MICROWAVE SPECTROSCOPY lecture 2

University of Babylon Undergraduate Studies
College of Science
Department of Chemistry
Course No. Chsc 424 Physical chemistry
Fourth year - Semester 2
Credit Hour: 3 hrs.
Scholar units: three units
Lectures of Molecular spectroscopy
Second Semester, Scholar year 2018-2017
Prof. Dr. Abbas A-Ali Draea
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Lecture No. Two: Microwave Spectroscopy
1-Introudction.
2-Advantages
3-Rotator molecules.
4- Intensities of Transitions and Selection Rules.
5-Classfication of molecules.
6-Applications.
1-Introudction.
Free atoms do not rotate or vibrate. For an oscillatory or a rotational motion of a pendulum, one end has to be tied or fixed to some point.
In molecules such a fixed point is the center of mass. The atoms in a molecule are held together by chemical bonds.
The rotational and vibrational energies are usually much smaller than the energies required to break chemical bonds. The rotational energies correspond to the microwave region of electromagnetic radiation (3x1010 to 3x1012 Hz; energy range around 10 to100 J/mol) and the vibrational energies are in the infrared region (3x1012 to 3x1014 Hz; energy range around 10kJ/mol) of the electromagnetic radiation.
For rigid rotors (no vibration during rotation) and harmonic oscillators (where in there are equal displacements of atoms on either side of the center of mass) there are simple formula characterizing the molecular energy levels.
In real life, molecules rotate and vibrate simultaneously and high speed rotations affect vibrations and vice versa.
Advantages:-
Rotational spectroscopy is primarily used for determine the molecular structure in gas phase.
It can be used to establish barriers to internal rotation such as that associated with the rotation of the CH3 group relative to the C7H7Cl group in chlorotoluene .
Hyperfine structure can be observed and the technique also provides information on the electronic structures of molecules.
Much of current understanding of the nature of weak molecular interactions such as van derWaals, hydrogen and halogen bonds have been established through rotational spectroscopy.
The measurement of bond length, mass of atoms, and isotopes.

Following figure represented the molecular energetic levels.

Molecular energetic levels.
2-Rotator molecules.
A molecule in the gas phase is free to rotate relative to a set of mutually orthogonal axes of fixed orientation in space, centered on the center of mass of the molecule. Free rotation is not possible for molecules in liquid or solid phases due to the presence of intermolecular forces. Rotation about each unique axis is associated with a set of quantized energy levels dependent on the moment of inertia about that axis and a quantum number. Thus, for linear molecules the energy levels are described by a single moment of inertia and a single quantum number, J, which defines the magnitude of the rotational angular momentum. Nonlinear molecules which are symmetric rotors (or symmetric tops, there are two moments of inertia and the energy also depends on a second rotational quantum number, K, which defines the vector component of rotational angular momentum along the principal symmetry axis. Analysis of spectroscopic data are expressed detailed results in quantitative determination of the values of the moments of inertia. From these precise values of the molecular structure and dimensions may be obtained. The rotational energy of a linear molecule, approximated as a rigid rotor is:
E= BJ (J+1) -----1, in joule units
Since J, is rotational quantum number and takes J = 0, 1, 2, 3…n, and B=h/8?2CI is the rotational constant cm-1 units.
For molecules other than hydrides, the moment of inertia I is such that B ? 1 cm-1, and the rotational levels are so close together that only “optical” spectrographs or spectrometers of the highest resolving power are capable of detecting the rotational structure on vibrational or vibronic transitions; and even these instruments fail when B << 1 cm-1 as is the case for most molecules containing four or more heavy atoms. Multiplication of B(cm-1 ) by the velocity of light c shows that in frequency units B is of the order or less than 30 GHz (1 GHz = 1 gigahertz = 109 cycles/sec). This places transitions between the pure rotational energy states of most molecules in the microwave region of the spectrum, where resolution of rotational structure is much better than that in the optical region. Just as in the classical problem where an oscillatory electrical field can cause an electric dipole to rotate with the frequency of the impressed field, the oscillatory electric vector of electromagnetic radiation can similarly “drive” a quantum mechanical rotor possessing a permanent electric dipole moment. Similarly, the magnetic vector of the electromagnetic wave can interact with a rotor possessing a permanent magnetic moment. Thus molecules such as OCS and BrCN, having electric moments, and O2, having a magnetic moment, have rotational spectra in the microwave region, while a molecule such as Carbon dioxide does not.
For a quantum mechanical rotor, the energy of the electromagnetic field is absorbed only when the frequency of the field is near that corresponding to the energy difference between two discrete energy states of the rotor. The resulting absorption lines for the quantum oscillator constitute the microwave spectrum that one observes. Working backward from the spectrum then, one can ascertain the rotational energy states of the molecule, the moments of inertia of the molecule, and therefore some information about the dimensions of the molecule. In certain cases, one can obtain sufficient information to obtain all the bond distances in the molecule, or for a nonlinear molecule, all the bond distances, bond angles, mass of isotopes(according to reduced mass) and moment of inertia. This is one of the primary goals of microwave spectroscopy.
3- Intensities of Transitions and Selection Rules:
The polar molecules (active microwave molecules) are interacted with electric vectors associated with electromagnetic radiation. The selection rules for pure rotational transitions in a linear rotor. These are ?J=±1, since rotational energy levels have constant distance between each two rotation levels that equal to 2B, this come out by differences of two levels through energy value as following:
??? = ??J+1 - ??J----2
??? = B J+1(J+1+1) - B J(J+1)
???=2B(J+1)-----3
There are constant distance between rotational levels 2B, 4B, 6B, and so on…. Can be make a table of energy measurements for several values of rotational quantum numbers:-
J Energy/??J Transition
J?J- Absorption spectral line cm-1
0 0 ------- --------- ground state
1 2B 0---1 First line at 2B
2 6B 1-----2 Second line at 4B
3 12B 2------3 Third line at 6B
4 20B 3------4 Fourth line at 8B


Rotational energy levels.

4-Classfication of molecules.



5-Applications.
1-//Rotation spectrum of 76Br19F has a serious lines in equal distance from each other (0.71433cm-1). Calculate the rotation constant, moment of inertia, and length bond of molecule.
Answer //
1-Equal distance= 2B =0.71433cm-1
Rotation constant=B=0.35717 cm -1
2- Moment of inertia=h/8?2BC ? I=7.83x10-96 kg.m2
3- Length bond of molecule= r = ?(I/?) = 0.1755nm

2//The microwave spectrum of 39K127I is consisted of a series of lines whose spacing is almost constant at 3634 MHz . Calculate the bond length of Potassium iodide, if you Know that 1 AMU=1.67x10-27 kg.
Answer//???? The rotational spacing for KI is given in Hz, a unit of frequency

3//Calculate the value of I and r of CO. 2B = 0.92118 cm-1.
Answer// I = h/(8?2 BC)
= 6.626 x 10 -34/(8 x 3.14152 x 1.92118 x 3 x 1010)
= 1.45579 x 10-46 kg m2
Since the value of B is in cm-1, the velocity of light C is taken in cm/s.
I = ?r2.
The atomic mass of C ? 12.0000 AMU, O ? 15.9994 AMU.
1 AMU = 1.6604 x 10-27 kg.
The reduced mass of CO can be calculated to be 1.13836 x 10-27 kg. Therefore r2 = I/µ = 1.45579 x 10-46/1.13826 x -27 m2
r = 1.131 ?