Lecture #6

Molecule energy

atom called the smallest particle chemical element with its chemical properties.

An atom consists of a positively charged nucleus and electrons moving in its field. The charge of the nucleus is equal to the charge of all the electrons. Ion of a given atom is called an electrically charged particle formed by the loss or acquisition of electrons of atoms.

molecule called the smallest particle of a homogeneous substance that has its basic chemical properties.

Molecules consist of identical or different atoms connected by interatomic chemical bonds.

In order to understand the reasons why electrically neutral atoms can form a stable molecule, we will confine ourselves to considering the simplest diatomic molecules, consisting of two identical or different atoms.

The forces that hold an atom in a molecule are caused by the interaction of the outer electrons. The electrons of the inner shells, when atoms are combined into a molecule, remain in the same states.

If the atoms are at a great distance from each other, then they do not interact with each other. When the atoms approach each other, the forces of their mutual attraction increase. At distances comparable to the size of atoms, mutual repulsive forces appear, which do not allow the electrons of one atom to penetrate too deeply into the electron shells of another atom.

Repulsive forces are more "short-range" than attractive forces. This means that as the distance between atoms increases, the repulsive forces decrease faster than the attractive forces.

Graph of attraction force, repulsion force and resulting force of interaction between atoms as a function of distance has the form:

The interaction energy of electrons in a molecule is determined by the mutual arrangement of the nuclei of atoms and is a function of distance, that is

The total energy of the entire molecule also includes the kinetic energy of the moving nuclei.

Hence,

.

This means that is the potential energy of the interaction of nuclei.

Then represents the force of interaction of atoms in a diatomic molecule.

Accordingly, the plot of the dependence of the potential energy of interaction of atoms in a molecule on the distance between atoms has the form:

The equilibrium interatomic distance in a molecule is called bond length. The value D is called dissociation energy of the molecule or connection energy. It is numerically equal to the work that must be done in order to break the chemical bonds of atoms into molecules and remove them beyond the action of interatomic forces. The dissociation energy is equal to the energy released during the formation of the molecule, but opposite in sign. The dissociation energy is negative, and the energy released during the formation of a molecule is positive.

The energy of a molecule depends on the nature of the motion of the nuclei. This movement can be divided into translational, rotational and oscillatory. At small distances between atoms in a molecule and a sufficiently large volume of the vessel provided to the molecules, translational energy has a continuous spectrum and its mean value is , that is .

Energy rotary motion has a discrete spectrum and can take the values

,

where I is the rotational quantum number;

J is the moment of inertia of the molecule.

Energy oscillatory motion also has a discrete spectrum and can take the values

,

where is the vibrational quantum number;

is the natural frequency of this type of vibration.

At , the lowest vibrational level has zero energy

The energy of rotational and translational motion corresponds to the kinetic form of energy, the energy of oscillatory motion - potential. Therefore, the energy steps of the vibrational motion of a diatomic molecule can be represented in a dependence plot.

The energy steps of the rotational motion of a diatomic molecule are similarly located, only the distance between them is much smaller than that of the same steps of the vibrational motion.

The main types of interatomic bond

There are two types of atomic bonds: ionic (or heteropolar) and covalent (or homeopolar).

Ionic bond occurs when the electrons in the molecule are arranged in such a way that an excess is formed near one of the nuclei, and their deficiency near the other. Thus, the molecule, as it were, consists of two ions of opposite signs, attracted to each other. An example of an ionically bonded molecule is NaCl, KCl, RbF, CsJ etc. formed by the combination of atoms of elements I-oh and VII-th group periodic system Mendeleev. In this case, an atom that has attached one or more electrons to itself acquires a negative charge and becomes a negative ion, and an atom that gives up the corresponding number of electrons turns into a positive ion. The total sum of the positive and negative charges of the ions is zero. Therefore, ionic molecules are electrically neutral. The forces that ensure the stability of the molecule are of an electrical nature.

In order for the ionic bond to be realized, it is necessary that the energy of electron detachment, that is, the work of creating a positive ion, would be less than the sum of the energy released during the formation of negative ions and the energy of their mutual attraction.

It is quite obvious that the formation of a positive ion from a neutral atom requires the least amount of work in the case when the detachment of electrons located in the electron shell that has begun to build up occurs.

On the other hand, the greatest energy is released when an electron is attached to halogen atoms, which lack one electron to fill the electron shell. Therefore, an ionic bond is formed in such a transfer of electrons that leads to the creation of filled electron shells in the formed ions.

Another type of connection is covalent bond.

In the formation of molecules consisting of identical atoms, the appearance of oppositely charged ions is impossible. Therefore, ionic bonding is impossible. However, in nature there are substances whose molecules are formed from identical atoms. H 2, O 2, N 2 etc. Bonding in substances of this type is called covalent or homeopolar(homeo - different [Greek]). In addition, a covalent bond is also observed in molecules with different atoms: hydrogen fluoride HF, nitric oxide NO, methane CH 4 etc.

The nature of the covalent bond can only be explained on the basis of quantum mechanics. The quantum mechanical explanation is based on the wave nature of the electron. The wave function of the outer electrons of an atom does not break off abruptly with increasing distance from the center of the atom, but gradually decreases. When the atoms approach each other, the blurred electron clouds of the outer electrons partially overlap, which leads to their deformation. Accurate calculation of the change in the state of electrons requires solving the Schrödinger wave equation for the system of all particles participating in the interaction. The complexity and cumbersomeness of this path force us to confine ourselves here to a qualitative consideration of phenomena.

In the simplest case s- state of the electron, the electron cloud is a sphere of some radius. If both electrons in a covalent molecule are exchanged so that electron 1, which previously belonged to the nucleus " A", will move to the place of electron 2, which belonged to the nucleus" b", and electron 2 will make the reverse transition, then nothing will change in the state of the covalent molecule.

The Pauli principle allows the existence of two electrons in the same state with oppositely directed spins. The merging of regions where both electrons can be means the appearance between them of a special quantum mechanical exchange interaction. In this case, each of the electrons in the molecule can alternately belong to one or the other nucleus.

As the calculation shows, the exchange energy of a molecule is positive if the spins of the interacting electrons are parallel, and negative if they are not parallel.

So, the covalent type of bond is provided by a pair of electrons with opposite spins. If in ionic communication it was about the transfer of electrons from one atom to another, then here communication is carried out by generalizing electrons and creating a common space for their movement.

Molecular spectra

Molecular spectra are very different from atomic ones. While atomic spectra are made up of single lines, molecular spectra are made up of bands that are sharp at one end and blurry at the other. Therefore, molecular spectra are also called striped spectra.

Bands in molecular spectra are observed in the infrared, visible and ultraviolet frequency ranges of electromagnetic waves. In this case, the stripes are arranged in a certain sequence, forming a series of stripes. There are a number of series in the spectrum.

Quantum mechanics gives an explanation of the nature of molecular spectra. The theoretical interpretation of the spectra of polyatomic molecules is very complicated. We confine ourselves to considering only diatomic molecules.

Earlier we noted that the energy of a molecule depends on the nature of the motion of the nuclei of atoms and identified three types of this energy: translational, rotational and vibrational. In addition, the energy of a molecule is also determined by the nature of the movement of electrons. This type of energy is called electronic energy and is a component of the total energy of the molecule.

Thus, the total energy of the molecule is:

A change in the translational energy cannot lead to the appearance of a spectral line in the molecular spectrum; therefore, we will exclude this type of energy in the further consideration of molecular spectra. Then

According to the Bohr frequency rule ( III– Bohr postulate) the frequency of a quantum emitted by a molecule when its energy state changes is equal to

.

Experience and theoretical studies showed that

Therefore, with weak excitations, only changes , with stronger - , with even stronger - . Let's discuss in more detail different kinds molecular spectra.

Rotational spectrum of molecules

Let's begin to investigate the absorption of electromagnetic waves from small portions of energy. Until the value of the energy quantum becomes equal to the distance between the two nearest levels, the molecule will not absorb. Gradually increasing the frequency, we will reach the quanta capable of lifting the molecule from one rotational step to another. This occurs in the region of infrared waves of the order of 0.1 -1 mm.

,

where and are the values ​​of the rotational quantum number at the -th and -th energy levels.

Rotational quantum numbers and can have the values ​​, i.e. their possible changes are limited by the selection rule

The absorption of a quantum by a molecule transfers it from one rotational energy level to another, higher one, and leads to the appearance of a spectral line of the rotational absorption spectrum. As the wavelength decreases (i.e., the number changes), more and more new lines of the absorption spectrum appear in this region. The totality of all lines gives an idea of ​​the distribution of the rotational energy states of the molecule.

So far we have considered the absorption spectrum of a molecule. The emission spectrum of the molecule is also possible. The appearance of lines of the rotational emission spectrum is associated with the transition of the molecule from the upper rotational energy level to the lower one.

Rotational spectra make it possible to determine interatomic distances in simple molecules with great accuracy. Knowing the moment of inertia and the masses of atoms, it is possible to determine the distances between atoms. For a diatomic molecule

Vibrational-rotational spectrum of molecules

Absorption by a substance of electromagnetic waves in the infrared region with a wavelength of microns causes transitions between vibrational energy levels and leads to the appearance of a vibrational spectrum of the molecule. However, when the vibrational energy levels of a molecule change, its rotational energy states also change simultaneously. Transitions between two vibrational energy levels are accompanied by a change in rotational energy states. In this case, a vibrational-rotational spectrum of the molecule arises.

If a molecule oscillates and rotates at the same time, then its energy will be determined by two quantum numbers And :

.

Taking into account the selection rules for both quantum numbers, we obtain the following formula for the frequencies of the vibrational-rotational spectrum (the previous formula /h and discard the previous energy level, i.e., the terms in brackets):

.

In this case, the sign (+) corresponds to transitions from a lower to a higher rotational level, and the sign (-) corresponds to the reverse position. The vibrational part of the frequency determines the spectral region in which the band is located; the rotational part determines the fine structure of the strip, i.e. splitting of individual spectral lines.

According to classical concepts, the rotation or vibration of a diatomic molecule can lead to the emission of electromagnetic waves only if the molecule has a nonzero dipole moment. This condition is satisfied only for molecules formed by two different atoms, i.e. for unsymmetrical molecules.

A symmetrical molecule formed by identical atoms has a dipole moment equal to zero. Therefore, according to classical electrodynamics, vibration and rotation of such a molecule cannot cause radiation. Quantum theory leads to a similar result.

Electronic vibrational spectrum of molecules

Absorption of electromagnetic waves in the visible and ultraviolet range leads to transitions of the molecule between different electronic energy levels, i.e. to the appearance of the electronic spectrum of the molecule. Each electronic energy level corresponds to a certain spatial distribution of electrons, or, as they say, a certain configuration of electrons, which has a discrete energy. Each configuration of electrons corresponds to a set of vibrational energy levels.

The transition between two electronic levels is accompanied by many accompanying transitions between vibrational levels. This is how the electronic-vibrational spectrum of the molecule arises, which consists of groups of close lines.

A system of rotational levels is superimposed on each vibrational energy state. Therefore, the frequency of a photon during an electronic-vibrational transition will be determined by a change in all three types of energy:

.

Frequency - determines the position of the spectrum.

The entire electronic-vibrational spectrum is a system of several groups of bands, often overlapping each other and forming a wide band.

The study and interpretation of molecular spectra allows you to understand the detailed structure of molecules and is widely used for chemical analysis.

Raman scattering of light

This phenomenon consists in the fact that in the scattering spectrum that occurs when light passes through gases, liquids or transparent crystalline bodies, along with light scattering with a constant frequency, a number of higher or lower frequencies appear, corresponding to the frequencies of vibrational or rotational transitions that scatter molecules.

The Raman scattering phenomenon has a simple quantum mechanical explanation. The process of light scattering by molecules can be considered as an inelastic collision of photons with molecules. When colliding, a photon can give or receive from a molecule only such amounts of energy that are equal to the differences between its two energy levels. If, upon collision with a photon, a molecule passes from a state with a lower energy to a state with a higher energy, then it loses its energy and its frequency decreases. This creates a line in the spectrum of the molecule, shifted relative to the main line towards longer wavelengths. If, after a collision with a photon, a molecule passes from a state with a higher energy to a state with a lower energy, a line is created in the spectrum that is shifted relative to the main one towards shorter wavelengths.

The study of Raman scattering provides information about the structure of molecules. Using this method, the natural vibration frequencies of molecules are easily and quickly determined. It also allows one to judge the nature of the symmetry of the molecule.

Luminescence

If the molecules of a substance can be brought into an excited state without increasing their average kinetic energy, i.e. without heating, then there is a glow of these bodies or luminescence.

There are two types of luminescence: fluorescence And phosphorescence.

Fluorescence called luminescence, immediately ceasing after the end of the action of the exciter of the glow.

During fluorescence, a spontaneous transition of molecules from an excited state to a lower level occurs. This type of glow has a very short duration (about 10 -7 sec.).

Phosphorescence is called luminescence long time after the action of the exciter.

During phosphorescence, the molecule passes from an excited state to a metastable state. Metastable a level is called, the transition from which to a lower level is unlikely. In this case, radiation can occur if the molecule returns to the excited level again.

The transition from a metastable state to an excited one is possible only in the presence of additional excitation. The temperature of the substance can be such an additional exciter. At high temperatures this transition occurs quickly, at low temperatures it is slow.

As we have already noted, luminescence under the action of light is called photoluminescence, under the influence of electron bombardment - cathodoluminescence, under the action of an electric field - electroluminescence, under the influence of chemical transformations - chemiluminescence.

Quantum amplifiers and radiation generators

In the mid-1950s, the rapid development of quantum electronics began. In 1954, the works of academicians N.G. Basov and A.M. Prokhorov, who described a quantum generator of ultrashort radio waves in the centimeter range, called maser(microware amplification by stimulated emission of radiation). A series of generators and light amplifiers in the visible and infrared regions, which appeared in the 60s, was called optical quantum generators or lasers(light amplification by stimulated emission of radiation).

Both types of devices work on the basis of the effect of stimulated or induced radiation.

Let us dwell on this type of radiation in more detail.

This type of radiation is the result of the interaction of an electromagnetic wave with the atoms of the substance through which the wave passes.

In atoms, transitions from higher energy levels to lower ones are carried out spontaneously (or spontaneously). However, under the action of incident radiation, such transitions are possible both in the forward and in the reverse direction. These transitions are called forced or induced. In a forced transition from one of the excited levels to a low energy level, a photon is emitted by the atom, additional to the photon under which the transition was made.

In this case, the direction of propagation of this photon and, consequently, of the entire stimulated radiation coincides with the direction of propagation of the external radiation that caused the transition, i.e. stimulated emission is strictly coherent with the stimulated emission.

Thus, a new photon resulting from stimulated emission amplifies the light passing through the medium. However, simultaneously with the induced emission, the process of light absorption occurs, because a photon of excitatory radiation is absorbed by an atom at a low energy level, while the atom goes to a higher energy level. And

The process of transferring the medium to the inverse state is called pumped amplifying medium. There are many methods for pumping an amplifying medium. The simplest of them is the optical pumping of the medium, in which atoms are transferred from the lower level to the upper excited level by irradiating light of such a frequency that .

In a medium with an inverted state, stimulated emission exceeds the absorption of light by atoms, as a result of which the incident light beam will be amplified.

Consider a device using such media, used as a wave generator in the optical range or laser.

Its main part is a crystal of artificial ruby, which is an aluminum oxide in which some aluminum atoms are replaced by chromium atoms. When a ruby ​​crystal is irradiated with light of a wavelength of 5600, chromium ions pass to the upper energy level.

The reverse transition to the ground state occurs in two stages. At the first stage, excited ions give up part of their energy to the crystal lattice and pass into a metastable state. At this level, the ions are longer than at the top. As a result, the inverse state of the metastable level is achieved.

The return of ions to the ground state is accompanied by the emission of two red lines: and . This return occurs like an avalanche under the action of photons of the same wavelength, i.e. with stimulated emission. This return occurs much faster than with spontaneous emission, so light amplification occurs.

The ruby ​​used in the laser has the form of a rod with a diameter of 0.5 cm and a length of 4-5 cm. The entire ruby ​​rod is located near a pulsed electron tube, which is used to optically pump the medium. Photons whose directions of motion form small angles with the ruby ​​axis experience multiple reflections from its ends.

Therefore, their path in the crystal will be very long, and photon cascades in this direction will be most developed.

Photons emitted spontaneously in other directions exit the crystal through its side surface without causing further radiation.

When the axial beam becomes sufficiently intense, a part of it emerges through the translucent end of the crystal to the outside.

A large amount of heat is released inside the crystal. Therefore, it has to be intensively cooled.

Laser radiation has a number of features. It is characterized by:

1. temporal and spatial coherence;

2. strict monochromaticity;

3. big power;

4. narrowness of the beam.

The high coherence of radiation opens up broad prospects for the use of lasers for radio communications, in particular, for directional radio communications in space. If a way can be found to modulate and demodulate light, it will be possible to transmit a huge amount of information. Thus, in terms of the amount of information transmitted, one laser could replace the entire communication system between the east and west coasts of the United States.

The angular width of the laser beam is so small that, using telescopic focusing, a spot of light with a diameter of 3 km can be obtained on the lunar surface. The high power and narrowness of the beam makes it possible, when focusing with a lens, to obtain an energy flux density 1000 times higher than the energy flux density that can be obtained by focusing sunlight. Such beams of light can be used for machining and welding, to influence the course chemical reactions etc.

The foregoing far from exhausts all the possibilities of the laser. It is a completely new type of light source and it is still difficult to imagine all the possible areas of its application.

In addition to the spectra corresponding to the radiation of individual atoms, there are also spectra emitted by whole molecules (§ 61). Molecular spectra are much more diverse and more complex in structure than atomic spectra. There are thickening sequences of lines, similar to the spectral series of atoms, but with a different frequency law and with lines so closely spaced that they merge into continuous bands (Fig. 279). In view of the peculiar nature of these spectra, they are called striped.

Rice. 279. Striped Spectrum

Along with this, sequences of equidistant spectral lines and, finally, multi-line spectra are observed, in which, at first glance, it is difficult to establish any regularities (Fig. 280). It should be noted that in the study of the spectrum of hydrogen, we always have a superposition of the molecular spectrum of Ha on the atomic spectrum, and special measures must be taken to increase the intensity of the lines emitted by individual hydrogen atoms.

Rice. 280. Molecular spectrum of hydrogen

From a quantum point of view, just as in the case atomic spectra, each line of the molecular spectrum is emitted during the transition of the molecule from one stationary energy level to another. But in the case of a molecule, there are many more factors on which the energy of the stationary state depends.

In the simplest case of a diatomic molecule, the energy consists of three parts: 1) the energy of the electron shell of the molecule; 2) vibrational energies of the nuclei of atoms that make up the molecule along the straight line connecting them; 3) the energy of rotation of nuclei around a common center of mass. All three types of energy are quantized, that is, they can only take on a discrete range of values. The electron shell of a molecule is formed as a result of the fusion of the electron shells of the atoms that make up the molecule. Energy electronic states of molecules can be considered as a limiting case

a very strong Stark effect caused by the interatomic interaction of atoms that form a molecule. Although the forces that bind atoms into molecules are purely electrostatic in nature, correct understanding chemical bonding turned out to be possible only within the framework of modern wave-mechanical quantum theory.

There are two types of molecules: homeopolar and heteropolar. Homeopolar molecules with increasing distance between the nuclei break up into neutral parts. Hemopolar molecules include molecules. Heteropolar molecules decompose into positive and negative ions as the distance between the nuclei increases. A typical example heteropolar molecules are molecules of salts, e.g. previous ed. § 21 and 24).

The energy states of the electron cloud of a homeopolar molecule are largely determined by the wave properties of the electrons.

Consider a very rough model of the simplest molecule (an ionized hydrogen molecule representing two potential "wells" located at a close distance from each other and separated by a "barrier" (Fig. 281).

Rice. 281. Two potential wells.

Rice. 282. Wave functions of an electron in the case of distant "holes".

Each of the "pits" depicts one of the atoms that make up the molecule. With a large distance between atoms, the electron in each of them has quantized energy values ​​corresponding to standing electron waves in each of the "wells" separately (§ 63). On fig. 282, a and b depict two identical wave functions describing the state of electrons in isolated atoms. These wave functions correspond to the same energy level.

As the atoms approach the molecule, the "barrier" between the "pits" becomes "transparent" (§ 63), because its width becomes commensurate with the length of the electron wave. As a result of this, there

the exchange of electrons between atoms through the "barrier", and it makes no sense to talk about the belonging of an electron to one or another atom.

The wave function can now have two forms: c and d (Fig. 283). Case c can be approximately considered as the result of the addition of curves a and b (Fig. 282), the case as the difference between a and b, but the energies corresponding to states c and d are no longer exactly equal to each other. The energy of the state is somewhat less than the energy of the state. Thus, two molecular electronic levels arise from each atomic level.

Rice. 283. Wave functions of an electron in the case of close "holes".

Until now, we have been talking about the ion of the hydrogen molecule, which has one electron. There are two electrons in a neutral hydrogen molecule, which leads to the need to take into account the mutual arrangement of their spins. In accordance with the Pauli principle, electrons with parallel spins seem to “avoid” each other, so the probability density of finding each electron is distributed according to Fig. 284, a, i.e., electrons are most often located outside the gap between the nuclei. Therefore, with parallel spins, a stable molecule cannot form. On the contrary, antiparallel spins correspond to the highest probability of finding both electrons inside the gap between the nuclei (Fig. 294, b). In this case, the negative electron charge attracts both positive nuclei to itself, and the whole system as a whole forms a stable molecule.

For heteropolar molecules, the pattern of electron charge density distribution has a much more classical character. An excess of electrons is grouped around one of the nuclei, and around the other, on the contrary, there is a shortage of electrons. Thus, two ions are formed in the composition of the molecule, positive and negative, which are attracted to each other: in, for example, and

The symbolism of the electronic states of molecules has many similarities with the atomic symbolism. Naturally, the main role in the molecule is played by the direction of the axis connecting the nuclei. Here the quantum number A is introduced, analogous to I in the atom. The quantum number characterizes the absolute value of the projection onto the axis of the molecule of the resulting orbital momentum of the electron cloud of the molecule.

There is a correspondence between the meanings and symbols of molecular electronic states, similar to that in atoms (§ 67):

The absolute value of the projection of the resulting spin of the electron cloud on the axis of the molecule is characterized by the quantum number 2, and the projection of the total rotational momentum of the electron shell is characterized by the quantum number. Obviously,

The quantum number is analogous to the internal quantum number of the atom (§ 59 and 67).

Rice. 284. Probability density of finding an electron at various points of a molecule.

Like atoms, molecules exhibit multiplicity caused by different orientations of the resulting spin with respect to the resulting orbital momentum.

Given these circumstances, the electronic states of molecules are written as follows:

where 5 is the value of the resulting spin, and means one of the symbols or A corresponding to different meanings quantum number A. For example, the normal state of the hydrogen molecule is 2, the normal state of the hydroxyl molecule is the normal state of the oxygen molecule is . During transitions between different electronic states, selection rules take place: .

The vibrational energy of a molecule associated with vibrations of nuclei is quantized based on the wave properties of nuclei. Assuming that the nuclei in a molecule are bound by a quasi-elastic force (the potential energy of a particle is proportional to the square of the displacement, § 63), we obtain from the Schrödinger equation the following permitted values ​​of the vibrational energy of this system (harmonic

oscillator):

where is the frequency of natural oscillations of the nuclei, determined as usual (Vol. I, § 57, 1959; in the previous ed. § 67):

where is the reduced mass of nuclei; the masses of both nuclei; quasi-elastic constant of the molecule; quantum number equal to Due to the large size of the mass, the frequency lies in the infrared region of the spectrum.

Rice. 285. Vibrational energy levels of a molecule.

The quasi-elastic constant depends on the configuration of the electron shell and is therefore different for different electronic states of the molecule. This constant is the greater, the stronger the molecule, i.e., the stronger the chemical bond.

Formula (3) corresponds to a system of equally spaced energy levels, the distance between which is equal to In fact, at large amplitudes of oscillations of the nuclei, deviations of the restoring force from Hooke's law already begin to affect. As a result, the energy levels are approaching (Fig. 285). At sufficiently large amplitudes, the dissociation of the molecule into parts occurs.

For a harmonic oscillator, transitions are allowed only at , which corresponds to the emission or absorption of frequency light. Due to deviations from harmonicity, transitions appear corresponding to

According to the quantum condition for frequencies (§ 58), overtones should appear in this case, which is observed in the spectra of molecules.

Vibrational energy is a relatively small addition to the energy of the electron cloud of the molecule. Vibrations of the nuclei lead to the fact that each electronic level is converted into a system of close levels corresponding to different values ​​of vibrational energy (Fig. 286). This does not exhaust the complexity of the system of energy levels of the molecule.

Rice. 286. Addition of vibrational and electronic energy of a molecule.

It is also necessary to take into account the smallest component of molecular energy - rotational energy. Permissible values ​​of rotational energy are determined, according to wave mechanics, based on the principle of torque quantization.

According to wave mechanics, the torque (§ 59) of any quantized system is equal to

In this case, replaces and is equal to 0, 1, 2, 3, etc.

Kinetic energy of a rotating body in prev. ed. § 42) will

where is the moment of inertia, w is the angular velocity of rotation.

But, on the other hand, the torque is equal. From here we get:

or, substituting expression (5) instead, we finally find:

On fig. 287 shows the rotational levels of the molecule; in contrast to vibrational and atomic levels, the distance between rotational levels increases with increasing transitions between rotational levels are allowed, while lines with frequencies are emitted

where Evrash corresponds corresponds

Formula (9) gives for frequencies

Rice. 287. Levels of rotational energy of a molecule.

We get equidistant spectral lines lying in the far infrared part of the spectrum. Measurement of the frequencies of these lines makes it possible to determine the moment of inertia of the molecule. It turned out that the moments of inertia of the molecules are of the order of magnitude.

centrifugal force increases with increasing speed of rotation of the molecule. The presence of rotations leads to the splitting of each vibrational energy level into a number of close sublevels corresponding to different values ​​of the rotational energy.

During the transitions of a molecule from one energy state to another, all three types of energy of the molecule can change simultaneously (Fig. 288). As a result, each spectral line that would be emitted during an electronic-vibrational transition acquires a fine rotational structure and turns into a typical molecular band.

Rice. 288. Simultaneous change of all three types of energy of a molecule

Such bands of equidistant lines are observed in vapors and water and lie in the far infrared part of the spectrum. They are observed not in the emission spectrum of these vapors, but in their absorption spectrum, because the frequencies corresponding to the natural frequencies of the molecules are absorbed more strongly than the others. On fig. 289 shows a band in the absorption spectrum of vapors in the near infrared region. This band corresponds to transitions between energy states that differ not only in the energy of rotation, but also in the energy of vibrations (at a constant energy of the electron shells). In this case, and and Ekol change simultaneously, which leads to large changes in energy, i.e., the spectral lines have a higher frequency than in the first case considered.

In accordance with this, lines appear in the spectrum that lie in the near infrared part, similar to those shown in Fig. 289.

Rice. 289. Absorption band.

The center of the band (corresponds to the transition at a constant Evrach; according to the selection rule, such frequencies are not emitted by the molecule. Lines with higher frequencies - shorter wavelengths - correspond to transitions in which the change in Europax is added to the change. Lines with lower frequencies (right side) correspond to the inverse relation: change rotational energy has the opposite sign.

Along with such bands, bands are observed corresponding to transitions with a change in the moment of inertia but with. In this case, according to formula (9), the line frequencies should depend on and the distances between the lines become unequal. Each stripe consists of a series of lines, thickening towards one edge,

which is called the strip head. As early as 1885, Delandre gave the following empirical formula for the frequency of an individual spectral line that is part of the band:

where is an integer.

The Delandre formula follows directly from the above considerations. The Delandre formula can be depicted graphically if one plots along one axis and along the other (Fig. 290).

Rice. 290. Graphic representation of the Delandre formula.

The corresponding lines are shown below, forming, as we see, a typical strip. Since the structure of the molecular spectrum strongly depends on the moment of inertia of the molecule, the study of molecular spectra is one of the reliable methods for determining this quantity. The slightest changes in the structure of a molecule can be detected by studying its spectrum. The most interesting circumstance is that molecules containing different isotopes (§ 86) of the same element must have different lines in their spectrum corresponding to different masses of these isotopes. This follows from the fact that the masses of atoms determine both the frequency of their oscillations in the molecule and its moment of inertia. Indeed, the lines of copper chloride bands consist of four components, respectively, to four combinations of copper isotopes 63 and 65 with chlorine isotopes 35 and 37:

Lines corresponding to molecules containing a heavy isotope of hydrogen were also found, despite the fact that the concentration of the isotope in ordinary hydrogen is

In addition to the mass of nuclei, other properties of nuclei also affect the structures of molecular spectra. In particular, the rotational moments (spins) of the nuclei play a very important role. If in a molecule consisting of identical atoms, the rotational moments of the nuclei are equal to zero, every second line of the rotational band falls out. Such an effect, for example, is observed in the molecule

If the angular moments of the nuclei are nonzero, they can cause an alternation of intensities in the rotational band, weak lines will alternate with strong ones.)

Finally, using the methods of radio spectroscopy, it was possible to detect and accurately measure the hyperfine structure of molecular spectra, related to the quadrupole electric moment of the nuclei.

The quadrupole electric moment arises as a result of the deviation of the shape of the nucleus from the spherical one. The nucleus may be in the form of an elongated or flattened ellipsoid of revolution. Such a charged ellipsoid can no longer be replaced by a simple point charge placed in the center of the nucleus.

Rice. 291. Absorbing device of "atomic" clocks: 1 - a rectangular waveguide with a cross-section of length closed on both sides by gas-tight bulkheads 7 and filled with ammonia at low pressure;

2 - crystal diode, which creates harmonics of the high-frequency voltage supplied to it; 3 - output crystal diode; 4 - generator of frequency-modulated high-frequency voltage; 5 - pipeline to the vacuum pump and ammonia gas holder; 6 - output to a pulse amplifier; 7 - bulkheads; And - indicator of the current of the crystal diode; B - vacuum gauge.

In addition to the Coulomb force, an additional force appears in the field of the nucleus, which is inversely proportional to the fourth power of the distance and depends on the angle with the direction of the symmetry axis of the nucleus. The appearance of an additional force is associated with the presence of a quadrupole moment at the nucleus.

For the first time, the presence of a quadrupole moment in the nucleus was established by conventional spectroscopy using certain details of the hyperfine structure of atomic lines. But these methods did not make it possible to accurately determine the magnitude of the moment.

In the radiospectroscopic method, the waveguide is filled with the investigated molecular gas and the absorption of radio waves in the gas is measured. The use of klystrons to generate radio waves makes it possible to obtain oscillations with a high degree of monochromaticity, which are then modulated. The absorption spectrum of ammonia in the region of centimeter waves was studied in particular detail. In this spectrum, a hyperfine structure was found, which is explained by the presence of a relationship between the quadrupole moment of the nucleus and electric field the molecule itself.

The fundamental advantage of radio spectroscopy is the low energy of photons corresponding to radio frequencies. Due to this, by the absorption of radio frequencies, it is possible to detect transitions between extremely close energy levels of atoms and molecules. In addition to nuclear effects, the method of radiospectroscopy is very convenient for determining the electric dipole moments of the entire molecule from the Stark effect of molecular lines in weak electric fields.

fields. Behind last years a huge number of works appeared devoted to the radiospectroscopic method of studying the structure of various molecules. The absorption of radio waves in ammonia was used to build ultra-precise "atomic" clocks (Fig. 291).

The duration of the astronomical day slowly increases and, in addition, fluctuates within the limits. It is desirable to build clocks with a more uniform course. "Atomic" clock is a quartz generator of radio waves with a frequency controlled by the absorption of the generated waves in ammonia. At a wavelength of 1.25 cm resonance occurs with the natural frequency of the ammonia molecule, which corresponds to a very sharp absorption line. The slightest deviation of the generator wavelength from this value breaks the resonance and leads to a strong increase in the transparency of the gas for radio emission, which is recorded by the appropriate equipment and activates the automation that restores the frequency of the generator. "Atomic" clocks have already given a course more uniform than the rotation of the Earth. It is assumed that it will be possible to achieve an accuracy of the order of fractions of a day.

MOLECULAR SPECTRA

Emission, absorption, and Raman scattering (Raman) spectra of free or weakly bonded molecules. Typical M. pages - striped, they are observed in the form of a set of more or less narrow bands in the UV, visible and IR regions of the spectrum; with sufficient resolution of spectral instruments pier. the stripes break up into a set of closely spaced lines. M.'s structure with. different for diff. molecules and becomes more complex with an increase in the number of atoms in the molecule. The visible and UV spectra of very complex molecules are similar and consist of a few broad continuous bands. M. s. arise during quantum transitions between energy levels?" and?" molecules according to the ratio:

where hv is the energy of an emitted or absorbed photon of frequency v. For Raman, hv is equal to the difference between the energies of the incident and scattered photons. M. s. much more complicated than atomic spectra, which is determined by the greater complexity of the internal. movements in the molecule, because in addition to the movement of electrons relative to two or more nuclei in the molecule, there is an oscillation. the movement of the nuclei (together with the internal elements surrounding them) about the equilibrium position and rotate. its movement as a whole. Electronic, oscillating and rotate. the movements of the molecule correspond to three types of energy levels? el,?

According to quant. mechanics, the energy of all types of motion in a molecule can only take on certain values ​​(quantized). What is the total energy of the molecule? approximately can be represented as a sum of quantized energy values ​​corresponding to three types of its internal. movements:

?? el +? count +? vr, (2) and in order of magnitude

El:?col:?vr = 1: ?m/M:m/M, (3)

where m is the mass of the electron, and M has the order of the mass of the nuclei of atoms in the molecule, i.e.

El -> ?count ->?vr. (4) Usually? e order several. eV (hundreds of kJ/mol), ?col = 10-2-10-1 eV, ?vr = 10-5-10-3 eV.

The system of energy levels of a molecule is characterized by sets of electronic energy levels far apart from each other (dec. ?el at?col=?vr=0). vibrational levels located much closer to each other (diff. ?col at a given?el and?rot=0) and rotational levels even closer to each other (values?rot at given?el and?col).

Electronic energy levels a to b in fig. 1 correspond to the equilibrium configurations of the molecule. Each electronic state corresponds to a certain equilibrium configuration and a certain value? el; smallest value corresponds to the main electronic state (basic electronic energy level of the molecule).

Rice. 1. Scheme of energy levels of a diatomic molecule, a and b - electronic levels; v" and v" - quantum. number of fluctuations. levels; J" and J" - quantum. rotation numbers. levels.

The set of electronic states of a molecule is determined by the St. you of its electronic shell. In principle, the values ​​\u200b\u200bof el can be calculated by quantum methods. chemistry, but this problem can be solved only approximately and for relatively simple molecules. Important information about the electronic levels of molecules (their location and their characteristics), determined by its chemical. a structure, receive, studying M. with.

A very important characteristic of the electronic energy level is the value of the quantum number 5, which determines abs. the value of the total spin moment of all e-new. Chemically stable molecules have, as a rule, an even number of electrons, and for them 5 = 0, 1, 2, . . .; for the main electronic level typically 5=0, for excited - 5=0 and 5=1. Levels with S=0 naz. singlet, with S=1 - triplet (because their multiplicity is c=2S+1=3).

In the case of diatomic and linear triatomic molecules, the electronic levels are characterized by the quantum value. number L, defining abs. the value of the projection of the total orbital momentum of all electrons onto the axis of the molecule. Levels with L=0, 1, 2, ... are denoted respectively by S, P, D, . . ., and and is indicated by the index at the top left (eg, 3S, 2П). For molecules with a center of symmetry (for example, CO2, CH6), all electronic levels are divided into even and odd (g and u, respectively) depending on whether the wave function that determines them retains its sign or not when reversing at the center of symmetry.

Vibrational energy levels can be found by quantizing the vibrations. movements, which are approximately considered harmonic. A diatomic molecule (one vibrational degree of freedom corresponding to a change in the internuclear distance r) can be considered as a harmonic. oscillator, quantization of which gives equidistant energy levels:

where v - main. harmonic frequency vibrations of the molecule, v=0, 1, 2, . . .- oscillate. quantum. number.

For each electronic state of a polyatomic molecule consisting of N?3 atoms and having f Colebat. degrees of freedom (f=3N-5 and f=3N-6 for linear and nonlinear molecules, respectively), it turns out / so-called. normal oscillations with frequencies vi(ill, 2, 3, . . ., f) and a complex system of oscillations. energy levels:

Set of frequencies of norms. fluctuations in the main. electronic state yavl. important characteristic of the molecule, depending on its chemical. buildings. To a certain standard. vibrations involve either all the atoms of the molecule, or part of them; atoms make harmonic. oscillations with the same frequency vi, but with diff. amplitudes that determine the shape of the oscillation. Norm. vibrations are divided by shape into valence (the lengths of chemical bonds change) and deformation (the angles between chemical bonds change - bond angles). For molecules of lower symmetry (see MOLECULE SYMMETRY) f=2 and all vibrations are non-degenerate; for more symmetrical molecules, there are double and triple degenerate vibrations, i.e., pairs and triples of vibrations coinciding in frequency.

The rotational energy levels can be found by quantizing the rotation. the motion of a molecule, considering it as TV. body with certain moments of inertia. In the case of a diatomic or linear triatomic molecule, its energy of rotation? vr \u003d M2 / 2I, where I is the moment of inertia of the molecule about an axis perpendicular to the axis of the molecule, and M is rotated. moment of the number of motion. According to the quantization rules,

M2=(h/4pi2)J(J+1),

where f=0, 1,2,. . .- rotational quantum. number; for?vr we get:

Вр=(h2/8pi2I)J(J+1) = hBJ(J+1), (7)

where they rotate. constant B=(h/8piI2)I

determines the scale of distances between energy levels, which decreases with increasing nuclear masses and internuclear distances.

Diff. M. types with. occur at different types of transitions between energy levels of molecules. According to (1) and (2):

D?=?"-?"==D?el+D?count+D?vr,

moreover, similarly to (4) D? el-> D? count-> D? When D? el? 0 obtained electronic M. s., observed in the visible and UV regions. Usually at D??0 simultaneously D?col?0 and D?vr?0; dec. D? count for a given D? el correspond to decomp. oscillating stripes (Fig. 2), and dec. D? vr at given D? el and D? number of otd. rotate lines into which oscillatory break up. stripes (Fig. 3).

Rice. 2. Electroino-oscillate. spectrum of the N2 molecule in the near UV region; groups of bands correspond to dec. values ​​Dv= v"-v".

The set of bands with a given D?el (corresponding to a purely electronic transition with a frequency nel=D?el/h) called. stripe system; stripes have different intensity depending on the relative. transition probabilities (see QUANTUM TRANSITION).

Rice. 3. Rotate. splitting of electron-kolsbat. bands 3805.0? N2 molecules.

For complex molecules, the bands of one system corresponding to a given electronic transition usually merge into one broad continuous band; can be superimposed on each other and several. such stripes. Characteristic discrete electronic spectra are observed in frozen organic solutions. connections.

Electronic (more precisely, electronic-vibrational-rotational) spectra are studied using spectral instruments with glass (visible region) and quartz (UV region, (see UV RADIATION)) optics. When D? el \u003d 0, and D? count? 0, oscillates are obtained. MS, observed in the near-IR region, usually in the absorption and Raman spectra. As a rule, at a given D? count D? vr? 0 and fluctuate. the band splits into rotate lines. Most intense in vibration. M. s. bands satisfying the condition Dv=v"-v"=1 (for polyatomic molecules Dvi=v"i-v"i=1 at Dvk=V"k-V"k=0; here i and k determine different normal vibrations). For purely harmonic fluctuations, these selection rules are strictly enforced; for anharmonic vibrations, bands appear, for which Dv> 1 (overtones); their intensity is usually low and decreases with increasing Dv. Swing. M. s. (more precisely, vibrational-rotational) are studied using IR spectrometers and Fourier spectrometers, and Raman spectra - using high-aperture spectrographs (for the visible region) using laser excitation. When D? el=0 and D? count=0 are obtained purely rotatable. spectra, consisting of lines. They are observed in the absorption spectra in the far IR region and especially in the microwave region, as well as in the Raman spectra. For diatomic, linear triatomic molecules, and sufficiently symmetrical nonlinear molecules, these lines are equidistant (on the frequency scale) from each other.

Purely rotate. M. s. studied using IR spectrometers with special. diffraction gratings (echelettes), Fourier spectrometers, spectrometers based on a backward wave lamp, microwave (microwave) spectrometers (see SUBMILLIMETER SPECTROSCOPY, MICROWAVE SPECTROSCOPY), and rotate. Raman spectra - using high-aperture spectrometers.

The methods of molecular spectroscopy, based on the study of M. s., make it possible to solve various problems of chemistry. Electronic M. with. give information about electron shells, excited energy levels and their characteristics, about the energy of dissociation of molecules (by the convergence of energy levels to the dissociation boundary). The study of fluctuations. spectra allows you to find the characteristic vibration frequencies corresponding to the presence in the molecule of certain types of chemical. bonds (e.g., double and triple C-C bonds, C-H connections, N-H for organic. molecules), define spaces. structure, distinguish between cis- and trans-isomers (see ISOMERIA OF MOLECULES). Particularly widespread methods of infrared spectroscopy - one of the most effective optical. methods for studying the structure of molecules. They provide the most complete information in combination with the methods of RAS spectroscopy. Rotate research. spectra, as well as rotation. structures of electronic and oscillatory. M. s. allows using the moments of inertia of molecules found from experience to find with great accuracy the parameters of equilibrium configurations - bond lengths and bond angles. To increase the number of parameters to be determined, the isotopic spectra are examined. molecules (in particular, molecules in which hydrogen is replaced by deuterium) that have the same parameters of equilibrium configurations, but decompose. moments of inertia.

M. s. are also used in spectral analysis to determine the composition of the Islands.

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MOLECULAR SPECTRA- absorption, emission or scattering spectra arising from quantum transitions molecules from one energetic. states to another. M. s. determined by the composition of the molecule, its structure, the nature of the chemical. communication and interaction with external fields (and, consequently, with the surrounding atoms and molecules). Naib. characteristic are M. s. rarefied molecular gases, when there is no spectral line broadening pressure: such a spectrum consists of narrow lines with a Doppler width.

Rice. 1. Scheme of energy levels of a diatomic molecule: a And b-electronic levels; u" And u"" - oscillatory quantum numbers; J" And J"" - rotational quantum numbers.

In accordance with the three systems of energy levels in a molecule - electronic, vibrational and rotational (Fig. 1), M. s. consist of a set of electronic, vibrating. and rotate. spectra and lie in a wide range of e-magn. waves - from radio frequencies to x-rays. region of the spectrum. The frequency of transitions between rotation. energy levels usually fall into the microwave region (in the scale of wave numbers 0.03-30 cm -1), the frequency of transitions between oscillations. levels - in the IR region (400-10,000 cm -1), and the frequencies of transitions between electronic levels - in the visible and UV regions of the spectrum. This division is conditional, because they often rotate. transitions also fall into the IR region, oscillate. transitions - in the visible region, and electronic transitions - in the IR region. Usually, electronic transitions are accompanied by a change in vibrations. energy of the molecule, and when vibrating. transitions changes and rotates. energy. Therefore, most often the electronic spectrum is a system of electron oscillations. stripes, and high resolution spectral equipment is detected by their rotation. structure. The intensity of lines and stripes in M. s. is determined by the probability of the corresponding quantum transition. Naib. the intense lines correspond to the transition allowed selection rules.K M. s. also include Auger spectra and X-rays. spectra of molecules (not considered in the article; see Auger effect, Auger spectroscopy, X-ray spectra, X-ray spectroscopy).

Electronic spectra. Purely electronic M. s. arise when the electronic energy of the molecules changes, if the vibrations do not change. and rotate. energy. Electronic M. with. are observed both in absorption (absorption spectra) and in emission (luminescence spectra). During electronic transitions, the electric current usually changes. dipole moment of the molecule. Electrical dipole transition between the electronic states of a molecule of type G symmetry " and G "" (cm. Symmetry of molecules) is allowed if the direct product Г " G "" contains the symmetry type of at least one of the components of the dipole moment vector d . In absorption spectra, transitions from the ground (totally symmetric) electronic state to excited electronic states are usually observed. Obviously, for such a transition to occur, the types of symmetry of the excited state and the dipole moment must coincide. T. to. electric Since the dipole moment does not depend on the spin, then the spin must be conserved during an electronic transition, i.e., only transitions between states with the same multiplicity are allowed (inter-combination prohibition). This rule, however, is broken

for molecules with strong spin-orbit interaction, which leads to intercombination quantum transitions. As a result of such transitions, for example, phosphorescence spectra arise, which correspond to transitions from an excited triplet state to the main state. singlet state.

Molecules in various electronic states often have different geom. symmetry. In such cases, the condition D " G "" G d must be performed for a point group of a low-symmetry configuration. However, when using a permutation-inversion (PI) group, this problem does not arise, since the PI group for all states can be chosen the same.

For linear molecules of symmetry With hu dipole moment symmetry type Г d=S + (dz)-P( d x , d y), therefore, only transitions S + - S +, S - - S -, P - P, etc. are allowed for them with a transition dipole moment directed along the axis of the molecule, and transitions S + - P, P - D, etc. with the moment of transition directed perpendicular to the axis of the molecule (for the designations of states, see Art. Molecule).

Probability IN electric dipole transition from the electronic level T to the electronic level P, summed over all oscillatory-rotating. electronic level levels T, is determined by f-loy:

dipole moment matrix element for the transition n-m,y en and y em- wave functions of electrons. Integral coefficient. absorption, which can be measured experimentally, is determined by the expression

Where Nm- the number of molecules in the beginning. able m, v nm- transition frequency TP. Often electronic transitions are characterized by the strength of the oscillator

Where e And t e are the charge and mass of the electron. For intense transitions f nm ~ 1. From (1) and (4) cf. excited state lifetime:

These f-ly are also valid for vibrations. and rotate. transitions (in this case, the matrix elements of the dipole moment should be redefined). For allowed electronic transitions, the coefficient is usually absorption for several orders more than for oscillating. and rotate. transitions. Sometimes the coefficient absorption reaches a value of ~10 3 -10 4 cm -1 atm -1, i.e., electron bands are observed at very low pressures (~10 -3 - 10 -4 mm Hg) and small thicknesses (~10-100 cm) layer of matter.

Vibrational spectra observed when the vibration changes. energy (electronic and rotational energies should not change). Normal vibrations of molecules are usually represented as a set of non-interacting harmonics. oscillators. If we confine ourselves to the linear terms of the expansion of the dipole moment d (in the case of absorption spectra) or polarizability a (in the case of combination scattering) along normal coordinates Qk, then the allowed vibrations. transitions are considered only transitions with a change in one of the quantum numbers u k per unit. Such transitions correspond to the main. oscillating stripes, they are oscillating. spectra max. intense.

Main oscillating bands of a linear polyatomic molecule corresponding to transitions from the main. oscillating states can be of two types: parallel (||) bands corresponding to transitions with a transition dipole moment directed along the molecular axis, and perpendicular (1) bands corresponding to transitions with a transition dipole moment perpendicular to the molecular axis. The parallel strip consists of only R- And R-branches, and in a perpendicular strip

resolved also Q-branch (Fig. 2). Main spectrum absorption bands of a symmetrical top molecule also consists of || And | stripes, but rotate. the structure of these bands (see below) is more complex; Q-branch in || lane is also not allowed. Allowed fluctuations. stripes represent vk. Band Intensity vk depends on the square of the derivative ( dd/dQ To ) 2 or ( d a/ dQk) 2 . If the band corresponds to the transition from an excited state to a higher one, then it is called. hot.

Rice. 2. IR absorption band v 4 SF 6 molecules, obtained on a Fourier spectrometer with a resolution of 0.04 cm -1 ; niche showing fine structure lines R(39) measured on a diode laser spectrometer with a resolution of 10 -4 cm -1.

When taking into account the anharmonicity of oscillations and nonlinear terms in the expansions d and a by Qk become probable and transitions forbidden by the selection rule for u k. Transitions with a change in one of the numbers u k on 2, 3, 4, etc. called. overtone (Du k=2 - first overtone, Du k\u003d 3 - second overtone, etc.). If two or more of the numbers u change during the transition k, then such a transition is called combinational or total (if all u To increase) and difference (if some of u k decrease). Overtone bands are denoted 2 vk, 3vk, ..., total bands vk + vl, 2vk + vl etc., and the difference bands vk - vl, 2vk - e l etc. Band intensities 2u k, vk + vl And vk - vl depend on the first and second derivatives d By Qk(or a by Qk) and cubic. coefficients of anharmonicity potent. energy; the intensities of higher transitions depend on the coefficient. more high degrees decomposition d(or a) and potent. energy by Qk.

For molecules that do not have symmetry elements, all vibrations are allowed. transitions both in the absorption of excitation energy and in combination. scattering of light. For molecules with an inversion center (eg, CO 2 , C 2 H 4 , etc.), transitions allowed in absorption are forbidden for combinations. scattering, and vice versa (alternative prohibition). The transition between oscillation energy levels of symmetry types Г 1 and Г 2 is allowed in absorption if the direct product Г 1 Г 2 contains the symmetry type of the dipole moment, and is allowed in combination. scattering if the product Г 1

Г 2 contains the symmetry type of the polarizability tensor. This selection rule is approximate, since it does not take into account the interaction of vibrations. movements with electronic and rotating. movements. Accounting for these interactions leads to the appearance of bands that are forbidden according to pure oscillations. selection rules.

The study of fluctuations. M. s. allows you to set the harmonic. oscillation frequencies, anharmonicity constants. According to fluctuations spectra is carried out conformation. analysis

chemical bonds and structure of molecules.

Molecule - the smallest particle of a substance, consisting of the same or different atoms connected to each other chemical bonds, and being the carrier of its basic chemical and physical properties. Chemical bonds are due to the interaction of external, valence electrons of atoms. There are two types of bonds most often found in molecules: ionic and covalent.

Ionic bond (for example, in molecules NaCl, KVR) is carried out by the electrostatic interaction of atoms during the transition of an electron from one atom to another, i.e. in the formation of positive and negative ions.

A covalent bond (for example, in H 2 , C 2 , CO molecules) is carried out when valence electrons are shared by two neighboring atoms (the spins of valence electrons must be antiparallel). The covalent bond is explained on the basis of the principle of indistinguishability of identical particles, such as electrons in a hydrogen molecule. The indistinguishability of particles leads to exchange interaction.

The molecule is quantum system; it is described by the Schrödinger equation, which takes into account the motion of electrons in a molecule, the vibrations of the atoms of the molecule, and the rotation of the molecule. The solution to this equation is very difficult task, which is usually divided into two: for electrons and nuclei. Energy of an isolated molecule:

where is the energy of motion of electrons relative to nuclei, is the energy of vibrations of nuclei (as a result of which the relative position of nuclei periodically changes), is the energy of rotation of nuclei (as a result of which the orientation of the molecule in space periodically changes). Formula (13.1) does not take into account the translational energy of the center of mass of the molecule and the energy of the nuclei of atoms in the molecule. The first of them is not quantized, so its changes cannot lead to the appearance of a molecular spectrum, and the second can be ignored if the hyperfine structure of the spectral lines is not considered. It is proved that eV, eV, eV, so >>>>.

Each of the energies included in expression (13.1) is quantized (it corresponds to a set of discrete energy levels) and is determined by quantum numbers. During the transition from one energy state to another, energy is absorbed or emitted D E=hv. During such transitions, the energy of electron motion, the energy of vibrations and rotation change simultaneously. It follows from theory and experiment that the distance between rotational energy levels D is much less than the distance between vibrational levels D, which, in turn, is less than the distance between electronic levels D. Figure 13.1 schematically shows the energy levels of a diatomic molecule (for example, only two electronic levels are considered are shown in bold lines).

The structure of molecules and the properties of their energy levels are manifested in molecular spectra– emission (absorption) spectra arising from quantum transitions between the energy levels of molecules. The emission spectrum of a molecule is determined by the structure of its energy levels and the corresponding selection rules.

Thus, different types of transitions between levels give rise to different types of molecular spectra. The frequencies of the spectral lines emitted by molecules can correspond to transitions from one electronic level to another (electronic spectra) or from one vibrational (rotational) level to another ( vibrational (rotational) spectra). In addition, transitions with the same values ​​are also possible And to levels having different values ​​of all three components, resulting in electronic-vibrational and vibrational-rotational spectra.

Typical molecular spectra are banded, which are a combination of more or less narrow bands in the ultraviolet, visible and infrared regions.

Using high-resolution spectral instruments, it can be seen that the fringes are such closely spaced lines that they are difficult to resolve. The structure of molecular spectra is different for different molecules and becomes more complicated with an increase in the number of atoms in a molecule (only continuous broad bands are observed). Only polyatomic molecules have vibrational and rotational spectra, while diatomic ones do not have them. This is explained by the fact that diatomic molecules do not have dipole moments (during vibrational and rotational transitions, there is no change in the dipole moment, which is a necessary condition for the transition probability to differ from zero). Molecular spectra are used to study the structure and properties of molecules, are used in molecular spectral analysis, laser spectroscopy, quantum electronics, etc.