When using the method molecular orbitals it is considered, in contrast to the method of valence bonds, that each electron is in the field of all nuclei. In this case, the bond is not necessarily formed by a pair of electrons. For example, the H 2 + ion consists of two protons and one electron. Between two protons there are repulsive forces (Fig. 30), between each of the protons and an electron - forces of attraction. A chemical particle is formed only if the mutual repulsion of protons is compensated by their attraction to the electron. This is possible if the electron is located between the nuclei - in the binding region (Fig. 31). Otherwise, the repulsive forces are not compensated by the forces of attraction - they say that the electron is in the region of antibonding, or loosening.

Two-center molecular orbitals

The molecular orbital method uses the idea of ​​a molecular orbital to describe the distribution of electron density in a molecule (similar to the atomic orbital for an atom). Molecular orbitals are the wave functions of an electron in a molecule or other polyatomic chemical particle. Each molecular orbital (MO), like the atomic orbital (AO), can be occupied by one or two electrons. The state of an electron in the binding region is described by the bonding molecular orbital, in the loosening region - by the loosening molecular orbital. The distribution of electrons in molecular orbitals follows the same rules as the distribution of electrons in atomic orbitals in an isolated atom. Molecular orbitals are formed by certain combinations of atomic orbitals. Their number, energy, and shape can be derived from the number, energy, and shape of the orbitals of the atoms that make up the molecule.

In the general case, the wave functions corresponding to molecular orbitals in a diatomic molecule are represented as the sum and difference of the wave functions of atomic orbitals multiplied by some constant coefficients that take into account the proportion of atomic orbitals of each atom in the formation of molecular orbitals (they depend on the electronegativity of atoms):

φ(AB) = s 1 ψ(A) ± s 2 ψ(B)

This method of calculating the one-electron wave function is called "molecular orbitals in the approximation of a linear combination of atomic orbitals" (MO LCAO).

So, when an H 2 + ion or a H 2 hydrogen molecule is formed from two s-orbitals of hydrogen atoms form two molecular orbitals. One of them is binding (it is denoted by σ st), the other is loosening (σ *).

The energies of the bonding orbitals are lower than the energies of the atomic orbitals used to form them. The electrons that populate the bonding molecular orbitals are predominantly located in the space between the bonded atoms, i.e. in the so-called binding region. The energies of the antibonding orbitals are higher than the energies of the initial atomic orbitals. The population of loosening molecular orbitals with electrons contributes to the weakening of the bond: a decrease in its energy and an increase in the distance between atoms in a molecule. The electrons of the hydrogen molecule, which have become common to both bonded atoms, occupy the bonding orbital.

Combination R-orbitals leads to two types of molecular orbitals. Of the two R-orbitals of interacting atoms directed along the bond line, bonding σ St - and loosening σ*-orbitals are formed. Combinations R-orbitals perpendicular to the bond lines give two bonding π- and two loosening π*-orbitals. Using the same rules when populating molecular orbitals with electrons as when filling atomic orbitals in isolated atoms, one can determine the electronic structure of diatomic molecules, for example, O 2 and N 2 (Fig. 35).

From the distribution of electrons in molecular orbitals, the bond order (ω) can be calculated. From the number of electrons located in the bonding orbitals, subtract the number of electrons located in the antibonding orbitals, and the result is divided by 2 n(based on n links):

ω = / 2 n

It can be seen from the energy diagram that for the H 2 molecule ω = 1.

The molecular orbital method gives the same chemical bond order values ​​as the valence bond method for O 2 (double bond) and N 2 (triple bond) molecules. At the same time, it allows non-integer values ​​of the link order. This is observed, for example, when a two-center bond is formed by one electron (in the H 2 + ion). In this case, ω = 0.5. The magnitude of the bond order directly affects its strength. The higher the bond order, the greater the bond energy and the shorter its length:

Regularities in changes in the order, energy and length of the bond can be traced on the examples of the molecule and molecular ions of oxygen.

The combination of the orbitals of two different atoms with the formation of a molecule is possible only if their energies are close, while the atomic orbitals of an atom of higher electronegativity in the energy diagram are always located lower.

For example, in the formation of a hydrogen fluoride molecule, the combination 1 s-AO of the hydrogen atom and 1 s-AO or 2 s-AO of the fluorine atom, since they differ greatly in energy. Closest in energy 1 s-AO of the hydrogen atom and 2 p-AO of the fluorine atom. The combination of these orbitals causes the appearance of two molecular orbitals: bonding σb and loosening σ*.

Remaining 2 R-orbitals of the fluorine atom cannot be combined with 1 s-AO of the hydrogen atom, since they have different symmetry relative to the internuclear axis. They form non-bonding π 0 -MOs having the same energy as the original 2 R-orbitals of the fluorine atom.

Not participating in LCAO s-orbitals of the fluorine atom form non-bonding σ 0 -MO. Population of nonbonding orbitals by electrons does not promote or prevent bond formation in the molecule. When calculating the link order, their contribution is not taken into account.

Multicenter molecular orbitals

In multicenter molecules, molecular orbitals are multicenter, as they are a linear combination of the orbitals of all the atoms involved in the formation of bonds. In the general case, molecular orbitals are not localized, that is, the electron density corresponding to each orbital is more or less evenly distributed throughout the entire volume of the molecule. However, with the help of mathematical transformations, it is possible to obtain localized molecular orbitals of a certain shape, corresponding to individual two- or three-center bonds or lone electrons.

The simplest example of a three-center bond is the molecular ion H 3 + . Of the three s-orbitals of hydrogen atoms, three molecular orbitals are formed: bonding, non-bonding and loosening. A pair of electrons populates a bonding orbital. The resulting bond is a two-electron three-center bond; the bond order is 0.5.

Chemical particles containing unpaired electrons have paramagnetic properties (in contrast to the diamagnetic properties of chemical particles, in which all electrons are paired). Paramagnets are all substances consisting of chemical particles with an odd number of electrons, such as NO. The method of molecular orbitals makes it possible to identify paramagnets among substances consisting of chemical particles with an even number of electrons, for example, O 2, in the molecule of which two unpaired electrons are located on two loosening π * orbitals.

Chemical species with unpaired electrons in outer orbitals are called free radicals. They are paramagnetic and highly reactive. Inorganic radicals with localized unpaired electrons, for example . H, . NH 2 are usually short lived. They are formed during photolysis, radiolysis, pyrolysis, electrolysis. Low temperatures are used to stabilize them. Short-lived radicals are intermediate species in many reactions.

Fig.1. Contour diagrams of electron density in H 2 +

Lecture No. 4. The concept of the molecular orbital method. Energy diagrams of molecular orbitals for binary homonuclear molecules. σ - and π- molecular orbitals. Dia- and paramagnetic molecules. Ionic bond.

Intermolecular interactions. Hydrogen bond.

The method of valence bonds quite clearly explains the formation and structure of many molecules, but it cannot explain many facts, for example, the existence of molecular ions (H2 +, He2+) or radicals (CH3, NH2), paramagnetism of molecules with an even number of electrons (O2, NO), which are explained within the framework of the molecular orbital method (MMO).

Molecular orbital method

The molecular orbital method, developed by Mulliken and Hund, is based on the assumption that each electron in a molecule is in the field of all the nuclei and electrons of the atoms that form the molecule, and its state is characterized by a wave function Ψ, called the molecular orbital. Each MO corresponds to a wave function that characterizes the region of the most probable stay of electrons of a certain energy in a molecule. Atomic s-, p-, d-, f-orbitals correspond to molecular σ-, π-, δ-, … orbitals, which are filled in accordance with the Pauli principle, Hund's rule, the principle of least energy.

by the most in a simple way formation of a molecular orbital (MO) is

linear combination of atomic orbitals (AO) (LCAO-MO method).

If in the field of two atomic nuclei A and B have one electron, then it can be either at one nucleus or at another, and its state can be described by two molecular orbitals Ψ and Ψ *, which are formed by a linear combination of atomic orbitals:

Ψ = Ψ A + Ψ B and Ψ * = Ψ A - Ψ B

A molecular orbital is called a bonding Ψ if it corresponds to an increase in the electron density in the region between the nuclei and thereby an increase in their attraction, and a loosening Ψ * if the electron density decreases between the nuclei and increases behind the nuclei, which is equivalent to an increase in the repulsion of the nuclei. The energy of the binding MO is lower than the energy of the initial AO, the energy of the loosening MO is higher than the energy of the initial atomic orbital.

On fig. 1 shows the contour diagrams of the electron density of the bonding Ψ

(a) and loosening Ψ * (b) molecular orbitals in the H2 + particle.

As in the MVS, the symmetry of molecular orbitals about the bonding line leads to the formation of σ - MO, in the direction perpendicular to the bonding line, - π - MO.

When d-orbitals overlap, δ-

On fig. Figure 2 shows the formation of σ - bonding and σ - loosening MOs with a combination of different atomic orbitals; 3 respectively π -MO and π* - MO.

The overlap of s-orbitals leads to the formation of two molecular orbitals: σs-bonding and σ*s-loosening.

The overlap of p-orbitals leads to the formation of six molecular orbitals of different symmetry. From two p-orbitals of interacting atoms, directed along the communication line, for example, the X axis, a bonding σ p z - and loosening σ * p z -orbitals are formed, along the Z and Y axes - πр z - and πp y - binding and π * р z - and π* p y - loosening MO.

The population of MOs with electrons occurs in accordance with the Pauli principle, the principle of least energy, and Hund's rule.

Rice. 2. Formation of σ - bonding and σ - loosening molecular orbitals

Due to the fact that for orbitals of the same type, the size of the overlapping region of orbitals decreases in the series σ > π > δ , then the splitting of energy levels during the formation of MO from AO decreases in the same order (Fig. 4), which leads to a change in the order of filling σр − and π - MO in molecules.

unpaired electrons with the same spins, for example B, C, N and their electronic counterparts, the sequence of filling MO is as follows:

σ(1s)< σ* (1s) < σ(2s) < σ* (2s) < π (2pz )= π (2py ) < σ(2px ) < π* (2pz )= π* (2py ) < σ* (2px )....

Rice. 3. Formation of π - bonding and π - loosening molecular orbitals

Rice. 4. Reducing the degree of splitting of energy levels in the series σ > π > δ

For homonuclear diatomic molecules of the second and subsequent periods, in which p - sublevels of atoms are filled paired electrons with antiparallel spins, for example (O - Ne) and their electronic counterparts, the sequence of filling MO changes somewhat:

σ(1s)< σ* (1s) < σ(2s) < σ* (2s) < σ(2px ) < π (2pz )= π (2py ) < π* (2pz )= π* (2py ) < σ* (2px )....

The electronic configuration of a molecule can be represented as an energy diagram or an electronic formula.

On fig. 5 shows the energy diagram of molecular orbitals for the hydrogen molecule H2, electronic formula which is written as follows: [σ(1s)]2 or (σ 1s )2 .

Rice. 5. Energy diagram of the H 2 molecule

The filling of the bonding molecular orbital σ 1s leads to an increase in the electron density between the nuclei and determines the existence of the H2 molecule.

The MO method substantiates the possibility of the existence of the molecular hydrogen ion H2 + and the impossibility of the existence of the He2 molecule, since in the latter case, the filling of the bonding and loosening σ 1s orbitals with two electrons does not lead to a change in the energy of isolated atoms: [(σ 1s )2 (σ * 1s )2 ] (Fig. 6). Therefore, the He2 molecule does not exist.

Rice. 6. Energy diagram confirming the impossibility of the existence of the He2 molecule

On fig. Figure 7 shows the energy diagram of molecular orbitals formed by the overlap of s- and p-orbitals of the second energy level for diatomic homonuclear molecules of the A2 type.

The arrows show the change in the order of occupation of the MO of molecules formed by atoms, in which the 2p sublevel is filled with unpaired electrons (B2, C2, N2), for which the binding π st (2py ) and π st (2pz ) are located below σst (2px ), and paired electrons (O2 , F2 , Ne2 ), for which the bonding π st (2py ) and π st (2pz ) are located above σst (2px ),

Rice. Fig. 7. MO energy diagram for homonuclear molecules of the 2nd period (arrows show the change in the filling order of the bonding σ- and π-MO)

In MMO, the concept is used - bond order, which is defined as the difference between the number of electrons in the bonding MO and the number of electrons in the loosening MO, divided by the number of atoms forming the bond.

					N − N*
	For diatomic molecules, the bond order n is: n =						Where N is the number
	electrons on bonding MOs, N* is the number of electrons on loosening MOs.
	For the H2 molecule, the bond order is, respectively,					2− 0		1 , for He2
		2− 2		Which confirms the impossibility of the existence of a diatomic

molecules. It is known that inert gases exist in the form of monatomic molecules. Using the same rules for populating molecular orbitals with electrons as

when filling atomic orbitals in isolated atoms (Pauli principle, minimum energy principle and Hund's rule)), one can determine the electronic structure of diatomic molecules, for example N2 and O2.

Let us write the electronic configurations of atoms in the ground state:

			or .
			or .
The electronic configurations of N2 and O2 molecules can be written as follows
		N + N → N2

O2 : O+O → O2

On fig. 8 shows the energy diagram of the formation of an oxygen molecule.

Fig.8. Energy diagram of an oxygen molecule

In the O2 molecule, two electrons with parallel spins ended up on two

degenerate (with the same energy) * -loosening molecular orbitals. Availability unpaired electrons determines the paramagnetic properties of the oxygen molecule, which become especially noticeable if oxygen is cooled to a liquid state.

Molecules of paramagnets have their own magnetic moment due to the internal movement of charges. In the absence of external magnetic field the magnetic moments of the molecules are randomly oriented, so the resulting magnetic field due to them is zero. The total magnetic moment of the substance is also equal to zero.

If the substance is placed in an external magnetic field, then under its influence the magnetic moments of the molecules acquire a predominant orientation in one direction, and the substance becomes magnetized - its total magnetic moment becomes different from zero.

Molecules of diamagnets do not have their own magnetic moments and are weakly magnetized when introduced into a magnetic field.

Paramagnets are all substances consisting of chemical particles with an odd number of electrons, for example, the NO molecule, molecular ions N2 +, N2 -, etc.

Most substances whose molecules contain an even number of electrons have diamagnetic properties(N2, CO).

The paramagnetic properties of oxygen and boron molecules containing an even number of electrons are explained on the basis of MMO. The O2 molecule has two unpaired electrons in the *-loosening molecular orbitals, and the B2 molecule has two unpaired electrons in the *-bonding molecular orbitals (see Table 1).

Chemical particles that have unpaired electrons in their outer orbitals are called free radicals. They are paramagnetic and highly reactive. Inorganic radicals with localized unpaired electrons, for example (.H), (.NH2), are usually short-lived. They are formed during photolysis,

radiolysis, pyrolysis, electrolysis. Low temperatures are used to stabilize them. Short-lived radicals are intermediate particles in many reactions, especially chain and catalytic ones.

The bond order in the N2 molecule, which has an excess of six electrons per

The concept of the order of a chemical bond in the MO method coincides with the concept of the multiplicity of bonds in the BC method (O2 is a double bond, N2 is a triple bond). The magnitude of the bond order affects the strength of the bond. The higher the bond order, the greater the bond energy and the shorter the bond length.

In table. 1 shows the electronic configurations and bond characteristics for homonuclear molecules of the first and second periods. As can be seen from the table, with an increase in the bond order in the series B2 - C2 - N2, the energy increases and the bond length decreases.

Table 1. Electronic configurations and some properties of molecules of the first and second periods

							Magnetic
	Molecule	Electronic configuration			disconnection,
							properties
		[(σ1s )2 ]					diamagnetic
		[(σ1s )2 (σ*1s )2 ]			Molecule does not exist
							diamagnetic
					Molecule does not exist
							paramagnetic
							diamagnetic
						diamagnetic

The MO method allows non-integer values ​​of the link order. This takes place in molecular ions, for example, in the molecular ion H2+, for which n = 0.5.

Regularities in changes in the order, energy and length of the bond can be traced on the examples of the molecule and molecular ions of oxygen.

The electronic configuration and bond order of the oxygen molecule are given in Table. 1. Electronic configurations and bond order of molecular oxygen ions

the following:
O2 - -			n = 1.5.
The decrease in the bond order in the series of particles O2 + , O2 , O2 - determines the decrease
bond strength and finds experimental confirmation:
O2+ :	n \u003d 2.5, E sv \u003d 629 kJ / mol,				d sv = 112 pm;
	n \u003d 2.0, E sv \u003d 494 kJ / mol,				d sv = 121 pm;
O2 - :	n \u003d 1.5, E sv \u003d 397 kJ / mol,				d sv \u003d 126 pm.

All particles have unpaired electrons and exhibit paramagnetic properties. Molecules that have the same number of valence electrons are called

isoelectronic particles. These include CO and N2 molecules, which have a total of 14 electrons; molecular ion N2 + and molecule CN, having 13 electrons. IMO assigns the same filling order to isoelectronic particles

electrons of molecular orbitals, the same bond order, which makes it possible to explain the closeness of the physical properties of molecules.

When a heteronuclear molecule of type AB is formed, the combination of orbitals of two different atoms, leading to the formation of a molecule, is possible only if the electron energies are close, while the orbitals of an atom with a higher electronegativity in the energy diagram are always located lower.

On fig. Figure 9 shows the energy scheme for the formation of a CO molecule.

Four 2p electrons of the oxygen atom and two 2p electrons of the carbon atom pass to the binding π - and σ - MO. The energy of the 2p electrons of the connecting atoms is not the same: the oxygen atom has a higher nuclear charge and electronegativity compared to the carbon atom, therefore the 2p electrons in the oxygen atom are more strongly attracted by the nucleus and their position on the energy diagram corresponds to a lower energy compared to the 2p orbitals of the carbon atom . All six electrons involved in bond formation are located on three bonding MOs; therefore, the bond multiplicity is three, which explains the significant similarity in the properties of free nitrogen and carbon monoxide (II) (Table 2).

Rice. 9. Energy scheme for the formation of the CO molecule

Table 2. Some physical properties CO and N2 molecules

Molecule	T pl , K	T bale, K	E St, kJ/mol	d sv , pm

Non-valent types of chemical bond

Ionic bond.

When the difference in the electronegativity of the interacting atoms is more than two units, the displacement of valence electrons is so large that we can talk about their transition from one atom to another with the formation of charged particles - cations and anions. These particles interact with each other according to the laws of electrostatics. The resulting bond is called ionic. Compounds with ionic bonds are significantly

less common than compounds with a covalent bond, characteristic of substances that exist in normal conditions in the crystalline state and having ionic conductivity in the molten or dissolved state. Ionic compounds primarily include typical salts - halides alkali metals having an ionic crystal lattice. Ionic molecules exist only at high temperatures in vapors of ionic compounds.

The ionic bond, unlike the covalent bond, is non-directional, since the ions form spherically symmetrical force fields, does not have saturation, since the interaction of ions of the opposite sign occurs in different directions, is delocalized, since no increased electron density is observed in the binding region.

Electrostatic model of ionic bond considers its formation as the interaction of oppositely charged ions, each of which is characterized

The formation energy of an AB molecule can be defined as the algebraic sum of several energies: the attraction energy of Az+ and Bz- ions, the repulsion energy of ions, the electron affinity energy of atom B, and the ionization energy of atom A.

ions in a molecule, n - takes into account the share of the repulsion energy, which is usually 10% of the attraction energy, E B - the energy of the electron affinity of the atom B, I A - the ionization energy of the atom A.

For a gaseous KCl molecule, the energy E AB was calculated without taking into account the polarization

ions: d \u003d 2.67 10-10 eV, E Cl \u003d 3.61 eV, I K \u003d 4.34 eV and the binding energy is E bond \u003d -E AB \u003d 4.06 eV ~ 391 kJ ..

The experimentally determined ionization energy of the KCl molecule is 422 kJ/mol.

In gases, liquids and crystals, each ion tends to surround itself largest number ions of opposite charge.

The location of ions in space is determined by the ratio of their radii. If the ratio of the cation radius to the anion radius is within

r + /r - = 0.41-0.73, then six ions of opposite charge are coordinated around the central atom - a cation or anion. This coordination is called octahedral, and the type of crystal lattice is designated as the NaCl type.

If the ratio of the cation radius to the anion radius is within

r + /r - = 0.73-1.37, then eight ions of opposite charge are coordinated around the central atom - a cation or anion. Such coordination is called cubic, and the type of crystal lattice is designated as the CsCl type.

When ions approach each other, their spherical electron shells are deformed, which leads to a displacement of the electric charge and the appearance of an induced electric moment in the particle. This phenomenon is called ion polarization. Ion polarization is a two-way process that combines the polarizability of ions and polarizing effect depending on the electronic structure, charge, and size of the ion. Polarizability is minimal for ions with an inert gas configuration (ns 2 np 6 ), which at the same time have the greatest polarizing effect. Significant polarizability of ions of d - elements is explained by the presence of a large number of valence electrons, as a result, the covalent component of the bond increases.

The polarization effect explains many differences in the properties of substances, for example, the poor solubility of silver chloride in water compared to alkali chlorides.

metals, differences in melting temperatures, for example, T pl, AgCl = 4550 C, T pl, NaCl = 8010 C. Electronic configurations of ions: Ag + - 4d 10 5s 0; Na+ - 3s 0 .

The less symmetric electronic configuration of the Ag+ ion due to the presence of 4d 10 electrons causes its stronger polarization, which leads to the appearance

directional covalent component of the bond compared to NaCl, in which the degree of ionicity of the bond is higher.

Metal connection.

The most important property of metals is high electrical conductivity, which decreases with increasing temperature. Metal atoms differ from atoms of other elements in that they retain their outer electrons relatively weakly. Therefore, in the crystal lattice of a metal, these electrons leave their atoms, turning them into positively charged ions. "Shared" electrons move in space between cations and keep them together. Interatomic distances in metals are greater than in their compounds with a covalent bond. Such a bond exists not only in metal crystals, but also in their melts and in the amorphous state. It is called

metallic, determines the electronic conductivity of metals.

Electrons in a metal move randomly, passing from one atom to another, forming an electron gas. Positively charged metal ions only slightly oscillate around their position in the crystal lattice, when the metal is heated, the vibrations of the cations increase and the electrical resistance of the metal increases. Due to the presence of free electrons not associated with certain atoms, metals conduct well electricity and warm.

Such physical properties of metals as high thermal and electrical conductivity, ductility and ductility, metallic luster can be explained based on the concept of electron gas. The metallic bond is quite strong, since most metals have a high melting point.

A more rigorous interpretation metallic bond lets give molecular orbital method. Recall that when two atomic orbitals interact, two molecular orbitals are formed: a bonding and an antibonding orbital. There is a splitting of the energy level into two. If four metal atoms interact simultaneously, four molecular orbitals are formed. With the simultaneous interaction of N particles contained in a crystal, N molecular orbitals are formed, and the value of N can reach huge values ​​comparable to the number

Avogadro (6 1023 ). Molecular orbitals formed by atomic orbitals of the same sublevel are so close that they practically merge, forming a certain

energy zone (Fig. 10).

Rice. 10. Formation of an energy band in a crystal

Consider the formation of energy bands on the example of metallic sodium,

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 more high energy than the original atoms.

MO diagrams of hydrogen and helium molecules

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.

MO diagram of a lithium molecule

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.

MO diagrams of diatomic molecules of elements 2 periods

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 2p orbital of the fluorine atom plays 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

Categories ,

Chronologically, the MO method appeared later than the VS method, since there were questions in the theory of covalent bonds that could not be explained by the VS method. Let's point out some of them.

As is known, the main position of the VS method 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 the molecular ion H 2 + one-electron bond. The VS method cannot explain the formation of a one-electron bond, it contradicts its main position.

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

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

4.5.1. The main provisions of mmo, mo.

1. In a molecule, all electrons are common. The molecule itself is a single whole, a collection of nuclei and electrons.

2. In a molecule, each electron corresponds to a molecular orbital, just as each electron in an atom corresponds to an atomic orbital. And the designations of the orbitals are similar:

AO s, p, d, f

MO σ, π, δ, φ

3. As a first approximation, a molecular orbital is a linear combination (addition and subtraction) of atomic orbitals. Therefore, they speak of the MO LCAO method (a molecular orbital is a linear combination of atomic orbitals), in which from N AO is formed N MO (this is the main provision of the method).

Rice. 12. Energy

mole formation scheme

cools of hydrogen H 2

Consideration of chemical bonds in the MO method consists in the distribution of electrons in a molecule along its orbitals. The latter are filled in ascending order of energy and taking into account the Pauli principle. This method assumes an increase in the electron density between the nuclei during the formation of a covalent bond.

Using provisions 1-3, we explain the formation of the H 2 molecule from the point of view of the MO method. With sufficient convergence of hydrogen atoms, their electron orbitals overlap. According to paragraph 3, from two identical ls-orbitals, two molecular orbitals are formed: one of them from the addition of atomic orbitals, the other from their subtraction (Fig. 12). Energy of the first E 1< E 2 , а энергия второй E 2 < E 3 .

A molecular orbital whose energy is less than the energy of an atomic orbital of an isolated atom is called binding(denoted by the symbol sv), and the electrons located on it - bonding electrons.

A molecular orbital whose energy is greater than that of an atomic orbital is called anti-binding or loosening(denoted by the symbol razr), and the electrons located on it - loosening electrons.

If the electron spins of the connecting hydrogen atoms are antiparallel, then they will occupy the binding MO, a chemical bond arises (Fig. 12), accompanied by the release of energy E 1 (435 kJ / mol). If the electron spins of hydrogen atoms are parallel, then, in accordance with the Pauli principle, they cannot be placed on the same molecular orbital: one of them will be placed on the bonding and the other on the loosening orbital, which means chemical bond cannot form.

According to the MO method, the formation of molecules is possible if the number of electrons in the bonding orbitals more number electrons in loosening orbitals. If the number of electrons in the bonding and loosening orbitals is the same, then such molecules cannot be formed. Thus, the theory does not allow the existence of the He 2 molecule, since in it two electrons would be in the bonding orbital and two in the loosening orbital. The always loosening electron negates the effect of the bonding electron.

In the notation of the MO method, the reaction of the formation of a hydrogen molecule from atoms is written as follows:

2H = H 2 [(σ CB 1s) 2 ],

those. symbols are used to express the placement of electrons in atomic and molecular orbitals. In this case, the symbol of each MO is enclosed in parentheses and above the brackets on the right is the number of electrons in this orbital.

The number of valence bonds is determined by the formula:

where: B is the number of connections;

N CB N RAS - respectively, the number of binding and loosening electrons in the molecule.

In a hydrogen molecule B \u003d (2-0): 2 \u003d 1, hydrogen is monovalent. The H 2 molecule is diamagnetic (electrons are paired).

Now the one-electron bond in the molecular ion H 2 + is easily explained (Fig. 13). The only electron of this ion occupies the energetically most favorable orbital St. 1s. Process equation:

H + H + = H 2 + [(σ St 1s) 1], ∆H = - 259.4 kJ

Rice. 13. Energy scheme 14. Energy scheme

formation of the molecular formation of the dihelium ion He 2

hydrogen ion H 2

The number of bonds in the H 2 + ion is ½ (bond by one electron). The H 2 + ion is paramagnetic (has one unpaired electron).

The existence of a molecular dihelium ion He 2 + is possible (Fig. 14). Equation of its formation

He + He + = He 2 + [(σ CB 1s) 2 (σ res 1s) 1], ∆H = - 292.8 kJ

This ion has been experimentally discovered. The number of links in it

Rice. 15 . Energy scheme for the formation of diatomic homonuclear molecules of elements of the second period

(2-1) : 2 = 1 / 2 . The ion is paramagnetic (has an unpaired electron).

4.5.2. The main diatomic homonuclear molecules of elements of the 2nd period. The considered principle of constructing an MO from two identical AOs is preserved in the construction of homonuclear molecules of elements of the 2nd period of the D.I. Mendeleev. They are formed as a result of the interaction of 2s- and 2p x -, 2p y - and 2p z-orbitals.

The participation of the inner electrons of the 1s orbitals can be neglected (they are not taken into account in the subsequent energy schemes). The 2s-orbital of one atom interacts only with the 2s-orbital of another atom (there must be closeness of the energies of the interacting orbitals), forming MO σ 2 s light and σ 2 s res. When the 2p orbitals of both atoms overlap (interact), MOs are formed:

(

Rice. 16. Energy scheme of the formation of the Li 2 molecule

Fig.15). Those. out of the six initial 2p orbitals, six MOs are formed—three bonding and three antibonding. MO formed from s- and p x -atomic orbitals are denoted by the letter , and from r y - and r z - - by the letter . With the help of fig. 15 it is easy to represent the electronic configurations of these molecules in the notation of the MO method.

Example 1 Lithium molecule Li 2 . The scheme of its formation is shown in Fig.16. It has two binding electrons, the molecule is diamagnetic (electrons are paired). The writing of the equation and formula can be simplified by denoting the internal level as K:

2Li = Li2

The number of links is 1.

Example 2 Beryllium Be 2 molecule. The eight electrons of the molecule are placed on the MO as follows:

Be 2

As can be seen, the number of bonds in the molecule is zero: two loosening electrons destroy the action of two binding ones. Such a molecule cannot exist, and it has not yet been discovered. It should be noted that diatomic molecules are impossible for all elements of the IIA group, palladium and inert elements, since their atoms have a closed electronic structure.

Example 3 Nitrogen molecule N 2 (Fig. 17). The distribution of 14 electrons by MO is written as follows:

N 2 [(σ CB 1s) 2 (σ cut 1s) 2 (σ CB 2s) 2 (σ cut 2s) 2 (π CB 2p y) 2 (π CB 2p z) 2 (σ CB 2p x) 2 ]

or abbreviated:

N 2 [CC (σ s CB)2 (σ s resp)2(π y CB)2(π z CB)2(σ x CB)2]

1 -1 +1 +1 +1=3

Rice. 17. Energy scheme for the formation of the N 2 molecule

Under the formula, the number of bonds in a molecule is indicated, based on the calculation that two electrons located on one MO form a valence bond; the plus sign denotes bonding orbitals, the minus sign denotes antibonding orbitals. The number of bonds in the molecule is 3. there are no unpaired electrons - the molecule is diamagnetic.

Example 4 O 2 molecule (Fig. 18). Electrons are placed along the MO in the sequence:

O 2 [CC(σ s CB)2(σ s res)2(π y CB)2(π z CB)2(σ x CB)2(π y res)1(π z res)1]

1 -1 +1 +1 +1 - 1 / 2 - 1 / 2 =2

Rice. 18. Energy scheme for the formation of the O 2 molecule

There are two valence bonds in a molecule. The last two electrons were placed in different π-loosening orbitals in accordance with Hund's rule. Two unpaired electrons determine the paramagnetism of the oxygen molecule.

4.5.3. Diatomic heteronuclear molecules of elements of the 2nd period. The energy scheme for the formation of MOs of heteronuclear diatomic molecules, consisting of atoms of elements of the 2nd period, is shown in Fig. . 19. It is similar to the scheme of formation of MO of homonuclear molecules.

The main difference is that the energy values ​​of the orbitals of the same name of atoms of different elements are not equal to each other, since the charges of the nuclei of atoms are different. As an example, consider the valence electronic configuration of CO and NO molecules.

Rice. 19 . Energy scheme for the formation of two atomic hetero-nuclear molecules of elements of the second period

Example 5 . CO molecule. The outer electron shell of the carbon atom has the configuration 2s 2 2p 2 , and oxygen 2s 2 2p 4 . Therefore, 4+6=10 electrons take part in filling the MO of a CO molecule. Of these, two are placed on the σ 2 s orbital, two on the σ 2 s orbital, four on the π y CB and π z CB orbitals, and the ninth and tenth are on the σ x light. Thus, the electronic valence configuration of a CO molecule can be expressed by the formula:

CO[CC(σ s CB)2 (σ s resp)2(π y CB)2(π z CB)2 (σ x CB)2]

1 -1 +1 +1 +1=3

As envisaged by the VS theory, there are three valence bonds in the CO molecule (compare with N 2). The molecule is diamagnetic - all electrons are paired.

Example 6 NO molecule. MO molecules of nitric oxide (II) should accommodate 11 electrons: five nitrogen - 2s 2 2p 3 and six oxygen - 2s 2 2p 4. Ten of them are placed in the same way as the electrons of the carbon monoxide (II) molecule (example 5), and the eleventh will be placed on one of the loosening orbitals - π y res or π Z res (these orbitals are energetically equivalent to each other). Then

NО[КК(σ s CB)2(σ s res)2(π y CB)2(π z CB)2(σ x CB)2(π y res)1]

1 -1 +1 +1 +1 - 1 / 2 =2 1 / 2

This means that the NO molecule has two and a half valence bonds, the binding energy is large - 677.8 kJ / mol. It is paramagnetic because it contains one unpaired electron.

The examples given serve to illustrate the possibilities of the MO method in explaining the structure and properties of molecules.

Example 7 What valency due to unpaired electrons (spinvalence) can phosphorus exhibit in the normal and excited states?

Solution. The distribution of electrons in the outer energy level of phosphorus 3s 2 3p 3 (taking into account the Hund rule,
) for quantum cells has the form:

3s 3px 3py 3pz

Phosphorus atoms have free d-orbitals, so the transition of one 3s-electron to the 3d-state is possible:

3s 3px 3py 3pz 3dxy

Hence, the valency (spinvalence) of phosphorus in the normal state is three, and in the excited state it is five.

Example 8 . What is valence orbital hybridization? What structure do molecules of type AB n have if the bond in them is formed due to sp-, sp 2 -, sp 3 -hybridization of the orbitals of the atom A?

Solution. The theory of valence bonds (VS) assumes participation in the formation of covalent bonds not only of pure AOs, but also of mixed, so-called hybrid, AOs. During hybridization, the initial shape and energy of the orbitals (electron clouds) mutually change and orbitals (clouds) of a new identical shape and with the same energy are formed. Number of hybrid orbitals (q) equal to the number of originals. See the answer in Table. 13.

Problem 241.
Describe the electronic structure of CO and CN molecules from the standpoint of the BC and MO methods. Which of the molecules is characterized by the greater bond multiplicity?
Solution:
a) Electronic structure of CO and CN molecules from the point of view of the VS method.
Electronic configuration of carbon atom 1s 2 2s 2 2p 2 , oxygen atom 1s 2 2s 2 2p 4 , nitrogen atom 1s 2 2s 2 2p 3 . The electronic structure of their valence orbitals in the unexcited state can be represented by the following graphical diagrams:
a) a carbon atom:

b) nitrogen atom:

When excited, the carbon atom goes into the state 1s 2 2s 1 2p 3, and the electronic structure of its valence orbitals corresponds to the scheme:

Two unpaired electrons of an unexcited carbon atom can participate in the formation of two covalent bonds by the usual mechanism with an oxygen atom that has two unpaired electrons to form a CO molecule. When a CN molecule is formed, two covalent bonds according to the usual mechanism due to two unpaired electrons of the carbon atom and two unpaired electrons of the nitrogen atom. Electronic circuits CO and CN:

b) Electronic structure of CO and CN molecules from the point of view of the MO method.

Energy schemes for the formation of molecules a) CO and b) CN:

It follows from the above schemes that the bond multiplicity in the CO molecule is 3 [(6 - 0)/2 = 3], and in the NO molecule it is 2.5[(5 - 0)/2 = 2.5]. Consequently, the CO molecule in relation to the NO molecule is characterized by greater stability, the greater the bond multiplicity, the shorter the bond. The CN molecule has one unpaired electron in the bonding orbital, hence it is paramagnetic. The CO molecule does not have unpaired electrons in bonding and loosening orbitals, which means that it diamagnetic.

Task 242.
Consider, from the standpoint of the MO method, the possibility of forming molecules B 2 , F 2 , BF. Which of these molecules is the most stable?
Solution:
Energy schemes for the formation of molecules a) B 2, b) F 2, c) BF:

From the compiled energy schemes B 2 , F 2 , BF it follows that the difference between the number of bonding and loosening electrons, respectively, is 2, 2 and 6, which corresponds to the bond multiplicity 1, 1 and 3, respectively. Therefore, the BF molecule is characterized by a larger bond multiplicity between atoms , it should be stronger than that of B 2 and F 2.