Molecular spectroscopy

Molecular spectroscopy-Pure rotational (Microwave) spectra-Vibrational (Infrared) spectra -Electronic (UV) Spectra-
Raman Spectra

1. Dr. P.Govindaraj Associate Professor and Head Department of Chemistry Saiva Bhanu Kshatriya College , Aruppukkottai 626101, Tamilnadu , I ndia . Molecular spectroscopy

2. Molecular Spectroscopy The study of interaction of electromagnetic radiations with matter is called M olecular spectroscopy. Types of Molecular spectroscopy: Pure rotational (Microwave) spectra Vibrational (Infrared) spectra Electronic (UV) Spectra Raman Spectra Nuclear Magnetic Resonance (NMR) spectra Electron Spin Resonance (ESR) Spectra

3. Rotational spectra of diatomic molecule Definition: The interaction between rotational energy levels of a gaseous molecule and microwave radiation causes transition between the rotational energy levels by the absorption of microwave radiation is called rotational spectra Condition: Molecules possess permanent dipole moment shows molecular spectra .The microwave spectra occur in the spectral range of 1-100 cm -1 Example : HCl , CO ,H 2 O , NO ,etc .

4. . Explanations : consider a diatomic molecule rotating about its center of gravity (C.G) . Where, r is the bond length m 1 is the mass of one atom m 2 is the mass of another atom r 1 is the distance of the atom 1 from the CG r 2 is the distance of the atom 2 from the CG . At center of gravity : m 1 r 1 = m 2 r 2 ---------- ( 1 ) Rotational spectra of diatomic molecule

5. Rotational spectra of diatomic molecule . T he moment of inertia I of a molecule is I = μr 2 ------- (2) where , μ = reduced mass of the molecule = . According to classical mechanics , the angular momentum (L) of a rotating molecule is L = Iω ------- (3) where , ω = angular velocities  

6. Rotational spectra of diatomic molecule . According to quantum mechanics L = ------- (4) where , J = rotational quantum number = 0,1,2,3,……. . T he energy of rotating molecule is E J = = = = E J = E J = ------- (5)  

7. Rotational spectra of diatomic molecule The equation (5) is divided by hc in order to express the energy in cm -1 cm -1 E J = cm -1 ------- (6) E J = BJ( J+1) cm -1 -------- (7) Where , B =  

8. Rotational spectra of diatomic molecule Substituting the rotational quantum number (J = 0 , 1 , 2 , 3 , ….) in the equation (7) we gets the quantized rotational energy levels of the rotating diatomic molecule when ; J = 0 , E = 0 J = 1 , E 1 = 2 Bcm -1 J = 2 , E 2 = 6 Bcm -1 J = 3 , E 3 = 12 Bcm -1 J = 4 , E 4 = 20 Bcm -1 J = 5 , E 5 = 30 Bcm -1 Since the rotational energy levels falls on the microwave region , the transition between rotational energy level takes place by the absorption of microwave radiation as per the selection rule ΔJ = ±1

9. Rotational spectra of diatomic molecule So, the energy for a transition J = 0 J = 1 is ΔE = E 1 – E ΔE 0-1 = 2B – 0 = 2B ; Since ΔE = γ γ 0-1 = 2B ;where, γ is frequency in cm -1 of the microwave causes transition Similarly for, J = 1 J = 2 is γ 1-2 = E 2 – E 1 γ 1-2 = 6B – 2B = 4B Similarly ; γ 2-3 = 6B , γ 3-4 = 8B

10. Rotational spectra of diatomic molecule The rotational spectrum of a rigid diatomic molecule appear at the following rotational frequencies 2B, 4B, 6B, 8B .etc.. And each are appeared as a lines in the detector . These lines are equally spaced by 2B i.e. the interspaceial distance of the spectral lines is 2B and it shown in the diagram

11. Relative intensities of rotational spectral lines The plot of versus J for a rigid diatomic molecule at room temperature is The value of J corresponding to the maximum in population is J max = ( 1/2 – ½  

12. Vibrational spectra of diatomic molecule Definition : The interaction between the vibrational energy levels of a molecule and the infrared radiation causes transition between the vibrational energy levels by the absorption of infrared radiation is called infrared radiation Condition : T he vibrations of a molecule involving changes in the dipole moment are IR active. These spectra occur in the spectral range of 500-4000 cm -1 Example : hetero diatomic molecule like CO , NO , CN , HCl ,(dipole moment) shows changes in dipole moment during vibration. i.e.. Homodiatomic molecule (H 2 , O 2 , N 2 etc.) are IR-inactive but hetero diatomic molecules are IR-active

13. Vibrational spectra of diatomic molecule Explanation : consider a vibrating diatomic molecule and the vibration is assumed to be simple harmonic vibration Where m 1 and m 2 are the masses of the atoms r e = equilibrium distance x = displacement of the atom during vibration(expansion and compression) from the equilibrium distance

14. Vibrational spectra of diatomic molecule The vibrational frequency of the vibrating molecule in term of cm -1 is γ = cm -1 ---------(1) Where , k = force constant , it is the restoring force acting on the molecule in order to come to original position during expansion and compression μ = reduced mass = According to Hooke's law , the potential energy ( V x ) of the vibrating molecule is a function of ‘x’ i.e.. V (x) = ½ kx 2 --------(2) where x = r - r e  

15. Vibrational spectra of diatomic molecule The plot of potential energy (V x ) versus x gives parabolic curve On solving the Schrodinger wave equation for a simple harmonic vibrator gives the vibrational energy level E V = ( v + ½ )h γ ----------(3) where v = vibrational quantum number = 0,1,2,3,…….. γ = vibrational frequency

16. Vibrational spectra of diatomic molecule Equation (3) is divided by hc to get the energy in cm -1 = (v + ½) = (v + ½) E v = (v + ½) ω e -----------(4) where ω e = equilibrium vibrational frequency By putting the value of v in equation (4) we get the energy of various vibrational level When ; v = 0 , E = called zero point energy v = 1 , E 1 = ; v = 2 , E 2 = v = 3 , E 3 = v = 4 , E 4 = v = 5 , E 5 =  

17. Vibrational spectra of diatomic molecule This shows the vibration energy levels are equally spaced by ω e . Since the vibrational energies are falling into IR region , the transition between vibrational energy levels takes place by the absorption of IR radiation as per the selection rule Δv = +1

18. Vibrational spectra of diatomic molecule The energy of the IR radiation in term of cm -1 ( γ )that causes the vibrational energy transition is equal to E v+1 – E v i.e.. For v = 0 ----- v = 1 For v = 1 ----- v = 2 γ = E 1 – E = – = ω e γ = E 2 – E 1 = – = ω e For v = 2 ----- v = 3 For v = 3 ----- v = 4 γ = E 3 – E 2 = – = ω e γ = E 4 – E 3 = – = ω e This shows all vibrational energies transition as per the selection rule Δv = ±1 occurs at only one frequency we called fundamental vibrational frequencies and gi v es only one vibrational spectrum line  

19. Vibrations of polyatomic molecules Total degree of freedom for polyatomic molecule = 3N where N is number of atoms The translational degree of freedom for polyatomic molecule = 3 The rotational degree of freedom for linear molecule = 2 non linear molecule = 3 So , the vibrational degree of freedom for polyatomic linear molecule = 3N – 5 polyatomic non linear molecule = 3N – 6

20. Vibrations of polyatomic molecules Linear CO 2 molecule N = 3 The vibrational degree of freedom = 3 N – 5 = (3 X 3) – 5 = 9 – 5 = 4 The four types vibrations in CO 2 molecule are IR active are shown in figure

21. Vibrations of polyatomic molecules 2. Linear H 2 O molecule N = 3 The vibrational degree of freedom = 3 N – 6 = (3 X 3) – 6 = 9 – 6 = 3 The three types vibrations in H 2 O molecule are IR active are shown in figure

22. Electronic spectra Definition : The interaction between the electronic energy levels in a molecule and the visible and ultra violet radiation causes transition between the electronic energy levels by the absorption of the visible (or) u.v radiation is called electronic spectra Conditions : Components containing π – bond shows electronic spectra. The electronic spectra in the visible region span 12,500-25,000 cm -1 ,those in the ultra violet region span 25,000-75,000 cm -1 Explanation : The total energy of a molecule in the ground state is E = E elc + E vib + E rot --------(1) (since E trans is not quantized , it is not included in equation 1 ) The total energy of a molecule in the excited state is E , = E , elc + E , vib + E , rot ---------(2)

23. Electronic spectra Equation (2) – (1) gives the energy required to make the electronic transition from E to E , i.e.. E , – E = ( E , elc – E elc ) + ( E , vib – E vib ) + ( E , rot – E rot ) ΔE = ΔE elc + ΔE vib + ΔE rot ---------(3) Since , ΔE elc >> ΔE vib >> ΔE rot ; the two electronic states transition is accompanied by simultaneous transition between the vibrational and rotational level. Divide equation (3) by hc we get the energy in terms of frequency for the electronic transition in cm -1 = = γ cm -1 ----------(4) The electronic energy levels transition will be governed by the Franck - Condon principle  

24. Electronic spectra – Franck C ondon principle Franck Condon principle states that an electronic transition takes place without any change in the internucler distance of the vibrating molecule .

25. Electronic spectra – Franck Condon principle Since the bonding in the excited state is weaker than in the ground state , the minimum in the potential energy curve for the excited state occurs at a slightly greater internucler distance than the corresponding minimum in the ground electronic state So , when a photon falls on the molecule , the most probable electronic transition according to Franck- C ondon principle is v ----- v , 2 and is shown in the above diagram as 0 ----- 2 Application : The unsaturated molecules containing C=C and C=O (aldehydes and ketone) are identified using electronic spectrum since they shows n – π* and π – π* electronic transition

26. Raman spectroscopy Definition : It is the branch of molecular spectroscopy which deals about the scattering of light radiation by the molecules in which the scattered light radiation will have either a higher or a lower frequency than the incident light radiation and this effect is called R aman effect Diagrammatically: Condition : Changes in polarisability of the molecule is the condition for getting R aman spectrum. Raman spectra are observed in the visible region, 12,500-25,000 cm -1

27. Raman spectroscopy – Quantum theory According to quantum theory , a photon of frequency ( γ ) falling on a molecule , collision takes place between the molecule and photon . If the collision is elastic , then the scattered photon will have the same energy and same frequency as the incident radiation . This scattering is called Rayleigh scattering If the collision is inelastic , the scattered photon will have either higher (or) lower energy and frequency then the incident radiation . This scattering is called Raman scattering

28. Raman spectroscopy – Quantum theory (a) (b) (c)

29. Raman spectroscopy – Quantum theory Figure b : when the molecule excited to the higher unstable vibrational energy level then returns to the original vibrational energy leve l of the ground state we get Rayleigh scattering Figure a : when the molecule excited to the higher unstable vibrational energy level then returns to the different vibrational energy level of the ground state we get Raman scattering called stokes lines Figure c : when the molecule , initially in the first excited vibrational energy level of the ground state is promoted to a higher unstable vibrational state and returns to the ground state we get Raman scattering called anti stokes line The shifts in frequency ( γ – γ , ) is called R aman shifts and it fall in the range 100 – 4,000 cm -1

30. Comparison between R aman spectrum and Infrared spectrum

31. Application of R aman spectra Using the mutual exclusion rule , it gives information about molecular vibrations which are IR inactive i.e.. Molecule having center of symmetry (H 2 , O 2 , CO 2 …) IR active vibrations are R aman inactive and IR inactive vibrations are Raman active Example : In CO 2 , the symmetric stretching vibration has no dipole moment so it is IR inactive but it gives R aman spectra

32. Application of Raman spectra 2. The existence of cis and trans isomers in dichloro ethylene can be confirmed by Raman's spectra Raman active IR active i.e.. i f the compound has trans isomer only , it gives R aman spectra only but dichloro ethylene gives both Raman and IR spectra. This indicates that the existence of cis and trans isomers in equilibrium

33. Application of Raman spectra 3. All the vibrations for CS 2 are R aman active and IR inactive . This indicates that the structure of CS 2 has center of symmetry like 4. All the vibrations for N 2 O are Raman active and IR active . This indicates that the structure of N 2 O has no center of symmetry like

34. Experimental technique for Raman spectroscopy As shown in the diagram is the experimental set-up for the Raman spectroscopy

35. Experimental technique for Raman spectroscopy Experiment : When a current discharge passes through the large spiral discharge tube emits intense monochromatic radiation allowed to fall on the cell containing a gaseous (or) liquid sample The scattered light is observed at right angles to the direction of incident radiation and allowed to pass through the filter and monochromator then finally fall on the detector The detector used is photographic plate

36. Pure Rotational R aman spectra The selection rule for Rotational Raman spectra is ΔJ = 0 , ± 2 when ΔJ = 0 → Rayleigh scattering ΔJ = +2 → stokes lines ΔJ = -2 → Anti stokes lines Raman scattering

37. Rotation – vibration Raman spectrum The selection rule for Rotation - vibration Raman spectra is Δv = +1 , ΔJ = 0 , ± 2 The transition with Δv = +1 and ΔJ = 0 is called Q - branch lines The transition with Δv = +1 and ΔJ = +2 is called S - branch lines The transition with Δv = +1 and ΔJ = -2 is called - branch lines

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