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

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

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

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

Chemical bonds and structure of molecules.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Molecular spectra.

Molecular spectra - optical spectra of emission and absorption, as well as Raman scattering of light (See. Raman scattering of light), belonging to free or loosely related 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.

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

Molecule energy

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

Formula (13.45) does not take into account the energy of the translational motion of the center of mass of molecules and the energy of the nuclei of atoms in a molecule. The first of them is not quantized, so its changes cannot lead to the appearance of a molecular spectrum, and the second can be ignored if the hyperfine structure of the spectral lines is not considered.

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

The structure of molecules and the properties of their energy levels are manifested in molecular spectra - emission (absorption) spectra arising from quantum transitions between the energy levels of molecules. The emission spectrum of a molecule is determined by the structure of its energy levels and the corresponding selection rules (for example, the change in quantum numbers corresponding to both vibrational and rotational motion should be equal to ± 1). Different types of transitions between levels give rise to different types of molecular spectra. The frequencies of the spectral lines emitted by molecules can correspond to transitions from one electronic level to another ( electronic spectra ) or from one vibrational (rotational) level to another [ vibrational (rotational) spectra ].

In addition, transitions with the same values ​​are also possible. E count and E rotation to levels having different values ​​of all three components, resulting in electronic oscillatory and vibrational-rotational spectra . Therefore, the spectrum of molecules is quite complex.

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

The structure of molecular spectra is different for different molecules and becomes more complicated with an increase in the number of atoms in a molecule (only continuous broad bands are observed). Only polyatomic molecules have vibrational and rotational spectra, while diatomic ones do not have them. This is explained by the fact that diatomic molecules do not have dipole moments (during vibrational and rotational transitions, there is no change in the dipole moment, which is a necessary condition for the transition probability to differ from zero).

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

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

Raman scattering of light.

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

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

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

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

Thus, the total energy of the molecule is:

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

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

.

Experience and theoretical studies 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.

Raman scattering of light

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

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

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

Luminescence

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

There are two types of luminescence: fluorescence and phosphorescence.

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

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

Phosphorescence 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.

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 is formed a complex system oscillating 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