Rotational spectroscopy or microwave spectroscopy studies the absorption and emission of electromagnetic radiation (typically in the microwave region of the electromagnetic spectrum) by molecules associated with a corresponding change in the rotational quantum number of the molecule. The use of microwaves in spectroscopy essentially became possible due to the development of microwave technology for RADAR during World War II. Rotational spectroscopy is only really practical in the gas phase where the rotational motion is quantized. In solids or liquids the rotational motion is usually quenched due to collisions. Absorption, in optics, is the process by which the energy of a photon is taken up by another entity, for example, by an atom whose valence electrons make a transition between two electronic energy levels. ... The word emission generally means sending something out. ... Electromagnetic radiation can be conceptualized as a self propagating transverse oscillating wave of electric and magnetic fields. ... Microwave image of 3C353 galaxy at 8. ... Legend: γ = Gamma rays HX = Hard X-rays SX = Soft X-Rays EUV = Extreme ultraviolet NUV = Near ultraviolet Visible light NIR = Near infrared MIR = Moderate infrared FIR = Far infrared Radio waves: EHF = Extremely high frequency (Microwaves) SHF = Super high frequency (Microwaves) UHF = Ultrahigh frequency VHF = Very high frequency HF = High frequency... In science, a molecule is the smallest particle of a pure chemical substance that still retains its chemical composition and properties. ... A quantum number describes the energies of electrons in atoms. ... This long range radar antenna, known as ALTAIR, is used to detect and track space objects in conjunction with ABM testing at the Ronald Reagan Test Site on the Kwajalein atoll[1]. Radar is a system that uses radio waves to detect, determine the distance of, and map, objects such... Combatants Allies: Poland, British Commonwealth, France/Free France, Soviet Union, United States, China, and others Axis Powers: Germany, Italy, Japan, and others Casualties Military dead: 17 million Civilian dead: 33 million Total dead: 50 million Military dead: 8 million Civilian dead: 4 million Total dead: 12 million World War II... A gas is one of the four main phases of matter (after solid and liquid, and followed by plasma), that subsequently appear as a solid material is subjected to increasingly higher temperatures. ... In the physical sciences, a phase is a set of states of a macroscopic physical system that have relatively uniform chemical composition and physical properties (i. ... This article is about rotation as a movement of a physical body. ... In physics, motion means a change in the position of a body with respect to time, as measured by a particular observer in a particular frame of reference. ... In physics, quantization is a procedure for constructing a quantum field theory starting from a classical field theory. ... A solid is a state of matter, characterized by a definite volume and a definite shape (i. ... A liquid will assume the shape of its container. ...

Rotational spectrum from a molecule (to first order) requires that the molecule have a dipole moment, that is a difference between the center of charge and the center of mass, or equivalently a separation between two unlike charges. It is this dipole moment that enables the electric field of the light (microwave) to exert a torque on the molecule causing it to rotate more quickly (in excitation) or slowly (in de-excitation). Diatomic molecules such as Oxygen (O₂), Hydrogen (H₂), etc. do not have a dipole moment and hence no pure-rotational spectrum. However, electronic excitation can lead to asymmetric charge distribution and thus providing a net dipole moment to the molecule. Under such circumstances, these molecules will exhibit a rotational spectrum. This article is about the electromagnetic phenomenon. ... Charge is a word with many different meanings. ... It has been suggested that this article or section be merged with Center of gravity. ... In physics, an electric field or E-field is an effect produced by an electric charge (or a time-varying magnetic field) that exerts a force on charged objects in the field. ... Prism splitting light Light is electromagnetic radiation with a wavelength that is visible to the eye (visible light) or, in a technical or scientific context, electromagnetic radiation of any wavelength. ... Microwave image of 3C353 galaxy at 8. ... In physics, torque can be thought of informally as rotational force. Torque is commonly measured in units of newton metres; although, centiNewton Meters (cNm), Foot Pounds (Lb-Ft), Inch Pounds (Lb-In) and Inch Ounces (Oz-In) are also frequently used expressions of torque. ... Excitation is the amount of energy (energy in a general sense, not energy as defined in physics) that something or someone has. ... A computer rendering of the Nitrogen Molecule, which is a diatomic molecule. ... General Name, Symbol, Number oxygen, O, 8 Chemical series Nonmetals, chalcogens Group, Period, Block 16, 2, p Appearance colorless Atomic mass 15. ... ‹ The template below has been proposed for deletion. ...

The simplest rotational spectra belongs to diatomic molecules Carbon monoxide (CO). The next simplest spectra belongs to linear triatomic molecule, such as Hydrogen cyanide (HC≡N). The next simplest spectra belongs to non-linear triatomic molecules, such as Hydrogen isocyanide (HN=C:). A computer rendering of the Nitrogen Molecule, which is a diatomic molecule. ... Carbon monoxide, chemical formula CO, is a colorless, odorless, tasteless, flammable and highly toxic gas. ... Flash point −17. ...

Understandint the rotational spectrum

In quantum mechanics the free rotation of a molecule is quantized, that is the rotational energy and the angular momentum can only take certain fixed values; what these values are is simply related to the moment of inertia, I, of the molecule. In general for any molecule, there are three moments of inertia viz. I_A, I_B and I_C about three mutually orthogonal axes A,B, and C with the origin at the center of mass of the system. A linear molecule is a special case in this regard. These molecules are cylindrically symmetric and one of the moment of inertia (I_A, which is the moment of inertia for a rotation taking place along the axis of the molecule) is negligible (i.e. I_A < < I_B = I_C). A simple introduction to this subject is provided in Basics of quantum mechanics. ... The rotational energy or angular kinetic energy is the kinetic energy due to the rotation of an object and is part of its total kinetic energy. ... In physics the angular momentum of an object with respect to a reference point is a measure for the extent to which, and the direction in which, the object rotates about the reference point. ... Moment of inertia (SI unit kilogram metre squared kg m2) quantifies the rotational inertia of an object, i. ... It has been suggested that this article or section be merged with Center of gravity. ...

Classification of molecules based on rotational behavior

The general convention is to define the axes such that the axis A has the smallest moment of inertia (and hence the highest rotational frequency) and other axes such that I_A < = I_B < = I_C. Sometimes the axis A may be associated with the symmetric axis of the molecule, if any. If such is the case, then I_A need not be the smallest moment of inertia. To avoid confusion, we will stick with the former convention for the rest of the article. The particular pattern of energy levels (and hence of transitions in the rotational spectrum) for a molecule is determined by its symmetry. A convenient way to look at the molecules is to divide them into four different classes (based on the symmetry of their structure). These are, A quantum mechanical system can only be in certain states, so that only certain energy levels are possible. ...

1. Linear molecules (or linear rotors)
2. Symmetric tops (or symmetic rotors)
3. Spherical tops (or spherical rotors) and
4. Asymmetric tops

Dealing with each in turn:

1. Linear molecules:
   • As mentioned earlier, for a linear molecule I_A < < I_B = I_C. For most of the purposes, I_A is taken to be zero. For a linear molecule, the separation of lines in the rotational spectrum can be related directly to the moment of inertia of the molecule, and for a molecule of known atomic masses, can be used to determine the bond lengths (structure) directly. For diatomic molecules this process is trivial, and can be made from a single measurement of the rotational spectrum. For linear molecules with more atoms, rather more work is required, and it is necessary to measure molecules in which more than one isotope of each atom have been substituted (effectively this gives rise to a set of simultaneous equations which can be solved for the bond lengths).
   • Examples or linear molecules: Oxygen (O=O), Carbon monoxide (O≡C^*), Hydroxy radical (OH), Carbon dioxide (O=C=O), Hydrogen cyanide (HC≡N), Carbonyl sulfide (O=C=S), Chloroethyne (HC≡CCl), Acetylene (HC≡CH)
2. Symmetric tops:
   • A symmetric top is a molecule in which two moments of inertia are the same. As a matter of historical convenience, spectroscopists divide molecules into two classes of symmetric tops, Oblate symmetric tops (saucer or disc shaped) with I_A = I_B < I_C and Prolate symmetric tops (rugby football, or cigar shaped) with I_A < I_B = I_C. The spectra look rather different, and are instantly recognizable. As for linear molecules, the structure of symmetric tops (bond lengths and bond angles) can be deduced from their spectra.
   • Examples of symmetric tops:
     • Oblate: Benzene (C₆H₆), Cyclobutadiene (C₄H₄), Ammonia (NH₃)
     • Prolate: Chloroform (CHCl₃), Propyne (CH₃C≡CH)
3. Spherical tops:
   • A spherical top molecule, can be considered as a special case of symmetric tops with equal moment of inertia about all three axes (I_A = I_B = I_C).
   • Examples of spherical tops: Phosphorus tetramer (P₄), Carbon tetrachloride (CCl₄), Nitrogen tetrahydride (NH₄), Ammonium ion (NH₄⁺), Sulfur hexafluoride (SF₆)
4. Asymmetric tops:
   • As you would have guessed a molecule is termed an asymmetric top if it has all three moments of inertia are different. Most of the larger molecules are asymmetric tops, even when they have a high degree of symmetry. Generally for such molecules a simple interpretation of the spectrum is not normally possible. Sometimes asymmetric tops have spectra that are similar to those of a linear molecule or a symmetric top, in which case the molecular structure must also be similar to that of a linear molecule or a symmetric top. For the most general case however, all that can be done is to fit the spectra to three different moments of inertia. If the molecular formula is known, then educated guesses can be made of the possible structure, and from this guessed structure, the moments of inertia can be calculated. If the calculated moments of inertia agree well with the measured moments of inertia, then the structure can be said to have been determined. For this approach to determining molecular structure, isotopic substitution is invaluable.
   • Examples of asymmetric tops: Anthracene (C₁₄H₁₀), Water (H₂O), Nitrogen dioxide (NO₂)

Bond length or bond distance in molecular geometry is the distance between two bonded atoms in a molecule. ... A computer rendering of the Nitrogen Molecule, which is a diatomic molecule. ... Bond length or bond distance in molecular geometry is the distance between two bonded atoms in a molecule. ... General Name, Symbol, Number oxygen, O, 8 Chemical series Nonmetals, chalcogens Group, Period, Block 16, 2, p Appearance colorless Atomic mass 15. ... Carbon monoxide, chemical formula CO, is a colorless, odorless, tasteless, flammable and highly toxic gas. ... Hydroxide is a functional group consisting of oxygen and hydrogen: -O−H It has a charge of 1-. The term hydroxyl group is used when the functional group -OH is counted as a substituent of an organic compound. ... Carbon dioxide is an atmospheric gas comprised of one carbon and two oxygen atoms. ... Flash point −17. ... Except where noted otherwise, data are given for materials in their standard state (at 25 °C, 100 kPa) Infobox disclaimer and references Carbonyl sulfide is a colourless gas at room temperature with an unpleasant odor. ... The chemical compound and unsaturated hydrocarbon acetylene, also known under IUPAC nomenclature (see IUPAC nomenclature of organic chemistry) as ethyne, was discovered in 1836 by Edmund Davy, in England. ... An oblate spheroid is ellipsoid having a shorter axis and two equal longer axes. ... A spheroid is a quadric surface in three dimensions obtained by rotating an ellipse about one of its principal axes. ... Bond length or bond distance in molecular geometry is the distance between two bonded atoms in a molecule. ... Geometry of the water molecule Molecular geometry or molecular structure is the three dimensional arrangement of the atoms that constitute a molecule, inferred from the spectroscopic studies of the compound. ... An oblate spheroid is ellipsoid having a shorter axis and two equal longer axes. ... Benzene, also known as C6H6, PhH, and benzol, is an organic chemical compound that is a colorless and flammable liquid with a pleasant, sweet smell. ... Cyclobutadiene is the smallest [n]-annulene ([4]-annulene), an extremely unstable hydrocarbon having a lifetime shorter than five seconds in the free state. ... Flash point 11°C R/S statement R: ? S: , , , , RTECS number BO0875000 Supplementary data page Structure and properties n, εr, etc. ... A spheroid is a quadric surface in three dimensions obtained by rotating an ellipse about one of its principal axes. ... PEL-TWA (OSHA) 50 ppm (240 mg/m3) IDLH (NIOSH) 500 ppm Flash point non-flammable RTECS number FS9100000 Supplementary data page Structure & properties n, εr, etc. ... Methylacetylene (propyne) is an alkyne with the chemical formula CH3C≡CH. It is a component of MAPP gas, which is commonly used in gas welding. ... R-phrases , , , , S-phrases , , , , , Flash point non flammable RTECS number FG4900000 Supplementary data page Structure and properties n, εr, etc. ... Fumes from hydrochloric acid and ammonia forming a white cloud of ammonium chloride Ammonium is also an old name for the Siwa oasis in western Egypt. ... Sulfur hexafluoride (SF6) is a gas whose molecules consist of one sulfur atom and six fluorine atoms. ... In chemistry, anthracene is a solid polycyclic aromatic hydrocarbon consisting of three benzene rings derived from coal-tar. ... Water has the chemical formula H2O, meaning that one molecule of water is composed of two hydrogen atoms and one oxygen atom. ... [1] R-phrases , S-phrases , , , , , Supplementary data page Structure and properties n, εr, etc. ...

Structure of rotational spectrum

• Linear molecules

These molecules have two degenerate modes of rotation (I_B = I_C, I_A = 0). Since we cannot distinguish between the two modes, we need only one rotational quantum number (J) to describe the rotational motion of the molecule.

The rotational energy levels () of the molecule based on rigid rotor model can be expressed as, The rigid rotor is a mechanical model that is used to explain rotating systems. ...

where is the rotational constant of the molecule and is related to the moment of inertia of the molecule I_B = I_C by,

Selection rules dictate that during emission or absorption the rotational quantum number has to change by unity i.e. . Thus the locations of the lines in a rotational spectrum will be given by,

where denotes the lower energy level and denotes higher energy level involved in the transition. The height of the lines is determined by the distribution of the molecules in the different levels and the probability of transition between two energy levels.

We observe that, for a rigid rotor, the transition lines are equally spaced in the wavenumber space. However, this is not always the case, except for the rigid rotor model. For non-rigid rotor model, we need to consider changes in the moment of inertia of the molecule. Two primary reasons for this are, The rigid rotor is a mechanical model that is used to explain rotating systems. ...

• Centrifugal distortion:

When a molecule rotates, the centrifugal force pulls the atoms apart. As a result, the moment of inertia of the molecule increases, thus decreasing . To account for this a centrifugal distortion correction term is added to the rotational energy levels of the molecule. Centrifugal force (from Latin centrum center and fugere to flee) is a term which may refer to two different forces which are related to rotation. ... Centrifugal force (from Latin centrum center and fugere to flee) is a term which may refer to two different forces which are related to rotation. ...

where is the centrifugal distortion constant.

Accordingly the line spacing for the rotational mode changes to,

• Effect of vibration on rotation:

A molecule is always in vibration. As the molecule vibrates, its moment of inertia changes. However as long as the vibrational quantum number does not change (i.e. the molecule is in only one state of vibration), the effect of vibration on rotation are not important, because the time for vibration is much greater than the time required for rotation.

• Symmetric Top

The rotational motion of a symmetric top molecule can be described by two independent rotational quantum number (since two axes have equal moment of inertia, the rotational motion about these axes requires only one rotational quantum number for complete description). Instead of defining the two rotational quantum number for two independent axes, we associate one of the quantum number (J) with the total angular momentum of the molecule and the other quantum number (K) with the angular momentum of the axis which has different moment of inertia (i.e. axis C for oblate symmetric top and axis A for prolate symmetric tops). The rotational energy of such a molecule, based on rigid rotor assumptions can be expressed in terms of the two previously defined rotational quantum number as follows,

where and for a prolate symmetric top molecule or for an oblate molecule.

Selection rule for the these molecules provide the guidelines for possible transitions. Accordingly,

.

This is so because K is associated with the axis about which the molecule is symmetric and hence has no net dipole moment in that direction. Thus there is no interaction of this mode with the light particles (photon).

This gives the transition wavenumbers of,

which is same as in case of linear molecule.

In case of non-rigid rotors, the first order centrifugal distortion correction is given by,

The suffixes on the centrifugal distortion constant D indicate the rotational mode involved and are not a function of the rotational quantum number. The location of the transition lines on a spectrum are given by,

• Spherical Tops

Unlike other molecules, spherical top molecules have no net dipole moment, and hence they do not exhibit any rotational spectrum.

• Asymmetric Tops

The spectrum for these molecules usually involves many lines due to three different rotational modes and there combinations. There is no general rule for studying the rotational spectum of these molecules.

Hyperfine interactions:

In addition to the main structure that is observed in microwave spectra that is due to the rotational motion of the molecules, a whole host of further interactions are responsible for small details in the spectra, and the study of these details provides a very deep understanding of molecular quantum mechanics. The main interactions responsible for small changes in the spectra (additional splittings and shifts of lines) are due to magnetic and electrostatic interactions in the molecule. The particular strength of such interactions differs in different molecules, but in general, the order of these effects (in decreasing significance) is:

1. electron spin - electron spin interaction (this occurs in molecules with two or more unpaired electrons, and is a magnetic-dipole / magnetic-dipole interaction)
2. electron spin - molecular rotation (the rotation of a molecule corresponds to a magnetic dipole, which interacts with the magnetic dipole moment of the electron)
3. electron spin - nuclear spin interaction (the interaction between the magnetic dipole moment of the electron and the magnetic dipole moment of the nuclei (if present)).
4. electric field gradient - nuclear electric quadrupole interaction (the interaction between the electric field gradient of the electron cloud of the molecule and the electric quadrupole moments of nuclei (if present)).
5. nuclear spin - nuclear spin interaction (nuclear magnetic moments interacting with one another).

These interactions give rise to the characteristic energy levels that are probed in "magnetic resonance" spectroscopy such as NMR and ESR, where they represent the "zero field splittings" which are always present. Nuclear Magnetic Resonance Spectroscopy most commonly known as NMR Spectroscopy is the name given to the technique which exploits the magnetic properties of nuclei. ... Electron Paramagnetic Resonance (EPR) or Electron Spin Resonance (ESR) is a spectroscopic technique which detects species that have unpaired electrons, generally meaning that it must be a free radical, if it is an organic molecule, or that it has transition metal ions if it is an inorganic complex. ...

Experimental determination of the spectrum

Applications

Resources

• Microwave Spectroscopy, Townes and Schawlow, Dover;
• Rotational Spectroscopy, Harry Kroto, Dover;
• Rotational Spectroscopy of Diatomic molecules, Brown and Carrington;
• Quantum Mechanics, Mcquarrie, Donald A.

See also

• Spectroscopy
• Rigid rotor
• Rovibronic excitation
• Vibrational spectroscopy
• Infrared spectroscopy

Extremely high resolution spectrum of the Sun showing thousands of elemental absorption lines (fraunhofer lines) Spectroscopy is the study of spectra, that is, the dependence of physical quantities on frequency. ... The rigid rotor is a mechanical model that is used to explain rotating systems. ... Rovibronic excitation stands for rotational vibrational electronic excitation of a molecule. ... The vibrational states of a molecule can be probed in a variety of ways. ... IR spectrum of a thin film of liquid ethanol. ...

External Links

• Hyperphysics article on Rotational Spectrum