atoms should overlap as much as possible. This means, for example, that it is impossible to combine p x – p y , p x – p z or p y – p z orbitals that do not have overlapping regions.

(a B C)

Rice. 4.17. Influence of the symmetry of atomic orbitals on the possibility

formation of molecular orbitals: MOs are formed (a, b),

not formed (in)

In the case of the interaction of two s-orbitals, the resulting s- and s-orbitals look like this (Fig. 3.18)

Rice. 4.18. Scheme for combining two 1s orbitals

The interaction of two p x -orbitals also gives an s-bond, because the resulting bond is directed along a straight line connecting the centers of atoms. The emerging molecular orbitals are designated respectively s and s, the scheme of their formation is shown in fig. 4.19.

Rice. 4.19. Scheme for combining two p x orbitals

With a combination of p y - p y or p z - p z -orbitals (Fig. 4.20), s-orbitals cannot be formed, because the regions of possible overlapping orbitals are not located on a straight line connecting the centers of atoms. In these cases, degenerate p y - and p z -, as well as p - and p - orbitals are formed (the term "degenerate" means in this case "the same in shape and energy").

Rice. 4.20. Scheme for combining two p z orbitals

When calculating the molecular orbitals of polyatomic systems, in addition, there may appear energy levels midway between bonding and loosening molecular orbitals. Such mo called non-binding .

As in atoms, electrons in molecules tend to occupy molecular orbitals corresponding to the minimum energy. So, in a hydrogen molecule, both electrons will transfer from the 1s orbital to the bonding s 1 s orbital (Fig. 4.14), which can be represented by the formula:

Like atomic orbitals, molecular orbitals can hold at most two electrons.

The MO LCAO method does not operate with the concept of valency, but introduces the term "order" or "link multiplicity".

Communication order (P)is equal to the quotient of dividing the difference between the number of bonding and loosening electrons by the number of interacting atoms, i.e. in the case of diatomic molecules, half of this difference. The bond order can take integer and fractional values, including zero (if the bond order is zero, the system is unstable and no chemical bond occurs).

Therefore, from the standpoint of the MO method, the chemical bond in the H 2 molecule, formed by two bonding electrons, should be considered as a single bond, which also corresponds to the method of valence bonds.

It is clear, from the point of view of the MO method, and the existence of a stable molecular ion H . In this case, the only electron passes from the atomic 1s orbital to the molecular s 1 S orbital, which is accompanied by the release of energy and the formation of a chemical bond with a multiplicity of 0.5.

In the case of molecular ions H and He (containing three electrons), the third electron is already placed on the antibonding s-orbital (for example, He (s 1 S) 2 (s) 1), and the bond order in such ions, according to the definition, is 0.5. Such ions exist, but the bond in them is weaker than in the hydrogen molecule.

Since there should be 4 electrons in a hypothetical He 2 molecule, they can only be located 2 in s 1 S - bonding and s - loosening orbitals, i.e. the bond order is zero, and diatomic molecules of helium, like other noble gases, do not exist. Similarly, Be 2 , Ca 2 , Mg 2 , Ba 2 etc. molecules cannot be formed.

Thus, from the point of view of the molecular orbital method, two interacting atomic orbitals form two molecular orbitals: bonding and loosening. For AO with principal quantum numbers 1 and 2, the formation of MOs presented in Table 1 is possible. 4.4.

Prerequisites for the emergence of the method

Chronologically, the method of molecular orbitals appeared later than the method of valence bonds, since there were questions in the theory of covalent bonds that could not be explained by the method of valence bonds. Let's consider some of them.

The main position of the method of valence bonds is that the bond between atoms is carried out due to electron pairs (binding two-electron clouds). But it is not always the case. In some cases, individual electrons are involved in the formation of a chemical bond. So, in a molecular ion H 2+ one-electron bond. The method of valence bonds cannot explain the formation of a one-electron bond, it contradicts its basic position.

The method of valence bonds also does not explain the role of unpaired electrons in a molecule. Molecules with unpaired electrons are paramagnetic, i.e. are drawn into the magnetic field, since the unpaired electron creates a permanent magnetic moment. If there are no unpaired electrons in the molecules, then they are diamagnetic - they are pushed out of the magnetic field. The oxygen molecule is paramagnetic, it has two electrons with parallel spins, which contradicts the method of valence bonds. It should also be noted that the method of valence bonds could not explain a number of properties of complex compounds - their color, etc.

To explain these facts, the molecular orbital method was proposed.

The main provisions of the method

According to the molecular orbital method, electrons in molecules are distributed in molecular orbitals, which, like atomic orbitals, are characterized by a certain energy (energy level) and shape. Unlike atomic orbitals, molecular orbitals cover not one atom, but the entire molecule, i.e. are two- or multicenter. If in the method of valence bonds the atoms of molecules retain a certain individuality, then in the method of molecular orbitals the molecule is considered as a single system.

The most widely used in the molecular orbital method is a linear combination of atomic orbitals. In this case, several rules are observed:

Schrödinger equation for a molecular system must consist of a kinetic energy term and a potential energy term for all electrons at once. But the solution of one equation with such a large number of variables (indices and coordinates of all electrons) is impossible, so the concept is introduced one-electron approximation.

The one-electron approximation assumes that each electron can be considered as moving in the field of the nuclei and the averaged field of the remaining electrons of the molecule. This means that every i th electron in a molecule is described by its own function ψ i and has its own energy Ei. In accordance with this, for each electron in the molecule, one can compose its own Schrödinger equation. Then for n electrons need to be solved n equations. This is carried out by methods of matrix calculus with the help of computers.

When solving the Schrödinger equation for a multicenter and multielectron system, solutions are obtained in the form of one-electron wave functions - molecular orbitals, their energies and the electronic energy of the entire molecular system as a whole.

Linear combination of atomic orbitals

In the one-electron approximation, the molecular orbital method describes each electron with its own orbital. Just as an atom has atomic orbitals, so a molecule has molecular orbitals. The difference is that molecular orbitals are multicenter.

Consider an electron located in a molecular orbital ψ i neutral molecule, at the moment when it is near the nucleus of some atom m. In this region of space, the potential field is created mainly by the nucleus of the atom m and nearby electrons. Since the molecule is generally neutral, the attraction between the electron in question and some other nucleus n is approximately compensated by the repulsion between the electron in question and the electrons near the nucleus n. This means that near the nucleus the motion of an electron will be approximately the same as in the absence of other atoms. Therefore, in the orbital approximation, the molecular orbital ψ i near the core m should be similar to one of the atomic orbitals of that atom. Since the atomic orbital has significant values ​​only near its nuclei, one can approximately represent the molecular orbital ψ i as linear combination of atomic orbitals individual atoms.

For the simplest molecular system consisting of two nuclei of hydrogen atoms, taking into account 1s-atomic orbitals describing the motion of an electron in an atom H, the molecular orbital is represented as:

Quantities c 1i and c 2i- numerical coefficients, which are the solution Schrödinger equations. They show the contribution of each atomic orbital to a particular molecular orbital. In the general case, the coefficients take values ​​in the range from -1 to +1. If one of the coefficients prevails in the expression for a particular molecular orbital, then this corresponds to the fact that an electron, being in a given molecular orbital, is mainly located near that nucleus and is described mainly by that atomic orbital, whose coefficient is greater. If the coefficient in front of the atomic orbital is close to zero, then this means that the presence of an electron in the region described by this atomic orbital is unlikely. According to the physical meaning, the squares of these coefficients determine the probability of finding an electron in the region of space and energies described by a given atomic orbital.

In the LCAO method, for the formation of a stable molecular orbital, it is necessary that the energies of the atomic orbitals be close to each other. In addition, it is necessary that their symmetry does not differ much. If these two requirements are met, the coefficients should be close in their values, and this, in turn, ensures the maximum overlap of electron clouds. When adding atomic orbitals, a molecular orbital is formed, the energy of which decreases relative to the energies of the atomic orbitals. This molecular orbital is called binding. The wave function corresponding to the bonding orbital is obtained by adding wave functions with the same sign. In this case, the electron density is concentrated between the nuclei, and the wave function takes on a positive value. When atomic orbitals are subtracted, the energy of the molecular orbital increases. This orbital is called loosening. The electron density in this case is located behind the nuclei, and between them is equal to zero. The wave function in the two formed electron clouds has opposite signs, which is clearly seen from the scheme of formation of the bonding and loosening orbitals.

When the atomic orbital of one of the atoms, due to a large difference in energy or symmetry, cannot interact with the atomic orbital of another atom, it passes into the energy scheme of the molecular orbitals of a molecule with the energy corresponding to it in the atom. This type of orbital is called non-binding.

Orbital classification

Classification of orbitals on σ or π produced according to the symmetry of their electron clouds. σ -orbital has such a symmetry of the electron cloud, in which turning it around the axis connecting the nuclei by 180 ° leads to an orbital that is indistinguishable from the original in shape. The sign of the wave function does not change. When π -orbital, when it is rotated by 180°, the sign of the wave function is reversed. Hence it follows that s-electrons of atoms, when interacting with each other, can form only σ -orbitals, and three (six) p- orbitals of an atom - one σ- and two π -orbitals, and σ -orbital occurs when interacting p x atomic orbitals, and π -orbital - during interaction r y and pz. Molecular π -orbitals are rotated relative to the internuclear axis by 90°.

In order to distinguish bonding and antibonding orbitals from each other, as well as their origin, the following notation has been adopted. The bonding orbital is denoted by the abbreviation "sv", located at the top right after the Greek letter denoting the orbital, and loosening - respectively "razr". One more designation is adopted: antibonding orbitals are marked with an asterisk, and bonding orbitals without an asterisk are marked. After the designation of the molecular orbital, the designation of the atomic orbital is written, to which the molecular orbital owes its origin, for example, π bit 2 py. This means that the molecular orbital π -type, loosening, formed during the interaction of 2 r y- atomic orbitals.

The position of an atomic orbital on the energy scale is determined by the value of the ionization energy of the atom, which corresponds to the removal of an electron described by this orbital to an infinite distance. This ionization energy is called orbital ionization energy. So, for an oxygen atom, types of ionization are possible when an electron is removed from 2p- or with 2s-electronic subshell.

The position of the molecular orbital in energy diagrams is also determined on the basis of quantum chemical calculations of the electronic structure of molecules. For complex molecules, the number of energy levels of molecular orbitals on energy diagrams is large, but for specific chemical problems it is often important to know the energies and composition of not all molecular orbitals, but only the most "sensitive" to external influences. These orbitals are molecular orbitals that contain the highest energy electrons. These electrons can easily interact with the electrons of other molecules, be removed from a given molecular orbital, and the molecule will go into an ionized state or change due to the destruction of one or the formation of other bonds. Such a molecular orbital is the highest occupied molecular orbital. Knowing the number of molecular orbitals (equal to the total number of all atomic orbitals) and the number of electrons, it is easy to determine the serial number of the HOMO and, accordingly, from the calculation data, its energy and composition. Also, the lowest free molecular orbital, i.e., is most important for the study of chemical problems. next in line to the HOMO on the energy scale, but a vacant molecular orbital. Other orbitals that are adjacent in energy to the HOMO and LUMO are also important.

Molecular orbitals in molecules, like atomic orbitals in atoms, are characterized not only by relative energy, but also by a certain total shape of the electron cloud. Just as atoms have s-, R-, d-, ... orbitals, the simplest molecular orbital, providing a connection between only two centers (two-center molecular orbital), can be σ -, π -, δ -, ... type. Molecular orbitals are divided into types depending on what symmetry they have with respect to the line connecting the nuclei of atoms relative to the plane passing through the nuclei of the molecule, etc. This leads to the fact that the electron cloud of the molecular orbital is distributed in space in various ways.

The physical meaning of the method

For any other system including k atomic orbitals, the molecular orbital in the approximation of the LCAO method will be written in general form as follows:

To understand the physical meaning of this approach, we recall that the wave function Ψ corresponds to the amplitude of the wave process characterizing the state of the electron. As you know, when interacting, for example, sound or electromagnetic waves, their amplitudes add up. As can be seen, the above equation for the decomposition of a molecular orbital into constituent atomic orbitals is equivalent to the assumption that the amplitudes of the molecular "electron wave" (i.e., the molecular wave function) are also formed by adding the amplitudes of the interacting atomic "electron waves" (i.e., adding the atomic wave functions ). In this case, however, under the influence of the force fields of the nuclei and electrons of neighboring atoms, the wave function of each atomic electron changes in comparison with the initial wave function of this electron in an isolated atom. In the LCAO method, these changes are taken into account by introducing the coefficients c iμ, where the index i defines a specific molecular orbital, and the index cm- specific atomic orbital. So when finding the molecular wave function, not the original, but the changed amplitudes are added - c iμ ψ μ.

Find out what form the molecular wave function will have Ψ 1, formed as a result of the interaction of wave functions ψ 1 and ψ 2 - 1s orbitals of two identical atoms. To do this, we find the sum c 11 ψ 1 + c 12 ψ 2. In this case, both considered atoms are the same, so that the coefficients from 11 and from 12 are equal in size ( from 11 = from 12 = c 1) and the problem is reduced to determining the sum c 1 (ψ 1 + ψ 2). Because the constant factor c 1 does not affect the form of the desired molecular wave function, but only changes its absolute values, we confine ourselves to finding the sum (ψ 1 + ψ 2). To do this, we place the nuclei of interacting atoms at the distance from each other (r) where they are located in the molecule, and depict the wave functions 1s-orbitals of these atoms (Figure a).

To find the molecular wave function Ψ 1, add the values ψ 1 and ψ 2: the result is the curve shown in (figure b). As can be seen, in the space between the nuclei, the values ​​of the molecular wave function Ψ 1 greater than the values ​​of the original atomic wave functions. But the square of the wave function characterizes the probability of finding an electron in the corresponding region of space, i.e., the density of the electron cloud. So the increase Ψ 1 compared to ψ 1 and ψ 2 means that during the formation of a molecular orbital, the density of the electron cloud in the internuclear space increases. As a result, a chemical bond is formed. Therefore, the molecular orbital of the type in question is called binding.

In this case, the region of increased electron density is located near the bond axis, so that the resulting molecular orbital belongs to σ -type. In accordance with this, the bonding molecular orbital obtained as a result of the interaction of two atomic 1s-orbitals, denoted σ 1s sv.

Electrons in a bonding molecular orbital are called bonding electrons.

Consider another molecular orbital Ψ 2. Due to the symmetry of the system, it should be assumed that the coefficients in front of the atomic orbitals in the expression for the molecular orbital Ψ 2 = c 21 ψ 1 + c 22 ψ 2 must be equal in modulus. But then they should differ from each other by a sign: from 21 = - from 22 = c 2.

Hence, except for the case where the signs of the contributions of both wave functions are the same, the case is also possible when the signs of the contributions 1s-atomic orbitals are different. In this case (fig. (a))contribution 1s-atomic orbital of one atom is positive, and the other is negative. When these wave functions are added together, the curve shown in Fig. (b). The molecular orbital formed during such an interaction is characterized by a decrease in the absolute value of the wave function in the internuclear space compared to its value in the initial atoms: even a nodal point appears on the bond axis, at which the value of the wave function, and, consequently, its square, turns into zero. This means that in the case under consideration, the density of the electron cloud in the space between the atoms will also decrease. As a result, the attraction of each atomic nucleus towards the internuclear region of space will be weaker than in the opposite direction, i.e. forces will arise that lead to mutual repulsion of the nuclei. Here, therefore, no chemical bond arises; the resulting molecular orbital is called loosening σ 1s *, and the electrons on it - loosening electrons.

Transfer of electrons from atomic 1s-orbitals to the bonding molecular orbital, leading to the appearance of a chemical bond, is accompanied by the release of energy. On the contrary, the transition of electrons from atomic 1s-orbitals per antibonding molecular orbital requires energy. Therefore, the energy of electrons in the orbital σ 1s sv below, but in orbital σ 1s * higher than nuclear 1s-orbitals. Approximately, we can assume that when passing 1s-electron is allocated to the bonding molecular orbital the same amount of energy as it is necessary to spend for its transfer to the loosening molecular orbital.

Communication order

In the molecular orbital method, to characterize the electron density responsible for the binding of atoms into a molecule, the value is introduced - communication order. The link order, in contrast to the link multiplicity, can take non-integer values. The bond order in diatomic molecules is usually determined by the number of bonding electrons involved in its formation: two bonding electrons correspond to a single bond, four bonding electrons to a double bond, etc. In this case, loosening electrons compensate for the action of the corresponding number of bonding electrons. So, if there are 6 binding and 2 loosening electrons in a molecule, then the excess of the number of binding electrons over the number of loosening electrons is four, which corresponds to the formation of a double bond. Therefore, from the standpoint of the molecular orbital method, a chemical bond in a hydrogen molecule formed by two bonding electrons should be considered as a simple bond.

For elements of the first period, the valence orbital is 1s-orbital. These two atomic orbitals form two σ -molecular orbitals - bonding and loosening. Consider the electronic structure of a molecular ion H2+. It has one electron, which will occupy a more energetically favorable s bonding orbital. In accordance with the rule for counting the multiplicity of bonds, it will be equal to 0.5, and since there is one unpaired electron in the ion, H2+ will have paramagnetic properties. The electronic structure of this ion will be written by analogy with the electronic structure of an atom as follows: σ 1s sv. The appearance of a second electron s-bonding orbitals will lead to an energy diagram describing the hydrogen molecule, an increase in the bond multiplicity to unity and diamagnetic properties. An increase in the multiplicity of bonds will also entail an increase in the dissociation energy of the molecule H2 and a shorter internuclear distance compared to that of the hydrogen ion.

diatomic molecule Not 2 will not exist, since the four electrons present in two helium atoms will be located on the bonding and loosening orbitals, which leads to a zero multiplicity of bonds. But at the same time the ion He2+ will be stable and the multiplicity of communication in it is equal to 0.5. Just like the hydrogen ion, this ion will have paramagnetic properties.

The elements of the second period have four more atomic orbitals: 2s, 2p x, 2p y, 2p z, which will take part in the formation of molecular orbitals. Energy Difference 2s- and 2p-orbitals are large, and they will not interact with each other to form molecular orbitals. This energy difference will increase as you move from the first element to the last. In connection with this circumstance, the electronic structure of diatomic homonuclear molecules of elements of the second period will be described by two energy diagrams that differ in the order of arrangement on them σ st 2p x and π sv 2p y,z. With relative energy proximity 2s- and 2p-orbitals observed at the beginning of the period, including the nitrogen atom, electrons located on σ res 2s and σ st 2p x-orbitals, repel each other. That's why π sv 2p y- and π sv 2p z orbitals are energetically more favorable than σ st 2p x-orbital. The figure shows both diagrams. Since participation 1s-electrons in the formation of a chemical bond is insignificant, they can be ignored in the electronic description of the structure of molecules formed by elements of the second period.

The second period of the system is opened by lithium and beryllium, in which the external energy level contains only s-electrons. For these elements, the scheme of molecular orbitals will not differ in any way from the energy diagrams of molecules and ions of hydrogen and helium, with the only difference that in the latter it is built from 1s-electrons, and Li 2 and Be 2- from 2s-electrons. 1s-electrons of lithium and beryllium can be considered as nonbonding, i.e. belonging to individual atoms. Here, the same patterns will be observed in changing the bond order, dissociation energy, and magnetic properties. And he Li2+ has one unpaired electron located on σ st 2s-orbitals - the ion is paramagnetic. The appearance of a second electron in this orbital will lead to an increase in the dissociation energy of the molecule Li 2 and an increase in the multiplicity of the bond from 0.5 to 1. The magnetic properties will acquire a diamagnetic character. Third s- the electron will be located on σ res-orbitals, which will help reduce the bond multiplicity to 0.5 and, as a consequence, lower the dissociation energy. Such an electronic structure has a paramagnetic ion Be 2+. Molecule Be 2, as well as He 2, cannot exist due to the zero order of the relationship. In these molecules, the number of binding electrons is equal to the number of loosening ones.

As can be seen from the figure, as the bonding orbitals are filled, the dissociation energy of molecules increases, and with the appearance of electrons in the antibonding orbitals, it decreases. The series ends with an unstable molecule Ne 2. The figure also shows that the removal of an electron from the antibonding orbital leads to an increase in the bond multiplicity and, as a consequence, to an increase in the dissociation energy and a decrease in the internuclear distance. The ionization of the molecule, accompanied by the removal of the binding electron, has the opposite effect.

We already know that electrons in atoms are in allowed energy states - atomic orbitals (AO). Similarly, electrons in molecules exist in allowed energy states − molecular orbitals (MO).

molecular orbital much more complicated than the atomic orbital. Here are a few rules that will guide us when building MO from AO:

• When compiling MOs from a set of atomic orbitals, the same number of MOs is obtained as there are AOs in this set.
• The average energy of MOs obtained from several AOs is approximately equal to (but may be greater or less than) the average energy of the taken AOs.
• MOs obey the Pauli exclusion principle: each MO cannot have more than two electrons, which must have opposite spins.
• AOs that have comparable energies combine most efficiently.
• The efficiency with which two atomic orbitals are combined is proportional to their overlap with each other.
• When an MO is formed by overlapping two nonequivalent AOs, the bonding MO contains a larger contribution from the AO with the lowest energy, while the antibonding orbital contains the contribution from the AO with a higher energy.

We introduce the concept communication order. In diatomic molecules, the bond order indicates how much the number of bonding electron pairs exceeds the number of antibonding electron pairs:

Now let's look at an example of how these rules can be applied.

Molecular orbital diagrams of the elements of the first period

Let's start with formation of a hydrogen molecule from two hydrogen atoms.

As a result of interaction 1s orbitals each of the hydrogen atoms form two molecular orbitals. During the interaction, when the electron density is concentrated in the space between the nuclei, a bonding sigma - orbital(σ). This combination has a lower energy than the original atoms. In the interaction, when the electron density is concentrated in the outside of the internuclear region, a antibonding sigma - orbital(σ*). This combination has a higher energy than the original atoms.

Electrons, according to Pauli principle, occupy first the orbital with the lowest energy σ-orbital.

Now consider formation of the He 2 molecule, when two helium atoms approach each other. In this case, the interaction of 1s-orbitals also occurs and the formation of σ * -orbitals, while two electrons occupy the bonding orbital, and the other two electrons occupy the loosening orbital. The Σ * -orbital is destabilized to the same extent as the σ -orbital is stabilized, so two electrons occupying the σ * -orbital destabilize the He 2 molecule. Indeed, it has been experimentally proven that the He 2 molecule is very unstable.

Next, consider formation of the Li 2 molecule, taking into account that the 1s and 2s orbitals differ too much in energy and therefore there is no strong interaction between them. The energy level diagram of the Li 2 molecule is shown below, where the electrons in the 1s-bonding and 1s-antibonding orbitals do not contribute significantly to bonding. Therefore, the formation of a chemical bond in the Li 2 molecule is responsible 2s electrons. This action extends to the formation of other molecules in which the filled atomic subshells (s, p, d) do not contribute to chemical bond. Thus, only valence electrons .

As a result, for alkali metals, the molecular orbital diagram will have a form similar to the diagram of the Li 2 molecule considered by us.

Communication order n in the Li 2 molecule is 1

Molecular orbital diagrams of the elements of the second period

Let us consider how two identical atoms of the second period interact with each other, having a set of s- and p-orbitals. It should be expected that 2s orbitals will connect only with each other, and 2p orbitals - only with a 2p orbitals. Because 2p orbitals can interact with each other in two different ways, they form σ and π molecular orbitals. Using the summary diagram below, you can set electronic configurations of diatomic molecules of the second period which are given in the table.

Thus, the formation of a molecule, for example, fluorine F 2 of atoms in the notation molecular orbital theory can be written like this:

2F =F 2 [(σ 1s) 2 (σ * 1s) 2 (σ 2s) 2 (σ * 2 s) 2 (σ 2px) 2 (π 2py) 2 (π 2pz) 2 (π * 2py) 2 ( π * 2pz) 2 ].

Because Since the overlap of 1s clouds is negligible, the participation of electrons in these orbitals can be neglected. Then the electronic configuration of the fluorine molecule will be:

F2,

where K is the electronic configuration of the K-layer.

Molecular orbitals of polar diatomic molecules

Doctrine of MO allows you to explain and education diatomic heteronuclear molecules. If the atoms in the molecule are not too different from each other (for example, NO, CO, CN), then you can use the diagram above for elements of the 2nd period.

With significant differences between the atoms that make up the molecule, the diagram changes. Consider HF molecule, in which the atoms differ greatly in electronegativity.

The energy of the 1s-orbital of the hydrogen atom is higher than the energy of the highest of the valence orbitals of fluorine, the 2p-orbital. The interaction of the 1s-orbital of the hydrogen atom and the 2p-orbital of fluorine leads to the formation bonding and antibonding orbitals, as it shown on the picture. A pair of electrons located in the bonding orbital of the HF molecule form polar covalent bond.

For the bonding orbital HF molecules The 2p orbital of the fluorine atom plays a more important role than the 1s orbital of the hydrogen atom.

For an antibonding orbital HF molecules vice versa: the 1s orbital of the hydrogen atom plays a more important role than the 2p orbital of the fluorine atom

The VS method is widely used by chemists. Within the framework of this method, a large and complex molecule is considered as consisting of separate two-center and two-electron bonds. It is assumed that the electrons that cause the chemical bond are localized (located) between two atoms. The VS method can be successfully applied to most molecules. However, there are a number of molecules to which this method is not applicable or its conclusions are in conflict with experiment.

It has been established that in a number of cases the decisive role in the formation of a chemical bond is played not by electron pairs, but by individual electrons. The existence of the H 2 + ion indicates the possibility of chemical bonding with the help of one electron. When this ion is formed from a hydrogen atom and a hydrogen ion, an energy of 255 kJ is released. Thus, the chemical bond in the H 2 + ion is quite strong.

If we try to describe a chemical bond in an oxygen molecule using the VS method, we will come to the conclusion that, firstly, it must be double (σ- and p-bonds), and secondly, all electrons in an oxygen molecule must be paired, i.e., .e. the O 2 molecule must be diamagnetic (for diamagnetic substances, the atoms do not have a permanent magnetic moment and the substance is pushed out of the magnetic field). A paramagnetic substance is that whose atoms or molecules have a magnetic moment, and it has the property of being drawn into a magnetic field. Experimental data show that the energy of the bond in the oxygen molecule is indeed double, but the molecule is not diamagnetic, but paramagnetic. It has two unpaired electrons. The VS method is powerless to explain this fact.

The molecular orbital (MO) method is most visible in its graphical model of a linear combination of atomic orbitals (LCAO). The MO LCAO method is based on the following rules.

1) When atoms approach each other to the distances of chemical bonds, molecular orbitals (AO) are formed from atomic orbitals.

2) The number of obtained molecular orbitals is equal to the number of initial atomic ones.

3) Atomic orbitals that are close in energy overlap. As a result of the overlap of two atomic orbitals, two molecular orbitals are formed. One of them has a lower energy compared to the original atomic ones and is called binding , and the second molecular orbital has more energy than the original atomic orbitals, and is called loosening .

4) When atomic orbitals overlap, the formation of both σ-bonds (overlap along the chemical bond axis) and π-bonds (overlap on both sides of the chemical bond axis) is possible.

5) A molecular orbital that is not involved in the formation of a chemical bond is called non-binding . Its energy is equal to the energy of the original AO.

6) On one molecular orbital (as well as atomic orbital) it is possible to find no more than two electrons.

7) Electrons occupy the molecular orbital with the lowest energy (principle of least energy).

8) The filling of degenerate (with the same energy) orbitals occurs sequentially with one electron for each of them.

Let us apply the MO LCAO method and analyze the structure of the hydrogen molecule.

Let's mentally overlap two atomic orbitals, forming two molecular orbitals, one of which (bonding) has a lower energy (located below), and the second (loosening) has a higher energy (located above)

Rice. eight Energy diagram of the formation of the H 2 molecule

The MO LCAO method makes it possible to visually explain the formation of H 2 + ions, which causes difficulties in the method of valence bonds. One electron of the H atom passes to the σ-bonding molecular orbital of the H 2 + cation with energy gain. A stable compound is formed with a binding energy of 255 kJ/mol. The multiplicity of the connection is ½. The molecular ion is paramagnetic. The ordinary hydrogen molecule already contains two electrons with opposite spins in σ cv 1s orbitals: The binding energy in H 2 is greater than in H 2 + - 435 kJ / mol. The H 2 molecule has a single bond, the molecule is diamagnetic.

Rice. 9 Energy diagram of the formation of the H 2 + ion

Using the MO LCAO method, we consider the possibility of the formation of the He 2 molecule

In this case, two electrons will occupy the bonding molecular orbital, and the other two will occupy the loosening orbital. Such a population of two orbitals with electrons will not bring a gain in energy. Therefore, the He 2 molecule does not exist.

Rice. ten Energy diagram illustrating the impossibility of forming a chemical

bonds between He atoms

The filling of molecular orbitals occurs in compliance with the Pauli principle and Hund's rule as their energy increases in the following sequence:

σ1s< σ*1s < σ2s < σ*2s < σ2p z < π2p x = π2p y < π*2p x =π*2p y < σ*2p z

The energy values ​​σ2p and π2p are close and for some molecules (B 2 , C 2 , N 2) the ratio is the opposite of the above: first π2p then σ2p

Table 1 Energy and bond order in molecules of elements of period 1

According to the MO method communication procedure in a molecule is determined by the difference between the number of bonding and loosening orbitals, divided by two. The bond order can be zero (the molecule does not exist), an integer or a positive fractional number. When the bond multiplicity is zero, as in the case of He 2 , no molecule is formed.

Figure 11 shows the energy scheme for the formation of molecular orbitals from atomic orbitals for diatomic homonuclear (of the same element) molecules of elements of the second period. The number of binding and loosening electrons depends on their number in the atoms of the initial elements.

Fig.11 Energy diagram for the formation of diatomic molecules

elements 2 periods

The formation of molecules from atoms of elements of period II can be written as follows

(K - internal electronic layers):

Li 2

The Be 2 molecule was not detected, as was the He 2 molecule

B 2 molecule is paramagnetic

C2

N 2

O 2 molecule is paramagnetic

F2

Ne 2 molecule not detected

Using the MO LCAO method, it is easy to demonstrate the paramagnetic properties of the oxygen molecule. In order not to clutter up the figure, we will not consider overlap 1 s-orbitals of oxygen atoms of the first (inner) electron layer. We take into account that p-orbitals of the second (outer) electron layer can overlap in two ways. One of them will overlap with a similar one with the formation of a σ-bond.

Two others p-AO overlap on both sides of the axis x with the formation of two π-bonds.

Rice. fourteen Energy diagram illustrating, using the MO LCAO method, the paramagnetic properties of the O 2 molecule

The energies of molecular orbitals can be determined from the absorption spectra of substances in the ultraviolet region. So, among the molecular orbitals of the oxygen molecule formed as a result of overlapping p-AO, two π-bonding degenerate (with the same energy) orbitals have less energy than the σ-bonding one, however, like π*-loosening orbitals, they have less energy compared to the σ*-loosening orbital.

In the O 2 molecule, two electrons with parallel spins ended up on two degenerate

(with the same energy) π*-antibonding molecular orbitals. It is the presence of unpaired electrons that determines the paramagnetic properties of the oxygen molecule, which will become noticeable if oxygen is cooled to a liquid state. So, the electronic configuration of O 2 molecules is described as follows:

О 2 [КК(σ s) 2 (σ s *) 2 (σ z) 2 (π x) 2 (π y) 2 (π x *) 1 (π y *) 1 ]

The letters KK show that four 1 s-electrons (two bonding and two loosening) have practically no effect on the chemical bond.

Since three hydrogen atoms have only three 1 s-orbitals, then the total number of formed molecular orbitals will be equal to six (three bonding and three loosening). Two electrons of the nitrogen atom will be in a non-bonding molecular orbital (lone electron pair).

The method of molecular orbitals (MO) is currently considered to be the best method for the quantum mechanical interpretation of a chemical bond. However, it is much more complicated than the VS method and is not as clear as the latter.

The existence of bonding and loosening MOs is confirmed by the physical properties of the molecules. The MO method makes it possible to foresee that if, during the formation of a molecule from atoms, the electrons in the molecule fall into bonding orbitals, then the ionization potentials of the molecules must be greater than the ionization potentials of atoms, and if the electrons fall into loosening orbitals, then vice versa. Thus, the ionization potentials of hydrogen and nitrogen molecules (bonding orbitals), 1485 and 1500 kJ/mol, respectively, are greater than the ionization potentials of hydrogen and nitrogen atoms, 1310 and 1390 kJ/mol, and the ionization potentials of oxygen and fluorine molecules (loosening orbitals) are 1170 and 1523 kJ/mol - less than that of the corresponding atoms - 1310 and 1670 kJ/mol. When molecules are ionized, the bond strength decreases if the electron is removed from the bonding orbital (H 2 and N 2), and increases if the electron is removed from the loosening orbital (O 2 and F 2).

Communication polarity

Between different atoms, a pure covalent bond can occur if the electronegativity (EO) of the atoms is the same. Such molecules are electrosymmetric, i.e. The "centers of gravity" of the positive charges of the nuclei and the negative charges of the electrons coincide at one point, therefore they are called non-polar.

If the connecting atoms have different EC, then the electron cloud located between them shifts from a symmetrical position closer to the atom with a higher EC:

The displacement of the electron cloud is called polarization. As a result of one-sided polarization, the centers of gravity of positive and negative charges in the molecule do not coincide at one point, a certain distance (l) appears between them. Such molecules are called polar or dipoles, and the bond between the atoms in them is called polar. For example, in the HCl molecule, the binding electron cloud is shifted towards the more electronegative chlorine atom. Thus, the hydrogen atom in hydrogen chloride is positively polarized, while the chlorine atom is negatively polarized.

A positive charge appears on the hydrogen atom δ= +0.18, and on the chlorine atom - a negative charge δ=-018. hence the bond in the hydrogen chloride molecule is 18% ionic.

A polar bond is a kind of covalent bond that has undergone a slight one-sided polarization. The distance between the "centers of gravity" of positive and negative charges in a molecule is called the dipole length. Naturally, the greater the polarization, the greater the length of the dipole and the greater the polarity of the molecules. To assess the polarity of molecules, a constant dipole moment µ is usually used, which is the product of the value of the elementary electric charge q and the length of the dipole (l), i.e. µ =q∙l. Dipole moments are measured in coulometers.

table 2 Electric moment of the dipole µ of some molecules

The total dipole moment of a complex molecule can be considered equal to the vector sum of the dipole moments of individual bonds. The dipole moment is usually considered to be directed from the positive end of the dipole to the negative. The result of the addition depends on the structure of the molecule. The dipole moent of highly symmetric BeCl 2 ,BF 3 ,CCl 4 molecules is equal to zero, although the Be-Cl,B-F,C-Cl bonds are highly polar. In the corner H 2 O molecule, the polar O-H bonds are located at an angle of 104.5 o. So the molecule is polar

(µ = 0.61∙10 -29 C∙m)

With a very large difference in electronegativity, the atoms have a clear unilateral polarization: the electron cloud of the bond shifts as much as possible towards the atom with the highest electronegativity, the atoms pass into oppositely charged ions, and an ionic molecule appears. The covalent bond becomes ionic. The electrical asymmetry of molecules increases, the length of the dipole increases, and the dipole moment increases.

The polarity of a bond can be predicted using the relative EO of atoms. The greater the difference between the relative EOs of atoms, the more pronounced the polarity. It is more correct to speak about the degree of ionicity of a bond, since bonds are not 100% ionic. Even in the CsF compound, the bond is only 89% ionic.

If we consider compounds of elements of any period with the same element, then as we move from the beginning to the end of the period, the predominantly ionic nature of the bond is replaced by a covalent one. For example, in fluorides of the 2nd period LiF, BeF 2 , CF 4 , NF 3 , OF 2 , F 2 the degree of ionicity of the bond from lithium fluoride gradually weakens and is replaced by a typically covalent bond in the fluorine molecule.

The electronegativity of sulfur is much less than the EO of oxygen. Therefore, the polarity of the H–S bond in H 2 S is less than the polarity of the H–O bond in H 2 O, and the length of the H–S bond (0.133 nm) is greater than H–O (0.56 nm) and the angle between the bonds approaches a straight line . For H 2 S it is 92 o, and for H 2 Se it is 91 o.

For the same reasons, the ammonia molecule has a pyramidal structure and the angle between the H–N–H valence bonds is greater than a straight one (107.3 o). In the transition from NH 3 to PH 3 , AsH 3 and SbH 3 the angles between the bonds are respectively 93.3 about; 91.8 o and 91.3 o.