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. with. - 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 decay with a 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 complicated with an increase in the number of atoms in a molecule. For highly 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 is the energy of the emitted absorbed Photon and the frequency ν ( h- The bar is constant). For Raman scattering hν is equal to the difference between the energies of the incident and scattered photons. M. s. much more complicated than the 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, there is an oscillatory movement of the nuclei (together with the internal electrons surrounding them) around the equilibrium positions and a rotational movement of the molecule as a whole. These three types of motions - 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 only take on certain values, that is, it is quantized. The total energy of the molecule E can be approximately represented as the sum of the quantized values ​​of the energies of the three types of its motion:

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

In order of magnitude

where m is the mass of the electron, and the quantity M has the order of the mass of the nuclei of atoms in the molecule, i.e. m/M Molecular spectra 10 -3 -10 -5, therefore:

E email >> E count >> E rotation (four)

Usually E el of the order of several ev(several hundred kJ/mol), E col Molecular spectra 10 -2 -10 -1 ev, E rotation 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 email 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 email and E count). On the rice. one the scheme of levels of a diatomic molecule is given; for polyatomic molecules, the system of levels becomes even more complicated.

Electronic energy levels ( E el in (2) and on the diagram rice. one 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. one in Art. Molecule). Each electronic state corresponds to a certain equilibrium configuration and a certain value E el; the smallest value corresponds to the main energy level.

The set of electronic states of a molecule is determined by the properties of its electron shell. Basically the values E el can be calculated by quantum chemistry methods (See Quantum Chemistry) , but given task can only be solved using approximate methods and for relatively simple molecules. The most important information about the electronic levels of a molecule (the arrangement of electronic energy levels and their characteristics), which is 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 have, as a rule, an even number of electrons, and for them S= 0, 1, 2... (for the main electronic level, the value S= 0, and for excited - S= 0 and S= 1). Levels from S= 0 are called singlets, with S= 1 - triplet (because the interaction in the molecule leads to their splitting into χ = 2 S+ 1 = 3 sublevels; see Multiplicity) . Free radicals usually have an odd number of electrons. S= 1 / 2 , 3 / 2 , ... and the value 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 Fig. 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 angular momentum of all electrons onto the axis of the molecule. Levels with λ = 0, 1, 2, ... are denoted respectively by Σ, П, Δ..., 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, such as 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 reversing at the center of symmetry or changes it).

Vibrational energy levels (values E kol) 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 equidistant 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, which takes on the values ​​0, 1, 2, ... On rice. one 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 non-linear molecules, respectively), it turns out f so-called. normal oscillations with frequencies ν i ( i = 1, 2, 3, ..., f) and a complex system 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 the atoms of the molecule or part of them participate in a certain normal vibration; atoms in this case make harmonic vibrations with one frequency v i , but with different amplitudes that determine the shape of the oscillation. Normal vibrations are divided according to their shape into valence (at which the lengths of bond lines change) and deformation (at which the angles between chemical bonds change - bond angles). The number of different vibrational frequencies for molecules of low symmetry (having no symmetry axes of order higher than 2) is 2, and all vibrations are non-degenerate, while for more symmetrical molecules there are double and triple degenerate vibrations (pairs and triplets of vibrations coinciding in frequency). For example, for a nonlinear triatomic molecule H 2 O ( rice. 2 , a) f= 3 and three nondegenerate vibrations are possible (two valence and one deformation). A more symmetrical linear triatomic CO 2 molecule ( rice. 2 , b) has f= 4 - two non-degenerate vibrations (valence) and one doubly degenerate (deformation). For a planar highly symmetric 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 valence and 6 deformation) and 6 non-planar deformation vibrations - perpendicular to this plane. An even more symmetrical tetrahedral CH 4 molecule ( rice. 2 , d) has f = 9 - one non-degenerate vibration (valence), one doubly degenerate (deformation) and two three times degenerate (one valence and one deformation).

The rotational energy levels can be found by quantizing rotary motion molecules, considering 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 about 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. one rotational levels are shown for each electronic-vibrational state.

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

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

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

Δ E email >> Δ E count >> Δ E rotation (9)

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

At Δ E el ≠ 0, electronic M. s are obtained, observed in the visible and in the ultraviolet (UV) regions. Usually at Δ E el ≠ 0 simultaneously Δ E count ≠ 0 and Δ E rotation ≠ 0; different Δ E count for a given Δ E el correspond to different vibrational bands ( rice. 3 ), and different Δ E rotation for given Δ E el and Δ E count - separate rotational lines into which this band breaks up; a characteristic striped structure is obtained ( rice. four ). The set of bands with a given Δ E el (corresponding to a purely electronic transition with a frequency v el = Δ E email / h) called the system of bands; individual bands have different intensities depending on the relative transition probabilities (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, and several such broad bands can overlap each other. Characteristic discrete electronic spectra are observed in frozen solutions of organic compounds (see the Shpol'skii 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 Fig. Spectral instruments).

At Δ E el = 0, and Δ E col ≠ 0, vibrational M. s are obtained, observed in a close (up to several micron) and in the middle (up to several tens micron) infrared (IR) region, usually in absorption, as well as in Raman scattering of light. As a rule, at the same time Δ E rotation ≠ 0 and for a given E If this is done, an oscillatory band is obtained, which breaks up into separate rotational lines. The most intense in vibrational 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 , forbidding other transitions are performed strictly; bands appear for anharmonic vibrations, for which Δ υ > 1 (overtones); their intensity is usually small 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 that are 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 col = 0, purely rotational M. s., consisting of individual lines, are obtained. They are observed in absorption in the distant (hundreds micron) IR region and especially in the microwave region, as well as in the Raman spectra. For diatomic and linear polyatomic molecules (as well as for sufficiently symmetric nonlinear polyatomic molecules), these lines are equally spaced (in the frequency scale) from each other with intervals Δν = 2 B in absorption spectra and Δν = 4 B in Raman spectra.

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

Methods of molecular spectroscopy, based on the study of molecular weight, make it possible to solve various problems in chemistry, biology, and other sciences (for example, to determine the composition of petroleum products, polymeric substances, and so on). In chemistry according to M. s. study the structure of molecules. Electronic M. with. make it possible to obtain information about the electron shells of molecules, to determine the excited levels and their characteristics, to find the dissociation energies of molecules (by the convergence of the vibrational levels of the molecule to the dissociation boundaries). Study of vibrational M. s. allows you to find the characteristic vibration frequencies corresponding to certain types of chemical bonds in a molecule (for example, simple double and triple C-C connections, C-H connections, 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, both infrared absorption spectra (IRS) 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 gives the most complete information in combination with the SRS method. The study of rotational molecular forces, as well as the rotational structure of electronic and vibrational spectra, makes it possible, from the values ​​of the moments of inertia of molecules found from experience [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 parameters to be determined, the spectra of isotopic molecules (in particular, in which hydrogen is replaced by deuterium) are studied, which have the same parameters of equilibrium configurations, but different moments of inertia.

As an example of M.'s application with. to determine the chemical structure of molecules, consider a benzene molecule C 6 H 6 . The study of 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), which has a sixth-order symmetry axis passing through the center of symmetry of the molecule perpendicular to its plane. Electronic M. with. 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 singlets ( rice. 5 ). The system of bands is most intense in the region 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 forbidden 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) ; obtained from electronic molecular spectra level diagram rice. 5 is in agreement with approximate quantum mechanical calculations. Vibrational M. s. C 6 H 6 correspond to the presence of a center of symmetry in the molecule - the vibrational frequencies that appear (active) in the ICS are absent (inactive) in the SKR and vice versa (the so-called alternative prohibition). Of the 20 normal vibrations of C6H6, 4 are active in the ICS and 7 are active in the TFR, the remaining 11 are inactive both in the ICS and in the TFR. The values ​​of the measured frequencies (in cm -1): 673, 1038, 1486, 3080 (in the ICS) and 607, 850, 992, 1178, 1596, 3047, 3062 (in the TFR). Frequencies 673 and 850 correspond to out-of-plane vibrations, all other frequencies correspond to plane vibrations. Particularly characteristic for planar vibrations are the frequency 992 (corresponding to the stretching vibration of the C-C bonds, which consists in periodic compression and stretching of the benzene ring), the frequencies 3062 and 3080 (corresponding to the stretching vibrations of the C-H bonds) and the frequency 607 (corresponding to the deformation 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 forms of all normal vibrations.

Similarly, with the help of M. s. determine the structure of various classes of organic and inorganic molecules, up to very complex ones, such as polymer molecules.

Lit.: Kondratiev 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; his, Vibrational and rotational spectra of polyatomic molecules, trans. from English, M., 1949; his, Electronic spectra and the structure of polyatomic molecules, trans. from English, M., 1969; Application of spectroscopy in chemistry, ed. V. Vesta, trans. from English, M., 1959.

M. A. Elyashevich.

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

Rice. 1. Scheme 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; in - C 6 H 6; d - CH 4 . Numbers indicate bond lengths (in Å) and bond angles.

Rice. 5. Scheme of electronic levels and transitions for the benzene molecule. The energy levels are given in ev. C - singlet levels; T - triplet level. The level parity is indicated by the letters g and u. For systems of absorption bands, the approximate wavelength ranges 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 ".

Great Soviet Encyclopedia. - M.: Soviet Encyclopedia. 1969-1978 .

See what "Molecular Spectra" is in other dictionaries:

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Molecular spectra due to the rotation of the molecule as a whole. Since the rotation of the molecule is quantized, V. s. consist of separate (almost equidistant) lines, i.e., they have a discrete character. V. s. observed in the far infrared Great Soviet Encyclopedia, Ochkin Vladimir Nikolaevich. Features are described and state of the art studies of low-temperature plasma by methods of classical and laser spectroscopy. The issues of physical interpretation of the results are considered…

spectrum called the sequence of energy quanta of electromagnetic radiation, absorbed, released, scattered or reflected by a substance during the transitions of atoms and molecules from one energy state to another.

Depending on the nature of the interaction of light with matter, the spectra can be divided into absorption (absorption) spectra; emissions (emission); scattering and reflection.

For the objects under study, optical spectroscopy, i.e. spectroscopy in the wavelength range 10 -3 ÷10 -8 m subdivided into atomic and molecular.

atomic spectrum is a sequence of lines, the position of which is determined by the energy of the transition of electrons from one level to another.

The energy of an atom can be represented as the sum of the kinetic energy of translational motion and electronic energy:

where - frequency, - wavelength, - wave number, - speed of light, - Planck's constant.

Since the energy of an electron in an atom is inversely proportional to the square of the principal quantum number , then for the line in the atomic spectrum we can write the equation:

.

(4.12)

Here - electron energies at higher and lower levels; - Rydberg constant; - spectral terms, expressed in units of wave numbers (m -1 , cm -1).

All lines of the atomic spectrum converge in the short-wavelength region to a limit determined by the ionization energy of the atom, after which there is a continuous spectrum.

Molecule energy in the first approximation can be considered as the sum of translational, rotational, vibrational and electronic energies:

(4.15)

For most molecules, this condition is satisfied. For example, for H 2 at 291 K, the individual components of the total energy differ by an order of magnitude or more:

309,5 kJ/mol,

=25,9 kJ/mol,

2,5 kJ/mol,

=3,8 kJ/mol.

The values ​​of photon energies in different regions of the spectrum are compared in Table 4.2.

Table 4.2 - Energy of absorbed quanta of different regions of the optical spectrum of molecules

The concepts of "oscillations of nuclei" and "rotation of molecules" are conditional. In fact, such types of motion only very approximately convey ideas about the distribution of nuclei in space, which is of the same probabilistic nature as the distribution of electrons.

A schematic system of energy levels in the case of a diatomic molecule is shown in Figure 4.1.

Transitions between rotational energy levels give rise to rotational spectra in the far IR and microwave regions. Transitions between vibrational levels within the same electronic level give vibrational-rotational spectra in the near-IR region, since a change in the vibrational quantum number inevitably entails a change in the rotational quantum number . Finally, transitions between electronic levels cause the appearance of electronic-vibrational-rotational spectra in the visible and UV regions.

In the general case, the number of transitions can be very large, but in fact, far from all appear in the spectra. The number of transitions is limited selection rules .

Molecular spectra provide a wealth of information. They can be used:

For the identification of substances in a qualitative analysis, as each substance has its own unique spectrum;

For quantitative analysis;

For structural group analysis, since certain groups, such as, for example, >C=O, _ NH 2 , _ OH, etc., give characteristic bands in the spectra;

To determine the energy states of molecules and molecular characteristics(internuclear distance, moment of inertia, natural oscillation frequencies, dissociation energies); a comprehensive study of molecular spectra makes it possible to draw conclusions about the spatial structure of molecules;

In kinetic studies, including for the study of very fast reactions.

- energies of electronic levels;

Energy of vibrational levels;

Energy of rotational levels

Figure 4.1 - Schematic arrangement of energy levels of a diatomic molecule

Bouguer-Lambert-Beer law

Quantitative molecular analysis using molecular spectroscopy is based on Bouguer-Lambert-Beer law , relating the intensity of the incident and transmitted light with the concentration and thickness of the absorbing layer (Figure 4.2):

or with a proportionality factor:

Integration result:

(4.19)

.

(4.20)

When the intensity of the incident light decreases by an order of magnitude

.

(4.21)

If \u003d 1 mol / l, then, i.e. the absorption coefficient is equal to the reciprocal thickness of the layer in which, at a concentration equal to 1, the intensity of the incident light decreases by an order of magnitude.

The absorption coefficients and depend on the wavelength. The type of this dependence is a kind of “fingerprint” of molecules, which is used in qualitative analysis to identify a substance. This dependence is characteristic and individual for a particular substance and reflects the characteristic groups and bonds included in the molecule.

Optical density D

expressed in %

4.2.3 Rotation energy of a diatomic molecule in the rigid rotator approximation. Rotational spectra of molecules and their application to determine molecular characteristics

The appearance of rotational spectra is due to the fact that the rotational energy of the molecule is quantized, i.e.

0

a

Energy of rotation of a molecule around the axis of rotation

Since the point O is the center of gravity of the molecule, then:

Introduction of the reduced mass notation:

(4.34)

leads to the equation

.

(4.35)

Thus, a diatomic molecule (Figure 4.7 a) rotating around the axis or , passing through the center of gravity, can be simply considered as a particle with mass , describing a circle with a radius around the point O(Figure 4.7 b).

The rotation of the molecule around the axis gives the moment of inertia, which is practically equal to zero, since the atomic radii are much smaller than the internuclear distance. Rotation about the axes or , mutually perpendicular to the bond line of the molecule, leads to equal moments of inertia:

where is a rotational quantum number that takes only integer values

0, 1, 2…. In accordance with selection rule for the rotational spectrum of a diatomic molecule, a change in the rotational quantum number upon absorption of an energy quantum is possible only by one, i.e.

transforms equation (4.37) into the form:

20 12 6 2

wavenumber of the line in the rotational spectrum corresponding to the absorption of a quantum upon transition from j energy level per level j+1, can be calculated by the equation:

Thus, the rotational spectrum in the approximation of the rigid rotator model is a system of lines located at the same distance from each other (Figure 4.5b). Examples of the rotational spectra of diatomic molecules estimated in the rigid rotator model are shown in Figure 4.6.

a b

Figure 4.6 - Rotational spectra HF (a) and CO(b)

For hydrogen halide molecules, this spectrum is shifted to the far IR region of the spectrum; for heavier molecules, it is shifted to the microwave region.

Based on the obtained patterns of the occurrence of the rotational spectrum of a diatomic molecule, in practice, first determine the distance between adjacent lines in the spectrum, from which they then find, and according to the equations:

,

(4.45)

where - centrifugal distortion constant , is related to the rotational constant by the approximate relationship . The correction should be taken into account only for very large j.

For polyatomic molecules, in the general case, the existence of three different moments of inertia is possible . In the presence of symmetry elements in the molecule, the moments of inertia can coincide or even be equal to zero. For example, for linear polyatomic molecules(CO 2 , OCS, HCN, etc.)

where - position of the line corresponding to the rotational transition in an isotopically substituted molecule.

To calculate the isotopic shift of the line, it is necessary to sequentially calculate the reduced mass of the isotopically substituted molecule, taking into account the change in the atomic mass of the isotope, the moment of inertia , rotational constant and the position of the line in the spectrum of the molecule according to equations (4.34), (4.35), (4.39) and (4.43), respectively , or estimate the ratio of the wave numbers of lines corresponding to the same transition in isotopically substituted and non-isotopically substituted molecules, and then determine the direction and magnitude of the isotopic shift using equation (4.50). If the internuclear distance is approximately constant , then the ratio of the wave numbers corresponds to the inverse ratio of the reduced masses:

where is the total number of particles, is the number of particles per i- that level of energy at temperature T, k- Boltzmann's constant, - statistical ve forces degree of degeneracy i-th energy level, characterizes the probability of finding particles at a given level.

For a rotational state, the population of a level is usually characterized by the ratio of the number of particles j- that energy level to the number of particles at the zero level:

,

(4.53)

where - statistical weight j-th rotational energy level, corresponds to the number of projections of the momentum of a rotating molecule on its axis - the communication line of the molecule, , energy of the zero rotational level . The function goes through a maximum when increasing j, as Figure 4.7 illustrates with the CO molecule as an example.

The extremum of the function corresponds to the level with the maximum relative population, the value of the quantum number of which can be calculated from the equation obtained after determining the derivative of the function in the extremum:

.

(4.54)

Figure 4.7 - Relative population of rotational energy levels

molecules CO at temperatures of 298 and 1000 K

Example. In the rotational spectrum of HI, the distance between adjacent lines is determined cm -1. Calculate the rotational constant, the moment of inertia, and the equilibrium internuclear distance in the molecule.

Solution

In the approximation of the rigid rotator model, in accordance with equation (4.45), we determine the rotational constant:

cm -1.

The moment of inertia of the molecule is calculated from the value of the rotational constant according to equation (4.46):

kg . m 2.

To determine the equilibrium internuclear distance, we use equation (4.47), taking into account that the masses of hydrogen nuclei and iodine expressed in kg:

Example. In the far IR region of the spectrum of 1 H 35 Cl, lines were found whose wavenumbers are:

Determine the average values ​​of the moment of inertia and the internuclear distance of the molecule. Attribute the observed lines in the spectrum to rotational transitions.

Solution

According to the rigid rotator model, the difference between the wave numbers of adjacent lines of the rotational spectrum is constant and equal to 2 . Let us determine the rotational constant from the average value of the distances between adjacent lines in the spectrum:

cm -1 ,

cm -1

We find the moment of inertia of the molecule (equation (4.46)):

We calculate the equilibrium internuclear distance (equation (4.47)), taking into account that the masses of hydrogen nuclei and chlorine (expressed in kg):

Using equation (4.43), we estimate the position of the lines in the rotational spectrum of 1 H 35 Cl:

We correlate the calculated values ​​of the wave numbers of the lines with the experimental ones. It turns out that the lines observed in the rotational spectrum of 1 H 35 Cl correspond to the transitions:

N lines
, cm -1	85.384	106.730	128.076	149.422	170.768	192.114	213.466
	3 4	4 5	5 6	6 7	7 8	8 9	9 10

Example. Determine the magnitude and direction of the isotopic shift of the absorption line corresponding to the transition from energy level, in the rotational spectrum of the 1 H 35 Cl molecule when the chlorine atom is replaced by the 37 Cl isotope. The internuclear distance in 1 H 35 Cl and 1 H 37 Cl molecules is considered to be the same.

Solution

To determine the isotopic shift of the line corresponding to the transition , we calculate the reduced mass of the 1 H 37 Cl molecule, taking into account the change in the atomic mass of 37 Cl:

then we calculate the moment of inertia, the rotational constant and the position of the line in the spectrum of the 1 H 37 Cl molecule and the value of the isotopic shift according to equations (4.35), (4.39), (4.43) and (4.50), respectively.

Otherwise, the isotope shift can be estimated from the ratio of the wave numbers of lines corresponding to the same transition in molecules (we assume that the internuclear distance is constant) and then the position of the line in the spectrum using equation (4.51).

For 1 H 35 Cl and 1 H 37 Cl molecules, the ratio of the wave numbers of a given transition is:

To determine the wave number of the line of an isotopically substituted molecule, we substitute the value of the transition wave number found in the previous example j → j+1 (3→4):

We conclude: the isotopic shift to the low-frequency or long-wave region is

85.384-83.049=2.335 cm -1 .

Example. Calculate the wave number and wavelength of the most intense spectral line of the rotational spectrum of the 1 H 35 Cl molecule. Match the line to the corresponding rotational transition.

Solution

The most intense line in the rotational spectrum of the molecule is associated with the maximum relative population of the rotational energy level.

Substituting the value of the rotational constant found in the previous example for 1 H 35 Cl ( cm -1) into equation (4.54) allows you to calculate the number of this energy level:

.

The wave number of the rotational transition from this level is calculated by equation (4.43):

We find the transition wavelength from the equation (4.11) transformed with respect to:

4.2.4 Multivariant task No. 11 "Rotational spectra of diatomic molecules"

1. Write a quantum mechanical equation to calculate the rotational energy of a diatomic molecule as a rigid rotator.

2. Derive an equation for calculating the change in the rotation energy of a diatomic molecule as a rigid rotator when it passes to the next, higher quantum level .

3. Derive an equation for the dependence of the wave number of rotational lines in the absorption spectrum of a diatomic molecule on the rotational quantum number.

4. Derive an equation for calculating the difference between the wave numbers of adjacent lines in the rotational absorption spectrum of a diatomic molecule.

5. Calculate the rotational constant (in cm -1 and m -1) of a diatomic molecule A by the wave numbers of two adjacent lines in the long-wavelength infrared region of the rotational absorption spectrum of the molecule (see Table 4.3) .

6. Determine the rotational energy of the molecule A at the first five quantum rotational levels (J).

7. Draw schematically the energy levels of the rotational motion of a diatomic molecule as a rigid rotator.

8. Plot on this diagram the rotational quantum levels of a molecule that is not a rigid rotator.

9. Derive an equation for calculating the equilibrium internuclear distance based on the difference between the wavenumbers of neighboring lines in the rotational absorption spectrum.

10. Determine the moment of inertia (kg. m 2) of a diatomic molecule A.

11. Calculate the reduced mass (kg) of the molecule A.

12. Calculate the equilibrium internuclear distance () of a molecule A. Compare the resulting value with the reference data.

13. Assign the observed lines in the rotational spectrum of the molecule A to rotational transitions.

14. Calculate the wavenumber of the spectral line corresponding to the rotational transition from the level j for a molecule A(see table 4.3).

15. Calculate the reduced mass (kg) of an isotopically substituted molecule B.

16. Calculate the wave number of the spectral line associated with the rotational transition from the level j for a molecule B(see table 4.3). Internuclear distances in molecules A and B consider equal.

17. Determine the magnitude and direction of the isotopic shift in the rotational spectra of molecules A and B for the spectral line corresponding to the rotational level transition j.

18. Explain the reason for the nonmonotonic change in the intensity of absorption lines as the rotational energy of the molecule increases

19. Determine the quantum number of the rotational level corresponding to the highest relative population. Calculate the wavelengths of the most intense spectral lines of the rotational spectra of molecules A and B.

MOLECULAR SPECTRA, spectra of emission and absorption of electromagnet. radiation and combinat. scattering of light belonging to free or weakly bound molecules. They have the form of a set of bands (lines) in the X-ray, UV, visible, IR and radio wave (including microwave) regions of the spectrum. The position of the bands (lines) in the spectra of emission (emission molecular spectra) and absorption (absorption molecular spectra) is characterized by frequencies v (wavelengths l \u003d c / v, where c is the speed of light) and wave numbers \u003d 1 / l; it is determined by the difference between the energies E "and E: those states of the molecule, between which a quantum transition occurs:

(h is Planck's constant). When combined scattering, the value of hv is equal to the difference between the energies of the incident and scattered photons. The intensity of the bands (lines) is related to the number (concentration) of molecules of a given type, the population of the energy levels E "and E: and the probability of the corresponding transition.

The probability of transitions with the emission or absorption of radiation is determined primarily by the square of the matrix element of the electric. dipole moment of the transition, and with a more accurate consideration - and the squares of the matrix elements of the magn. and electric quadrupole moments of the molecule (see Quantum transitions). When combined In light scattering, the transition probability is related to the matrix element of the induced (induced) dipole moment of the transition of the molecule, i.e. with the matrix element of the polarizability of the molecule .

states of the pier. systems, transitions between to-rymi are shown in the form of these or those molecular spectra, have the different nature and strongly differ on energy. The energy levels of certain types are located far from each other, so that during transitions the molecule absorbs or emits high-frequency radiation. The distance between the levels of other nature is small, and in some cases, in the absence of external. field levels merge (degenerate). At small energy differences, transitions are observed in the low-frequency region. For example, the nuclei of atoms of certain elements have their own. magn. torque and electric spin-related quadrupole moment. Electrons also have a magnet. the moment associated with their spin. In the absence of external magnetic orientation fields moments are arbitrary, i.e. they are not quantized and the corresponding energetic. states are degenerate. When applying external permanent magnet. field, degeneracy is lifted and transitions between energy levels are possible, which are observed in the radio-frequency region of the spectrum. This is how NMR and EPR spectra arise (see Nuclear magnetic resonance, Electron paramagnetic resonance).

Kinetic distribution energies of electrons emitted by the pier. systems as a result of irradiation with X-ray or hard UV radiation, gives X-rayspectroscopy and photoelectron spectroscopy. Additional processes in the mall. system, caused by the initial excitation, lead to the appearance of other spectra. Thus, Auger spectra arise as a result of relaxation. electron capture from ext. shells to.-l. atom per vacant ext. shell, and the released energy turned into. in the kinetic energy other electron ext. shell emitted by an atom. In this case, a quantum transition is carried out from a certain state of a neutral molecule to a state they say. ion (see Auger spectroscopy).

Traditionally, only the spectra associated with the optical properties are referred to as molecular spectra proper. transitions between electronic-vibrational-rotate, energy levels of the molecule associated with three main. energy types. levels of the molecule - electronic E el, vibrational E count and rotational E vr, corresponding to three types of ext. movement in a molecule. For E el take the energy of the equilibrium configuration of the molecule in a given electronic state. The set of possible electronic states of a molecule is determined by the properties of its electron shell and symmetry. Swing. the motion of the nuclei in the molecule relative to their equilibrium position in each electronic state is quantized so that at several vibrations. degrees of freedom, a complex system of vibrations is formed. energy levels E col. The rotation of the molecule as a whole as a rigid system of bound nuclei is characterized by rotation. the moment of the number of motion, which is quantized, forming a rotation. states (rotational energy levels) E temp. Usually the energy of electronic transitions is of the order of several. eV, vibrational -10 -2 ... 10 -1 eV, rotational -10 -5 ... 10 -3 eV.

Depending on between which energy levels there are transitions with emission, absorption or combinations. electromagnetic scattering. radiation - electronic, oscillating. or rotational, distinguish between electronic, oscillating. and rotational molecular spectra. The articles Electronic spectra , Vibrational spectra , Rotational spectra provide information about the corresponding states of molecules, selection rules for quantum transitions, methods of pier. spectroscopy, as well as what characteristics of molecules can be. obtained from molecular spectra: St. islands and symmetry of electronic states, vibrate. constants, dissociation energy, molecular symmetry, rotation. constants, moments of inertia, geom. parameters, electrical dipole moments, data on the structure and ext. force fields, etc. Electronic absorption and luminescence spectra in the visible and UV regions provide information on the distribution

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. bands, and with a high resolution of the spectral equipment, their rotation is detected. 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 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 AT 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 N m- 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 + v l, 2vk + v l etc., and the difference bands vk - v l, 2vk - e l etc. Band intensities 2u k, vk + v l and vk - v l depend on the first and second derivatives d on 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

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 mutual arrangement nuclei of atoms and is a function of distance, i.e.

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

Consequently,

.

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 dependency graph potential energy 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 .

Rotational energy 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 of 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 of the periodic system of 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 there is a detachment of electrons located in the electron shell that has begun to build up.

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 provides an explanation for 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 have shown that

Therefore, with weak excitations, only changes , with stronger - , with even stronger - . Let us discuss in more detail the various types of 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.

The 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.

For every vibrational energy state a system of rotational levels is superimposed. 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.

combinational light scattering

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 called luminescence, which remains luminous for a long time after the action of the luminescence causative agent.

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 an interaction electromagnetic wave with the atoms of the matter 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 optical pumping 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.