Molecular spectra are. Structure and spectra of molecules
MOLECULAR SPECTRA- absorption, emission or scattering spectra arising from quantum transitions molecules from one energetic. states to another. M. s. determined molecular composition, 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 + vl, 2vk
+ vl etc., and the difference bands vk
- vl, 2vk - e l etc. Band intensities 2u k,
vk + vl and vk
- vl depend on the first and second derivatives d on Qk(or a by Qk) and cubic. coefficients of anharmonicity potent. energy; the intensities of higher transitions depend on the coefficient. higher degrees of 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
MOLECULAR SPECTRA
Emission, absorption, and Raman scattering (Raman) spectra of free or weakly bonded molecules. Typical M. pages - striped, they are observed in the form of a set of more or less narrow bands in the UV, visible and IR regions of the spectrum; with sufficient resolution of spectral instruments pier. the stripes break up into a set of closely spaced lines. M.'s structure with. different for diff. molecules and becomes more complex with an increase in the number of atoms in the molecule. The visible and UV spectra of very complex molecules are similar and consist of a few broad continuous bands. M. s. occur when quantum transitions between energy levels?" and?" molecules according to the ratio:
where hv is the energy of an emitted or absorbed photon of frequency v. For Raman, hv is equal to the difference between the energies of the incident and scattered photons. M. s. much more complicated than atomic spectra, which is determined by the greater complexity of the internal. movements in the molecule, because in addition to the movement of electrons relative to two or more nuclei in the molecule, there is an oscillation. the movement of the nuclei (together with the internal elements surrounding them) about the equilibrium position and rotate. its movement as a whole. Electronic, oscillating and rotate. the movements of the molecule correspond to three types of energy levels? el,?
According to quant. mechanics, the energy of all types of motion in a molecule can only take on certain values (quantized). What is the total energy of the molecule? approximately can be represented as a sum of quantized energy values corresponding to three types of its internal. movements:
?? el +? count +? vr, (2) and in order of magnitude
El:?col:?vr = 1: ?m/M:m/M, (3)
where m is the mass of the electron, and M has the order of the mass of the nuclei of atoms in the molecule, i.e.
El -> ?count ->?vr. (4) Usually? e order several. eV (hundreds of kJ/mol), ?col = 10-2-10-1 eV, ?vr = 10-5-10-3 eV.
The system of energy levels of a molecule is characterized by sets of electronic energy levels far apart from each other (dec. ?el at?col=?vr=0). vibrational levels located much closer to each other (diff. ?col at a given?el and?rot=0) and even closer to each other rotational levels (values?rot at given?el and?col).
Electronic energy levels a to b in fig. 1 correspond to the equilibrium configurations of the molecule. Each electronic state corresponds to a certain equilibrium configuration and a certain value? el; smallest value corresponds to the main electronic state (basic electronic energy level of the molecule).
Rice. 1. Scheme of energy levels of a diatomic molecule, a and b - electronic levels; v" and v" - quantum. number of fluctuations. levels; J" and J" - quantum. rotation numbers. levels.
The set of electronic states of a molecule is determined by the St. you of its electronic shell. In principle, the values \u200b\u200bof el can be calculated by quantum methods. chemistry, but this problem can be solved only approximately and for relatively simple molecules. Important information about the electronic levels of molecules (their location and their characteristics), determined by its chemical. a structure, receive, studying M. with.
A very important characteristic of the electronic energy level is the value of the quantum number 5, which determines abs. the value of the total spin moment of all e-new. Chemically stable molecules have, as a rule, an even number of electrons, and for them 5 = 0, 1, 2, . . .; for the main electronic level typically 5=0, for excited - 5=0 and 5=1. Levels with S=0 naz. singlet, with S=1 - triplet (because their multiplicity is c=2S+1=3).
In the case of diatomic and linear triatomic molecules, the electronic levels are characterized by the quantum value. number L, defining abs. the value of the projection of the total orbital momentum of all electrons onto the axis of the molecule. Levels with L=0, 1, 2, ... are denoted respectively by S, P, D, . . ., and and is indicated by the index at the top left (eg, 3S, 2П). For molecules that have a center of symmetry (for example, CO2, CH6), all electronic levels are divided into even and odd (g and u, respectively) depending on whether or not the defining wave function sign when reversing at the center of symmetry.
Vibrational energy levels can be found by quantizing the vibrations. movements, which are approximately considered harmonic. A diatomic molecule (one vibrational degree of freedom corresponding to a change in the internuclear distance r) can be considered as a harmonic. oscillator, quantization of which gives equidistant energy levels:
where v - main. harmonic frequency vibrations of the molecule, v=0, 1, 2, . . .- oscillate. quantum. number.
For each electronic state of a polyatomic molecule consisting of N?3 atoms and having f Colebat. degrees of freedom (f=3N-5 and f=3N-6 for linear and nonlinear molecules, respectively), it turns out / so-called. normal oscillations with frequencies vi(ill, 2, 3, . . ., f) and a complex system of oscillations. energy levels:
Set of frequencies of norms. fluctuations in the main. electronic state yavl. important characteristic of the molecule, depending on its chemical. buildings. To a certain standard. vibrations involve either all the atoms of the molecule, or part of them; atoms make harmonic. oscillations with the same frequency vi, but with diff. amplitudes that determine the shape of the oscillation. Norm. vibrations are divided according to their shape into valence (the lengths of chemical bonds change) and deformation vibrations (the angles between chemical bonds change - bond angles). For molecules of lower symmetry (see MOLECULE SYMMETRY) f=2 and all vibrations are non-degenerate; for more symmetrical molecules, there are double and triple degenerate vibrations, i.e., pairs and triples of vibrations coinciding in frequency.
The rotational energy levels can be found by quantizing the rotation. the motion of a molecule, considering it as TV. body with certain moments of inertia. In the case of a diatomic or linear triatomic molecule, its energy of rotation? vr \u003d M2 / 2I, where I is the moment of inertia of the molecule about an axis perpendicular to the axis of the molecule, and M is rotated. moment of the number of motion. According to the quantization rules,
M2=(h/4pi2)J(J+1),
where f=0, 1,2,. . .- rotational quantum. number; for?vr we get:
Вр=(h2/8pi2I)J(J+1) = hBJ(J+1), (7)
where they rotate. constant B=(h/8piI2)I
determines the scale of distances between energy levels, which decreases with increasing nuclear masses and internuclear distances.
Diff. M. types with. occur at different types of transitions between energy levels of molecules. According to (1) and (2):
D?=?"-?"==D?el+D?count+D?vr,
moreover, similarly to (4) D? el-> D? count-> D? When D? el? 0 obtained electronic M. s., observed in the visible and UV regions. Usually at D??0 simultaneously D?col?0 and D?vr?0; dec. D? count for a given D? el correspond to decomp. oscillating stripes (Fig. 2), and dec. D? vr at given D? el and D? number of otd. rotate lines into which oscillatory break up. stripes (Fig. 3).
Rice. 2. Electroino-oscillate. spectrum of the N2 molecule in the near UV region; groups of bands correspond to dec. values Dv= v"-v".
The set of bands with a given D?el (corresponding to a purely electronic transition with a frequency nel=D?el/h) called. stripe system; stripes have different intensity depending on the relative. transition probabilities (see QUANTUM TRANSITION).
Rice. 3. Rotate. splitting of electron-kolsbat. bands 3805.0? N2 molecules.
For complex molecules, the bands of one system corresponding to a given electronic transition usually merge into one broad continuous band; can be superimposed on each other and several. such stripes. Characteristic discrete electronic spectra are observed in frozen organic solutions. connections.
Electronic (more precisely, electronic-vibrational-rotational) spectra are studied using spectral instruments with glass (visible region) and quartz (UV region, (see UV RADIATION)) optics. When D? el \u003d 0, and D? count? 0, oscillates are obtained. MS, observed in the near-IR region, usually in the absorption and Raman spectra. As a rule, at a given D? count D? vr? 0 and fluctuate. the band splits into rotate lines. Most intense in vibration. M. s. bands satisfying the condition Dv=v"-v"=1 (for polyatomic molecules Dvi=v"i-v"i=1 at Dvk=V"k-V"k=0; here i and k determine different normal vibrations). For purely harmonic fluctuations, these selection rules are strictly enforced; for anharmonic vibrations, bands appear, for which Dv> 1 (overtones); their intensity is usually low and decreases with increasing Dv. Swing. M. s. (more precisely, vibrational-rotational) are studied using IR spectrometers and Fourier spectrometers, and Raman spectra - using high-aperture spectrographs (for the visible region) using laser excitation. When D? el=0 and D? count=0 are obtained purely rotatable. spectra, consisting of lines. They are observed in the absorption spectra in the far IR region and especially in the microwave region, as well as in the Raman spectra. For diatomic, linear triatomic molecules, and sufficiently symmetrical nonlinear molecules, these lines are equidistant (in the frequency scale) from each other.
Purely rotate. M. s. studied using IR spectrometers with special. diffraction gratings (echelettes), Fourier spectrometers, spectrometers based on a backward wave lamp, microwave (microwave) spectrometers (see SUBMILLIMETER SPECTROSCOPY, MICROWAVE SPECTROSCOPY), and rotate. Raman spectra - using high-aperture spectrometers.
The methods of molecular spectroscopy, based on the study of M. s., make it possible to solve various problems of chemistry. Electronic M. with. give information about electron shells, excited energy levels and their characteristics, about the energy of dissociation of molecules (by the convergence of energy levels to the dissociation boundary). The study of fluctuations. spectra allows you to find the characteristic vibration frequencies corresponding to the presence in the molecule of certain types of chemical. bonds (e.g. double and triple C-C connections, C-H connections, N-H for organic. molecules), define spaces. structure, distinguish between cis- and trans-isomers (see ISOMERIA OF MOLECULES). Particularly widespread methods of infrared spectroscopy - one of the most effective optical. methods for studying the structure of molecules. Most full information they give in combination with the methods of RAS spectroscopy. Rotate research. spectra, as well as rotation. structures of electronic and oscillatory. M. s. allows using the moments of inertia of molecules found from experience to find with great accuracy the parameters of equilibrium configurations - bond lengths and bond angles. To increase the number of parameters to be determined, the isotopic spectra are examined. molecules (in particular, molecules in which hydrogen is replaced by deuterium) that have the same parameters of equilibrium configurations, but decompose. moments of inertia.
M. s. are also used in spectral analysis to determine the composition of the Islands.
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Studies of molecular spectra make it possible to determine the forces acting between atoms in a molecule, the dissociation energy of a molecule, its geometry, internuclear distances, etc. , i.e. provide extensive information about the structure and properties of the molecule.
Under the molecular spectrum, in a broad sense, is understood the distribution of the probability of transitions between two separate energy levels of the molecule (see Fig. 9) depending on the energy of the transition. Since in what follows we will deal with optical spectra, each such transition must be accompanied by the emission or absorption of a photon with energy
E n \u003d hn \u003d E 2 - E 1, 3.1
where E 2 and E 1 are the energies of the levels between which the transition occurs.
If radiation, consisting of photons emitted by gas molecules, is passed through a spectral device, then the emission spectrum of the molecule will be obtained, consisting of individual bright (maybe colored) lines. Moreover, each line will correspond to the corresponding transition. In turn, the brightness and position of the line in the spectrum depend on the transition probability and energy (frequency, wavelength) of the photon, respectively.
If, on the contrary, radiation consisting of photons of all wavelengths (continuous spectrum) is passed through this gas, and then through a spectral device, then an absorption spectrum will be obtained. In this case, this spectrum will be a set of dark lines against the background of a bright continuous spectrum. The contrast and position of the line in the spectrum here also depend on the transition probability and photon energy.
Based on the complex structure of the energy levels of the molecule (see Fig. 9), all transitions between them can be divided into separate types, which give a different character of the spectrum of molecules.
A spectrum consisting of lines corresponding to transitions between rotational levels (see Fig. 8) without changing the vibrational and electronic states of the molecule is called the rotational spectrum of the molecule. Since the energy of rotational motion lies in the range of 10 -3 -10 -5 eV, the frequency of the lines in these spectra should lie in the microwave region of radio frequencies (far infrared region).
A spectrum consisting of lines corresponding to transitions between rotational levels belonging to different vibrational states of a molecule in the same electronic state is called the vibrational-rotational or simply vibrational spectrum of the molecule. These spectra, at vibrational motion energies of 10 -1 -10 -2 eV, lie in the infrared region of frequencies.
Finally, the spectrum, consisting of lines corresponding to transitions between rotational levels belonging to different electronic and vibrational states of the molecule, is called the electronic-vibrational-rotational or simply electronic spectrum of the molecule. These spectra lie in the visible and ultraviolet frequency regions, since the energy of the electronic motion is a few electron volts.
Since the emission (or absorption) of a photon is an electromagnetic process, its necessary condition is the presence or, more precisely, the change in the electric dipole moment associated with the corresponding quantum transition in the molecule. Hence it follows that rotational and vibrational spectra can only be observed for molecules with an electric dipole moment, i.e. composed of dissimilar atoms.
Chemical bonds and structure of molecules.
Molecule - the smallest particle of a substance, consisting of the same or different atoms connected to each other chemical bonds, and being the carrier of its basic chemical and physical properties. Chemical bonds are due to the interaction of external, valence electrons of atoms. There are two types of bonds most often found in molecules: ionic and covalent.
Ionic bond (for example, in molecules NaCl, KVR) is carried out by the electrostatic interaction of atoms during the transition of an electron from one atom to another, i.e. in the formation of positive and negative ions.
A covalent bond (for example, in H 2 , C 2 , CO molecules) is carried out when valence electrons are shared by two neighboring atoms (the spins of valence electrons must be antiparallel). The covalent bond is explained on the basis of the principle of indistinguishability of identical particles, such as electrons in a hydrogen molecule. The indistinguishability of particles leads to exchange interaction.
The molecule is 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.
Thus, different types of transitions between levels give rise to different types of molecular spectra. The frequencies of the spectral lines emitted by molecules can correspond to transitions from one electronic level to another (electronic spectra) or from one vibrational (rotational) level to another ( vibrational (rotational) spectra). In addition, transitions with the same values are also possible and to levels having different values of all three components, resulting in electronic-vibrational and vibrational-rotational spectra.
Typical molecular spectra are banded, which are a combination of more or less narrow bands in the ultraviolet, visible and infrared regions.
Using high-resolution spectral instruments, it can be seen that the fringes are such closely spaced lines that they are difficult to resolve. The structure of molecular spectra is different for different molecules and becomes more complicated with an increase in the number of atoms in a molecule (only continuous broad bands are observed). Only polyatomic molecules have vibrational and rotational spectra, while diatomic ones do not have them. This is explained by the fact that diatomic molecules do not have dipole moments (during vibrational and rotational transitions, there is no change in the dipole moment, which is a necessary condition for the transition probability to differ from zero). Molecular spectra are used to study the structure and properties of molecules, are used in molecular spectral analysis, laser spectroscopy, quantum electronics, etc.
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 line atomic spectra, which is determined by the greater complexity internal movements 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) ,
however, this problem can be solved only with the help of approximate methods and for relatively simple molecules. The most important information about the electronic levels of a molecule (the arrangement of the 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 odd number electrons, for them 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 of vibrational levels: where υ
i = 0, 1, 2, ... are the corresponding vibrational quantum numbers. The set of frequencies of normal vibrations in the ground electronic state is a very important characteristic of a molecule, depending on its chemical structure. All 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 - valence 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 vibrations; 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 the rotational motion of the molecule, considering it as solid 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 organic compounds(see Shpolsky effect). Electronic (more precisely, electronic-vibrational-rotational) spectra are studied experimentally using spectrographs and spectrometers with glass (for the visible region) and quartz (for the UV region) optics, in which prisms or diffraction gratings are used to decompose light into a spectrum (see 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 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 oscillation frequencies corresponding to certain types chemical bonds in a molecule (for example, simple double and triple C-C bonds, C-H, N-H, O-H bonds for organic molecules), various groups of atoms (for example, CH 2, CH 3, NH 2), determine the spatial structure molecules, to 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 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) ;
level diagram derived from electronic molecular spectra 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 IKS) 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 plane vibrations is the frequency 992 (corresponding to the stretching vibration of C-C bonds, which consists in periodic compression and tension benzene ring), frequencies 3062 and 3080 (corresponding to stretching vibrations of C-H bonds), and frequency 607 (corresponding to bending vibrations 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; band groups correspond different meanings Δ v = v" - v ". Big soviet encyclopedia. - M.: Soviet Encyclopedia.
1969-1978
.
See what "Molecular Spectra" is in other dictionaries:
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Spectra of optical absorption, emission and Raman scattering of light arising from the transitions of molecules from one energy level to another. M. s. consist of more or less wide stripes, images. many closely spaced. spectral ... ... Big encyclopedic polytechnic dictionary
optical emission, absorption and scattering spectra of light belonging to free or weakly bound molecules. They consist of spectral bands and lines, the structure and arrangement of which are typical of the molecules that emit them. Occur during quantum ... ... Natural science. encyclopedic Dictionary
Spectra el. magn. radiation in the IR, visible and UV ranges of the electromagnetic wave scale. S. o. divided into emission spectra (also called emission spectra, or emission spectra), absorption spectra (absorption spectra), scattering and ... ... Physical Encyclopedia
Spectra electromagnetic radiation in the infrared, visible and ultraviolet ranges of the scale of electromagnetic waves (See Electromagnetic waves). S. o. divided into emission spectra (also called spectra ... Great Soviet Encyclopedia
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…