§ii.2. valence bond method. valence. Valence bond method (BC method) Basic principles of the valence bond method

VALENCE BOND METHOD

(valence circuit method), method of approximate solution of the electronic Schrödinger equation for multielectron molecular systems. Based on the concept of two-center chemistry. bonds between atoms in a molecule formed by two electrons. These ideas are a generalization to polyatomic molecules of the Heitler-London approximation, which was first possible using quantum mechanics. methods to explain chemistry. bond in the H 2 molecule.

Basic physical idea V. s. m. consists in the fact that the wave function of a molecule is expressed through the wave functions of its constituent atoms. Chemistry education connection is considered as a 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 line connecting atoms A and B in the structural f-le of the molecule corresponds to a two-electron function of the valence bond X AB (1,2), which is represented as the product of two wave functions: spatial F (1,2 ), symmetric with respect to the permutation of electron coordinates, and spin (1,2), antisymmetric with respect to such a permutation and describing a system of two electrons with opposite spins; numbers 1 and 2 in these notations indicate spaces. coordinates or spin variables of the first and second electrons, or both at the same time. Hence,

For the simplest H2 molecule, the function Ф(1,2) is built from the 1s-orbitals of H atoms, denoted for different nuclei as and , and the function (1,2) is built from one-electron spin functions and (spin functions ), describing states of electrons with oppositely directed spins:

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

where E H is the energy of the H atom, -orbital overlap integral ( dV- volume element in the coordinate space of one electron), I and K-t. called Coulomb and exchange integrals, respectively. The Coulomb integral takes into account the contribution to the binding energy due to electrostatics. interaction undistorted electron clouds of atoms between each other 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 the product of all two-electron functions of type X AB (1,2) antisymmetrized in accordance with the Pauli principle and functions describing the state of internal electrons. shells, lone electron pairs and unpaired electrons not occupied in two-center bonds. The distribution of “valence” lines that connect atoms in a molecule corresponding to this function is called. valence scheme. This approach is called ideal pairing approximation or localized electron pair approximation. Electrons are assigned to individual atoms and in accordance with the basic principle. With the idea of the Heitler-London approximation, their states are described by atomic orbitals. According to the variational principle (see. Variational method), the approximate wave function is chosen so that it gives a minimum. electronic energy of the system or, accordingly, max. binding energy value. This condition, generally speaking, is achieved at max. overlap of orbitals belonging to the same bond. Thus, V. s. m provides justification for the max. criterion. orbital overlap 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 of “pure” s-, p-or d-orbitals, but of their linear combinations localized along the chemical directions. bonds formed by a given atom.

Intraatomic contributions to the energy of a molecule, similar to E H, usually exceed the free energy. atoms by an amount called 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 a chemical. bonds, namely: the transition of electrons to energetically less favorable atomic orbitals (for example, from 2s to 2p) during pairing of electrons, the transition from the most. favorable orbitals in free. atom to less favorable hybrid orbitals. Chemistry education bonding is explained by the fact that the gain in binding energy compensates for the energy costs for promoting atoms.

Further refinement of the description of molecular systems within the framework of V. s. m. is associated with the use of linear combinations of wave functions of several. valence schemes. This approach is usually called by the method of valence schemes. Coefficients in a linear combination of functions corresponding in the approximation of ideal pairing decomp. 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, so-called. Dewar structures with “long” bonds, in which electrons belonging to non-neighboring atoms are formally paired, as well as structures of the ionic type, in which electrons are formally transferred from one atom to another. On this basis, V. s. m. is often considered as a mat. justification of the theory of resonance. One of the simple ways to construct all valence schemes is given by Rumer's rules: each singly occupied orbital is associated with 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 a molecule, all Rumer diagrams with non-intersecting arrows are taken into account. Rumer's diagrams provide a convenient graphic. method of calculating the matrix elements of the Hamiltonian on the functions of valence circuits through Coulomb, exchange and other integrals. In semi-empirical variants of V. s. m. Coulomb and exchange integrals are considered as parameters determined from spectroscopic parameters. and thermochemical data, in non-empirical options, everything is calculated accurately (see. Semi-empirical methods, Non-empirical methods).

Consistent An increase in the number of basic atomic orbitals and the inclusion of an increasing number of valence schemes and electronic configurations in the calculation make it possible to obtain almost accurate ab initio. solution to the Schrödinger equation.

Advantages of V. s. m. - visibility of qualities. descriptions of molecules with localized bonds, directly. analogy between valence schemes and structural phases, the possibility of explaining many empirical additive laws in chemistry. However, this method is often preferred to those that are simpler in structure. molecular orbital methods.

Lit.: Peacock T., Electronic properties of aromatic and heterocyclic molecules, trans. from English, M., 1969; McWeeney 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 .

The valence bond (VB) method is based on the following principles:

The electronic structure of chemical compounds is considered as a set of individual two-center, two-electron chemical bonds localized between neighboring atoms;

Each individual chemical bond between two neighboring atoms is formed as a result of the sharing of an electron pair with oppositely directed spins. Such a common electron pair can be formed both as a result of the interaction of two atoms, each of which is characterized by the presence of an unpaired electron in overlapping valence orbitals (exchange mechanism), and due to a pair of electrons of one atom - donor - and a free orbital of another atom - acceptor (donor -acceptor mechanism);

Depending on the symmetry of the electron density distribution of a common electron pair with respect to the line of chemical bond between interacting atoms, s, p and d bonds are distinguished. Since no more than one s, two p and one d bonds can be formed between two atoms, chemical bonds can be: one- (s), two- (s+p), three- (s+2p) and four-fold (s+ 2p+d);

Since the energy (E) of an individual two-center two-electron chemical bond is greater, the greater the overlap between the atomic orbitals of interacting atoms, the bond is formed in the direction of maximum overlap and is characterized by focus in space. Due to the difference in the efficiency of overlap of atomic orbitals: E(s) > E(p) > E(d);

A quantitative measure of the ability of an atom of a chemical element to form chemical bonds – valence- is determined by the number of two-electron two-center chemical bonds formed by an atom of a chemical element with its partners in a chemical compound. Taking into account the exchange and donor-acceptor mechanisms of the formation of chemical bonds, the valence of an atom in a chemical compound is equal to the number of its valence orbitals used in bonding, regardless of their occupancy with electrons. The maximum possible valence of an atom of a chemical element cannot exceed the number of its valence orbitals, which determines the saturation of covalent chemical bonds.

Example 1. Describe the electronic structure and justify the non-monotonic nature of the change in binding energy (kJ/mol) in halogen molecules: F 2 (159)< Cl 2 (243) >Br 2 (199) > I 2 (151) > At 2 (117).

Solution. The interaction of two F 2s 2 2p 5 atoms, each of which is characterized by the presence of one unpaired electron in the valence 2p orbitals, determines the formation of a single s-type chemical bond in the F 2 molecule by the exchange mechanism:

For Cl, Br, I and At atoms, the valence orbitals are not only ns 2 np 5, but also free nd orbitals. This determines the presence in the molecules of these halogens, along with an s type chemical bond based on the exchange mechanism, an additional p type bond according to the donor-acceptor mechanism due to the lone electron pair of one atom and the free 3d orbital of the other:

The presence of additional p binding determines the natural increase in the multiplicity [†] and binding energy during the transition from the F 2 molecule to Cl 2 . A further decrease in the binding energy in the Cl 2 ®Br 2 ®I 2 ®At 2 series is associated with a decrease in the efficiency of overlap of the valence orbitals of interacting halogen atoms as a result of an increase in the size of the valence orbitals.

Example 2. Describe the electronic structure and determine the valency of phosphorus in its compounds with fluorine: PF 3, PF 5 and -. Which of the following compounds can form nitrogen?

Solution. The ground state P 3s 2 3p 3 3d 0 is characterized by the presence of an electron pair, three unpaired electrons and five free valence orbitals. The interaction of three fluorine atoms, each of which has one unpaired electron F 2s 2 2p 5, with three unpaired electrons of the phosphorus atom in the ground state determines the formation of three s bonds in the PF 3 compound by the exchange mechanism:

In the excited state, the phosphorus atom P* 3s 1 3p 3 3d 1 is characterized by the presence of five unpaired electrons in the valence orbitals and, as a consequence of this, can participate in the formation of five s bonds by the exchange mechanism when interacting with five fluorine atoms in the PF 5 compound:

It should be noted that the relatively small energy gap between the valence 3s, 3p and 3d orbitals leads to small energy costs for excitation of the atom, which are more than compensated for by the formation of additional chemical bonds.

Ion formation occurs as a result of the donor-acceptor interaction of the F - 2s 2 2p 6 ion, which provides an electron pair, and PF 5, characterized by the presence of a free d orbital on the phosphorus atom:

In accordance with the number of two-electron chemical bonds formed by the phosphorus atom with partners, the valence of phosphorus in the compounds PF 3, PF 5 and - is 3, 5 and 6, respectively.

Unlike the phosphorus atom, the valence capabilities of the element of the second period of nitrogen N 2s 2 2p 3 are limited by the possibility of forming no more than four chemical bonds involving four valence orbitals - three by the exchange mechanism due to three unpaired electrons on the 2p valence orbitals and one by the donor-acceptor mechanism due to an electron pair in 2s orbitals. This determines the existence of only the NF 3 compound for nitrogen.

When atoms of different chemical elements interact, the generalized electron pair is shifted to a more electronegative atom, which leads to the appearance of excess negative and positive charges on atoms of equal magnitude (q). A quantitative characteristic of the polarity of such a chemical bond is the value dipole moment(m) – the product of the absolute value of the excess charge q and the distance l between the centers of positive and negative charges in the dipole (dipole length): m = q×l[‡][KB1] .

Example 3. Determine the effective charges on the fluorine and hydrogen atoms in the HF molecule if the dipole moment and H-F bond length are 1.91 D and 92 pm.

Solution. The effective charge of hydrogen and fluorine atoms forming a polar covalent bond can be calculated as a fraction of the electron charge using the relation:

q = m exp/m ion,

where q is the value of the effective charge of the H and F atoms; m ion – the value of the dipole moment of the molecule, calculated under the assumption that HF consists of H + and F - ions with charges equal to the electron charge e = 1.602×10 -19 C; m exp is the experimental value of the dipole moment of the HF molecule.

q = e×l/m exp = (1.91×3.34×10 -30)/ 1.602×10 -19 ×9.2×10 -11 = 0.43.

Thus, the effective charges in the molecule are: H +0.43 F -0.43, which indicates the ionic-covalent nature of the chemical bond - 43% ionicity and 57% covalency.

Since the dipole moment of a chemical bond is a vector quantity directed from the positive to the negative end of the dipole, the dipole moment of a chemical compound is determined by the vector sum of the dipole moments of individual chemical bonds and depends not only on the polarity of each bond, but also on the spatial arrangement of the bonds in the compound. Thus, despite the polarity of individual bonds A d + -B d - , with a symmetrical geometric structure of AB n molecules:

the vector sum of the dipole moments of bonds is 0, which leads to non-polarity of the compounds.

The magnitude of the dipole moment and the polarity of polyatomic molecules is also influenced by the presence of lone electron pairs in the electronic structure of the molecule.

Example 4. Justify the difference in dipole moments and polarity of isostructural trigonal pyramidal molecules: NH 3 (1.5 D) and NF 3 (0.2 D).

Solution. In NH 3 and NF 3 molecules, the nitrogen atom participates in the formation of three s bonds with partners and are characterized by the presence of a lone pair of electrons. Taking into account the difference in electronegativity of nitrogen atoms compared to hydrogen c(N) > c(H) and fluorine c(N)< c(F), дипольные моменты связей N-H направлены в сторону азота, а дипольные моменты связей N-F – в сторону фтора:

Since the direction of the vector sum of dipole moments of N-H bonds for NH 3 coincides with the direction of the lone electron pair localized on the nitrogen atom, the dipole moment and polarity of ammonia are enhanced. In the NF 3 molecule, the direction of the vector sum of the dipole moments of N-F bonds is directly opposite to the direction of the electron pair, which determines the decrease in the dipole moment and polarity of NF 3.

To justify the energy equivalence and symmetrical spatial orientation of two-center two-electron chemical bonds formed as a result of overlap different(s, p, d) valence orbitals of the central atom with ligand orbitals, the concept is used hybridization of valence atomic orbitals, based on the following provisions:

In the formation of chemical bonds s of the type of the central atom with ligands, not the original atomic orbitals (s, p, d), which differ in energy and shape, can take part, but equivalent hybrid orbitals, the shape of which ensures the most effective overlap with the orbitals of the ligands;

Since the hybridization of atomic orbitals of the central atom requires energy expenditure, which is compensated by the formation of stronger chemical bonds, the efficiency of hybridization decreases with increasing energy gap between the original atomic orbitals and increasing their size. As a result of this, both by period (increase in the energy gap between ns, np and nd valence orbitals) and by group (increase in the size of valence orbitals), the efficiency of hybridization of the orbitals of atoms of chemical elements decreases;

The number of hybrid orbitals is determined by the number of initial atomic orbitals that participated in hybridization: s + p = 2sp, s + 2p = 3sp 2, s + 3p = 4sp 3, s + 2p + d = 4sp 2 d, s + 3p + d = 5sp 3 d, s + 3p + 2d = 6sp 3 d 2 ;

For compounds of non-transition elements, the type of hybridization of atomic orbitals of the central atom, the spatial arrangement of hybrid orbitals and, consequently, the stereochemical structure of the compounds are mainly determined by the minimum repulsive energy of electron pairs ensuring the formation of s bonds of the central atom with ligands, as well as lone valence pairs of the central atom (model of localized electron pairs). Since the electron pair of a chemical s bond occupies a smaller volume than a lone electron pair (n), the repulsion between electron pairs increases in the series: s-s< s-n < n-n.

Example 5. Describe the electronic structure, determine the geometric shape and multiplicity of bonds in the following compounds: a) H 2 O, b) CO 2, c) SO 2, d) NO 3 -; e) BrF 4 -, f) PCl 5, g) SF 6.

Solution. Taking into account the concept of hybridization, when analyzing the electronic structure, geometric shape and bond multiplicity in compounds of non-transition elements, it is recommended to adhere to the following sequence:

1. Write the electronic formulas of the central atom and ligands in the ground state and, based on the electronic structure of the ligands, determine the number of s and p bonds in the compound:

a) H 2 O - O 2s 2 2p 4, 2H 1s 1 with 2 unpaired electrons form 2s bonds with the O atom according to the exchange mechanism;

b) CO 2 - C 2s 2 2p 2, 2O 2s 2 2p 4 with 4 unpaired electrons form 2s and 2p bonds with the C atom according to the exchange mechanism;

c) SO 2 - S 3s 2 3p 4 3d 0, 2O 2s 2 2p 4 with 4 unpaired electrons form 2s and 2p bonds with the S atom according to the exchange mechanism;

d) NO 3 - - N 2s 2 2p 3, 2O 2s 2 2p 4 and O - 2s 2 2p 5 are characterized by 5 unpaired electrons and, therefore, must form 5 two-electron bonds with the central nitrogen atom. However, as for atoms of other chemical elements of period 2, the maximum number of two-electron bonds (maximum valency) for nitrogen cannot exceed 4. This determines the need to reduce the number of unpaired electrons on the ligands as a result of the redistribution of the number of electrons between the ligands and the nitrogen atom: NO 3 - - N + 2s 2 2p 2, O 2s 2 2p 4 and 2O - 2s 2 2p 5 – such a system is characterized by 4 unpaired electrons on the ligands, which can participate in the formation of 3s and 1p bonds with the N + cation via an exchange mechanism;

e) BrF 4 - - Br 4s 2 4p 5 4d 0, 3F 2s 2 2p 5 with 3 unpaired electrons and F - 2s 2 2p 6 form 4s bonds with the Br atom: 3 by exchange and 1 by donor-acceptor mechanism;

f) PCl 5 - P 3s 2 3p 3 3d 0, 5Cl 3s 2 3p 5 with 5 unpaired electrons form 5s bonds with the P atom according to the exchange mechanism;

g) SF 6 – S 3s 2 3p 4 3d 0, 6F 2s 2 5p 5 with 6 unpaired electrons form 6s bonds with the S atom according to the exchange mechanism.

2. To form the required number of s and p bonds by the exchange mechanism, if necessary, transfer the central atom to an excited state and equalize the number of unpaired electrons of the central atom and ligands:

a) H 2 O - the central atom O 2s 2 2p 4 and the 2H 1s 1 ligands contain the same number of unpaired electrons;

b) CO 2 – 4 unpaired electrons of the ligands 2O 2s 2 2p 4 determine the need to excite the carbon atom C* 2s 1 2p 3;

c) SO 2 - 4 unpaired electrons of the ligands 2O 2s 2 2p 4 determine the need to excite the sulfur atom S* 3s 2 3p 3 3d 1;

d) NO 3 - - 4 unpaired electrons of the O 2s 2 2p 4 and 2O - 2s 2 2p 5 ligands determine the need to excite the N + * 2s 1 2p 3 cation;

e) BrF 4 - - 3 unpaired electrons of the ligands 3F 2s 2 2p 5 determine the need to excite the Br * 4s 2 4p 4 4d 1 atom;

e) PCl 5 – 5 unpaired electrons of the 5Cl 3s 2 3p 5 ligands determine the need to excite the P * 3s 1 3p 3 3d 1 atom;

g) SF 6 – 6 unpaired electrons of the 6F 2s 2 2p 5 ligands determine the need to excite the S * 3s 1 3p 3 3d 2 atom.

3. Based on the sum of the number s of bonds of the central atom with ligands and the number of lone electron pairs in the valence orbitals of the central atom, determine the number of hybrid orbitals, and based on the nature of the orbitals of the central atom participating in the formation of s bonds and containing lone pairs - the type of hybridization:

a) H 2 O – O forms 2s bonds with H atoms and contains 2 lone pairs - a total of 4 hybrid orbitals formed from s and three p orbitals, sp 3 hybridization;

b) CO 2 – C* in an excited state forms 2s bonds with O atoms and does not contain lone pairs - only 2 hybrid ones, formed from s and one p orbitals, sp hybridization;

c) SO 2 – S* in the excited state forms 2s bonds with O atoms and contains one lone electron pair - a total of 3 hybrid orbitals formed from s and two p orbitals, sp 2 hybridization;

d) NO 3 - - the N + cation in an excited state forms 3s bonds with one atom and two oxygen ions, there are no lone electron pairs - only 3 hybrid orbitals formed from s and two p orbitals, sp 2 hybridization;

e) BrF 4 - - Br* in the excited state forms 3s bonds with F atoms by the exchange mechanism and 1s bond with the F ion by the donor-acceptor mechanism, contains 2 lone electron pairs - a total of 6 hybrid orbitals formed from s, three p and two d orbitals, sp 3 d 2 hybridization;

e) PCl 5 – P* in the excited state forms 5s bonds with Cl atoms and does not contain lone electron pairs - only 5 hybrid orbitals formed from s, three p and one d orbitals, sp 3 d hybridization;

g) SF 6 – S* in the excited state forms 6s bonds with F atoms and does not contain lone electron pairs - only 6 hybrid orbitals formed from s, three p and two d orbitals, sp 3 d 2 hybridization;

4. Taking into account the energy equivalence and spatial orientation of hybrid orbitals, give electron-graphical and structural-graphic formulas of compounds; taking into account the number of s and p bonds of the central atom with ligands and the delocalization of p bonds, determine the multiplicity of bonds (K):

K = 2 K = 1 1/3

Example 6. Why do the bond angles РНЭН decrease in the series of hydrogen compounds of group VI p-elements H 2 E: H 2 O (104.5 0) > H 2 S (92.2 0) > H 2 Se (91.0 0) > H 2 Te (90 0)?

Solution. The electronic structure of H 2 E molecules is characterized by the presence of two s E-H bonds and two lone electron pairs localized on the atoms of p-elements of group VI. The magnitude of the bond angle РНЭН is determined, on the one hand, by the nature and spatial orientation of the orbitals of the central atom, which take part in the formation of s E-H bonds, and on the other hand, by the effect of interelectron repulsion between lone and s bonding electron pairs.

The presence of 2 s bonds and 2 lone electron pairs determines the possibility of participation in the formation of s bonds either sp 3 hybridized valence orbitals of the central atom, characterized by a tetrahedral spatial orientation with an angle РНЭН = 109 0, or the original atomic p orbitals located at an angle of 90 0. Since the size of the orbitals increases with an increase in the principal quantum number of valence orbitals of the central atom, the efficiency of their hybridization decreases, which leads to a decrease in the bond angle РНЭН from close to tetrahedral 104.5 0 for H 2 O to 90 0 for H 2 Te. The slightly smaller value of the bond angle РНОН = 104.5 0 compared to the tetrahedral 109 0 is due to the effect of electron-electron repulsion of two lone electron pairs onto s bonding electron pairs.

The description of the electronic structure of complex compounds of transition metals by the BC method is characterized by the following features:

The formation of chemical bonds between the central metal ion complexing agent and the ligands occurs as a result of the donor-acceptor interaction of free hybrid orbitals of the metal ion (acceptor) and the orbitals of the ligands (donors) filled with a pair of electrons;

The type of hybridization of valence orbitals of the central metal ion is determined by the number s of bonds of the metal ion with ligands (coordination number) without taking into account lone electron pairs on the valence orbitals of the metal;

Depending on the nature of the valence orbitals of the metal ion involved in hybridization and the formation of s bonds with ligands, the formation of two types of complexes is possible: outer orbital(high-spin), characterized by an unchanged distribution of electrons over d-orbitals compared to a free metal ion, and intra-orbital(low-spin) with a changed distribution of electrons over d-orbitals as a result of the participation of part of the d-orbitals in the formation of donor-acceptor bonds with ligands.

Example 7. Describe the electronic structure, determine the geometric shape and magnetic properties of the following complex compounds of transition metals: a) 2- and 2-, b) 3+ and 3+.

Solution. When analyzing the electronic structure, geometric shape and magnetic properties of complex compounds of transition metals, adhere to the following sequence:

1. Determine the charge of the central metal ion and write down its electronic graphic formula:

2. Determine the number s of bonds of the metal ion with ligands and possible types of hybridization of valence orbitals of the metal ion:

a) 2- and 2- - 4s bonds, sp 3 and dsp 2 hybridization;

b) 3+ and 3+ - 6s bonds, sp 3 d 2 and d 2 sp 2 hybridization.

3. Based on an analysis of the nature of the metal ion and ligands, determine the nature of the complex - outer-orbital (high-spin) or intra-orbital (low-spin) and the type of hybridization of the metal ion orbitals that is realized:

A) 2- - Cl - is a weak-field ligand and with the 3d ion Ni 2+ forms a high-spin - outer-orbital complex with an unchanged distribution of electrons over 3d orbitals compared to the free ion, which corresponds to sp 3 hybridization of Ni 2+ orbitals:

2- - CN - is a strong field ligand and with the 3d Ni 2+ ion forms a low-spin - intra-orbital complex, characterized as a result of pairing of electrons in 3d orbitals, the presence of one free 3d orbital, which determines the dsp 2 type of hybridization of Ni 2+ orbitals:

B) 3+ - H 2 O is a weak field ligand and with the 3d ion Co 3+ forms a high-spin - outer-orbital complex with an unchanged distribution of electrons over 3d orbitals compared to the free ion, which corresponds to sp 3 d 2 hybridization of Co 3+ orbitals:

3+ - 5d ion Ir 3+, regardless of the strength of the ligand field, forms low-spin - intra-orbital complexes, characterized, as a result of pairing of electrons in 5d orbitals, by the presence of two free 5d orbitals, which determines d 2 sp 3 hybridization of Ir 3+ orbitals:

4. Show the formation of donor-acceptor bonds of ligands with hybridized orbitals of the metal ion, the geometric shape of the complex and indicate its magnetic properties:

paramagnetic,

diamagnetic;

paramagnetic;

Basic principles of the valence bond method

Lecture No. 4. Fundamentals of the theory of chemical bonds. Valence bond method

A chemical bond is the interaction of nuclei and electrons, leading to the formation of a stable collection of atoms - molecular particles or atomic aggregates. The driving force for the formation of a chemical bond is the system’s desire to minimize energy when the atoms reach the completed electron shell of the inert gas (s 2 or s 2 p 6). Taking into account the dependence on the method of approaching a system of atomic particles to a stable state, three types of chemical bonds are distinguished: covalent, ionic and metallic. In the theory of chemical bonding, the forces of intermolecular interaction (van der Waals forces), which are inherently physical interactions, and the hydrogen bond, which lies on the border of physical and chemical phenomena, are usually also considered.

With the development of quantum mechanical concepts in the theory of chemical bonds, two methods for describing covalent bonds emerged: the valence bond method (BC method) and the molecular orbital method (MO method).

According to the BC method, the atoms that make up a molecule retain their individuality, and chemical bonds arise as a result of the interaction of their valence electrons and valence orbitals. The MO method considers a molecule as a single formation in which each electron belongs to the molecular particle as a whole and moves in the field of all its nuclei and electrons. The BC and MO methods, despite significant differences in approaches to the description of molecules, complement each other well. In many cases they ultimately lead to the same results.

¨ A covalent bond is realized through the formation of a common electron pair.

¨ A shared electron pair is formed when the electron orbitals of interacting atoms overlap.

The degree of overlap and bond strength depends on the energetic and geometric correspondence of the orbitals. All other things being equal, the bond strength increases with a decrease in the energy difference between interacting orbitals and an increase in the density of the electron cloud:

1s - 1s > 1s - 2s > 1s - 3s 1s - 1s > 2s - 2s > 3s - 3s

A necessary condition for the effective overlap of orbitals is their proper orientation in space and the coincidence of the mathematical sign of the wave function:

Effective overlap Zero overlap Ineffective overlap

There are two mechanisms for the formation of a common electron pair - exchange and donor-acceptor. When implementing the exchange mechanism, each of the interacting atoms provides an unpaired electron occupying a valence orbital for the formation of a common electron pair:

When a covalent bond is formed according to the donor-acceptor mechanism, one of the atoms (D) acts as a donor, providing for common use a lone pair of electrons located on one of its valence orbitals. The second atom - the acceptor (A) - provides a vacant orbital for bond formation, accepting the electron pair of the donor partner onto it:

Based on the number of common electron pairs connecting atoms, simple, double and triple bonds are distinguished:

H2N : NH 2 or H 2 N-NH 2 HN :: NH or HN=NH N ::: N or NºN

There are a few known examples of compounds containing fourfold metal-metal bonds, for example,

Based on the nature of the overlap of electronic orbitals, three types of covalent bonds are distinguished:

s-Communication, during the formation of which the overlapping of orbitals occurs along the bond line (the line connecting the nuclei of interacting atoms).

p-Communication, during the formation of which the overlap of orbitals occurs in the plane containing the communication line (lateral overlap).

d-Communication, during the formation of which the overlap of orbitals occurs in a plane perpendicular to the communication line.

The physical characteristics of a chemical bond and molecular species are bond energy, bond length and bond angle, as well as polarity and polarizability. The energy of a chemical bond is the amount of energy that is critical to breaking the bond.. The same amount of energy is released when a bond is formed. So the dissociation energy of a hydrogen molecule is 435 kJ/mol, respectively, E H-H = 435 kJ/mol. The distance between the nuclei of chemically bonded atoms is usually called the bond length. The bond length is measured in nm (nanometer, 1×10 -9 m) or pm (picometer, 1×10 -12 m). The angle between conventional lines connecting the nuclei of chemically bonded atoms (bond lines),usually called valence. For example, a water molecule has an angular shape

with a HOH bond angle of 104.5° and an O-H bond length of 96 pm. The energy required for complete dissociation of a molecule is ᴛ.ᴇ. for the process H 2 O ® 2H + O, is 924 kJ/mol, the average O-H bond energy is 462 kJ/mol (924/2).

In the case when a covalent bond is formed by atoms with the same electronegativity, the shared electron pair belongs equally to both partners. Such a bond is usually called a nonpolar covalent bond. If the atoms forming a bond differ in electronegativity, the common electron pair is shifted to the atom with higher electronegativity. The resulting bond is usually called polar covalent. Due to the asymmetric distribution of electron density, diatomic molecules with a polar covalent bond are dipoles - electrically neutral particles in which the centers of gravity of positive and negative charge do not coincide. When writing formulas, the polarity of a covalent bond is conveyed in several ways:

A quantitative characteristic of the polarity of a bond is its dipole moment, or more precisely the electric dipole moment:

where q e is the electron charge, l is the bond length.

The unit of dipole moment is Kl×m (SI) or the off-system unit - Debye (D = 3.34×10 -30 Kl×m). The dipole moment of a molecule is defined as the vector sum of the dipole moments of its bonds and lone electron pairs. As a result, molecular particles that have the same shape, but bonds of different polarity, can have different dipole moments. Eg:

m = 1.47 D m = 0.2 D

An important characteristic of a covalent bond, which largely determines its reactivity, is polarizability - the ability of a bond to change polarity (redistribute electron density) under the influence of an external electrostatic field, the source of which can be a catalyst, reagent, solvent, etc. The induced dipole of a particle is related to the external field strength ( E) by a simple relation: m = aE. Proportionality factor a is a quantitative characteristic of polarizability.

A covalent bond has two important properties - saturation and directionality. Saturability A covalent bond is essentially that atoms are capable of forming a finite number of covalent bonds. The reason for the saturation of a covalent bond is the limited number of valence orbitals of an atom necessary for the formation of a bond both by the exchange and donor-acceptor mechanisms.

Quantitatively, the saturation of a covalent bond is characterized by covalency. Covalency(structural valency - v) is equal to the number of covalent bonds formed by an atom both by exchange and donor-acceptor mechanisms.

Knowing the number of orbitals in valence electronic levels, we can calculate the maximum theoretically possible valence for elements of different periods. Atoms of elements of the first period have only one orbital (1s) at the valence (first) level; therefore, hydrogen in all its compounds is monovalent. Helium, the atom of which has a completely completed first level, does not form chemical compounds.

For elements of the second period, the valence level is the second energy level, containing four orbitals - 2s, 2p x, 2p y, 2p z. For this reason, the maximum covalency of elements of the second period is four. For example, for nitrogen:

v N = 3; v N = 4

Focus covalent bonding is due to the desire of atoms to form bonds in the direction of greatest overlap of orbitals, which ensures maximum energy gain. This leads to the fact that molecules formed with the participation of covalent bonds have a strictly defined shape. For example, the formation of sulfur-hydrogen bonds in a hydrogen sulfide molecule occurs due to the overlap of the electron clouds of the 1s orbitals of hydrogen atoms and two 3p orbitals of the sulfur atom, located at right angles to each other. As a result, the hydrogen sulfide molecule has an angular shape and a bond angle HSH close to 90°.

Since the shape of a number of molecules cannot be explained by the formation of covalent bonds involving a standard set of atomic orbitals, L. Pauling developed the theory of hybridization of atomic orbitals. According to this theory, the process of formation of a molecular particle is accompanied by equalization of the lengths and energies of covalent bonds due to the process of hybridization of atomic orbitals, which can be represented as mixing the wave functions of basic atomic orbitals with the formation of a new set of equivalent orbitals. The hybridization process requires energy, but the formation of bonds involving hybrid orbitals is energetically beneficial, since it ensures more complete overlap of electron clouds and minimal repulsion of the resulting common electron pairs. The condition for stable hybridization is the proximity of the initial atomic orbitals in energy. Moreover, the lower the energy of the electronic level, the more stable the hybridization is.

The simplest one is sp hybridization, which is realized by mixing the wave functions of the s- and one p-orbital:

The resulting sp-hybrid orbitals are oriented along the same axis in different directions, which ensures minimal repulsion of electron pairs; therefore, the angle between the bonds formed with the participation of these orbitals is 180°.

Participation in the hybridization of s- and two p-orbitals leads to the formation of three hybrid orbitals ( sp 2 hybridization), oriented from the center to the vertices of a regular triangle. The bond angle between bonds formed with the participation of hybrid orbitals of this type is 120°.

sp 3 -Hybridization leads to the formation of a set of four energetically equivalent orbitals, oriented from the center to the vertices of the tetrahedron at an angle of 109.5° relative to each other:

Let us consider, as an example, the structure of some molecules formed with the participation of sp 3 hybrid orbitals.

Methane molecule - CH 4

From the energy diagram of the carbon atom it follows that the existing two unpaired electrons are not enough to form four covalent bonds according to the exchange mechanism; therefore, the formation of a methane molecule occurs with the participation of a carbon atom in an excited state.

The equivalence of bonds and the tetrahedral geometry of the methane molecule indicate the formation of bonds involving sp 3 hybrid orbitals of the central atom.

Ammonia molecule - NH 3

The atomic orbitals of nitrogen in the ammonia molecule are in a state of sp 3 hybridization. Three orbitals are involved in the formation of nitrogen-hydrogen bonds, and the fourth contains a lone electron pair, and therefore the molecule has a pyramidal shape. The repulsive effect of the lone pair of electrons leads to a decrease in the bond angle from the expected 109.5 to 107.3°.

The presence of a lone electron pair on the nitrogen atom allows it to form another covalent bond via the donor-acceptor mechanism. Thus, the formation of the molecular ammonium cation - NH 4 + occurs. The formation of the fourth covalent bond leads to the alignment of bond angles (a = 109.5°) due to the uniform repulsion of hydrogen atoms:

The symmetry of the ammonium cation, as well as the geometric and energetic equivalence of nitrogen-hydrogen bonds indicates the equivalence of covalent bonds formed by the exchange and donor-acceptor mechanisms.

Water molecule - H2O

The formation of a water molecule occurs with the participation of sp 3 -hybrid orbitals of the oxygen atom, two of which are occupied by lone electron pairs and, therefore, do not contribute to the geometry of the molecule. The overlap of one-electron clouds of two hybrid oxygen orbitals and the 1s orbitals of two hydrogen atoms results in the formation of a corner molecule. The repulsive action of the two lone pairs of electrons reduces the bond angle of HOH to 104.5°.

The presence of two lone pairs of electrons allows the water molecule to form another oxygen-hydrogen bond via the donor-acceptor mechanism, adding a hydrogen cation and forming a molecular hydronium cation:

H 2 O + H + ® H 3 O +

The considered examples illustrate the advantages of the BC method, first of all, its clarity and simplicity of considering the structure of the molecule at a qualitative level. The BC method also has disadvantages:

· The BC method does not allow one to describe the formation of one-electron bonds, for example, in the molecular cation H 2 +.

· The BC method does not allow one to describe the formation of delocalized multicenter bonds. To describe molecules with delocalized bonds within the framework of the BC method, they are forced to resort to a special technique - valence circuit resonance. According to the concept of resonance, the structure of molecules of this type is conveyed not by one formula, but by the superposition of several valence schemes (formulas). For example, the structure of a nitric acid molecule containing a delocalized three-center bond

in the VS method, it is transmitted by the superposition (resonance) of two valence schemes:

· The valence bond method does not always adequately reflect the physical properties of molecules, in particular, their magnetic behavior. For example, according to the BC method, the oxygen molecule must be diamagnetic, since all the electrons in it are paired. In reality, the oxygen molecule is a diradical and is paramagnetic.

· The BC method cannot explain the absorption spectra and color of substances, since it does not consider the excited states of molecules.

· The mathematical apparatus of the valence bond method is quite complex and cumbersome.

Literature: p. 109 - 135; With. 104 - 118; With. 70 - 90

Lecture No. 4. Fundamentals of the theory of chemical bonds. Valence bond method

A chemical bond is the interaction of nuclei and electrons, leading to the formation of a stable collection of atoms - molecular particles or atomic aggregates. The driving force for the formation of a chemical bond is the system’s desire to minimize energy when the atoms reach the completed electron shell of the inert gas (s 2 or s 2 p 6). Depending on the method of approaching a system of atomic particles to a stable state, three types of chemical bonds are distinguished: covalent, ionic and metallic. In the theory of chemical bonding, the forces of intermolecular interaction (van der Waals forces), which are inherently physical interactions, and the hydrogen bond, which lies on the border of physical and chemical phenomena, are usually also considered.

According to the BC method, the atoms that make up a molecule retain their individuality, and chemical bonds arise as a result of the interaction of their valence electrons and valence orbitals. The MO method considers a molecule as a single entity in which each electron belongs to the molecular particle as a whole and moves in the field of all its nuclei and electrons. The BC and MO methods, despite significant differences in approaches to the description of molecules, complement each other well. In many cases they ultimately lead to the same results.

¨ A covalent bond is realized through the formation of a common electron pair.

¨ A shared electron pair is formed when the electron orbitals of interacting atoms overlap.

1s - 1s > 1s - 2s > 1s - 3s 1s - 1s > 2s - 2s > 3s - 3s

A necessary condition for the effective overlap of orbitals is their proper orientation in space and the coincidence of the mathematical sign of the wave function:

Effective overlap Zero overlap Ineffective overlap

When a covalent bond is formed by the donor-acceptor mechanism, one of the atoms (D) acts as a donor, sharing a lone pair of electrons located in one of its valence orbitals. The second atom - the acceptor (A) - provides a vacant orbital for bond formation, accepting the electron pair of the donor partner onto it:

Based on the number of common electron pairs connecting atoms, simple, double and triple bonds are distinguished:

H2N : NH 2 or H 2 N-NH 2 HN :: NH or HN=NH N ::: N or NºN

There are a few known examples of compounds containing fourfold metal-metal bonds, for example,

Based on the nature of the overlap of electronic orbitals, three types of covalent bonds are distinguished:

s-Communication, during the formation of which the overlapping of orbitals occurs along the bond line (the line connecting the nuclei of interacting atoms).

p-Communication, during the formation of which the overlap of orbitals occurs in the plane containing the communication line (lateral overlap).

d-Communication, during the formation of which the overlap of orbitals occurs in a plane perpendicular to the communication line.

The physical characteristics of a chemical bond and molecular species are bond energy, bond length and bond angle, as well as polarity and polarizability. The energy of a chemical bond is the amount of energy required to break it. The same amount of energy is released when a bond is formed. So the dissociation energy of a hydrogen molecule is 435 kJ/mol, respectively, E H-H = 435 kJ/mol. The distance between the nuclei of chemically bonded atoms is called the bond length. The bond length is measured in nm (nanometer, 1×10 -9 m) or pm (picometer, 1×10 -12 m). The angle between conventional lines connecting the nuclei of chemically bonded atoms (bond lines),called valence. For example, a water molecule has an angular shape

with a HOH bond angle of 104.5° and an O-H bond length of 96 pm. The energy required for complete dissociation of the molecule, i.e. for the process H 2 O ® 2H + O, is 924 kJ/mol, the average O-H bond energy is 462 kJ/mol (924/2).

In the case when a covalent bond is formed by atoms with the same electronegativity, the shared electron pair belongs equally to both partners. Such a bond is called a nonpolar covalent bond. If the atoms forming a bond differ in electronegativity, the shared electron pair is shifted to the atom with higher electronegativity. The resulting bond is called polar covalent. Due to the asymmetric distribution of electron density, diatomic molecules with a polar covalent bond are dipoles - electrically neutral particles in which the centers of gravity of positive and negative charge do not coincide. When writing formulas, the polarity of a covalent bond is conveyed in several ways:

A quantitative characteristic of the polarity of a bond is its dipole moment, or more precisely the electric dipole moment:

where q e is the electron charge, l is the bond length.

m = 1.47 D m = 0.2 D

A covalent bond has two important properties - saturation and directionality. Saturability covalent bonding is that atoms are capable of forming a finite number of covalent bonds. The reason for the saturation of a covalent bond is the limited number of valence orbitals of an atom necessary for the formation of a bond both by the exchange and donor-acceptor mechanisms.

Knowing the number of orbitals in valence electronic levels, we can calculate the maximum theoretically possible valence for elements of different periods. Atoms of elements of the first period have only one orbital (1s) at the valence (first) level, therefore hydrogen in all its compounds is monovalent. Helium, the atom of which has a completely completed first level, does not form chemical compounds.

For elements of the second period, the valence level is the second energy level, containing four orbitals - 2s, 2p x, 2p y, 2p z. For this reason, the maximum covalency of elements in the second period is four. For example, for nitrogen:

v N = 3; v N = 4

The simplest one is sp hybridization, which is realized by mixing the wave functions of the s- and one p-orbital:

The resulting sp-hybrid orbitals are oriented along the same axis in different directions, which ensures minimal repulsion of electron pairs, therefore the angle between the bonds formed with the participation of these orbitals is 180°.

Let us consider, as an example, the structure of some molecules formed with the participation of sp 3 hybrid orbitals.

Methane molecule - CH 4

From the energy diagram of the carbon atom it follows that the existing two unpaired electrons are not enough to form four covalent bonds according to the exchange mechanism, therefore the formation of a methane molecule occurs with the participation of a carbon atom in an excited state.

The equivalence of bonds and the tetrahedral geometry of the methane molecule indicate the formation of bonds involving sp 3 hybrid orbitals of the central atom.

Ammonia molecule - NH 3

The atomic orbitals of nitrogen in the ammonia molecule are in a state of sp 3 hybridization. Three orbitals are involved in the formation of nitrogen-hydrogen bonds, and the fourth contains a lone electron pair, so the molecule has a pyramidal shape. The repulsive effect of the lone pair of electrons leads to a decrease in the bond angle from the expected 109.5 to 107.3°.

The presence of a lone electron pair on the nitrogen atom allows it to form another covalent bond through the donor-acceptor mechanism. Thus, the formation of the molecular ammonium cation - NH 4 + occurs. The formation of the fourth covalent bond leads to the alignment of bond angles (a = 109.5°) due to the uniform repulsion of hydrogen atoms:

Water molecule - H2O

The formation of a water molecule occurs with the participation of sp 3 hybrid orbitals of the oxygen atom, two of which are occupied by lone electron pairs and therefore do not contribute to the geometry of the molecule. The overlap of one-electron clouds of two hybrid oxygen orbitals and the 1s orbitals of two hydrogen atoms results in the formation of a corner molecule. The repulsive action of the two lone pairs of electrons reduces the bond angle of HOH to 104.5°.

The presence of two lone pairs of electrons allows the water molecule to form another oxygen-hydrogen bond through the donor-acceptor mechanism, adding a hydrogen cation and forming a molecular hydronium cation:

H 2 O + H + ® H 3 O +

· The BC method does not allow one to describe the formation of one-electron bonds, for example, in the molecular cation H 2 +.

in the VS method, it is transmitted by the superposition (resonance) of two valence schemes:

· The BC method cannot explain the absorption spectra and color of substances, since it does not consider the excited states of molecules.

· The mathematical apparatus of the valence bond method is quite complex and cumbersome.

Literature: p. 109 - 135; With. 104 - 118; With. 70 - 90

The valence bond method is considered one of the fundamental principles of inorganic chemistry. Let's identify its features and application options.

Theoretical provisions

A chemical bond is considered to be a bond between atoms accompanied by the release of thermal energy.

Let's look at the basic principles of the valence bond method.

The covalent species is created by two electrons having opposite spin directions.

The formed electron pair is shared; it is formed as a result of the pairing of free electrons that belong to two different atoms, thereby forming a covalent bond.

The valence bond method also explains the bonding mechanism in which one atom has a free electron pair. The second element has an empty atomic orbital and is an acceptor.

Characteristics of covalent bond

How strong is a chemical bond? The valence bond method explains the relationship between the strength of a covalent bond and the degree of overlap of interacting electron clouds. The formation of this type of connection occurs in the direction where complete interaction of electron clouds is observed.

The valence bond method uses hybridization of the orbitals of the main chemical element. Bond formation often occurs after a change in the state of the valence orbitals.

Features of education

The unequal original atomic orbitals “mix” to form hybrid orbitals that have the same amount of energy. The hybridization process is accompanied by the elongation of the cloud towards the interacting electron atom, which leads to the overlap of the hybrid cloud with an ordinary electron of a neighboring atom.

The valence bond method is characterized by the formation of a strong bond. The process is accompanied by the release of energy, compensated by the costs of the hybridization process.

The basic principles of the valence bond method, presented above in the article, fully explain the structure of molecules that have a covalent bond. It is directed towards the greatest overlap of orbitals.

Valence possibilities

The valence bond method allows us to understand what valences a specific chemical element may have. In an unexcited state, valence possibilities are limited by the number of unpaired electrons located at the last energy level. When heated, a transition of an atom from a normal state to an excited state is observed. The process is accompanied by an increase in the number of unpaired electrons.

Excitation energy in chemistry is the quantity that is necessary for the complete transition of an atom with a low energy reserve to a higher form. The bond multiplicity is understood as the number of electron pairs that are shared by nearby atoms as a result of the formation of a covalent chemical bond.

Ϭ and π bonds are approximate descriptions of various types of covalent bonds in molecules. A simple (Ϭ connection) is formed between hybrid clouds. It is characterized by the maximum distribution of the density of the electron cloud along the axis along which the nuclei of atoms are connected.

Complex (π coupling) involves lateral overlap of non-hybrid electron clouds. During its formation, the density of the electron cloud has a maximum value in all directions.

Process characteristics

Bond hybridization is the process of displacement of orbitals of various types in a polyatomic molecule, resulting in the formation of clouds that have the same thermodynamic characteristics.

What is the application of the valence bond method? Examples of organic and inorganic substances indicate its importance for explaining the structure, as well as the characteristic chemical properties of compounds.

Types of hybridization

Depending on how many unpaired electrons are mixed with each other, there are several main types of hybridization.

The sp-type variant involves mixing one s- and p-orbitals with each other. As a result of the process, two identical hybrid orbitals are formed, which overlap each other at an angle of 180 degrees. Thus, they are directed from the nucleus of the atom in different directions.

Sp2 hybridization occurs when two p orbitals are mixed with one s. As a result, three identical hybrid orbitals are formed, which are directed to the vertices of the triangle at the same angle (its value is 120 degrees).

In sp3 hybridization, 3p and one s orbital are mixed. As a result of the process, four identical hybrid clouds are formed, which form a tetrahedron. The bond angle in this case is 109 degrees 28 minutes.

Important aspects of the method

Let us highlight several important points characterizing the valence bond method. To form a covalent chemical bond, two electrons with opposite spin directions are required. For example, if we consider the formation of a hydrogen molecule, it is associated with the overlap of individual electron orbitals of two atoms, the appearance of one common electron pair between them.

When analyzing a covalent bond formed according to the donor-acceptor type, we will use the formation of an ammonium cation as an example. The donor in this case is nitrogen, which has its own electron pair, and the acceptor is the hydrogen proton contained in acids. In the resulting ammonium cation, three bonds are formed due to hybrid clouds, and one is formed by overlapping in a donor-acceptor type. The electron density is distributed evenly, so all bonds are considered covalent.

Conclusion

During the formation of bonds between nonmetal atoms, overlap of electron wave functions is observed. The strength of the connection depends on the completeness of the interaction of electronic clouds. In the normal state, the valence of an atom is characterized by the number of unpaired electrons that participate in the formation of common electron pairs with other atoms.

For an atom in a heated (excited) state, it is related to the number of free (unpaired) electrons, as well as the number of unoccupied orbitals.

To summarize, we note that the method of valence bonds allows us to explain the process of formation of molecules of inorganic and organic substances. The number of chemical bonds with which it is connected to other elements is used as a measure of valence bonds.

Valence electrons are considered to be only those located at the outer level. This statement is relevant for elements of the main subgroups. If we consider the elements located in the periodic table in the secondary subgroup, then the valence will be determined by the electrons located on the outermost energy levels.

When considering any molecule, using the method of valence bonds, you can create an electronic formula, as well as assume the chemical activity and properties of the compound. Depending on how many clouds are involved in the process, a different number of hybrid orbitals are formed. This leads to the appearance of single, double, and triple bonds in the molecules of inorganic and organic substances.

Here we briefly examined the method of valence bonds and its provisions.