Microwave spectroscopy

The microwave spectroscopy or (pure) of rotation spectroscopy is one of the group of molecular spectroscopy belonging investigation method, which provides information on rotations of molecules. From this, molecules can be identified and other basic properties such as B. gain the bond strength. It is primarily used to investigate gases and liquids . The method is based on the absorption of electromagnetic waves in the wavelength range from approx. 1 cm - 100 µm ( frequency range from approx. 0.5–100 GHz) through the excitation of molecular rotationsand associated transitions between the levels of hyperfine structure . In contrast to electronic and vibration spectroscopy , which can also contain rotational splitting, the disruptive Doppler spread is smaller at the low frequencies of the microwaves.

theory

Theoretically, the rotation spectrum can usually be well described by the model of the rigid rotator . Here, molecules are divided into linear, spherical, symmetrical and asymmetrical rotator according to their structure and symmetry.

Spherical and linear rotator

The rotation of a molecule in which moments of inertia coincide around all three main axes of inertia (spherical rotator, e.g. CH ₄ , CCl ₄ ) or in which the angular momentum with respect to the main axis becomes zero (linear rotator, e.g. CO ₂ , HCl , C ₂ H ₂ ) can be described by a rigid rotator with its rotational energy : ${\ displaystyle E _ {\ mathrm {red}}}$

{\ displaystyle E _ {\ text {red}} = {\ frac {| {\ vec {L}} | ^ {2}} {2I}} = {\ frac {\ hbar ^ {2} J (J + 1 )} {2I}} = hc \ cdot BJ (J + 1)}

It is the moment of inertia about the rotational axis, the rotational quantum number, the Planck's constant , the speed of light and the rotational constant. As molecules rotate, the atoms experience centrifugal forces, which leads to centrifugal distortion. In reality, this effect is negligible for transitions between low rotation levels.

{\ displaystyle I}

{\ displaystyle J = 0,1,2, \ ldots}

{\ displaystyle h}

{\ displaystyle c}

{\ displaystyle B = {\ frac {\ hbar ^ {2}} {2Ihc}}}

Symmetrical rotator

The symmetrical rotator (e.g. CH ₃ Cl, NH ₃ , C ₆ H ₆ ) can be divided into two components with regard to its moments of inertia: two identical and one different moment of inertia. The rotational energy is now described by the following equation: ${\ displaystyle I _ {\ perp}}$ ${\ displaystyle I _ {\ parallel}}$

{\ displaystyle E _ {\ text {red}} = {\ frac {\ hbar ^ {2} J (J + 1)} {2I _ {\ perp}}} + {\ biggl (} {\ frac {1} { 2I _ {\ parallel}}} - {\ frac {1} {2I _ {\ perp}}} {\ biggr)} \ cdot (K \ hbar) ^ {2} = hc \ cdot BJ (J + 1) + ( AB) \ cdot K ^ {2}}

Here is the quantum number of the angular momentum with respect to the main axis, the constant of rotation and refined to the following expressions:

{\ displaystyle K}

{\ displaystyle A}

{\ displaystyle B}

{\ displaystyle A = {\ frac {\ hbar ^ {2}} {2I _ {\ parallel} hc}} \ qquad B = {\ frac {\ hbar ^ {2}} {2I _ {\ perp} hc}}}

Rotation spectrum

Energy levels and emission wavenumbers according to the linear rigid rotator model.

The adjacent picture shows the relationship between the energetic rotation level and a rotation spectrum. The difference between two rotation levels corresponds to the energy of a rotation transition , which is visible in the spectrum through a peak. This shows the linear dependence of the energy levels on the constant of rotation. The line spacings are always the same distance from , which facilitates the interpretation of rotational spectra. ${\ displaystyle E _ {\ mathrm {red}} (J)}$ ${\ displaystyle E _ {\ mathrm {red}} (J + 1) -E _ {\ mathrm {red}} (J)}$ ${\ displaystyle 2B}$

The intensity of the individual peaks results from the population of the rotation level from which the transition occurs. Since molecules always have a certain temperature , the occupation of the rotation levels is given according to the Boltzmann distribution . The population of the rotation levels, which results from the intensity of the individual transitions, can therefore also provide information about the sample temperature. ${\ displaystyle T> 0 ~ \ mathrm {K}}$

Experimental implementation

As a measuring method, the absorption can be measured at different frequencies, or the Fourier transformation is used and a time-dependent absorption is evaluated according to the frequencies contained therein (analogous to NMR spectroscopy ). Because the spontaneous transition probability for emission is extremely small due to the low transition frequency, rotational spectroscopy is usually measured in absorption.

Sample shape

In general, only molecules that have a dipole moment are suitable for microwave spectroscopy . Microwave spectra of gases are characterized by sharp absorption lines, as the molecules can rotate freely. In order to obtain exact absorption spectra that can be assigned as clearly as possible, the interaction between the molecules (see pressure broadening ) must be minimized. For this reason, small amounts of gaseous species are usually used in large measuring containers under low pressure.

Microwave spectroscopy can also be used to elucidate the structure and dynamics of liquids. The spectra of liquids are distinguished from others by very broad absorption bands that go through several frequency ranges. In the microwave spectrum, a contribution is made by molecules that have a dipole moment. The strength of the dipole moment is preferably included in the strength of the absorption, whereas the speed of the molecular movement (tumbling rotation) determines the position of the absorption band on the frequency scale. There is generally a relationship between the viscosity of a liquid and the speed of movement of the dipoles.

Experimental setup

Low-noise microwaves in the range from 1 to 100 GHz can be generated by a reflex klystron . In this case, the spectral variation is difficult, which, on the other hand, carcinotrons and magnetrons allow. Microwave generators made of semiconductors such as GaAs ( Gunn diode ) or InP ( avalanche diode ) are also used. The signal is usually detected using a microwave diode. To further improve the signal-to-noise ratio , the sample to be examined can be exposed to an alternating electric field. The energy levels of the molecules are consequently shifted by the Stark effect . The measurement signal obtained is corrected by the known frequency of the field modulation and compared with an experiment without an alternating electric field.

interpretation

By applying the model that is suitable for the corresponding molecular symmetry (spherical, linear, symmetrical, etc.), the desired molecular sizes can be determined. Usually, microwave spectra can be described mathematically with a superposition of Debye functions (named after Peter Debye ), with each individual Debye function being assigned a movement process.

application

With the help of microwave spectroscopy of gases information can be obtained, such as: B .:

Bond lengths in simply structured molecules
Conformations of certain chemical compounds that have so-called rotational hyperfine structures in the absorption spectrum,
Structures of short-lived, non-isolable species, which also result in rotational hyperfine structures, with the help of the molecular beam method ,
Electronic environment or electron density distribution around certain atomic nuclei, which have so-called quadrupole hyperfine structures in the absorption spectrum.

Microwave spectroscopy is mainly used in physical chemistry to research molecular properties that cannot or can only be obtained with difficulty using other methods. This is the case in astrophysics and radio astronomy , for example , to identify molecules in space or to determine the temperature of matter in space. In today's research, microwave spectroscopy has increasingly been replaced by electronic or vibrational spectroscopy with rotational resolution.

history

About half a century after the discovery and understanding of microwave radiation by Michael Faraday , James Clerk Maxwell and Heinrich Hertz , microwave spectroscopy was used for the first time in 1946.

In 1963, a radio telescope was used to detect OH ^- as the first molecule in space. In the following years a number of emissions from unknown crossings were measured. While the molecules OH ^- and NH ₃ showed vibrational transitions, all other measured transitions of the molecules with permanent dipole moments were pure rotational transitions. The assignment was made by comparison with laboratory tests. Since the molecules in space have a certain speed compared to the radio telescope, the spectra had to be corrected for the Doppler effect . Linear and cyclic molecules with an atomic number of 2 to 13 were found. In the nebula Sagittarius B2 , which moves at a speed of 60 km / s, z. B. detected cyanoacetylene .

literature

Reinhard Demuth , Friedhelb Kober: Basics of spectroscopy . Moritz Diesterweg / Otto Salle and Sauerländer, Frankfurt / Main 1977, ISBN 3-425-05481-3 , p. 48-63 .
Wolfgang Demtröder: Molecular Physics: Theoretical Foundations and Experimental Methods . Oldenbourg Wissenschaftsverlag, 2003, ISBN 978-3-486-24974-3 , p. 362-366 .
J. Michael Hollas: Modern Spectroscopy . 4th edition. Wiley, Chichester 2004, ISBN 978-0-470-84416-8 , pp. 103-135 .
Claus Czeslik, Heiko Semann, Roland Winter: Basic knowledge of physical chemistry . Teubner, Wiesbaden 2007, ISBN 978-3-8351-0047-3 , p. 310-313 .
CH Townes, AL Schawlow: Microwave Spectroscopy . Courier Corporation, Chichester 2013, ISBN 978-0-486-16231-7 .

Individual evidence

^ Alan Carrington: Rotational spectroscopy of diatomic molecules . Cambridge University Press, Cambridge 2003, ISBN 0-511-06420-9 .
↑ ^a ^b Heiko Seemann, Roland Winter: Basic knowledge of physical chemistry . 2., revised. Ed. Teubner, Wiesbaden 2007, ISBN 3-8351-0047-5 .
^ Julio De Paula: Physical chemistry. 9th ed.WH Freeman and Co, New York 2010, ISBN 978-1-4292-1812-2 .
↑ ^a ^b ^c Hans Christoph Wolf: Molecular Physics and Quantum Chemistry: Introduction to the experimental and theoretical basics . 5th edition. Springer, Berlin 2006, ISBN 3-540-30314-6 .
^ Walter Gordy: Microwave spectroscopy. Introductory paper: quadrupole couplings, dipole moments and the chemical bond . In: Discussions of the Faraday Society . tape 19 , 1955, ISSN 0366-9033 , p. 14 , doi : 10.1039 / df9551900014 .
↑ J. Michael Hollas: Modern Spectroscopy . 4th edition. Wiley, Chichester 2004, ISBN 978-0-470-84416-8 .

[1] Alan Carrington: Rotational spectroscopy of diatomic molecules . Cambridge University Press, Cambridge 2003, ISBN 0-511-06420-9 .

[:0-2] Heiko Seemann, Roland Winter: Basic knowledge of physical chemistry . 2., revised. Ed. Teubner, Wiesbaden 2007, ISBN 3-8351-0047-5 .

[3] Julio De Paula: Physical chemistry. 9th ed.WH Freeman and Co, New York 2010, ISBN 978-1-4292-1812-2 .

[:1-4] Hans Christoph Wolf: Molecular Physics and Quantum Chemistry: Introduction to the experimental and theoretical basics . 5th edition. Springer, Berlin 2006, ISBN 3-540-30314-6 .

[5] Walter Gordy: Microwave spectroscopy. Introductory paper: quadrupole couplings, dipole moments and the chemical bond . In: Discussions of the Faraday Society . tape 19 , 1955, ISSN 0366-9033 , p. 14 , doi : 10.1039 / df9551900014 .

[6] J. Michael Hollas: Modern Spectroscopy . 4th edition. Wiley, Chichester 2004, ISBN 978-0-470-84416-8 .