Electronic vibrational and rotational spectra of molecules. Infrared spectra, their origin. Obtaining IR spectra

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 ext. fields (and, therefore, with the surrounding atoms and molecules). Naib. characteristic are M. s. rarefied molecular gases when absent broadening of spectral lines pressure: such a spectrum consists of narrow lines with Doppler width.

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

In accordance with three systems of energy levels in a molecule - electronic, vibrational and rotational (Fig. 1), M. p. consist of a collection of electronic vibrations. and rotate. spectra and lie in a wide range of electromagnets. waves - from radio frequencies to X-rays. areas of the spectrum. The frequencies of the transitions between rotate. energy levels usually fall into the microwave region (in the wave number scale of 0.03-30 cm -1), the frequency of transitions between vibrations. levels - in the IR region (400-10000 cm -1), and the frequencies of transitions between electronic levels - in the visible and UV regions of the spectrum. This division is conditional, since they are often rotated. transitions also fall into the IR region, vibrate. transitions to the visible region, and electronic transitions to the IR region. Usually, electronic transitions are accompanied by a change in vibrations. the energy of the molecule, and when they vibrate. transitions change and rotate. energy. Therefore, most often the electronic spectrum is an electron-vibrational system. bands, and at a high resolution of the spectral equipment, they are rotated. structure. Intensity of lines and bands in M. c. is determined by the probability of the corresponding quantum transition. Naib. intense lines correspond to the transition allowed selection rules.K M. s. also include Auger spectra and X-rays. molecular spectra(not considered in the article; see. Auger effect, Auger spectroscopy, X-ray spectra, X-ray spectroscopy).

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

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 the excited triplet state to the ground. singlet state.

Molecules in decomp. electronic states often have different geomes. symmetry. In such cases, the condition Г " G "" G d should 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 xy type of symmetry of the dipole moment Г d= S + (d z) -P ( d x, d y), therefore, only the S + - S +, S - - S -, P - P, etc. transitions with the transition dipole moment directed along the axis of the molecule and the S + - P, P - D, etc. transitions are allowed for them. with the moment of transition directed perpendicular to the axis of the molecule (for the designation of states, see Art. Molecule).

Probability V electric dipole transition from electronic level T to the electronic level NS summed over all vibrational-rotate. electronic level levels T, is determined by f-loy:

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

where N m- the number of molecules in the beginning. condition m, v nm- transition frequency TNS... Often electronic transitions are characterized by

Rotational spectra

Consider the rotation of a two atomic molecule around its axis. The molecule has the lowest energy in the absence of rotation. This state corresponds to a rotational quantum number j = 0. The nearest excited level (j = 1) corresponds to a certain rotation speed. To transfer a molecule to this level, it is necessary to expend energy E 1. At j = 2,3,4… the rotation speed is 2,3,4… times higher than at j = 0. The internal energy of the molecule increases with the speed of rotation and the distance between the levels increases. The energy difference between neighboring levels is constantly increasing by the same value E 1. In this regard, the rotational spectrum consists of separate lines; for the first line ν 1 = Е 1 / ħ, and for the next 2ν 1, 3 ν 1, etc. The energy difference between the rotational levels is very small, so even at room temperature the kinetic energy of the molecules during their collision turns out to be sufficient to excite the rotational levels. The molecule can absorb a photon and move to a higher rotational level. In this way, absorption spectra can be investigated.

The frequency depends on the mass of the molecule and its size. With increasing mass, the distance between the levels decreases and the entire spectrum shifts towards longer wavelengths.

Rotational spectra can be observed for substances in a gaseous state. In liquid and solid bodies, there is practically no shaped rotation. The need to convert the analyte into a gaseous state without destroying it severely limits the use of rotational spectra (as does the difficulty of working in the far IR region).

If the molecule is given additional energy, less than the bond cleavage energy E chem, then the atoms will vibrate around the equilibrium position, and the vibration amplitude will have only certain values. The vibrational spectra exhibit bands rather than individual lines (as for atoms or in rotational spectra). The fact is that the energy of a molecule depends both on the positions of individual atoms and on the rotation of the entire molecule. So any vibrational level turns out to be complex and splits into a number of simple levels.

Separate lines of the rotational structure are clearly visible in the vibrational spectra of gaseous substances. There are no specific rotational levels in liquids and solids. So one wide band is observed in them. Vibrations of polyatomic molecules are much more complicated than 2-atomic ones, because the number of possible vibration modes grows rapidly with the number of atoms in the molecule.

For example, a linear CO 2 molecule has 3 types of vibrations.

The first 2 types are valence (one is symmetric, the other is antisymmetric). During vibrations of the third type, the bond angles change and the atoms are displaced in directions perpendicular to the valence bonds, the length of which remains almost constant. Such vibrations are called deformation vibrations. To excite bending vibrations, less energy is required than for stretching vibrations. The absorption bands associated with the excitation of deformation transitions have a frequency 2-3 times lower than the frequencies of stretching vibrations. Oscillations in CO 2 affect all atoms at once. Such vibrations are called skeletal. They are characteristic only for a given molecule and the corresponding bands do not even coincide with substances with a similar structure.

In complex molecules, vibrations are also distinguished in which only small groups of atoms participate. The bands of such vibrations are characteristic of certain groups and their frequencies change little when the structure of the rest of the molecule changes. So in the absorption spectra of chemical compounds, it is easy to detect the presence of certain groups.

So, any molecule has its own specific absorption spectrum in the infrared region of the spectrum. It is almost impossible to find 2 substances with the same spectra.

Simultaneously with the change in the vibrational state of the molecule, its rotational state also changes. A change in vibrational and rotational states leads to the appearance of rotational-vibrational spectra. The vibrational energy of molecules is approximately one hundred times greater than its rotational energy, so rotation does not violate the vibrational structure of molecular spectra. The superposition of energetically small rotational quanta on relatively large in energy vibrational quanta, shifts the lines of the vibrational spectrum to the near infrared region of the electromagnetic spectrum and turns them into bands. For this reason, the rotational-vibrational spectrum, which is observed in the near infrared region, has a line-striped structure.

Each band of such a spectrum has a central line (dashed line), the frequency of which is determined by the difference in the vibrational terms of the molecule. The set of such frequencies represents the pure vibrational spectrum of the molecule. Quantum-mechanical calculations associated with the solution of the Schrödinger wave equation, taking into account the mutual influence of the rotational and vibrational states of the molecule, lead to the expression:

where and are not constant for all energy levels and depend on the vibrational quantum number.

where and are constants smaller in magnitude than and. Due to the smallness of the parameters and, in comparison with the quantities and, the second terms in these ratios can be neglected and the actual rotational-vibrational energy of the molecule can be considered as the sum of the vibrational and rotational energy of a rigid molecule, then, respectively, the expression:

This expression conveys the structure of the spectrum well and leads to distortion only at large values ​​of the quantum numbers and. Consider the rotational structure of the rotational-vibrational spectrum. So, during radiation, a molecule passes from higher energy levels to lower ones, and lines with frequencies appear in the spectrum:

those. for the frequency of the line of the rotational-vibrational spectrum, we can write down accordingly:

the set of frequencies gives a rotational-vibrational spectrum. The first term in this equation expresses the spectral frequency that occurs when only vibrational energy changes. Let us consider the distribution of rotational lines in the spectral bands. Within the boundaries of one strip, its fine rotational structure is determined only by the value of the rotational quantum number. For such a strip, it can be written as:

According to Pauli's selection rule:

the entire band is divided into two groups of spectral series, which are located relatively on both sides. Indeed, if:

those. when:

then we get a group of lines:

those. when:

then we get a group of lines:

In the case of transitions when the molecule passes from the first rotational level to the rotational energy level, a group of spectral lines with frequencies appears. This group of lines is called the positive or - branch of the spectrum band, starting with. During transitions, when the molecule passes from the th to the energy level, a group of spectral lines with frequencies appears. This group of lines is called negative or - the branch of the spectrum band, starting with. This is due to the fact that the meaning that is responsible has no physical meaning. - and - the branches of the strip, based on equations of the form:

consist of lines:

Thus, each band of the rotational-vibrational spectrum consists of two groups of equidistant lines with a distance between adjacent lines:

for a real non-rigid molecule, given the equation:

for the frequency of the lines - and - of the band branches, we get:

As a result, the lines - and - of the branches are bent and not equidistant lines are observed, but - branches that diverge and - branches that converge to form the edge of the strip. Thus, the quantum theory of molecular spectra turned out to be capable of decoding spectral bands in the near infrared region, interpreting them as the result of a simultaneous change in rotational and vibrational energy. It should be noted that molecular spectra are a valuable source of information on the structure of molecules. By studying molecular spectra, it is possible to directly determine various discrete energy states of molecules and, based on the data obtained, make reliable and accurate conclusions regarding the motion of electrons, vibration and rotation of nuclei in a molecule, as well as obtain accurate information regarding the forces acting between atoms in molecules, internuclear distances and geometric the arrangement of nuclei in molecules, the dissociation energy of the molecule itself, etc.

They are represented by a model of two interacting point masses m 1 and m 2 with an equilibrium distance r e between them (bond length), and vibrate. the motion of the nuclei is considered harmonic and is described by the unity, the coordinate q = r-r e, where r is the current internuclear distance. Potential energy dependence is staggering. motions of V from q are determined in the harmonic approximation. oscillator [oscillating material point with reduced mass m = m 1 m 2 / (m 1 + m 2)] as f-tion V = l / 2 (K e q 2), where K e = (d 2 V / dq 2) q = 0 - harmonic. force constant

Rice. 1. Dependence of the potential energy V of a harmonic oscillator (dashed line) and a real diatomic molecule (solid line) on the internuclear distance r (r with equilibrium value r); horizontal straight lines indicate oscillation. levels (0, 1, 2, ... values ​​of the vibrational quantum number), vertical arrows - some vibrations. transitions; D 0 - dissociation energy of the molecule; the shaded area corresponds to the continuous spectrum. molecules (dashed line in Fig. 1). According to the classic. mechanics, the frequency is harmonic. hesitation Quantum mech. consideration of such a system gives a discrete sequence of equidistant energy levels E (v) = hv e (v + 1/2), where v = 0, 1, 2, 3, ... is the vibrational quantum number, v e is harmonic. vibrational constant of a molecule (h is Planck's constant). When moving between adjacent levels, according to the selection rule D v = 1, a photon with energy hv = D E = E (v + 1) -E (v) = hv e (v + 1 + 1/2) -hv e (v + 1/2) = hv e, i.e., the frequency of the transition between any two adjacent levels is always one and the same, and coincides with the classic. frequency harmonic. hesitation. Therefore, v e is called. also harmonious. frequency. For real molecules, the potential energy curve is not the indicated quadratic function q, i.e., a parabola. Oscillation. the levels approach more and more as we approach the dissociation limit of the molecule and for the anharmonic model. oscillators are described by the equation: E (v) =, where X 1 is the first constant anharmonicity. The frequency of transitions between neighboring levels does not remain constant, and, in addition, transitions that meet the selection rules are possible D v = 2, 3, .... Frequency of transition from the level v = 0 to the level v = 1 called. fundamental, or fundamental, frequency, transitions from the level v = 0 to levels v> 1 give overtone frequencies, and transitions from levels v> 0 - the so-called. hot frequencies. In the IR absorption spectrum of diatomic molecules vibrate. frequencies are observed only in heteronuclear molecules (HCl, NO, CO, etc.), and the selection rules are determined by changing their electr. dipole moment during oscillations. In the Raman spectra vibrate. frequencies are observed for any diatomic molecules, both homonuclear and heteronuclear (N 2, O 2, CN, etc.), since for such spectra, the selection rules are determined by the change in the polarizability of molecules during vibrations. Determined from vibrational harmonic spectra. constants Ke and v e, constants of anharmonicity, as well as the dissociation energy D 0 - important characteristics of the molecule, necessary, in particular, for thermochemical. calculations. The study is vibrational-rotate. spectra of gases and vapors allows you to determine rotate. constants В v (see Rotational spectra), moments of inertia and internuclear distances of diatomic molecules. Polyatomic molecules are considered as systems of bound point masses. Oscillation. the motion of nuclei relative to equilibrium positions with a fixed center of mass in the absence of rotation of the molecule as a whole is usually described using the so-called. int. natures. coordinates q i, chosen as changes in bond lengths, bond and dihedral angles of spaces, model of a molecule. A molecule consisting of N atoms has n = 3N - 6 (for a linear molecule 3N - 5) vibrate. degrees of freedom. In the space of natures. coordinates q i complex oscillate. the movement of nuclei can be represented by n separate oscillations, each with a certain frequency v k (k takes values ​​from 1 to n), with which all natures change. coordinates q i at the amplitudes q 0 i and phases determined for the given oscillation. Such fluctuations are called. normal. For example, a triatomic linear molecule AX 2 has three normal vibrations:


Oscillation v 1 is called. symmetric stretching vibration (bond stretching), v 2 - deformed vibration (change in the bond angle), v 3 antisymmetric stretching vibration. In more complex molecules, there are other normal vibrations (changes in dihedral angles, torsional vibrations, pulsations of cycles, etc.). Quantization is shaking. energy of a polyatomic molecule in the approximation of multidimensional harmonic. an oscillator leads to a trace, a system to oscillate. energy levels:
where v ek is harmonic. sway. constants, v k - oscillate. quantum numbers, d k - the degree of degeneracy of the energy level along the k-th oscillation. quantum number. Main the frequencies in the vibrational spectra are due to transitions from the zero level [all v k = 0, vibrate. energy to levels characterized by

such sets of quantum numbers v k, in which only one of them is equal to 1, and all the others are equal to 0. As in the case of diatomic molecules, in anharmonic. approximation, overtone and "hot" transitions are also possible and, in addition, the so-called. combined, or compound, transitions involving levels, for which two or more of the quantum numbers v k are nonzero (Fig. 2).

Rice. 2. System of vibrational terms E / hc (cm "; c is the speed of light) of the H2O molecule and some transitions; v 1, v 2. V 3 - vibrational quantum numbers.

Interpretation and Application. Vibrational spectra of polyatomic molecules are highly specific and present a complex picture, although the total number of experimentally observed bands may be. significantly less than their possible number, which theoretically corresponds to the predicted set of levels. Usually DOS. frequencies correspond to more intense bands in the vibrational spectra. The selection rules and the probability of transitions in the IR and Raman spectra are different, since related acc. with changes in electric the dipole moment and polarizability of the molecule at each normal vibration. Therefore, the appearance and intensity of bands in the IR and Raman spectra depend differently on the type of symmetry of vibrations (the ratio of the configurations of a molecule arising as a result of vibrations of nuclei to symmetry operations that characterize its equilibrium configuration). Some of the bands of vibrational spectra can be observed only in the IR or only in the Raman spectrum, others with different intensities in both spectra, and some are not observed experimentally at all. So, for molecules that do not have symmetry or have low symmetry without a center of inversion, all basic. frequencies are observed with different intensities in both spectra; for molecules with an inversion center, none of the observed frequencies is repeated in the IR and Raman spectra (the rule of alternative exclusion); some of the frequencies may be absent in both spectra. Therefore, the most important of the applications of vibrational spectra is the determination of the symmetry of the molecule from a comparison of the IR and Raman spectra, along with the use of other experiments. data. Given the models of a molecule with different symmetry, one can theoretically calculate in advance for each of the models how many frequencies in the IR and Raman spectra should be observed, and on the basis of comparison with experiment. data to make the appropriate choice of model. Although every normal wobble, by definition, is wobbling. the movement of the entire molecule, some of them, especially in large molecules, can most of all affect only K.-L. fragment of a molecule. The amplitudes of the displacement of the nuclei not included in this fragment are very small with such a normal vibration. This is the basis of the widely used structural analyte. research concept of the so-called. group, or characteristic, frequencies: certain funkts. groups or fragments repeating in molecules decomp. Comm., are characterized by approximately the same frequencies in the vibrational spectra, according to which m. their presence in the molecule of the given substance has been established (though not always with the same high degree of reliability). For example, the carbonyl group is characterized by a very intense band in the IR absorption spectrum in the region of ~ 1700 (b 50) cm -1, related to the stretching vibration. The absence of absorption bands in this region of the spectrum proves that there is no group in the molecule of the investigated substance. At the same time, the presence of K.-L. bands in this region is not yet unambiguous evidence of the presence of a carbonyl group in the molecule, since frequencies of other vibrations of the molecule may accidentally appear in this region. Therefore, structural analysis and determination of conformations by fluctuate. frequencies func. groups should rely on several. characteristic frequencies, and the proposed structure of the molecule must be confirmed by data from other methods (see Structural chemistry). There are reference books containing numerous. structural and spectral correlations; there are also data banks and corresponding programs for information retrieval systems and structural analytes. research using computers. Isotopic helps to correctly interpret vibrational spectra. substitution of atoms, leading to a change in vibrations. frequencies. So, the replacement

VIBRATIONAL SPECTRA, they say. spectra due to quantum transitions between vibrational energy levels of molecules. Experimentally observed as IR absorption spectra and spectra of combinations. scattering (CR); range of wave numbers ~ 10-4000 cm -1 (vibrational transition frequencies 3. 10 11 -10 14 Hz). Oscillation. energy levels are determined by quantizing the vibrational motion of atomic nuclei. Diatomic molecules. In the simplest case, a diatomic molecule is represented by a model of two interacting point masses m 1 and m 2 with an equilibrium distance r e between them (bond length), and the vibrational motion of nuclei is considered harmonic and described by the units, coordinate q = rr e, where r is the current internuclear distance ... The dependence of the potential energy of the vibrational motion V on q is determined in the harmonic approximation. oscillator [oscillating material point with reduced mass m = m 1 m 2 / (m 1 + m 2)] as a function of V = l / 2 (K eq 2), where K e = (d 2 V / dq 2) q = 0 - harmonious. force constant

Rice. 1. The dependence of the potential energy V is harmonic. an oscillator (dashed curve) and a real diatomic molecule (solid curve) from the internuclear distance r (r with the equilibrium value of r); horizontal straight lines show vibrational levels (0, 1, 2, ... values ​​of the vibrational quantum number), vertical arrows - some vibrational transitions; D 0 - dissociation energy of the molecule; the shaded area corresponds to the continuous spectrum. molecules (dashed line in Fig. 1).

According to the classic. mechanics, the frequency is harmonic. hesitation The quantum mechanical consideration of such a system gives a discrete sequence of equidistant energy levels E (v) = hv e (v + 1/2), where v = 0, 1, 2, 3, ... is the vibrational quantum number, v e is harmonic. vibrational constant of a molecule (h is Planck's constant). When passing between neighboring levels, according to the selection rule D v = 1, a photon with energy hv = DE = E (v + 1) -E (v) = hv e (v + 1 + 1/2) -hv e (v + 1/2) = hv e, i.e., the frequency of the transition between any two adjacent levels is always the same, and coincides with the classical one. frequency harmonic. hesitation. Therefore, v e is also called harmonic. frequency. For real molecules, the potential energy curve is not the indicated quadratic function of q, i.e., a parabola. Oscillation. the levels approach more and more as we approach the dissociation limit of the molecule and for the anharmonic model. oscillators are described by the equation: E (v) =, where X 1 is the first constant of anharmonicity. The frequency of the transition between neighboring levels does not remain constant, and, in addition, transitions are possible that meet the selection rules D v = 2, 3, .... The frequency of the transition from the level v = 0 to the level v = 1 is called the fundamental, or fundamental, frequency , the transitions from the v = 0 level to the v> 1 levels give overtone frequencies, and the transitions from the v> 0 levels give the so-called hot frequencies. In the IR absorption spectrum of diatomic molecules, vibrational frequencies are observed only in heteronuclear molecules (HCl, NO, CO, etc.), and the selection rules are determined by the change in their electrical. dipole moment during oscillations. In Raman spectra, vibrational frequencies are observed for any diatomic molecules, both homonuclear and heteronuclear (N 2, O 2, CN, etc.), since for such spectra the selection rules are determined by the change in the polarizability of molecules during vibrations. Determined from VIBRATIONAL SPECTRA c. harmonious. the constants Ke and v e, the anharmonicity constants, and the dissociation energy D 0 are important characteristics of the molecule, which are necessary, in particular, for thermochemical calculations. The study of the vibrational-rotational spectra of gases and vapors makes it possible to determine the rotational constants B v (see Rotational spectra), moments of inertia, and internuclear distances of diatomic molecules. Polyatomic molecules are considered as systems of bound point masses. Oscillation. the motion of nuclei relative to equilibrium positions with a fixed center of mass in the absence of rotation of the molecule as a whole is usually described using the so-called int. natures. coordinates q i, chosen as changes in bond lengths, bond and dihedral angles of spaces, model of a molecule. A molecule consisting of N atoms has n = 3N - 6 (for a linear molecule 3N - 5) vibrational degrees of freedom. In the space of natures. coordinates q i the complex oscillatory motion of nuclei can be represented by n separate oscillations, each with a certain frequency v k (k takes values ​​from 1 to n), with which all natures change. coordinates q i at the amplitudes q 0 i and phases determined for the given oscillation. Such fluctuations are called normal. For example, a triatomic linear molecule AX 2 has three normal vibrations:


Oscillation v 1 is called symmetric stretching vibration (bond stretching), v 2 - deformed vibration (change in the bond angle), v 3 antisymmetric stretching vibration. In more complex molecules, there are other normal vibrations (changes in dihedral angles, torsional vibrations, pulsations of cycles, etc.). Quantization of vibrational energy of a polyatomic molecule in the multidimensional harmonic approximation. The oscillator leads to a trace, a system of vibrational energy levels:

where v ek is harmonic. vibrational constants, v k - vibrational quantum numbers, d k - the degree of degeneracy of the energy level with respect to the k-th vibrational quantum number. Main frequencies to VIBRATORY SPECTRA s. due to transitions from the zero level [all v k = 0, vibrational energy to levels characterized by

such sets of quantum numbers v k, in which only one of them is equal to 1, and all the others are equal to 0. As in the case of diatomic molecules, in anharmonic. In the approximation, overtone and "hot" transitions are also possible and, in addition, the so-called combined, or compound, transitions involving levels for which two or more of the quantum numbers v k are nonzero (Fig. 2).

Rice. 2. The system of vibrational terms E / hc (cm "; c is the speed of light) of the H2O molecule and some transitions; v 1, v 2. v 3 - vibrational quantum numbers.

Interpretation and Application. VIBRATIONAL SPECTRA p. polyatomic molecules are highly specific and present a complex picture, although the total number of experimentally observed bands can be significantly less than their possible number, theoretically corresponding to the predicted set of levels. Usually, the main frequencies correspond to more intense bands in VIBRATORY SPECTRA s. The selection rules and the probability of transitions in the IR and Raman spectra are different, since they are associated, respectively, with changes in electric. the dipole moment and polarizability of the molecule at each normal vibration. Therefore, the appearance and intensity of bands in the IR and Raman spectra depend differently on the type of symmetry of vibrations (the ratio of the configurations of a molecule arising as a result of vibrations of nuclei to symmetry operations that characterize its equilibrium configuration). Some of the bands VIBRATIONAL SPECTRA c. can be observed only in the IR or only in the Raman spectrum, others with different intensities in both spectra, and some are not observed experimentally at all. So, for molecules that do not have symmetry or have low symmetry without an inversion center, all fundamental frequencies are observed with different intensities in both spectra; for molecules with an inversion center, none of the observed frequencies is repeated in the IR and Raman spectra (the rule of alternative exclusion); some of the frequencies may be missing in both spectra. Therefore, the most important of the applications VIBRATIONAL SPECTRA c. - determination of the symmetry of the molecule from the comparison of IR and Raman spectra, along with the use of other experiments. data. Given the models of a molecule with different symmetry, one can theoretically calculate in advance for each of the models how many frequencies in the IR and Raman spectra should be observed, and on the basis of comparison with experiment. data to make the appropriate choice of model. Although each normal vibration, by definition, is the vibrational motion of the entire molecule, some of them, especially in large molecules, can most of all affect only c.-l. fragment of a molecule. The amplitudes of the displacement of the nuclei not included in this fragment are very small with such a normal vibration. This is the basis of the widely used structural analyte. studies, the concept of the so-called group, or characteristic, frequencies: certain functional groups or fragments repeating in molecules of various compounds are characterized by approximately the same frequencies in VIBRATIONAL SPECTRA s., by which their presence in the molecule of a given substance can be established ( however, not always with the same high degree of reliability). For example, the carbonyl group is characterized by a very intense band in the IR absorption spectrum in the region of ~ 1700 (b 50) cm -1, related to the stretching vibration. The absence of absorption bands in this region of the spectrum proves that there is no group in the molecule of the investigated substance. At the same time, the presence of K.-L. bands in the indicated region is not yet unambiguous evidence of the presence of a carbonyl group in the molecule, since the frequencies of other vibrations of the molecule may accidentally appear in this region. Therefore, structural analysis and determination of conformations by vibrational frequencies of func. groups should rely on several characteristics. frequencies, and the proposed structure of the molecule must be confirmed by data from other methods (see Structural chemistry). There are reference books containing numerous structural-spectral correlations; there are also data banks and corresponding programs for information retrieval systems and structural analytes. research using computers. CORRECT INTERPRETATION VIBRATIONAL SPECTRA p. isotopic helps. substitution of atoms, leading to a change in vibrational frequencies. So, replacing hydrogen with deuterium leads to a decrease in the frequency of the X-H stretching vibration by about 1.4 times. When isotopic. substitution, the force constants of the molecules Ke are retained. There are a number of isotopes. rules that allow the observed vibrational frequencies to be attributed to one or another type of symmetry of vibrations, functional groups, etc. Model calculations VIBRATIONAL SPECTRA p. (frequencies and intensities of bands) at given force constants, which are used to determine the structure of molecules, constitute the direct problem of vibrational spectroscopy. The required force constants and the so-called electro-optical parameters (dipole moments of bonds, components of the polarizability tensor, etc.) are transferred from studies of molecules with similar structures or obtained by solving an inverse problem, which consists in determining sets of force constants and electro-optical parameters of polyatomic molecules from the observed vibrational frequencies , intensities, and other experiments. data. Determination of sets of fundamental frequencies VIBRATIONAL SPECTRA p. necessary to calculate the vibrational contributions to the thermodynamic function of substances. These data are used in calculating chemical equilibria and for modeling technology. processes. VIBRATIONAL SPECTRA p. allow you to study not only intramol. dynamics, but also intermolecular interactions. From them receive data on the surfaces of potential energy, int. the rotation of molecules, the movements of atoms with large amplitudes. By VIBRATIONAL SPECTRA p. investigate the association of molecules and the structure of complexes of various natures. VIBRATIONAL SPECTRA p. depend on the state of aggregation of matter, which makes it possible to obtain information about the structure of various condensates. phases. The frequencies of the vibrational transitions are clearly recorded for the pier. forms with a very short lifetime (up to 10 -11 s), for example, for conformers with a potential barrier height of several kJ / mol. Therefore, VIBRATIONAL SPECTRA with. used to study conformational isomerism and rapidly establishing equilibria. On the use of VIBRATIONAL SPECTRA p. for quantitative analysis and other purposes, as well as for modern techniques of vibrational spectroscopy, see Art. Infrared spectroscopy, Raman spectroscopy.