The method of valence bonds sun. Open Library - open library of educational information

Evolution of the valence bond method

First approximate solution Schrödinger equations for one of the simplest molecules, the hydrogen molecule, was produced in 1927. V. Geytler and F. London. These authors first considered a system of two hydrogen atoms located at a great distance from each other. Under this condition, only the interaction of each electron with its “own” nucleus can be taken into account, and all other interactions (mutual repulsion of nuclei, attraction of each electron to a “foreign” nucleus, interaction between electrons) can be neglected. Then it becomes possible to express the dependence of the wave function of the system under consideration on the coordinates and thereby determine the density of the general electron cloud (electron density) at any point in space.

Further Geytler and London assumed that the dependence of the wave function on the coordinates found by them is also preserved when the hydrogen atoms approach each other. In this case, however, it is also necessary to take into account those interactions (between nuclei, between electrons, etc.) that could be neglected at a considerable distance of atoms from each other. These additional interactions are considered as some corrections ("perturbations") to the initial state of electrons in free hydrogen atoms.

As a result, equations were obtained that make it possible to find the dependence of the potential energy E system consisting of two hydrogen atoms, on the distance r between the nuclei of these atoms. It turned out that the results of the calculation depend on whether the spins of the interacting electrons are the same or opposite in sign. With the same direction of spins, the approach of atoms leads to a continuous increase in the energy of the system. In the latter case, the approach of the atoms requires an expenditure of energy, so that such a process turns out to be energetically unfavorable and no chemical bond between the atoms arises. With oppositely directed spins, the approach of atoms up to a certain distance r is accompanied by a decrease in the energy of the system. At r = r0 the system has the lowest potential energy, i.e. is in the most stable state; further approach of the atoms again leads to an increase in energy. But this also means that in the case of oppositely directed electron spins, a molecule is formed H 2- a stable system of two hydrogen atoms located at a certain distance from each other.

The formation of a chemical bond between hydrogen atoms is the result of the interpenetration ("overlapping") of electron clouds, which occurs when interacting atoms approach each other. As a result of such interpenetration, the density of the negative electric charge in the internuclear space increases. Positively charged atomic nuclei are attracted to the region of overlapping electron clouds. This attraction prevails over the mutual repulsion of like-charged electrons, so that a stable molecule is formed as a result.

Thus, the study made it possible to conclude that the chemical bond in the hydrogen molecule is carried out by the formation of a pair of electrons with oppositely directed spins belonging to both atoms. The theory of chemical bond developed on this basis and for more complex molecules was called valence bond method. The important point is that whenever a chemical bond is formed, the spins of a pair of electrons must be antiparallel. This is in line with Pauli principle and emphasizes that when a chemical bond is formed, electrons pass into a new quantum state.

The presence of paired electrons is an "indicator" of the presence of a chemical bond, but not the cause of its formation. The study of the cause of the formation of a chemical bond has so far shown that the energy of a system of two atoms decreases when the electrons are more likely to be in the internuclear space (as if "delayed" in this region). Such a delay leads to a decrease in their kinetic energy, as a result, the negative component of the total energy of the molecule prevails, the molecule becomes stable or, as they say, a chemical bond is formed.

The method of valence bonds gave a theoretical explanation of the most important properties of a covalent bond, made it possible to understand the structure of a large number of molecules. Although this method did not turn out to be universal and in some cases is not able to correctly describe the structure and properties of molecules, it nevertheless played an important role in the development of the quantum mechanical theory of chemical bonding and has not lost its significance to date in a qualitative understanding of the nature of chemical bonding.

Basic provisions of the method of valence bonds

The method of valence bonds describes the mechanism of occurrence of a covalent bond and is based on the following basic principles:

1. A chemical bond between two atoms occurs through one or more shared electron pairs.

Both electrons of a common electron pair are held simultaneously by two nuclei, which is energetically more favorable than the presence of each electron in the field of “its own” nucleus.

Such a chemical bond is two-center.

for instance, depict the formation of a molecule F2 with the help of quantum cells of the external energy level (the electronic formula of the atom F: 1s 2 2s 2 2p 5):

Paired electrons of the outer level of an atom must be separated (steered) to form chemical bonds with other atoms. The atom will go into a new valence state. The energy expended on such a process of excitation of an atom is compensated by the energy released during the formation of a chemical bond (it should be remembered that the possibilities of excitation of atoms are limited by the number of free orbitals in the corresponding energy sublevels).

1. The covalent bond has the property of saturation, as a result of which the molecules have a well-defined composition.

for instance, during the formation of a methane molecule CH 4 each of the four unpaired electrons of the excited carbon atom connected with the electron of the hydrogen atom, 4 covalent bonds were formed; more electron pairs in this case cannot be formed, molecules CH 5, CH 6 etc. does not exist.

(Note: the interaction of valence-saturated compounds with each other is possible with the formation of one or more additional donor-acceptor bonds according to a special mechanism).

1. The covalent bond is directed in space, which determines the spatial structure of molecules (directivity property).

Depending on which electrons are bonding - s-, p-, d- or f- electrons, bond energies, bond lengths, as well as their direction in space are significantly different.

Electron clouds have a different shape, so their mutual overlap is carried out in several ways: σ- (sigma), π- (pi) and δ (delta)-bonds.

If the overlap of electron clouds occurs along the line connecting the nuclei - this is σ- connection; if clouds overlap outside this line, there are π- and δ -connections.

If one common electron pair has arisen between atoms (usually σ- connection), such a connection is called single, if two or more, then multiple: double, triple.

for instance, the formation of a nitrogen molecule N 2 carried out by three common electron pairs. For each nitrogen atom, 3 unpaired bonds are involved in the formation of bonds R-electron directed in three-dimensional space at an angle of 90 0 to each other and oriented respectively along the axes x, y, z(these are the properties R- sublevel and R-orbitals dictated by the magnetic quantum number).

Two nitrogen atoms joining into a molecule N 2, can form one σ- communication (clouds oriented along the axis overlap) X) and two π- connections (clouds oriented along the axes of at and z).

Hybridization of atomic orbitals

The structure of molecules depends primarily on the type and properties of those orbitals that atoms provide for the formation of chemical bonds. But, in addition to this factor, the phenomenon of hybridization of orbitals affects the spatial structure of molecules.

hybridization called the formation of new orbitals of equal shape and energy from orbitals of different types. Mixed, hybrid orbitals in the diagrams are conventionally depicted:

sp hybridization

From one s-orbitals and one R-orbitals form two hybrid, mixed orbitals sp-type, directed with respect to each other by 180°.

For instance: molecules have a linear shape Ven 2 and SnCl 2 With sp-hybridization of the atom of beryllium and tin, respectively.

sp 2 hybridization

From one s-orbitals and two R three orbitals are formed sp 2 hybrid orbitals located in the same plane at an angle of 120° to each other.

Mutual orientation of three sp 2-hybrid orbitals - trigonal. concept sp 2-hybridizations are used to describe planar trigonal molecules.

For instance: aluminum fluoride molecule A1F3. The excitation of the aluminum atom is accompanied by steaming s2- electrons of the outer level on p-sublevel. Therefore, the electronic configuration of the outer level of an aluminum atom in an excited state is 3s 1 3p 2. The orbitals of the aluminum atom populated with electrons hybridize and orient themselves in the same plane at an angle of 120° to each other. Each of the three hybrid electron clouds sp 2-orbitals overlap with electron clouds p-orbitals of three fluorine atoms.

sp 3 hybridization

sp 3-hybridization occurs when combined s-orbital and three R-orbitals; four sp 3-hybrid orbitals, oriented no longer in one plane, but in the volume of the tetrahedron and directed from the center of the tetrahedron to its 4 vertices; the bond angle between two chemical bonds is 109°28".

For instance: structure of the methane molecule CH 4. An excited carbon atom has four unpaired electrons: one s- and three R- electron. It would seem that the four chemical bonds formed by them with s- electrons of four hydrogen atoms must be unequal. However, it has been experimentally established that all 4 bonds in the molecule CH 4 completely identical in length and energy, and the angles between the bonds are 109 ° 28 ". Therefore, in the molecule CH 4 takes place sp 3-hybridization.

More complex cases of hybridization involving d-electrons, (for example, sp 3 d 2- hybridization).

The phenomenon of hybridization, i.e. mixing, equalization of electron density, energetically beneficial for the atom, since the hybrid orbitals have a deeper overlap and stronger chemical bonds are formed. A small amount of energy spent on excitation of the atom and hybridization of orbitals is more than offset by the energy released when chemical bonds occur. Bond angles are dictated by considerations of maximum symmetry and stability.

On hybrid orbitals, as well as on ordinary orbitals, not only one electron can be located, but also two. For example, four sp 3-hybrid orbitals of the oxygen atom O are such that two of them contain a pair of electrons, and two - one unpaired electron. From the modern standpoint, the structure of the water molecule is considered taking into account the hybridization of the atomic orbitals O and tetrahedral structure of the molecule H 2 O generally.

Valence by the exchange mechanism of the method

The ability of an atom to attach or replace a certain number of other atoms to form chemical bonds is called valence. According to the exchange mechanism of the valence bond method, each atom donates one unpaired electron to form a common electron pair (covalent bond). The quantitative measure of valency in the exchange mechanism of the method of valence bonds is the number of unpaired electrons in an atom in the ground or excited state of the atom. These are the unpaired electrons in the outer shells of s- and p- elements, outer and pre-outer shells d- elements, outer, pre-outer and pre-outer shells of f-elements.

When a chemical bond is formed, an atom can go into an excited state as a result of the separation of a pair (or pairs) of electrons and the transition of one electron (or several electrons equal to the number of disconnected pairs) into a free orbital of the same shell.

For instance: The electronic configuration of calcium in the ground state is written as:

1s 2 2s 2 2p 6 3s 2 3p 6 4s 2

In accordance with the exchange mechanism of the method of valence bonds, its valency is zero B=0. At the calcium atom in the fourth shell ( n=4) there are vacant R- orbitals. When an atom is excited, electrons are depaired and one of 4s- electrons goes into free 4p-orbital. The valency of calcium in the excited state is equal to two, i.e. when steaming, the valency increases by two units:

Unlike oxygen and fluorine, whose electron pairs cannot be separated, since there are no vacant orbitals in the second shell, the electron pairs of sulfur and chlorine atoms can be paired into vacant orbitals 3d-subshells, respectively, sulfur, in addition to the valency of the ground state 1 and 2, also has valencies 4 and 6 in the excited state, and chlorine, in addition to valence 1 in the ground state, has valences 3, 5 and 7 in the excited state.

Electronic configurations of atoms of some elements in the ground and excited states

Element	Basic state					excited state
	Electronic configuration	Orbital filling			Valence	Electronic configuration	Orbital filling			Valence
		s	p	d			s	p	d
Hydrogen	1s 1				1
Helium	1s2				0
Beryllium	2s 2				0	2s 1 2p 1				2
Carbon	2s 2 2p 2				1,2	2s 1 2p 3				1,2,4
Oxygen	2s 2 2p 4				1,2
Fluorine	2s 2 2p 5				1
Sulfur	3s 2 3p 4				1,2	3s 1 3p 3 3d 2				1,2,4,6
Chlorine	3s 2 3p 5				1	3s 1 3p 3 3d 3				1,3,5,7

Most atoms d- and f-elements on the outer shells in the ground state there are no unpaired electrons, therefore their valency in the ground state is zero, despite the fact that on the pre-outer d- and f subshells contain unpaired electrons. The latter cannot form electron pairs with the electrons of other atoms, since they are closed by the electrons of the outer shell. When an atom is excited, the paired electrons of the outer shell enter into a chemical bond and open the inner electron shells.

For instance: the valency of iron in the ground state is zero:

In the excited state, disconnection occurs 4s-pairs of electrons:

The valency of iron in an excited state is determined not only 4s-, 4p-, but also 3d- unpaired electrons. However, a couple 3d-electrons cannot be separated because there are no vacant orbitals in the third shell, so the maximum valency of iron is six.

In osmium, when excited, not only external 6s-electrons, but also preexternal 5d-electrons, because in the fifth shell there is also 5f-subshell with free orbitals, so the maximum valency of osmium is eight:

The first quantum mechanical theory of two-electron bonding was the theory of the hydrogen molecule, proposed by W. G. Geitler and F. London in 1927. This theory in the 1930s. was developed by L. K. Pauling and other researchers into a comprehensive theory of chemical bonding, called by the method of valence bonds (MVS).

The MVS proceeds from the following provisions:

• 1) a chemical covalent bond is formed due to the pairing of two free electrons that have opposite spins and belong to different atoms;
• 2) when a chemical bond is formed, the atomic orbitals of the interacting atoms overlap, the electron density increases in the internuclear space, the atoms are attracted to each other, which leads to a decrease in the potential energy of the system, when a molecule is formed, the electronic structure of its constituent atoms is basically preserved, with the exception of outer shells;
• 3) the covalent bond is directed towards the greatest overlap of atomic orbitals.

All chemical bonds in a molecule can be represented as fixed (localized) two-center two-electron bonds. Each such bond in the schemes is depicted by a short line, and the electronic structure of the molecule looks like a set of different valence schemes (VS), in connection with which this method is also called method of localized electron pairs.

So, hydrogen is a system of two electrons and two protons. If two hydrogen atoms are separated from each other by some distance, then in the MVS, when constructing the wave function of electrons, the molecules proceed from the wave functions of the electrons of the constituent atoms. Denoting the wave functions of the electrons of isolated atoms H A and H b through |/ L(1) and |/ B(2) accordingly, we obtain an expression for the wave function of the molecular system:

Since the electrons in N.; are indistinguishable, then there is no reason to believe that in this molecule electron 1 belongs to the nucleus of the Hl atom, and electron 2 belongs to the nucleus of the Hg atom. Consequently, the inverse distribution is also probable, so equation (4.1) is equivalent to the equation

According to Heitler and London, the wave function of the hydrogen molecule is a linear combination of the function G ( and |/. ; :

In addition to the covalent structure (I), for the H 2 molecule, the existence of two ionic structures (II) and (III) can also be assumed, which, respectively, can be characterized by the wave functions / 3 and / 4:

The existence of structures (II) and (III) is possible under the condition that electrons are shifted towards the atom A(I) and the atom V(III).

The wave function for ionic structures can be written as

Ultimately, the total wave function of the H 2 molecule, taking into account all the structures, can be represented as

Equation (4.5) takes into account all the valence schemes for the hydrogen molecule simultaneously, so the function |/ 1b is a superposition of structures (I), (II), and (III). Therefore, the concept of resonance becomes important: if a molecule can be represented by two or more structures, differing only in the distribution of electrons, those. structures, in which the atomic nuclei are arranged in the same way, then resonance becomes possible.

The molecule is a hybrid of these structures and cannot be satisfactorily represented by any of them. Each of the resonant structures contributes to the hybrid, which is more stable than any of the structures participating in the resonance. It should be taken into account that the concept of resonance arises as a consequence of the construction of the wave function in the MHS.

When a bond is formed, the electrons must be between the nuclei of atoms, i.e. in the binding area. When the electrons are outside the binding region, then it is called anti-bonding, or loosening, and the bond is not formed. Since in the binding state, electrons are drawn into the region between the nuclei, and in the loosening state they are pushed out, the wave function H 2 is denoted by / +, and the function |/ describes the loosening state. Therefore, equation (4.3) can be written as two independent expressions:

From equation (4.6) it is clear that the permutation of the electronic coordinates (1) and (2) does not affect the sign of the function |/ + . Such a function is called symmetrical. In equation (4.7), the permutation of the coordinates of the electrons leads to a change in the function u/_. Therefore, the function |/_ is called antisymmetric (Fig. 4.11).

Rice. 4.11.

For |/ +, the electrons in the atom are characterized by different spin quantum numbers, i.e. have antiparallel backs. Symmetric and antisymmetric wave functions correspond to different distributions of the electron cloud in H 2 between the nuclei of atoms. So, in a symmetric wave function, there are antiparallel electron spins, so their wave functions are summed (see formula (4.6)), which, in turn, leads to an increase in the electron density between the nuclei. Consequently, when / + takes place, then there is an overlap of the wave functions of electrons, or, as they say otherwise, an overlap of electron clouds.

For an antisymmetric wave function, electrons are characterized by parallel spins; therefore, a decrease in the electron density between the nuclei of atoms is observed, which indicates the absence of the possibility of the formation of a chemical bond. In this case, the electron density between the nuclei drops to zero.

Since the theory of valence bonds is based on the concept of the formation of covalent bonds as a result of the overlap of atomic orbitals, the criterion of positive overlap of atomic orbitals is of exceptional value for establishing the possibility of bond formation (see formulas (4.6), (4.7)).

The orbitals are called overlapping, if the interacting atoms are so close that one of the orbitals has a significant amplitude in the space common to both atoms. Depending on the properties of the orbitals, the amount of overlap can be positive, negative, or zero (Figure 4.12).

A positive overlap occurs when the overlapping regions of both orbitals have the same sign; a negative overlap value occurs if the overlapping regions of both orbitals have opposite signs. If there are absolutely equal areas of negative and positive overlap, then, in general, zero overlap is characteristic. In the area of

Rice. 4.12.

positive overlap, the electron density between the nuclei of atoms increases, so the attraction of the nuclei to the binding electrons prevails over mutual repulsion and a binding interaction occurs.

The positive overlap of two orbitals should be considered as a new one, so-called molecular orbital(MO). With negative overlap, the electron density between the nuclei of interacting atoms decreases, so the internuclear repulsion increases, which leads to excessive repulsion between them. When the overlap is zero, then there is neither a decrease nor an increase in electron density between the atoms, as a result of which there is neither repulsion nor additional attraction. Such a state is called non-binding interaction.

The fundamentals of the VS method were developed in 1927 by Walter Geitler ( Heitler) and Fritz London ( London). The model particle for this method is the hydrogen molecule H 2 . When constructing the wave function of a molecule in the method of valence bonds, it is considered that: 1) the atoms in the molecule retain their individuality - each electron belongs to the nucleus of its atom, 2) the wave functions of the electrons of the atom A (Y A) and the atom B (Y B) are known - atomic orbitals, 3) it is believed that particles (electrons and nuclei of atoms) are indistinguishable.

Schrödinger equation for the hydrogen molecule. Let us compose the Schrödinger equation for the hydrogen molecule. The potential energy included in it includes the sum of the energies of the electrostatic interaction of all particles with each other (two electrons -e and two cores + e). From fig. 3.3 it can be seen that the total potential energy consists of two positive terms: the energy of repulsion of electrons and nuclei between themselves and four negative ones - the energies of attraction of electrons to nuclei:

Where r AB ; r 12 - distances between the nuclei of atoms A and B and between the first and second electrons; r A1; r A2 are the distances between the nucleus of the atom A and the first and second electrons, respectively; r B1; r B2 are the distances between the nucleus of the B atom and the first and second electrons, respectively.

Rice. 3-3 Scheme of the electrostatic interaction of electrons and nuclei in a hydrogen molecule

Thus, the Schrödinger equation for the hydrogen molecule has the form

The analytical solution of this equation is practically impossible, therefore, finding the chemical bond energy D E(r) and the wave function of electrons, showing the distribution of electron density in the molecule, is produced by an approximate method.

First approximation function. Since the probability of finding an electron in an elementary volume is proportional to the Y-function, and according to the conditions of the VS method, atoms retain their atomic orbitals during the formation of a bond, then, in the first approximation, the function describing the state of electrons in a hydrogen molecule can be represented as a product of the wave functions of electrons in separate isolated hydrogen atoms:

,

where Y 1 is a function describing the states of electrons in a hydrogen molecule; Y А (1) is a function describing the states of electron 1 belonging to the А atom (Y 1s is the function of the ground state of the hydrogen atom); Y В (2) is a function describing the states of electron 2 belonging to atom В (Y 1s).

Since the electrons and nuclei of atoms are fundamentally indistinguishable, it does not matter which of them will be located at a particular nucleus. Therefore, it is necessary to create a second function:

.

The first function considers 1 electron as belonging to atom A, and 2 to atom B, the second function, on the contrary, considers that 2 electron belongs to atom A, and 1 to atom B. Both functions are solutions of the Schrödinger equation. For simplicity of presentation, the normalization factors are taken equal to unity.

The calculation using these functions qualitatively correctly described the hydrogen molecule, but the values ​​of the energy and bond length differed greatly from the values ​​determined experimentally.

A more accurate approximation to the true wave function was a linear combination of the first and second functions:

The physical meaning of these two functions is as follows: Y S– symmetric function – corresponds to the case when the electrons in the hydrogen molecule have different sign values ​​of the spin quantum number, – the spins of the electrons are antiparallel. Y A– antisymmetric function – describes the state when both electrons have the same value of the spin number - the spins of the electrons are parallel.

The change in the energy of a system of two interacting hydrogen atoms is described by the expression

– for a symmetrical function,

– for the antisymmetric function,

Q– "Coulomb integral", which characterizes the change in the energy of the system due to the electrostatic interaction of electrons and nuclei with each other. I- "exchange integral", an integral characterizing the decrease in the energy of the system due to the indistinguishability of electrons; S– “overlap integral”, which characterizes the change in the energy of the system due to the overlap of atomic orbitals.

To clarify the physical meaning of these integrals, we analyze their expressions.

"Overlap Integral"

characterizes the region of space of overlapping atomic orbitals.

"Coulomb integral"

shows the change in the energy of the system as a result of the repulsion of nuclei from each other (the first term of the sum), electrons (the second term) and the attraction of electrons to the nuclei of a "non-own atom" (the third and fourth terms). The last two integrals are equal because the atoms are the same. The physical meaning of the integrals is obvious: y i 2 dVj is the probability of finding j-electron in an elementary volume of space, e xy i 2 dVj is the amount of charge. According to Coulomb's law, the energy of electrostatic interaction is directly proportional to the product of the magnitude of the charges and inversely proportional to the distance between them.

The energy of attraction of electrons to the nuclei of “own atom” is the energy of non-interacting atoms ( E 0) - is not taken into account in the chemical bond energy (the total energy of the hydrogen molecule E= 2× E 0+D E(r)).

"Exchange Integral"

S- "overlap integral".

The “exchange integral” is similar to the “Coulomb integral”, but instead of the square of the wave function for a given electron, there is a product of the wave functions of different atoms, which gives it a rather abstract character - “non-classical electrostatic interaction”. The energy of the system changes due to the indistinguishability of electrons, that is, the possibility of replacing one electron with another leads to a change in the energy of the system.

At distances r®¥ Coulomb, exchange and overlap integrals tend to zero: Q®0, I®0 and S®0. At distances close to the bond length, the Coulomb and exchange integrals are negative Q<0; I<0, причем ½Q½<½I½; at r®0 they become positive. The overlap integral is always positive and less than one: £0 S<1.

In the case of a symmetric function (electron spins are antiparallel), the dependences D E(r) there is a minimum (potential well), and the electron density between atoms increases - a chemical bond is formed, the molecule is stable (Fig. 3.4).

		Y A

Rice. 3-4 The dependence of the change in the energy of the molecule and the distribution of electron density in the hydrogen molecule in the case of a description of a symmetric system (Y S) and an antisymmetric function (Y A)

In the case of an antisymmetric function (electron spins are parallel), the minimum in the dependence D E(r) is absent, the electron density between the nuclei is equal to zero - the bond is not formed.

Example. The energy and bond length in the hydrogen molecule, determined experimentally and calculated taking into account various factors that complicate the explicit form of the wave functions:

Based on the ideas developed in the calculation of the hydrogen molecule, the basic principles(postulates) valence bond method, which allow describing the formation of a covalent chemical bond in more complex molecules:

1. A single chemical bond is formed by a common pair of electrons with opposite (antiparallel) spins.

2. The common electron pair is localized (concentrated) between atoms in the direction of maximum overlap of atomic orbitals.

3. The binding energy is determined only by the forces of electrostatic interaction of electrons and nuclei and depends on the amount of overlapping orbitals.

Thus, the number of bonds (valency) that an atom can form is determined by the number of unpaired electrons in the outer energy level of the atom in the ground or excited state. A covalent bond has the property saturation(an atom can form a limited number of single covalent bonds). A covalent chemical bond has the property focus(the location in space of a common electron pair is determined by the spatial orientation of the overlapping valence orbitals). Atoms are mutually arranged in such a way that the overlap of valence orbitals is maximum. Of the two bonds, the stronger one is where the overlap of valence orbitals is greater.

VALENCE BONDS METHOD

(the method of valence schemes), the method of approximate solution of the electronic Schrödinger equation for many-electron molecular systems. Based on the concept of two-center chem. bonds between atoms in a molecule formed by two electrons. These representations are a generalization to polyatomic molecules of the Heitler-London approximation, which made it possible for the first time with the help of quantum mechanics. methods to explain the chem. bond in the H 2 molecule.

Main physical V.'s idea with. m. is that the wave function of the molecule is expressed through the wave function of its constituent atoms. The formation of a chem. bonds are considered as the result of pairing of free spins. electrons of atoms. Thus, V. s. m. gives justification for one of the main. provisions of the theory of valence: a neutral atom is equal to the number of free. electrons in its valence shell. Each valence stroke connecting atoms A and B in the structural f-le of the molecule corresponds to the two-electron function of the valence bond X AB (1.2), which is represented as a product of two wave functions: spatial F (1.2 ), which is symmetric with respect to a permutation of the electron coordinates, and spin (1.2), which is antisymmetric with respect to such a permutation and describes a system of two electrons with opposite spins; the numbers 1 and 2 in these designations indicate spaces. coordinates or spin variables of the first and second electrons, or both. Hence,

For the simplest molecule H 2, the f-tion F (1,2) is built from the 1s-orbitals of the H atoms, denoted for different nuclei as and , and the f-tion (1,2) - from single-electron spin functions and (spin functions ), which describe the states of electrons with oppositely directed spins:

The energy of the molecule, calculated with such a two-electron wave function X(1,2), is equal to:

where E H is the energy of the atom H, -orbital overlap integral ( dv- volume element in the coordinate space of one electron), I and Kt. called Coulomb and exchange integrals, respectively. The Coulomb integral takes into account the contribution to the binding energy due to electrostatic. interaction undistorted electron clouds of atoms between themselves and with the nucleus of a neighboring atom, exchange - the contribution due to the deformation of the electron cloud during the formation of a bond and its movement into the space between the nuclei (> 90% of the bond energy); see also Molecular integrals.

For more complex molecules, the multielectron wave function is represented as an antisymmetrized product in accordance with the Pauli principle of all two-electron functions of the type X AB (1.2) and functions describing the state of the electrons ext. shells, unshared electron pairs and unpaired electrons not involved in two-center bonds. Corresponding to this function, the distribution of "valence" strokes connecting atoms in a molecule, called. valent scheme. Such an approach is called ideal pairing approximation or approximation of localized electron pairs. Electrons are assigned to individual atoms and in accordance with the main. by the idea of ​​the Heitler-London approximation, their states are described by atomic orbitals. According to the variational principle (cf. variational method), approximate wave function is chosen so that it gives a minimum. electronic energy of the system or, respectively, max. the value of the bond energy. This condition, generally speaking, is achieved at max. overlapping orbitals belonging to the same bond. Thus, V. s. m. gives justification for the criterion of max. overlapping orbitals in the theory of directed valences. Better overlap of orbitals corresponding to a given valence bond is facilitated by hybridization of atomic orbitals, i.e. participation in the bond is not "pure" s-, p-or d-orbitals, but their linear combinations, localized along the directions of chemical. bonds formed by a given atom.

Intraatomic contributions to the energy of the molecule, analogous to E H, usually exceed the energy free. atoms by a value called the promotion energy. This excess is due to the electronic rearrangement of the atom during its transition to the valence state, i.e., to the state required for the formation of chemical. bonds, namely: the transition of electrons to energetically less favorable atomic orbitals (eg, from 2s to 2p) during the depairing of electrons, the transition from the most. profitable orbitals in free. atom to less favorable hybrid orbitals. The formation of a chem. bonding is explained by the fact that the gain in binding energy compensates for the energy spent on the promotion of atoms.

Further refinement of the description of molecular systems in the framework of V. s. m. is associated with the use of linear combinations of wave functions of several. valent schemes. This approach is usually called by the method of valence schemes. Coefficients in a linear combination of functions corresponding to the ideal pairing approximation dec. The valence schemes possible for a given molecule are determined by the variational method. Valence schemes include all schemes of covalent (so-called Kekul) structures with the maximum possible number of valence bonds between neighboring atoms, the so-called. Dewar structures with "long" bonds, in which electrons belonging to non-adjacent atoms are formally paired, as well as structures of the ionic type, in which formally transferred from one atom to another. On this basis, V. s. m. is often considered as a mat. substantiation of the theory of resonance. One of the simple ways of constructing all valence schemes is given by Rumer's rules: each singly occupied orbital is assigned a point on a certain circle, each pairing of electrons is associated with an arrow connecting two such points. The resulting diagram is called. Rumer's diagram. When constructing the complete wave function of the molecule, all Rumer diagrams with non-intersecting arrows are taken into account. Rumer's diagrams give a convenient graphic. a method for calculating the matrix elements of the Hamiltonian on functions of valence schemes through Coulomb, exchange, and other integrals. In the semi-empirical V.'s options with. m. Coulomb and exchange integrals are considered as parameters determined from spectroscopic. and thermochem. data, in non-empirical all options are accurately calculated (see. Semi-empirical methods, Non-empirical methods).

Consistent an increase in the number of basic atomic orbitals and the inclusion in the calculation of an increasing number of valence schemes and electronic configurations make it possible to obtain an almost exact non-empirical. solution of the Schrödinger equation.

V.'s advantages with. m. - visibility of qualities. descriptions of molecules with localized bonds, directly. analogy between valence schemes and structural f-lam, the possibility of explaining many empiric. additive regularities in chemistry. However, this method is often preferred to simpler ones in their structure. molecular orbital methods.

Lit.: Peacock T., Electronic properties of aromatic and heterocyclic molecules, trans. from English, M., 1969; McWeeny R., Sutcliffe B., Quantum mechanics of molecules, trans. from English, M., 1971 A. A. Bagaturyants.

Chemical encyclopedia. - M.: Soviet Encyclopedia. Ed. I. L. Knunyants. 1988 .

3.4. Molecular orbital method

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 -bonds (overlapping along the chemical bond axis) and -bonds (overlapping 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 us depict the energy levels of the atomic orbitals of the initial hydrogen atoms on two parallel diagrams (Fig. 3.5).

It can be seen that there is a gain in energy compared to unbound atoms. Both electrons lowered their energy, which corresponds to the unit of valency in the method of valence bonds (a bond is formed by a pair of electrons).
The MO LCAO method makes it possible to visually explain the formation of ions and , which causes difficulties in the method of valence bonds. One electron of the H atom passes to the -bonding molecular orbital of the cation with a gain in energy (Fig. 3.7).

In an anion, three electrons must already be placed in two molecular orbitals (Fig. 3.8).

If two electrons, having descended to the bonding orbital, give a gain in energy, then the third electron has to increase its energy. However, the energy gained by two electrons is greater than that lost by one. Such a particle may exist.
It is known that alkali metals in the gaseous state exist in the form of diatomic molecules. Let us try to verify the possibility of the existence of a diatomic Li 2 molecule using the MO LCAO method. The original lithium atom contains electrons at two energy levels - the first and second (1 s and 2 s) (Fig. 3.9).

Overlapping identical 1 s-orbitals of lithium atoms will give two molecular orbitals (bonding and loosening), which, according to the principle of minimum energy, will be completely populated by four electrons. The gain in energy resulting from the transition of two electrons to the bonding molecular orbital is not able to compensate for its losses during the transition of two other electrons to the antibonding molecular orbital. That is why only the electrons of the outer (valence) electron layer contribute to the formation of a chemical bond between lithium atoms.
Overlapping valence 2 s-orbitals of lithium atoms will also lead to the formation of one
-bonding and one loosening molecular orbitals. The two outer electrons will occupy the bonding orbital, providing an overall gain in energy (the bond multiplicity is 1).
Using the MO LCAO method, let us consider the possibility of the formation of the He 2 molecule (Fig. 3.10).

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.
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 -bond (Fig. 3.11).

Two others p-AO overlap on both sides of the axis x with the formation of two -bonds (Fig. 3.12).

The energies of the constructed molecular orbitals can be determined from the data of 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 -bonding degenerate (with the same energy) orbitals have less energy than the -bonding one, however, like the *-loosening orbitals, they have less energy in comparison with the *-loosening orbital (Fig. 3.13).

In the O 2 molecule, two electrons with parallel spins ended up in two degenerate (with the same energy) *-loosening 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.
Among the diatomic molecules, one of the strongest is the CO molecule. The MO LCAO method easily makes it possible to explain this fact (Fig. 3.14, see p. eighteen).

The result of the overlap p-orbitals of the O and C atoms is the formation of two degenerate
-bonding and one -bonding orbital. These molecular orbitals will occupy six electrons. Therefore, the multiplicity of the bond is three.
The MO LCAO method can be used not only for diatomic molecules, but also for polyatomic ones. Let us analyze, as an example, within the framework of this method, the structure of the ammonia molecule (Fig. 3.15).

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).

3.5. Geometric shapes of molecules

When talking about the shapes of molecules, first of all, they mean the relative position in space of the nuclei of atoms. It makes sense to talk about the shape of a molecule when the molecule consists of three or more atoms (two nuclei are always on the same straight line). The shape of molecules is determined on the basis of the theory of repulsion of valence (external) electron pairs. According to this theory, the molecule will always take the form in which the repulsion of external electron pairs is minimal (the principle of minimum energy). In doing so, the following assertions of the theory of repulsion must be borne in mind.

1. Lone electron pairs undergo the greatest repulsion.
2. The repulsion between the unshared pair and the pair involved in bond formation is somewhat less.
3. Least repulsion between the electron pairs involved in bond formation. But even this is not enough to separate the nuclei of atoms involved in the formation of chemical bonds to the maximum angle.

As an example, consider the forms of hydrogen compounds of elements of the second period: BeH 2, BH 3, CH 4, C 2 H 4, C 2 H 2, NH 3, H 2 O.
Let's start by determining the shape of the BeH 2 molecule. Let's depict its electronic formula:

from which it is clear that there are no unshared electron pairs in the molecule. Therefore, for electron pairs that bind atoms, it is possible to repel to the maximum distance at which all three atoms are on the same straight line, i.e. the HBeH angle is 180°.
The BH 3 molecule consists of four atoms. According to its electronic formula, there are no lone pairs of electrons in it:

The molecule will acquire such a shape in which the distance between all bonds is maximum, and the angle between them is 120°. All four atoms will be in the same plane - the molecule is flat:

The electronic formula of the methane molecule is as follows:

All atoms of a given molecule cannot be in the same plane. In this case, the angle between the bonds would be 90°. There is a more optimal (from an energy point of view) arrangement of atoms - tetrahedral. The angle between the bonds in this case is 109°28".
The electronic formula of ethene is:

Naturally, all angles between chemical bonds take on a maximum value of 120°.
Obviously, in an acetylene molecule, all atoms must be on the same straight line:

H:C:::C:H.

The difference between the ammonia molecule NH 3 and all the previous ones is the presence in it of a lone pair of electrons at the nitrogen atom:

As already mentioned, the electron pairs involved in bond formation are more strongly repelled from the lone electron pair. The lone pair is located symmetrically with respect to the hydrogen atoms in the ammonia molecule:

The HNH angle is smaller than the HCH angle in the methane molecule (due to the stronger electron repulsion).
There are already two lone pairs in a water molecule:

This is due to the angular shape of the molecule:

As a consequence of the stronger repulsion of lone electron pairs, the HOH angle is even smaller than the HNH angle in the ammonia molecule.
The given examples quite clearly demonstrate the possibilities of the theory of repulsion of valence electron pairs. It makes it relatively easy to predict the shapes of many inorganic and organic molecules.

3.6. Exercises

1 . What types of bonds can be classified as chemical?
2. What are the two main approaches to the consideration of chemical bonds do you know? What is their difference?
3. Define valency and oxidation state.
4. What are the differences between simple covalent, donor-acceptor, dative, metallic, ionic bonds?
5. How are intermolecular bonds classified?
6. What is electronegativity? From what data is electronegativity calculated? What do the electronegativity of atoms forming a chemical bond allow us to judge? How does the electronegativity of atoms of elements change when moving in the periodic table of D.I. Mendeleev from top to bottom and from left to right?
7. What rules should be followed when considering the structure of molecules by the MO LCAO method?
8. Using the method of valence bonds, explain the structure of hydrogen compounds of elements
2nd period.
9. The dissociation energy in the series of Cl 2, Br 2, I 2 molecules decreases (239 kJ/mol, 192 kJ/mol, 149 kJ/mol, respectively), but the dissociation energy of the F 2 molecule (151 kJ/mol) is much less than the dissociation energy Cl 2 molecules, and falls out of the general pattern. Explain the given facts.
10. Why, under normal conditions, CO 2 is a gas, and SiO 2 is a solid, H 2 O is a liquid,
and H 2 S is a gas? Try to explain the state of aggregation of substances.
11. Using the MO LCAO method, explain the occurrence and features of the chemical bond in the molecules B 2 , C 2 , N 2 , F 2 , LiH, CH 4 .
12. Using the theory of repulsion of valence electron pairs, determine the shapes of the molecules of oxygen compounds of elements of the 2nd period.