General characteristics of molecular spectra. General characteristics of molecular spectra Spectra of molecules and their features

In addition to the spectra corresponding to the radiation of individual atoms, spectra emitted by whole molecules are also observed (§ 61). Molecular spectra are much more diverse and complex in structure than atomic spectra. Here condensed sequences of lines are observed, 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). Due to the peculiar nature of these spectra, they are called striped.

Rice. 279. Striped spectrum

Along with this, sequences of equally spaced spectral lines and, finally, multiline spectra are observed, in which, at first glance, it is difficult to establish any patterns (Fig. 280). It should be noted that when studying the spectrum of hydrogen, we always have a superposition of the molecular spectrum of Ha on the atomic spectrum, and special measures have to 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, as in the case of atomic spectra, each line of the molecular spectrum is emitted when a molecule transitions 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 is composed of three parts: 1) the energy of the electron shell of the molecule; 2) the energy of vibrations 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 series 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 forming a molecule. Although the forces that bind atoms into molecules are of a purely electrostatic nature, a correct understanding of the chemical bond turned out to be possible only within the framework of modern wave-mechanical quantum theory.

There are two types of molecules: homeopolar and heteropolar. As the distance between the nuclei increases, homeopolar molecules disintegrate into neutral parts. Hemopolar molecules include molecules. Heteropolar molecules, as the distance between the nuclei increases, disintegrate into positive and negative ions. A typical example of heteropolar molecules are molecules of salts, for example, etc. (vol. I, § 121, 130, 1959; in the previous edition, § 115 and 124, etc. II, § 19, 22, 1959 ; in the previous edition § 21 and 24).

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

Let's consider a very rough model of the simplest molecule (an ionized hydrogen molecule representing two potential “holes” located at a close distance from each other and separated by a “barrier” (Fig. 281).

Rice. 281. Two potential holes.

Rice. 282. Wave functions of an electron in the case of distant “wells”.

Each of the “holes” represents 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). In Fig. 282, a and b, two identical wave functions are depicted that describe the state of electrons located in isolated atoms. These wave functions correspond to the same energy level.

When atoms come together to form a molecule, the “barrier” between the “holes” becomes “transparent” (§ 63), because its width becomes commensurate with the length of the electron wave. As a result of this there is

exchange of electrons between atoms through a “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), 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 slightly less than the energy of the state. Thus, from each atomic level two molecular electronic levels arise.

Rice. 283. Wave functions of an electron in the case of close “wells”.

So far we have been talking about the ion of a hydrogen molecule, which has one electron. A neutral hydrogen molecule has two electrons, which leads to the need to take into account the relative positions of their spins. In accordance with the Pauli principle, electrons with parallel spins seem to “avoid” each other, therefore 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 be formed. 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 electronic charge attracts both positive nuclei and the entire system as a whole forms a stable molecule.

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

The symbolism of the electronic states of molecules has many similarities with atomic symbolism. Naturally, in a molecule the main role 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.

Between the values ​​and symbols of molecular electronic states there is a correspondence similar to that in atoms (§ 67):

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

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

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

Just like atoms, molecules exhibit multiplicity caused by different orientations of the resulting spin relative to the resulting orbital momentum.

Taking these circumstances into account, 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 values ​​of the quantum number A. For example, the normal state of a hydrogen molecule is 2, the normal state of a hydroxyl molecule is the normal state of an oxygen molecule is . During transitions between different electronic states, the following selection rules apply: .

The vibrational energy of a molecule associated with vibrations of nuclei is quantized, taking into account 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 the following allowed values ​​from the Schrödinger equation vibrational energy this system (harmonic

oscillator):

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

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

Rice. 285. Levels of vibrational energy 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 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 In fact, at large amplitudes of nuclear oscillations, deviations of the restoring force from Hooke’s law already begin to affect. As a result, the energy levels come closer together (Fig. 285). At sufficiently large amplitudes, the molecule dissociates into parts.

For a harmonic oscillator, transitions are allowed only at , which corresponds to the emission or absorption of light of frequency. Due to deviations from harmonicity, transitions appear that correspond 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 a molecule. Vibrations of nuclei lead to the fact that each electronic level turns 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 a 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. The permissible values ​​of rotational energy are determined, according to wave mechanics, based on the principle of quantization of torque.

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 the previous. ed. § 42) will be

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

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

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

In 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, and 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. Measuring 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 molecules are of the order of magnitude. It should be noted that the moment of inertia I itself due to the action

centrifugal forces 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 rotational energy.

When a molecule transitions from one energy state to another, all three types of energy of the molecule can simultaneously change (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 in all three types of energy of a molecule

Such bands of equally spaced lines are observed in vapor 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 others. In Fig. 289 shows a band in the vapor absorption spectrum in the near infrared region. This band corresponds to transitions between energy states that differ not only in rotational energy, but also in vibrational energy (at a constant energy of electron shells). In this case, and and Ecol 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 lying in the near infrared region, similar to those shown in Fig. 289.

Rice. 289. Absorption band.

The center of the band ( corresponds to a transition at a constant EUR; 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 EUR is added to the change. Lines with lower frequencies (right side) correspond to the inverse relationship: 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 frequencies of the lines should depend on and the distances between the lines become unequal. Each stripe consists of a series of lines condensing towards one edge,

which is called the head of the strip. For the frequency of an individual spectral line included in the band, Delander back in 1885 gave an empirical formula of the following form:

where is an integer.

Delandre's formula follows directly from the above considerations. Delandre's formula can be depicted graphically if we plot it along one axis and along the other (Fig. 290).

Rice. 290. Graphic representation of Delandre's formula.

Below are the corresponding lines, forming, as we see, a typical stripe. Since the structure of the molecular spectrum strongly depends on the moment of inertia of the molecule, research molecular spectra is one of the reliable ways to determine this value. The slightest changes in the structure of a molecule can be detected by studying its spectrum. The most interesting is the fact that molecules containing different isotopes (§ 86) of the same element should 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 vibrations in the molecule and its moment of inertia. Indeed, the copper chloride band lines consist of four components, corresponding 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 discovered, despite the fact that the concentration of the isotope in ordinary hydrogen is equal to

In addition to the mass of nuclei, other properties of nuclei also influence 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 drops out. This effect, for example, is observed in the molecule

If the rotational moments of the nuclei are non-zero, they can cause an alternation of intensities in the rotational band, weak lines alternating with strong ones.)

Finally, using radiospectroscopy methods, it was possible to detect and accurately measure the hyperfine structure of molecular spectra associated with the quadrupole electric moment of nuclei.

The quadrupole electric moment arises as a result of the deviation of the nuclear shape from spherical. The core can have the shape of an elongated or oblate ellipsoid of revolution. Such a charged ellipsoid can no longer be replaced simply by a point charge placed in the center of the nucleus.

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

2 - crystal diode that 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; I - crystal diode current indicator; B - vacuum gauge.

In addition to the Coulomb force, an additional force appears in the nuclear field, inversely proportional to the fourth power of the distance and depending on the angle with the direction of the symmetry axis of the nucleus. The appearance of 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 a nucleus was established by conventional spectroscopy using some 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, a waveguide is filled with the molecular gas being studied 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 centimeter wave region was studied in particular detail. A hyperfine structure was discovered in this spectrum, which is explained by the presence of a connection between the quadrupole moment of the nucleus and the electric field of the molecule itself.

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

fields. Behind last years A huge number of works have appeared devoted to the radio spectroscopic method of studying the structure of a wide variety of molecules. The absorption of radio waves in ammonia has been used to construct 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 rate. An “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 disrupts 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 moved more uniformly than the rotation of the Earth. It is assumed that it will be possible to achieve accuracy of the order of a fraction of a day.

Lecture No. 6

Molecule energy

Atom called the smallest particle chemical element possessing 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 electrons. Ion of a given atom is an electrically charged particle formed when atoms lose or gain electrons.

Molecule is the smallest particle of a homogeneous substance that has its basic chemical properties.

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

In order to understand the reasons why electrically neutral atoms can form a stable molecule, we will limit 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 external electrons. When atoms combine into a molecule, the electrons of the inner shells remain in their previous states.

If atoms are at a great distance from each other, then they do not interact with each other. As atoms come closer together, the forces of their mutual attraction increase. At distances comparable to the sizes of atoms, mutual repulsion 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.

The graph of the attractive force, the repulsive force and the resulting interaction force between atoms as a function of distance looks like this:

The interaction energy of electrons in a molecule is determined by the mutual arrangement of atomic nuclei 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 it is the potential energy of interaction between nuclei.

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

Accordingly, the graph 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 connection length. The quantity D is called molecular dissociation energy or bond 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 is 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, forward energy has a continuous spectrum and its average value is equal to , that is.

Rotational energy has a discrete spectrum and can take values

,

where I is the rotational quantum number;

J is the moment of inertia of the molecule.

Energy of vibrational motion also has a discrete spectrum and can take values

,

where is the vibrational quantum number;

– natural frequency of this type of oscillation.

When 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 corresponds to the potential form. Consequently, the energy steps of the vibrational motion of a diatomic molecule can be represented on a graph.

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

Main types of interatomic bonds

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

Ionic bond occurs in cases where electrons in a molecule are arranged in such a way that an excess is formed near one of the nuclei, and a deficiency near the other. Thus, the molecule seems to consist of two ions of opposite signs, attracted to each other. Examples of molecules with ionic bonds are NaCl, KCl, RbF, CsJ etc. formed by combining atoms of elements I-oh and VII-th group of Mendeleev's periodic system. In this case, an atom that has added one or more electrons to itself acquires a negative charge and becomes a negative ion, and an atom that donates 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 electrical in nature.

For an ionic bond to take place, it is necessary that the energy of electron removal, that is, the work of creating a positive ion, 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 work in the case when electrons located in the electron shell that has begun to build up occur.

On the other hand, the greatest energy is released when an electron attaches to halogen atoms, which lack one electron before filling the electron shell. Therefore, an ionic bond is formed through the transfer of electrons, which leads to the creation of filled electron shells in the resulting ions.

Another type of connection - covalent bond.

When molecules consisting of identical atoms are formed, the formation of oppositely charged ions is impossible. Therefore, ionic bonding is not possible. 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, covalent bonds are also observed in molecules with different atoms: hydrogen fluoride HF, nitric oxide NO, methane CH 4 etc.

The nature of covalent bonds 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 stop abruptly as the distance from the center of the atom increases, but gradually decreases. As atoms approach each other, the fuzzy electron clouds of outer electrons partially overlap, causing them to deform. An accurate calculation of the change in 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 limit ourselves here to only a qualitative consideration of phenomena.

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

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

As calculations show, the exchange energy of a molecule is positive if the spins of 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 the ionic bond we were talking about the transfer of electrons from one atom to another, then here the connection is carried out by the generalization of electrons and the creation of a common space for their movement.

Molecular spectra

Molecular spectra are very different from atomic spectra. While atomic spectra consist of individual lines, molecular spectra consist 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 provides an explanation for the nature of molecular spectra. The theoretical interpretation of the spectra of polyatomic molecules is very complex. We will limit ourselves to considering only diatomic molecules.

Earlier, we noted that the energy of a molecule depends on the nature of the movement of atomic nuclei 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 translational energy cannot lead to the appearance of a spectral line in the molecular spectrum, therefore we will exclude this type of energy in further consideration of molecular spectra. Then

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

.

Experience and theoretical research showed that

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

Rotational spectrum of molecules

Let's start exploring the absorption of electromagnetic waves with 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 quanta capable of raising a 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 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 in 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 rotational energy states of the molecule.

We have so far considered the absorption spectrum of the molecule. The emission spectrum of the molecule is also possible. The appearance of lines in 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 mass of atoms, it is possible to determine the distances between atoms. For a diatomic molecule

Vibrational-rotational spectrum of molecules

Absorption of electromagnetic waves by a substance 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 simultaneously change. Transitions between two vibrational energy levels are accompanied by changes in rotational energy states. In this case, a vibrational-rotational spectrum of the molecule appears.

If a molecule simultaneously vibrates and rotates, 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. 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 opposite 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, 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 asymmetric molecules.

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

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 with discrete energy. Each configuration of electrons corresponds to many vibrational energy levels.

A 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, consisting 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 making up a wide band.

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

Raman scattering

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

The phenomenon of Raman scattering has a simple quantum mechanical explanation. The process of light scattering by molecules can be considered as an inelastic collision of photons with molecules. During a collision, 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, when colliding with a photon, a molecule moves from a state with lower energy to a state with higher energy, it loses its energy and its frequency decreases. This creates a line in the spectrum of the molecule, shifted relative to the main one towards longer wavelengths. If, after a collision with a photon, a molecule passes from a state with higher energy to a state with lower energy, a line is created in the spectrum that is shifted relative to the main one towards shorter wavelengths.

Raman scattering studies provide information about the structure of molecules. Using this method, the natural vibrational 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 the glow of these bodies or luminescence occurs.

There are two types of luminescence: fluorescence And phosphorescence.

Fluorescence called luminescence, which stops immediately after the end of the action of the luminescence exciter.

With 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 seconds).

Phosphorescence called luminescence, which retains its glow for a long time after the action of the luminescence exciter.

During phosphorescence, a molecule moves from an excited state to a metastable level. Metastable This is a level from which a transition to a lower level is unlikely. Emission can occur if the molecule returns to the excited level again.

The transition from a metastable state to an excited state is possible only in the presence of additional excitation. Such an additional pathogen may be the temperature of the substance. At high temperatures this transition occurs quickly, at low temperatures it occurs slowly.

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

Quantum amplifiers and radiation generators

In the mid-50s of our century, the rapid development of quantum electronics began. In 1954, the works of academicians N.G. Basov and A.M. appeared in the USSR. Prokhorov, in which 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 amplifiers of light in the visible and infrared regions, which appeared in the 60s, were called optical quantum generators or lasers(light amplification by stimulated emission of radiation).

Both types of devices operate based on the effect of stimulated or stimulated radiation.

Let's look at 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 occur spontaneously (or spontaneously). However, under the influence of incident radiation, such transitions are possible both direct and reverse direction. These transitions are called forced or induced. During a forced transition from one of the excited levels to a low energy level, the atom emits a photon that is additional to the photon under the influence of which the transition was made.

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

Thus, the 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 The driving photon is absorbed by an atom located at a low energy level, and the atom moves to a higher energy level. And

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

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

Let us consider a device that uses 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 wavelength 5600, chromium ions move to the upper energy level.

The return 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 enter a metastable state. The ions remain at this level for a longer time than at the upper level. As a result, an inverse state of a 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 influence of photons of the same wavelength, i.e. with stimulated emission. This return occurs much faster than with spontaneous emission, so the light is amplified.

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 flat ends of this rod are polished and silvered so that they form two mirrors facing each other, one of them being translucent. 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 axis of the ruby ​​experience multiple reflections from its ends.

Therefore, their path in the crystal will be very long, and cascades of photons in this direction will receive the greatest development.

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

When the axial beam becomes intense enough, part of it exits through the translucent end of the crystal to the outside.

A large amount of heat is generated 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 monochromatic;

3. high power;

4. beam narrowness.

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 to modulate and demodulate light is found, it will be possible to transmit a huge amount of information. Thus, in terms of the volume of transmitted information, 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, it is possible to obtain a spot of light with a diameter of 3 km on the lunar surface. The high power and narrowness of the beam allows, when focusing using 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 of chemical reactions, etc.

The above does not exhaust all the capabilities 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.

1. Unlike optical line spectra with their complexity and diversity, the X-ray characteristic spectra of various elements are simple and uniform. With increasing atomic number Z element, they monotonically shift towards the short-wavelength side.

2. The characteristic spectra of different elements are of a similar nature (of the same type) and do not change if the element of interest to us is in combination with others. This can only be explained by the fact that the characteristic spectra arise during electron transitions into internal parts atom, parts having a similar structure.

3. Characteristic spectra consist of several series: TO,L, M, ... Each series consists of a small number of lines: TO A , TO β , TO γ , ... L a , L β , L y , ... etc. in descending order of wavelength λ .

Analysis of the characteristic spectra led to the understanding that atoms are characterized by a system of X-ray terms TO,L, M, ...(Fig. 13.6). The same figure shows a diagram of the appearance of characteristic spectra. Excitation of an atom occurs when one of the internal electrons is removed (under the influence of electrons or photons of sufficiently high energy). If one of the two electrons escapes K-level (n= 1), then the vacated space can be occupied by an electron from some higher level: L, M, N, etc. As a result, there arises K-series. Other series arise in a similar way: L, M,...

Series TO, as can be seen from Fig. 13.6, is certainly accompanied by the appearance of the remaining series, since when its lines are emitted, electrons are released at the levels L, M etc., which in turn will be filled with electrons from higher levels.

Molecular spectra. Types of bonds in molecules, molecule energy, energy of vibrational and rotational motion.

Molecular spectra.

Molecular spectra - optical spectra of emission and absorption, as well as Raman scattering of light (See. Raman scattering), belonging to free or loosely connected Molecule m. M. s. have a complex structure. Typical M. s. - striped, they are observed in emission and absorption and in Raman scattering in the form of a set of more or less narrow bands in the ultraviolet, visible and near infrared regions, which break up with sufficient resolving power of the spectral instruments used into a set of closely spaced lines. The specific structure of M. s. is different for different molecules and, generally speaking, becomes more complex as the number of atoms in the molecule increases. For very complex molecules, the visible and ultraviolet spectra consist of a few broad continuous bands; the spectra of such molecules are similar to each other.

From the solution of the Schrödinger equation for hydrogen molecules under the above assumptions, we obtain the dependence of the energy eigenvalues ​​on the distance R between cores, i.e. E =E(R).

Molecule energy

Where E el - energy of movement of electrons relative to nuclei; E count - energy of nuclear vibrations (as a result of which the relative position of the nuclei periodically changes); E rotation - the energy of rotation of nuclei (as a result of which the orientation of the molecule in space periodically changes).

Formula (13.45) does not take into account the energy of translational motion of the center of mass of the molecules 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 spectral lines is not considered.

It has been proven that E email >> E count >> E rotate, while E el ≈ 1 – 10 eV. Each of the energies included in expression (13.45) is quantized and a set of discrete energy levels corresponds to them. When transitioning from one energy state to another, energy Δ is absorbed or emitted E = hν. From theory and experiment it follows that the distance between rotational energy levels Δ E rotation is much less than the distance between vibrational levels Δ E count, which, in turn, is less than the distance between electronic levels Δ E email

The structure of molecules and the properties of their energy levels are manifested in molecular spectra - emission (absorption) spectra arising during quantum transitions between energy levels of molecules. The emission spectrum of a molecule is determined by the structure of its energy levels and the corresponding selection rules (for example, the change in quantum numbers corresponding to both vibrational and rotational motion must be equal to ± 1). With different types of transitions between levels, different types of molecular spectra arise. The frequencies of 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 E count And E rotate to levels that have different values ​​of all three components, resulting in electronic vibrational And vibrational-rotational spectra . Therefore, the spectrum of molecules is quite complex.

Typical molecular spectra - striped , are a collection of more or less narrow bands in the ultraviolet, visible and infrared regions. Using high-resolution spectral instruments, one can see that the bands are lines so closely spaced that they are difficult to resolve.

The structure of molecular spectra is different for different molecules and becomes more complex as the number of atoms in the molecule increases (only continuous broad bands are observed). Only polyatomic molecules have vibrational and rotational spectra, while diatomic molecules 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 differences from zero transition probability).

Molecular spectra are used to study the structure and properties of molecules; they are used in molecular spectral analysis, laser spectroscopy, quantum electronics, etc.

TYPES OF BONDS IN MOLECULES Chemical bond- interaction phenomenon atoms, caused by overlap electron clouds binding particles, which is accompanied by a decrease total energy systems. Ionic bond- durable chemical bond, formed between atoms with a large difference electronegativities, at which the total electron pair completely passes to an atom with greater electronegativity. This is the attraction of ions as oppositely charged bodies. Electronegativity (χ)- a fundamental chemical property of an atom, a quantitative characteristic of the ability atom V molecule shift towards oneself shared electron pairs. Covalent bond(atomic bond, homeopolar bond) - chemical bond, formed by the overlap (socialization) of a pair valence electron clouds. The electronic clouds (electrons) that provide communication are called shared electron pair.Hydrogen bond- connection between electronegative atom and hydrogen atom H, related covalently with another electronegative atom. Metal connection - chemical bond, due to the presence of relatively free electrons. Characteristic for both clean metals, so do them alloys And intermetallic compounds.

Raman scattering of light.

This is the scattering of light by a substance, accompanied by a noticeable change in the frequency of the scattered light. If the source emits a line spectrum, then at K. r. With. In the spectrum of scattered light, additional lines are detected, the number and location of which are closely related to the molecular structure of the substance. With K. r. With. the transformation of the primary light flux is usually accompanied by the transition of scattering molecules to other vibrational and rotational levels , Moreover, the frequencies of new lines in the scattering spectrum are combinations of the frequency of the incident light and the frequencies of vibrational and rotational transitions of the scattering molecules - hence the name. "TO. R. With.".

To observe the spectra of K. r. With. it is necessary to concentrate an intense beam of light on the object being studied. A mercury lamp is most often used as a source of exciting light, and since the 60s. - laser ray. The scattered light is focused and enters the spectrograph, where the red spectrum is With. recorded by photographic or photoelectric methods.

While atomic spectra consist of individual lines, molecular spectra, when observed with an instrument of average resolving power, appear to consist of (see Fig. 40.1, which shows a section of the spectrum resulting from a glow discharge in air).

When using high-resolution instruments, it is discovered that the bands consist of a large number of closely spaced lines (see Fig. 40.2, which shows the fine structure of one of the bands in the spectrum of nitrogen molecules).

In accordance with their nature, the spectra of molecules are called striped spectra. Depending on the change in which types of energy (electronic, vibrational or rotational) causes the emission of a photon by a molecule, three types of bands are distinguished: 1) rotational, 2) vibrational-rotational and 3) electronic-vibrational. Stripes in Fig. 40.1 belong to the electronic vibrational type. This type of stripe is characterized by the presence of a sharp edge called the edge of the stripe. The other edge of such a strip turns out to be blurred. The edging is caused by the condensation of lines forming a strip. Rotational and oscillatory-rotational bands do not have an edge.

We will limit ourselves to considering the rotational and vibrational-rotational spectra of diatomic molecules. The energy of such molecules consists of electronic, vibrational and rotational energies (see formula (39.6)). In the ground state of the molecule, all three types of energy have a minimum value. When a molecule is given a sufficient amount of energy, it goes into an excited state and then, making a transition allowed by the selection rules to one of the lower energy states, emits a photon:

(it must be borne in mind that both and differ for different electronic configurations of the molecule).

In the previous paragraph it was stated that

Therefore, with weak excitations, it changes only with stronger ones - and only with even stronger excitations does the electronic configuration of the molecule change, i.e.

Rotational stripes. Lowest energy have photons corresponding to transitions of a molecule from one rotational state to another (the electronic configuration and vibration energy do not change):

Possible changes in the quantum number are limited by the selection rule (39.5). Therefore, the frequencies of lines emitted during transitions between rotational levels can have the following values:

where is the quantum number of the level to which the transition occurs (it can have the values: 0, 1, 2, ...), and

In Fig. Figure 40.3 shows a diagram of the occurrence of a rotational band.

The rotational spectrum consists of a series of equally spaced lines located in the very far infrared region. By measuring the distance between the lines, you can determine the constant (40.1) and find the moment of inertia of the molecule. Then, knowing the masses of the nuclei, one can calculate the equilibrium distance between them in a diatomic molecule.

The distance between the Lie lines is of the order of magnitude, so that for the moments of inertia of molecules, values ​​of the order of magnitude are obtained. For example, for a molecule, which corresponds to .

Vibrational-rotational bands. In the case when both the vibrational and rotational state of the molecule changes during the transition (Fig. 40.4), the energy of the emitted photon will be equal to

For the quantum number v the selection rule (39.3) applies, for J the rule (39.5) applies.

Since photon emission can be observed not only at and at . If the photon frequencies are determined by the formula

where J is the rotational quantum number of the lower level, which can take the following values: 0, 1, 2, ; B - value (40.1).

If the formula for the photon frequency has the form

where is the rotational quantum number of the lower level, which can take the values: 1, 2, ... (in this case it cannot have the value 0, since then J would be equal to -1).

Both cases can be covered by one formula:

The set of lines with frequencies determined by this formula is called a vibrational-rotational band. 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., the splitting of individual lines. The region in which the vibrational-rotational bands are located extends from approximately 8000 to 50000 A.

From Fig. 40.4 it is clear that the vibrational-rotational band consists of a set of relatively symmetrical lines spaced apart from each other by only in the middle of the band the distance is twice as large, since a line with frequency does not appear.

The distance between the components of the vibrational-rotational band is related to the moment of inertia of the molecule by the same relationship as in the case of the rotational band, so that by measuring this distance, the moment of inertia of the molecule can be found.

Note that, in full accordance with the conclusions of the theory, rotational and vibrational-rotational spectra are observed experimentally only for asymmetrical diatomic molecules (i.e., molecules formed by two different atoms). For symmetric molecules, the dipole moment is zero, which leads to the prohibition of rotational and vibrational-rotational transitions. Electronic vibrational spectra are observed for both asymmetric and symmetric molecules.

Molecular spectra

optical spectra of emission and absorption, as well as Raman scattering of light (See Raman scattering of light) , belonging to free or weakly interconnected Molecule m. M. s. have a complex structure. Typical M. s. - striped, they are observed in emission and absorption and in Raman scattering in the form of a set of more or less narrow bands in the ultraviolet, visible and near infrared regions, which break up with sufficient resolving power of the spectral instruments used into a set of closely spaced lines. The specific structure of M. s. is different for different molecules and, generally speaking, becomes more complex as the number of atoms in the molecule increases. For very complex molecules, the visible and ultraviolet spectra consist of a few broad continuous bands; the spectra of such molecules are similar to each other.

hν = E‘ - E‘’, (1)

Where hν - energy of emitted absorbed Photon and frequency ν ( h- The plank is constant). With Raman scattering hν is equal to the difference between the energies of the incident and scattered photons. M. s. much more complex than line atomic spectra, which is determined by the greater complexity of internal motions in a molecule than in atoms. Along with the movement of electrons relative to two or more nuclei in molecules, vibrational motion of the nuclei (together with the internal electrons surrounding them) occurs around equilibrium positions and rotational motion of the molecule as a whole. These three types of motion - electronic, vibrational and rotational - correspond to three types of energy levels and three types of spectra.

According to quantum mechanics, the energy of all types of motion in a molecule can take only certain values, i.e. it is quantized. Total energy of a molecule E can be approximately represented as the sum of quantized energy values ​​of three types of its motion:

E = E email + E count + E rotate (2)

By order of magnitude

Where m is the mass of the electron, and the magnitude M has the order of mass of atomic nuclei in a molecule, i.e. m/M Molecular spectra 10 -3 -10 -5, therefore:

E email >> E count >> E rotate (4)

Usually E el about several ev(several hundred kJ/mol), E count Molecular spectra 10 -2 -10 -1 eV, E rotate Molecular spectra 10 -5 -10 -3 ev.

In accordance with (4), the system of energy levels of a molecule is characterized by a set of electronic levels far apart from each other (different values E el at E count = E rotation = 0), vibrational levels located much closer to each other (different values E count at a given E l and E rotation = 0) and even more closely spaced rotational levels (different values E rotation at given E el and E count). On rice. 1 a diagram of the levels of a diatomic molecule is shown; For polyatomic molecules, the level system becomes even more complicated.

Electronic energy levels ( E el in (2) and on the diagram rice. 1 correspond to the equilibrium configurations of the molecule (in the case of a diatomic molecule, characterized by the equilibrium value r 0 internuclear distance r, cm. rice. 1 in Art. Molecule). Each electronic state corresponds to a certain equilibrium configuration and a certain value E el; the lowest value corresponds to the basic energy level.

The set of electronic states of a molecule is determined by the properties of its electron shell. In principle the values E el can be calculated by quantum chemistry methods (See Quantum chemistry) , however, this problem can only be solved using approximate methods and for relatively simple molecules. The most important information about the electronic levels of a molecule (the location of the electronic energy levels and their characteristics), determined by its chemical structure, is obtained by studying its molecular structure.

A very important characteristic of a given electronic energy level is the value of the quantum number (See Quantum numbers) S, characterizing the absolute value of the total spin moment of all electrons of the molecule. Chemically stable molecules usually have an even number of electrons, and for them S= 0, 1, 2... (for the main electronic level the typical value is S= 0, and for excited ones - S= 0 and S= 1). Levels with S= 0 are called singlet, with S= 1 - triplet (since the interaction in the molecule leads to their splitting into χ = 2 S+ 1 = 3 sublevels; see Multiplicity) . Free radicals, as a rule, have an odd number of electrons, for them S= 1 / 2, 3 / 2, ... and the value is typical for both the main and excited levels S= 1 / 2 (doublet levels splitting into χ = 2 sublevels).

For molecules whose equilibrium configuration has symmetry, the electronic levels can be further classified. In the case of diatomic and linear triatomic molecules having an axis of symmetry (of infinite order) passing through the nuclei of all atoms (see. rice. 2 , b) , electronic levels are characterized by the values ​​of the quantum number λ, which determines the absolute value of the projection of the total orbital momentum of all electrons onto the axis of the molecule. Levels with λ = 0, 1, 2, ... are designated Σ, П, Δ..., respectively, and the value of χ is indicated by the index at the top left (for example, 3 Σ, 2 π, ...). For molecules with a center of symmetry, for example CO 2 and C 6 H 6 (see rice. 2 , b, c), all electronic levels are divided into even and odd, denoted by indices g And u(depending on whether the wave function retains its sign when inverted at the center of symmetry or changes it).

Vibrational energy levels (values E count) can be found by quantizing the oscillatory motion, which is approximately considered harmonic. In the simplest case of a diatomic molecule (one vibrational degree of freedom, corresponding to a change in the internuclear distance r) it is considered as a harmonic oscillator ; its quantization gives equally spaced energy levels:

E count = hν e (υ +1/2), (5)

where ν e is the fundamental frequency of harmonic vibrations of the molecule, υ is the vibrational quantum number, taking values ​​0, 1, 2, ... On rice. 1 vibrational levels for two electronic states are shown.

For each electronic state of a polyatomic molecule consisting of N atoms ( N≥ 3) and having f vibrational degrees of freedom ( f = 3N- 5 and f = 3N- 6 for linear and nonlinear molecules, respectively), it turns out f so-called normal vibrations with frequencies ν i ( i = 1, 2, 3, ..., f) and a complex system of vibrational levels:

Where υ i = 0, 1, 2, ... are the corresponding vibrational quantum numbers. The set of frequencies of normal vibrations in the ground electronic state is a very important characteristic of a molecule, depending on its chemical structure. All or part of the atoms of the molecule participate in a certain normal vibration; the atoms perform harmonic vibrations with the same frequency v i, but with different amplitudes that determine the shape of the vibration. Normal vibrations are divided according to their shape into stretching (in which the lengths of bond lines change) and bending (in which the angles between chemical bonds - bond angles - change). The number of different vibration frequencies for molecules of low symmetry (without symmetry axes of order higher than 2) is equal to 2, and all vibrations are non-degenerate, while for more symmetric molecules there are doubly and triply degenerate vibrations (pairs and triplets of vibrations that match in frequency). For example, in a nonlinear triatomic molecule H 2 O ( rice. 2 , A) f= 3 and three non-degenerate vibrations are possible (two stretching and one bending). A more symmetrical linear triatomic CO 2 molecule ( rice. 2 , b) has f= 4 - two non-degenerate vibrations (stretching) and one doubly degenerate (deformation). For a flat highly symmetrical molecule C 6 H 6 ( rice. 2 , c) it turns out f= 30 - ten non-degenerate and 10 doubly degenerate oscillations; of these, 14 vibrations occur in the plane of the molecule (8 stretching and 6 bending) and 6 out-of-plane bending vibrations - perpendicular to this plane. An even more symmetrical tetrahedral molecule CH 4 ( rice. 2 , d) has f = 9 - one non-degenerate vibration (stretching), one doubly degenerate (deformation) and two triply degenerate (one stretching and one deformation).

Rotational energy levels can be found by quantizing the rotational motion of a molecule, treating it as a solid body with certain moments of inertia (See Moment of Inertia). In the simplest case of a diatomic or linear polyatomic molecule, its rotational energy

Where I is the moment of inertia of the molecule relative to an axis perpendicular to the axis of the molecule, and M- rotational moment of momentum. According to the quantization rules,

where is the rotational quantum number J= 0, 1, 2, ..., and therefore for E rotation received:

where is the rotational constant rice. 1 rotational levels for each electronic vibrational state are shown.

Various types of M. s. arise during various types of transitions between energy levels of molecules. According to (1) and (2)

Δ E = E‘ - E‘’ = Δ E el + Δ E count + Δ E rotate, (8)

where changes Δ E el, Δ E count and Δ E rotation of electronic, vibrational and rotational energies satisfy the condition:

Δ E el >> Δ E count >> Δ E rotate (9)

[distances between levels are of the same order as the energies themselves E el, E ol and E rotation, satisfying condition (4)].

At Δ E el ≠ 0, electronic microscopy is obtained, observable in the visible and ultraviolet (UV) regions. Usually at Δ E el ≠ 0 simultaneously Δ E count ≠ 0 and Δ E rotation ≠ 0; different Δ E count at a given Δ E el correspond to different vibrational bands ( rice. 3 ), and different Δ E rotation at given Δ E el and Δ E count - individual rotational lines into which this strip breaks up; a characteristic striped structure is obtained ( rice. 4 ). A set of stripes with a given Δ E el (corresponding to a purely electronic transition with a frequency v el = Δ E email/ h) called the strip system; individual bands have different intensities depending on the relative probabilities of transitions (see Quantum transitions), which can be approximately calculated by quantum mechanical methods. For complex molecules, the bands of one system corresponding to a given electronic transition usually merge into one wide continuous band; several such wide bands can overlap each other. Characteristic discrete electronic spectra are observed in frozen solutions of organic compounds (see Shpolsky effect). Electronic (more precisely, electronic-vibrational-rotational) spectra are studied experimentally using spectrographs and spectrometers with glass (for the visible region) and quartz (for the UV region) optics, in which prisms or diffraction gratings are used to decompose light into a spectrum (see. Spectral devices).

At Δ E el = 0, and Δ E count ≠ 0, oscillatory magnetic resonances are obtained, observed in close range (up to several µm) and in the middle (up to several tens µm) infrared (IR) region, usually in absorption, as well as in Raman scattering of light. As a rule, simultaneously Δ E rotation ≠ 0 and at a given E The result is a vibrational band that breaks up into separate rotational lines. They are most intense in oscillatory M. s. bands corresponding to Δ υ = υ ’ - υ '' = 1 (for polyatomic molecules - Δ υ i = υ i' - υ i ''= 1 at Δ υ k = υ k ’ - υ k '' = 0, where k≠ i).

For purely harmonic oscillations these Selection rules , prohibiting other transitions are carried out strictly; for anharmonic vibrations, bands appear for which Δ υ > 1 (overtones); their intensity is usually low and decreases with increasing Δ υ .

Vibrational (more precisely, vibrational-rotational) spectra are studied experimentally in the IR region in absorption using IR spectrometers with prisms transparent to IR radiation or with diffraction gratings, as well as Fourier spectrometers and in Raman scattering using high-aperture spectrographs ( for the visible region) using laser excitation.

At Δ E el = 0 and Δ E count = 0, purely rotational magnetic systems are obtained, consisting of individual lines. They are observed in absorption at a distance (hundreds of µm) IR region and especially in the microwave region, as well as in Raman spectra. For diatomic and linear polyatomic molecules (as well as for fairly symmetrical nonlinear polyatomic molecules), these lines are equally spaced (on the frequency scale) from each other with intervals Δν = 2 B in absorption spectra and Δν = 4 B in Raman spectra.

Pure rotational spectra are studied in absorption in the far IR region using IR spectrometers with special diffraction gratings (echelettes) and Fourier spectrometers, in the microwave region using microwave (microwave) spectrometers (see Microwave spectroscopy) , as well as in Raman scattering using high-aperture spectrographs.

Methods of molecular spectroscopy, based on the study of microorganisms, make it possible to solve various problems in chemistry, biology, and other sciences (for example, determining the composition of petroleum products, polymer substances, etc.). In chemistry according to MS. study the structure of molecules. Electronic M. s. make it possible to obtain information about the electronic shells of molecules, determine excited levels and their characteristics, and find the dissociation energies of molecules (by the convergence of the vibrational levels of a molecule to the dissociation boundaries). Study of oscillatory M. s. allows you to find characteristic vibration frequencies corresponding to certain types of chemical bonds in the molecule (for example, simple double and triple C-C connections, C-H bonds, N-H, O-H for organic molecules), various groups of atoms (for example, CH 2, CH 3, NH 2), determine the spatial structure of molecules, distinguish between cis- and trans-isomers. For this purpose, both infrared absorption spectra (IR) and Raman spectra (RSS) are used. The IR method has become especially widespread as one of the most effective optical methods for studying the structure of molecules. It provides the most complete information in combination with the SKR method. The study of rotational magnetic resonances, as well as the rotational structure of electronic and vibrational spectra, makes it possible to use experimentally found values ​​of the moments of inertia of molecules [which are obtained from the values ​​of rotational constants, see (7)] to find with great accuracy (for simpler molecules, for example H 2 O) parameters of the equilibrium configuration of the molecule - bond lengths and bond angles. To increase the number of determined parameters, the spectra of isotopic molecules (in particular, in which hydrogen is replaced by deuterium) having the same parameters of equilibrium configurations, but different moments of inertia, are studied.

As an example of the use of M. s. To determine the chemical structure of molecules, consider the benzene molecule C 6 H 6 . Studying her M. s. confirms the correctness of the model, according to which the molecule is flat, and all 6 C-C bonds in the benzene ring are equivalent and form a regular hexagon ( rice. 2 , b), having a sixth-order symmetry axis passing through the center of symmetry of the molecule perpendicular to its plane. Electronic M. s. absorption C 6 H 6 consists of several systems of bands corresponding to transitions from the ground even singlet level to excited odd levels, of which the first is triplet, and the higher ones are singlet ( rice. 5 ). The system of stripes is most intense in the area of ​​1840 Å (E 5 - E 1 = 7,0 ev), the system of bands is weakest in the region of 3400 Å (E 2 - E 1 = 3,8ev), corresponding to the singlet-triplet transition, which is prohibited by the approximate selection rules for the total spin. Transitions correspond to the excitation of the so-called. π electrons delocalized throughout the benzene ring (see Molecule) ; level diagram obtained from electronic molecular spectra rice. 5 is in agreement with approximate quantum mechanical calculations. Oscillatory M. s. C 6 H 6 correspond to the presence of a center of symmetry in the molecule - vibrational frequencies that appear (active) in the IRS are absent (inactive) in the SRS and vice versa (the so-called alternative prohibition). Of the 20 normal vibrations of C 6 H 6 4 are active in the ICS and 7 are active in the SCR, the remaining 11 are inactive in both the ICS and the SCR. Measured frequency values ​​(in cm -1): 673, 1038, 1486, 3080 (in ICS) and 607, 850, 992, 1178, 1596, 3047, 3062 (in TFR). Frequencies 673 and 850 correspond to non-plane vibrations, all other frequencies correspond to plane vibrations. Particularly characteristic of planar vibrations are the frequency 992 (corresponding to the stretching vibration of C-C bonds, consisting of periodic compression and stretching of the benzene ring), frequencies 3062 and 3080 (corresponding to the stretching vibrations of C-H bonds) and frequency 607 (corresponding to the bending vibration of the benzene ring). The observed vibrational spectra of C 6 H 6 (and similar vibrational spectra of C 6 D 6) are in very good agreement with theoretical calculations, which made it possible to give a complete interpretation of these spectra and find the shapes of all normal vibrations.

In the same way, you can use M. s. determine the structure of various classes of organic and inorganic molecules, up to very complex ones, such as polymer molecules.

Lit.: Kondratyev V.N., Structure of atoms and molecules, 2nd ed., M., 1959; Elyashevich M. A., Atomic and molecular spectroscopy, M., 1962; Herzberg G., Spectra and structure of diatomic molecules, trans. from English, M., 1949; him, Vibrational and rotational spectra of polyatomic molecules, trans. from English, M., 1949; him, Electronic spectra and structure of polyatomic molecules, trans. from English, M., 1969; Application of spectroscopy in chemistry, ed. V. Vesta, per. from English, M., 1959.

M. A. Elyashevich.

Rice. 4. Rotational splitting of the electronic-vibrational band 3805 Å of the N 2 molecule.

Rice. 1. Diagram of energy levels of a diatomic molecule: a and b - electronic levels; v" And v" - quantum numbers of vibrational levels. J" And J" - quantum numbers of rotational levels.

Rice. 2. Equilibrium configurations of molecules: a - H 2 O; b - CO 2; c - C 6 H 6; g - CH 4 . Numbers indicate bond lengths (in Å) and bond angles.

Rice. 5. Diagram of electronic levels and transitions for a benzene molecule. The energy levels are given in ev. C - singlet levels; T - triplet level. The parity of the level is indicated by the letters g and u. For systems of absorption bands, approximate wavelength regions in Å are indicated; more intense systems of bands are indicated by thicker arrows.

Rice. 3. Electronic-vibrational spectrum of the N 2 molecule in the near ultraviolet region; groups of bands correspond to different values ​​of Δ v = v" - v ".

Big Soviet encyclopedia. - M.: Soviet Encyclopedia. 1969-1978 .

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