The method of valence bonds (BC) considers a chemical bond as a result of the attraction of the nuclei of two atoms to one or more electron pairs common to them. Such a two-electron and two-center (binuclear) bond, localized between two atoms, is called covalent.
In principle, two mechanisms for the formation of a covalent bond are possible: 1) pairing of electrons of two atoms under the condition of opposite orientation of their spins; 2) donor-acceptor interaction, in which a ready electron pair of one of the atoms (donor) becomes common in the presence of an energetically favorable free orbital of another atom (acceptor).
The reason for the formation of any type of chemical bond is the decrease in the energy of the system that accompanies this process. The difference between the energies of the initial and final states is called the binding energy (E CB) and is determined by the amount of heat released during its formation. Experimentally, it is more convenient to find this value by the amount of energy that is spent on breaking this bond. The energy of chemical bonds is estimated at values of the order of 125-1050 kJ/mol.
The distance between the nuclei of two atoms, at which the attractive forces are balanced by the repulsive forces and the system has a minimum energy, is called the equilibrium or bond length d. The bond length and energy depend on its multiplicity, which is determined by the number of electron pairs that bind two atoms. With an increase in the multiplicity, the bond length decreases and its energy increases, for example, these values \u200b\u200bfor the С-С 1 С=С 1 С=С bonds, respectively, are (in nm and kJ) 0.154 and 548, 0.155 and 598, 0.120 and 838. On the contrary, an increase in the radii of the atoms forming a bond leads to an increase in its length and a decrease in energy.
In many cases, the number of unpaired electrons in an atom is less than the number of bonds formed by it. This is explained by the fact that when an atom is excited, one or more electron pairs are depaired, followed by the transition of one electron from each to a free and energetically accessible orbital of a higher sublevel. Such a process is called promotion, and the energy that is spent on this is the promotion energy E prom. For the sulfur atom, in addition to the ground state (2), two excited states S(4) and S(6) are possible due to the transition of one or two electrons, respectively, to the 3d orbitals.
Properties of a covalent bond: saturation, directivity and polarizability.
The saturation of a covalent bond is due to the limited valence capabilities of atoms, i.e. their ability to form a strictly defined number of bonds, which usually ranges from 1 to 6. The total number of valence orbitals in an atom, i.e. those that can be used to form chemical bonds determines the maximum possible covalence of the element. The number of orbitals already used for this determines the covalence of an element in a given compound.
If an atom forms all bonds only due to the pairing of electrons, then one usually speaks simply of its valency, which is determined by the number of one-electron orbitals or the number of unpaired electrons of its atom in the ground or excited state.
The nature of the participation of each type of AO in bond formation (pairing, donor and acceptor functions) is graphically depicted by signs:
Elements of the 2nd period of the periodic system have only 4 valence AOs (one 2S- and three 2P), so their maximum covalence is 4. The number of valence electrons in the atoms of elements located to the left of carbon is less than the number of AOs, and in the atoms of elements located to the right on the contrary, more. Therefore, the former can be acceptors, while the latter can be donors of electron pairs. In its usual valence state, the carbon atom has 4 unpaired electrons, which coincides with the number of valence AOs, so it does not form bonds in the donor-acceptor organism.
The orientation of the covalent bond is the result of the desire of atoms to form the strongest bond due to the highest possible electron density between the nuclei. This is achieved with such a spatial orientation of the overlap of electron clouds, which coincides with their own. The exception is s-electron clouds, since their spherical shape makes all directions equivalent. For p- and d-electron clouds, the overlap is carried out along the axis along which they are extended, and the bond formed in this case is called a δ-bond. The δ bond has axial symmetry, and both atoms can rotate along the bond line, i.e. that imaginary line that passes through the nuclei of chemically bonded atoms. This excludes the possibility of the formation of spatial isomers.
After the formation of a δ bond between two atoms, for the rest of the electron clouds of the same shape and with the same principal quantum number, only the possibility of lateral overlap on both sides of the bond line remains, through which in this case one nodal plane passes. As a result, a π bond is formed. Thus, each multiple bond always contains only one δ-bond. An example would be the nitrogen molecule. The number of δ-bonds that form the central atom in complex molecules or ions determines the value of the coordination number for it. For example, in the NH 3 molecule and the NH 4 + ion for the nitrogen atom, it is equal to three.
The formation of δ-bonds fixes the spatial position of atoms relative to each other, therefore the number of δ-bonds and the angles between the bond lines, which are called valence, determine the spatial geometric configuration of molecules and complex ions, which is reflected in the corresponding geometric models.
The bonds formed by an atom due to orbitals with different values of ℓ must be energetically unequal, which, however, is not confirmed by experiment. The contradiction is eliminated by the idea of hybridization (L. Pauling), according to which, when bonds are formed, orbitals of different symmetry mix and transform into hybrid AOs of the same shape and the same average energy, which ensures the equivalence of the bonds they form. The possibility of hybridization is determined by three conditions:
1. a small difference in the energy of the initial AO, with an increase in this difference, the stability of their hybrid state and the strength of the bonds formed by them decrease;
2. sufficient density of electron clouds, which is determined by the value of the main quantum number;
3. a sufficient degree of overlapping of hybrid AOs with the orbitals of other atoms during the formation of bonds, which fixes the hybrid state and makes it more stable.
The number of hybrid orbitals is equal to the number of original ones. They can be found by the method of linear combination (addition and subtraction) of the initial AO (LCAO). The greater the contribution of the AO to the initial wave function, the more similar the hybrid orbital is to it. The asymmetric shape of hybrid orbitals is due to the fact that, on the one hand, from the nucleus, the electron density increases due to the addition of wave functions with the same signs, and on the other hand, it decreases due to the addition of the same functions with different signs, which is equivalent to their subtraction. This form of hybrid orbitals is beneficial for the formation of stronger bonds.
The relative spatial position of hybrid orbitals in an atom is determined by the charge and spin correlation of electrons, according to which electrons with parallel spins tend to be as far apart as possible from each other, which reduces the repulsive forces and thus lowers the energy of the system. In the case of two hybrid orbitals, their position along one straight line with orientation in opposite directions will be the most energetically favorable, which determines the linear configuration of the corresponding molecules.
Sp 2 hybridization gives three hybrid orbitals, which are directed from the center to the vertices of a regular triangle and the bond angle in this case is 120 0 . Such hybridization of valence orbitals is carried out in BF 3 and BCl 3 molecules.
Four Sp 3 hybrid orbitals δ are directed to the vertices of a regular tetrahedron at an angle of 109 0 . Examples of tetrahedral molecules are CH 4 , CCl 4 and the NH 4 + ion.
Hybridization can involve not only one-electron, but also two-electron AOs. In this case, the number of unshared orbitals remains on the hybrid orbitals, i.e. not taking part in the formation of bonds, electron pairs (EP), which was on the original AO. Free AO and those of the one-electron ones that form π-bonds do not take part in hybridization.
The geometric configuration of molecules is completely determined by the type of hybridization of the orbitals of the central atom only under the condition that all hybrid AOs participate in the formation of bonds. If an unshared electron pair remains on at least one of them, then the configuration determined by the type of hybridization is realized incompletely. So, in the presence of the same type of Sp 3 hybridization, depending on the number of lone pairs, four different geometric configurations of molecules are possible, as shown in Table 2.
table 2
Possible geometric configuration of molecules during Sp 3 - hybridization
Molecules with multiple bonds contain π-bonds, which, without participating in hybridization and without affecting the geometric configuration of molecules, stabilize the hybrid state of atoms. The number of all π bonds in a molecule is equal to the bond multiplicity minus one (one δ bond). The number of δ-bonds is determined by the total sum of single and multiple bonds. So, in the POCI 3 molecule there is one double and three single bonds, therefore it contains 3δ and one π-bond.
To determine the type of hybridization, it is necessary to know the number of hybridizing orbitals of the central atom. It can be found by subtracting from the total number of valence AOs the number of one-electron ones forming π-bonds. In schemes of electronic configurations, they are counted from right to left, since π-bonds form, first of all, α-, and then p-AO. All remaining valence orbitals participate in hybridization.
The presence of unshared electron pairs in molecules affects the magnitude of bond angles. This is due to the fact that the repulsion forces are greater than between relatively fixed binding electron pairs (BPs). According to the decreasing repulsion force, electron pairs can be arranged in the following order:
NP - NP > NP-SP > SP-SP. As a result, the NPs, to a certain extent, put pressure on the bond electron pairs, which leads to some decrease in the bond angle. The greater the number of NPs, the stronger their effect. So, in the NH 3 molecule, one NP reduces the tetrahedral angle (~ 109 0) to 107 0, and in the H 2 O 2NP molecule, it is reduced to 104.5 0. The length of single and double bonds between the central atom and other identical atoms turns out to be the same according to experimental data. This can be explained by the delocalization of π bonds, i.e. their uniform distribution among all bonds, which is indicated in the formulas by a dotted line.
In these cases, the bond multiplicity is expressed as a fractional number, in the sulfate ion it is equal to 1.5. This corresponds to the experimentally found bond length (0.149 nm), which in its value is intermediate between a simple (0.160 nm) and a double (0.143 nm). Simultaneously with the delocalization of π-bonds, the delocalization of charges also occurs, therefore, in oxoacid ions, they are concentrated not on oxygen atoms, but are evenly distributed throughout the volume of the entire ion.
Polarizability is considered on the basis of the notion that a covalent bond can be non-polar (purely covalent) or polar. In the first case, a bond is formed between identical atoms, and the symmetrical distribution of the electron density in the internuclear space leads to the coincidence of the centers of gravity of positive and negative charges. A polar bond is formed when the internuclear electron density shifts to an atom with a higher electronegativity. Then the centers of gravity (+) and (-) of the charges do not coincide and a system (electric dipole) arises of two equal in magnitude, but opposite in sign charges (δ + and δ-), the distance between which is called the length of the dipole ℓ. The degree of polarity of such a connection is estimated by the value of the electric moment of the dipole μ, equal to the product of the absolute charge of the electron (q = 1.60∙10 -19 C) by the length of the dipole: μ = q∙ ℓ. So, if ℓ(Н-СI)=0.022 nm or 22∙10 -12 m, then μ(Н-СI)=1.60∙10 -19 ∙22∙10 -12 = 3.52∙10 -30 C ∙m.
Experimentally, the electric moments of the dipoles are usually determined and the length of the dipole is found from them: ℓ= μ / q.
Dipole moments are vector quantities, i.e. characterized by directivity (conditionally from positive to negative charge).
The electric moments of the dipoles of molecules are determined by the geometric (vector) sum of the moments of the bond dipoles. For example, μ of a linear CO 2 molecule is: μ (CO) + μ (CO) \u003d 0 or for a water molecule in which μ H-O bonds are directed at an angle of 104.5 0, μ \u003d 6.13 ∙ 10 -30 Cl∙m.
The polarizability of a covalent bond is its ability to become polar or more polar under the action of an external electric field. The constant moment of the polar coupling dipole μ n in the electric field becomes larger by the value μ i equal to the time moment of the induced or induced dipole: μ =μ n + μ i .
The role of an external electric field can be played by charged particles that are part of the compound itself (ions or atoms with a large effective charge δ).
The polarizing effect of the ion leads to deformation of the electron shell of its neighbors, which is the greater, the greater their polarizability, i.e. capacity for such deformation. The greater the charge of the ion and the smaller the radius, the greater its polarizing effect and the lower the actual polarizability.
The formation of cations and anions from atoms is accompanied by a decrease and an increase in the radius, respectively. For example, r (Na)= 0.189 and r (Na +)= 0.098 nm; r (Cl)= 0.099 and r (Cl -)= 0.181 nm. These relationships lead to the fact that the interaction of ions is mainly accompanied by polarization of the anion by the cation. For complex anions, due to their large effective radii, the polarizing effect and intrinsic polarizability are relatively small and are usually not taken into account.
According to the increasing strength of the polarizing action, all cations can be grouped into three groups:
1. Cations with a completed stable outer electron layer of the noble gas type;
2. Cations with an incomplete outer electron layer - ions of α-elements (Cr 3+, Fe 2+, Fe 3+, Mn 2+, etc.), ions of p-elements (TI +, Pb 2+, Bi 3+ and others);
3. Cations with an 18-electron layer (Ag + , Zn 2+ , TI 3+ etc.). Some of the ions of the last group, for example Hg 2+, are easily deformed, and then the polarized anion induces a dipole in them, which, in turn, enhances the deformation of the anion's electron shell, which is called the additional polarization effect.
Basic provisions of the VS method.
1. A single chemical bond is formed by two electrons with opposite spins belonging to different atoms. The connection is formed due to the overlap of their wave functions and the formation of a common electron pair. As a result, a zone of increased negative charge appears between the nuclei of atoms, since the residence time of electrons in this region is longer than at other points in the molecular space. The formation of a common electron pair leads to a decrease in the total energy of the system as a whole and the formation of a covalent bond.
2. The connection is oriented in space and is located in the direction where the possibility of overlapping wave functions is maximum.
3. Of the two atomic orbitals, the stronger bond is formed by the one that overlaps more with the orbital of the second atom. The greater the overlap of orbitals, the more energy is released during the formation of a bond, the stronger it is.
Characteristics of a covalent bond.
1. Bond energy E St, kJ/mol.
2. Communication polarity.
3. Bond saturation.
Let's consider them in more detail.
Communication energy.
The resistance of a diatomic molecule to decay into atoms is characterized by the value of its dissociation energy, or the strength of the bond. In a hydrogen molecule, the binding energy is numerically equal to the energy that is released during the formation of an H 2 molecule from H + H = H 2 + 432 kJ atoms. The same energy must be expended to break the bond H 2 = H + H − 432 kJ.
In molecules of composition AB n the successive detachment of the "B" atoms is accompanied by an uneven expenditure of energy.
For example, the energy values (kJ/mol) of successive elimination of hydrogen atoms from a methane molecule differ significantly:
In this case, the C-H bond energy is defined as the average value of the energy expended at all stages: CH 4 =C+4H; ∑=1660kJ/mol;
E(С−Н) = 1660 / 4 = 415 kJ/mol.
The binding energy of a particular pair of atoms, for example C-H, depends on which molecule this pair is included in. However, the changes in this energy in different molecules are small. This confirms the assumption that the electron pairs that bind the atoms are localized between the atoms.
If we compare the C-H bond energies in many molecules, then the average value will be 413 kJ / mol, which is not too different from that calculated for the C-H bond in the CH 4 molecule (415 kJ / mol).
The higher the energy of a chemical bond, the stronger the bond. The bond is considered strong or strong if its energy exceeds 500 kJ/mol (for example, 942 kJ/mol for N 2), weak - if its energy is less than 100 kJ/mol (for example, 69 kJ/mol for NO 2). If during the interaction of atoms an energy of less than 15 kJ/mol is released, then it is considered that a chemical bond is not formed, but an intermolecular interaction is observed (for example, 2 kJ/mol for Xe 2). Bond strength usually decreases with increasing length (Table 4.1).
Table 4.1
Values of bond length and energy for hydrohalic acids
A single bond is always weaker than multiple bonds - double and triple bonds between the same atoms.
Communication polarity
If a covalent bond is formed by two atoms of the same element, then the total electron density is located absolutely symmetrically in the field of both nuclei. If a common pair binds atoms of two different elements, then the electron density is not symmetrical. It is biased towards an atom of a more electronegative element. As a result, an excess (partial) negative charge is induced on this atom, and a partial positive charge is induced on the opposite atom. As a result, two oppositely charged poles are formed in the molecule. The greater the difference in the electronegativity of the atoms, the more polar the bond is.
Polar molecules having positive and negative poles separated in space are called DIPOLES. The distance between the poles in a dipole is called its longitude ( L).
The product of the charge of one of the poles and the length of the dipole is called the dipole moment (Cl∙m).
μ = Z∙L.(4.1)
The dipole moment is a vector quantity. In chemistry, the direction of the dipole moment is taken from the positive pole to the negative. For example, in a hydrogen chloride molecule, excess (+) is concentrated on the hydrogen atom, and excess (-) H δ + → Cl δ - is concentrated on the chlorine atom. For polyatomic molecules, the dipole moment can be calculated as the vector sum of the dipole moments of individual bonds, neglecting their mutual influence. The moments of individual bonds can either reinforce or compensate each other, changing the total moment.
For example, linear BeCl 2 and CO 2 molecules are non-polar. Although each of the bonds is polar. These molecules include the molecules of methane CH 4 and sulfur hexafluoride SF 6, in which the dipole moments of individual bonds
compensate each other and the total dipole moment of the molecule is zero.
In the limiting case, the shared electron pair is completely localized at one of the atoms. As a result, two oppositely charged ions are formed. An atom that has lost an electron turns into a cation (A +), and an atom that captures an alien electron turns into an anion (A -). As a result of the mutual attraction of two oppositely charged particles, an ionic bond arises.
Ionic bond is formed due to electrostatic attraction between particles with charges of the opposite sign, which are formed due to the transfer of one or more electrons from one atom to another. According to Kossel's theory (1916), an atom of any element, entering into a compound, losing or gaining an appropriate number of electrons, seeks to acquire the electron shell of an atom of the nearest (in the Periodic system) noble gas ns 2 or ns 2 np 6. As a result of the addition or loss of electrons, an anion or a cation is formed, respectively.
For example, for an ionic crystal NaCl, the formation of Na ions + and Cl - from neutral atoms shows that the sodium atom loses an electron, and the chlorine atom gains it. As a result, Na + (2 s 2 2p 6 – Ne shell) and Cl - (3 s 2 3p 6 – Ar shell). These ions form a regular three-dimensional structure inside the crystal.
The ions in the crystal are in equilibrium positions, so the forces of Coulomb attraction between them must be compensated by the repulsive forces of their electron shells.
It is known that a perfect ionic bond does not exist. Even in those compounds that are usually referred to as ionic, there is no complete transfer of electrons from one atom to another. Electrons always partially remain in common use.
For example, the bond in lithium fluoride is 80% ionic and 20% covalent. For this reason, it is more correct to speak of the degree of ionicity of a chemical bond.
A dominant ionic bond appears only if the interacting atoms (for example, sodium and chlorine) differ greatly in ionization energies and electron affinities (metal-nonmetal).
The interaction between cations and anions in an ionic crystal does not depend on the direction, so the ionic bond is said to be non-directional. Each cation can attract any number of anions, and vice versa. For this reason, the ionic bond is non-directional and unsaturated, and the number of interactions between ions in the solid state is limited only
crystal sizes. Therefore, the "molecule" of an ionic compound should be considered the entire crystal.
For this reason, ionic crystals are very hard and brittle and have high lattice energies.
If you try to deform the ionic lattice, then one of the layers will shift relative to the other until like-charged ions are too close to each other. This leads to a sharp increase in the repulsive forces, and the lattice is rapidly destroyed.
Communication saturation
A covalent bond is the most common type of chemical bond that occurs in compounds of various types. It is customary to distinguish two possible mechanisms for its formation: the exchange mechanism, when each of the interacting atoms supplies one electron, and the donor-acceptor one, if an electron pair is transferred for common use by one atom (donor) to another atom (acceptor) that has a free electron orbital.
1. Exchange mechanism A ∙ + ∙ B = A : AT
2. Donor-acceptor mechanism A + : B = A : AT
The hydrogen molecule is the simplest possible example of the formation of a covalent bond by the exchange mechanism.
Within the framework of Lewis' ideas about the exchange mechanism, the valency of an element is determined by the number of common electron pairs formed by an atom in a molecule.
In some cases, both electrons during the formation of a covalent bond are supplied by only one of the atoms. It is called donor valence. Once such a bond is formed, it becomes indistinguishable from any other covalent bond. The donor-acceptor bond is realized in many molecules and ions.
During the formation of the ammonium ion NH 4 + and the BF 3 NH 3 molecule, the nitrogen atom in the ammonia molecule NH 3 has a non-bonding 2 S 2 electron pair. Hydrogen ion H + - free 1 S orbital, and the boron atom in the BF 3 molecule is free 2 R orbital.
H++ : NH 3 → H : N H F 3 B + : NH3 → BF3 : NH3
In the NH 4 + ion, the H + ion serves as an acceptor, and in the BF 3 NH 3 molecule, the boron atom (B) serves. The nitrogen atom, which is part of the ammonia molecule, in both cases acts as a donor.
The donor-acceptor interaction between different molecules can be accompanied by the formation of complex compounds:
А1С1 3 + : NH 3 \u003d [A1 (NH 3)] C1 3
The nitrogen atom in NH 3 has a lone pair of electrons and plays the role of a donor, and the A1 atom in the A1C1 3 molecule has a free orbital and plays the role of an acceptor.
All this suggests that the valence of atoms depends not only on the number of unpaired electrons, but also on the presence of vacant orbitals and the number of unshared electron pairs, respectively.
In the NH 4 + ion, all bonds of the central nitrogen atom N-H, despite their different origin, are equivalent and indistinguishable, which clearly proves the same nature of covalent and donor-acceptor bonds.
The bonds formed by the donor-acceptor mechanism are usually formed after the donor atom has used its unpaired electrons to form bonds by the exchange mechanism. This is explained by the fact that during the formation of common electron pairs with the participation of electrons of another atom, the valence level of the donor atom is saturated, while its electronegativity decreases and it more easily gives up its non-bonding pairs for the formation of bonds by the donor-acceptor mechanism.
Free acceptor orbitals are characterized by a very low energy value. This explains their tendency to be filled with electrons according to the donor-acceptor mechanism. Donor-acceptor interaction underlies such processes as the polymerization of some molecules during the transition from a gaseous to a liquid state, the formation of complex compounds, and the hydrolysis of anions.
Direction of communication
The formation of a covalent bond is the result of the overlap of valence electron clouds (AO atomic orbitals), which are characterized by certain orientations in space, and therefore the covalent bond has a strictly defined direction.
The direction of covalent bonds is characterized by valence angles - the angles between the lines connecting the centers of the bonded atoms. By itself, the graphic formula of a molecule or ion does not carry information about bond angles. For example, in the 2− ion, the bond angles between the S-O bonds are equal to 109.5 o, and in the 2− Pd-Cl ion - 90 o; the BF 3 molecule is flat triangular, NF 3 is pyramidal, and C1F 3 has a T-shape, although all three of the last molecules have the composition AF 3.
The combination of bond lengths and bond angles in a molecule determines its spatial equilibrium structure, in which there is an equality of forces
attraction and repulsion, and which provides the optimal spatial structure and the minimum value of the energy of the molecule.
The overlap of atomic orbitals along the line connecting the nuclei of atoms leads to the formation of σ-bonds. Only one σ-bond is possible between two atoms in a chemical particle. All σ-bonds have axial symmetry about the internuclear axis.
Fragments of chemical particles can rotate around the internuclear axis without violating the degree of overlap of atomic orbitals that form σ-bonds.
A set of directed, strictly oriented in space σ - bonds creates a spatial structure of particles.
Rice. 4.2. Schemes of the formation of σ-bonds with the participation of electrons of various types
With additional overlapping of atomic orbitals perpendicular to the line connecting the nuclei of interacting atoms, π-bonds are formed, in which r-r, p - d and d-d-orbitals (Fig. 4.3).
With the appearance of a π-bond that does not have axial symmetry, the free rotation of fragments of a chemical particle around the σ-bond becomes impossible, since it should lead to the rupture of the π-bond.
The number of bonds formed between atoms is called multiplicity, or communication order, and is determined by the number of common electron pairs .
It has been found that the average distance between bonded atoms (bond length) decreases with an increase in the number of shared electron pairs.
Rice. 4.3. Schemes of the formation of π-bonds with the participation of electrons of various types
This is due to the fact that the electron density between two positively charged nuclei increases, as a result of which the attraction between the nuclei also increases, and, consequently, increases binding energy(Table 4.2).
2. As a result of the AO overlap, an electron pair common to two atoms with antiparallel (ie, opposite in sign) spins appears, which provides one chemical bond.
3. In the course of interaction, AOs can undergo hybridization (in this case, GAOs are obtained - hybrid atomic orbitals).
In fact, the MVS is a more perfect version of the theory of covalent bonds. In MVS, a chemical bond can also be formed in two ways:
1. Exchange mechanism
2. Donor-acceptor mechanism
Bonds formed by the same atoms in different ways are absolutely indistinguishable from each other. So, a hydrogen molecule can be obtained both by exchange and by donor-acceptor mechanisms:
The MVS gives a clear and precise interpretation of the concept of valency. Valence- this is the number of AO of a given atom that took part in the overlap with AO of other atoms through the exchange or donor-acceptor mechanisms.
Atoms can form bonds both in the normal (unexcited) state and in the excited state. The transition of an atom to an excited state is associated with a jump of valence electrons from one valence sublevel to another. In this case, an additional number of unpaired electrons appears and the valence possibilities of the atom increase according to the exchange mechanism.
Example: a phosphorus atom in its normal state has an electronic structure 1s 2 2s 2 2p 6 3s 2 3p 3 or [ Ne] 3s 2 3p 3. The valence electrons of phosphorus ( 3s 2 3p 3) are distributed over valence orbitals as follows:
An unexcited phosphorus atom can form 3 bonds by the exchange mechanism and 1 bond by the donor-acceptor mechanism (due to a pair of electrons 3s 2). Therefore, such a phosphorus atom may have a valence of either III or IV.
The excited phosphorus atom ( R *) can form 5 bonds by the exchange mechanism, that is, its valence is V. And, indeed, phosphorus in its compounds exhibits valency III ( PH 3- phosphine), IV ( P- phosphonium ion), V ( H3PO4- phosphoric acid). Other valencies for phosphorus are uncharacteristic.
If atoms do not undergo hybridization in the course of chemical interaction, then the description of the formation of bonds from the positions of MHS is carried out as follows:
a) an orbital diagram of the formation of bonds is compiled;
b) the overlapping of orbitals in space is schematically depicted.
Example: molecule Cl 2 .
This diagram shows that in a molecule Cl2 there is one covalent bond formed by the exchange mechanism. The graphic formula of this molecule is: Cl - Cl.
Spatial structure of the molecule Cl2(shown only 3p- orbitals):
According to the type of orbital overlap, s-bonds, p-bonds and d-bonds are distinguished.
s - bond is formed at the “frontal” overlapping of orbitals, i.e. the AO overlap maximum is on a straight line connecting the atomic nuclei. s - the connection is the strongest. It can be formed by overlapping orbitals of any kind:
In the case of a p-bond, the AO overlap maxima are located in 2 regions lying on a plane passing through the nuclei of atoms:
In the case of a d-bond, the AO overlap maxima are located in 4 regions lying on 2 mutually perpendicular planes passing through the nuclei of atoms. Relationships of this type can only occur when overlapping d- and f- orbitals and have been studied very little.
Attempts to use MVS in the simplest version described above to describe the chemical structure of most molecules consisting of 3 or more atoms were unsuccessful. In many cases, the theory did not match the experimental data at all. To eliminate this contradiction, the theory of hybridization was developed.
Hybridization is a deep rearrangement of AO that occurs when an atom passes from a normal to an excited state. In this case, AOs are converted into GAOs (hybrid atomic orbitals). GAOs differ sharply from the original AOs in terms of energy, shape, and orientation in space. At the same time, GAOs of one atom are absolutely identical in energy and form to each other.
Example : sp 3- hybridization of the carbon atom:
All GAOs are shaped like an asymmetric dumbbell (i.e. extended in one direction). Only the orbitals of the valence sublevels can undergo hybridization. During hybridization from n AO are obtained n GAO. GAO participate in the formation of only s-bonds, and these bonds are stronger than similar s-bonds involving non-hybrid AO.
Currently, about 20 different types of hybridization have been found in various substances. But most often there are 6 types of hybridization:
| Type of hybridization | Mutual location of GAO in space | Structural forms |
| sp | ||
| sp 2 | ||
| sp 3 | ||
| sp 3 d 1 | ||
| sp 3 d 2 | ||
| spd 2 |
The presence of hybridization and its type in one or another atom in a molecule cannot generally be predicted.
To solve this problem unambiguously, in most cases you need to know:
1. How many bonds between each pair of atoms (the first bond is always s - bond, the second and third - p - bonds).
2. What are the bond angles (the angles between bonds) or at least what is the dipole moment of the molecule (the sum of the dipole moments of the bonds).
Example 1 . It is known that the molecule CCl 4 non-polar (½m½ = 0). Angles between bonds C - Cl are the same and equal to 109°28¢. All connections C-Cl identical in length and energy. All these data support the fact that the carbon in this molecule is in the state sp3- hybridization.
So the orbital diagram looks like this:
Spatial structure CCl 4- atoms Cl form a regular shape (tetrahedron). Nothing can be said about the possible hybridization of chlorine atoms, since the initial data is not enough for this.
Example 2 . The H 2 O molecule is polar (çm ç ¹ 0), the angle between the H-O bonds is 105°30¢. Hydrogen cannot hybridize because it has only one valence orbital. Oxygen can be unhybridized (then the angle between the bonds must be 90°) or have one of 3 types of hybridization (others are impossible due to the lack of valence d and f- orbitals): sp- hybridization (bond angle 180°), sp 2- hybridization (120°), sp 3- hybridization (109°28¢).
Since the bond angle in the water molecule is closest to that for the case sp3- hybridization, the orbital diagram of this molecule is as follows:
The bond angle in such a molecule differs from the standard tetrahedral angle (109°28¢) due to the fact that oxygen HAOs are unequal: two of them are binding (take part in the formation of bonds IS HE), and two are non-binding:
The non-bonding atomic orbitals of oxygen strongly repel each other, and this leads to the fact that the bond angle in the water molecule is 5 ° less than the standard for sp 3 - hybridization.
Example 3: Molecule CO 2 non-polar (çm ç = 0). This is quite enough to describe the structure of this molecule. Every connection C - O is polar because the carbon and oxygen atoms are very different in electronegativity. For the molecule as a whole to be nonpolar, it is necessary that the bonds C - O had a bond angle of 180°:
When adding 2 vectors of the same length and opposite in direction, zero is obtained. Angle 180° corresponds to sp-hybridization of the carbon atom. Hence follows the orbital diagram.
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
An 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, – electron spins are antiparallel. Y BUT– 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).
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Rice. 3-4 The dependence of the change in the energy of the molecule and the distribution of the electron density in the hydrogen molecule in the case of describing 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 the electrostatic interaction of electrons and nuclei and depends on the amount of orbital overlap.
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.
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 some distance apart, then in the MVS, when constructing the wave function of the 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 BUT 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; therefore, 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 BUT(I) and the atom AT(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 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 area
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.
