Atomic and Molecular Physics Course Code: PHYS4009

Lecture Topic Molecular Spectroscopy By Prof. Sunil Kumar Srivastava Department of Physics Mahatma Gandhi Central University Motihari, Bihar-845401 Please see the video lecture at https://www.youtube.com/watch?v=A2DQ_OxJ2Og Outline Questions that comes in our mind ?

What is the term Spectroscopy? What does light do to the molecules? How can you produce a molecular spectrum? What information does the molecular spectrum give?

What we achieve?

Understanding of: - How light interacts with molecules - Molecular Energy States - How to use spectroscopy to quantitatively characterize molecule - How to extract molecular information SPECTROSCOPY Spectroscopy is the study of electromagnetic spectra – the wavelength composition of light – due to atomic and molecular interactions. Interaction of radiation with matter

Reflection Interaction of radiation with matter

Transmission Interaction of radiation with matter

Absorption Interaction of radiation with matter

Scattering Interaction of radiation with matter

Photoluminescence Spectroscopy is the study of matter (atom or molecule or any substance ) by investigating light, sound, or particles that are absorbed, emitted or scattered by the matter under investigation with the help of spectroscopic instruments Light : Electromagnetic Radiation

E = E0 sin(kx −t)

B = B0 sin(kx −t) 2 k =  = 2  Energy of Photon c E = h = h = hc~  h = 6.626 × 10−34 js c = 2.997 × 108 m/s

c Wave frequency  =  

1 Wavenumber (cm−1) ~ = (cm) Molecular Interaction with Light

E´ E´ Absorption ΔE = hν hν E E

E´ E´ Emission ΔE = hν hν E E

Scattering hν hν Molecular Energy States

Electronic excited state Energy Electronic transition Vibrational state (in visible or UV) Electronic ground state Rotational transition Vibrational (in microwave) transition (in infrared) Rotational state

Internuclear Separation Molecular Rotation in Diatomic Molecule

I = R2 m m  = 1 2 m1 + m2

Permanent dipole moment

The electric field of an electromagnetic wave exerts a torque on a electric dipole Molecular Rotational Energy 1 1 1 E = I2 + I2 + I2 2 x 2 y 2 z Angular momentum L = I

+

L2 J (J +1)2 H =  =  J is Rotational Quantum Number 2I 2I J (J +1)2 E = 2I 퐸 _ h 퐹 퐽 = = 퐵퐽 퐽 + 1 푐푚 1 For rigid rotor B = ℎ푐 8 2cI E _ F(J ) = = BJ (J +1) − DJ 2 (J +1)2 + 푐푚 1 For non-rigid rotor hc B is Rotational constant and D is centrifugal distortion constant Rotational Energy Level Rigid Rotor Non-Rigid Rotor _ _ 퐹 퐽 = 퐵퐽 퐽 + 1 푐푚 1 J 퐹 퐽 = 퐵퐽 퐽 + 1 − 퐷퐽2 퐽 + 1 2 … . 푐푚 1 6 J 6

5 5

4 Selection rule 4 J = 1 3 3

2 2 1 1 0 0 0 4B 8B 12B 0 4B 8B 12B

2B 6B 10B 2B 6B 10B cm-1 → cm-1 → Molecular Rotation in Polyatomic Molecule

The rotational spectra of molecules can be classified according to their principal moments of inertia c 2 b I =  M i Ri i a

Ic  Ib  Ia

The particular pattern of energy levels and hence the transitions in the rotational spectrum for a molecule is determined by its symmetry. Based on the symmetry of their structure, molecules are divided into four different classes. Linear molecules

Ic = Ib  Ia = 0

c b

a

O C O Symmetric top

Ic  Ib = Ia Ic = Ib  Ia Oblate Prolate

BF3 CH3Cl Spherical top

Ic = Ib = Ia

CH4

Asymmetric top

Ic  Ib  Ia

H2O Books for Further Reading

1. Fundamentals of Molecular Spectroscopy by C. N. Banwell (McGraw Hill)

2. Basic Atomic & Molecular Spectroscopy by J. M. Hollas (Royal Society of Chemistry)

References: http://hyperphysics.phy-astr.gsu.edu/hbase/index.html Bruker application notes