1. RAMAN SPECTROSCOPY THREE EFFECTS OF RADIATION OF LIGHT ON MOLECULES CAN OCCUR. (i) RADIATION OF LIGHT ON TO MOLECULES, SOME OF THE LIGHT WILL BE REFLECTED WITH WAVELENGTH UNCHANGED. THIS IS RALEIGH SCATTERING. (ii)SOME OF THE LIGHT IS REFLECTED WITH WAVELENGTH INCREASED. (iii)SOME OF THE IS REFLECTED WITH THE LENGTH REDUCED.

2. RAMAN SPECTROSCOPY THE LEAST TWO PHENOMENA ARE CAUSED BY LIGHT INTERACTION WITH MOLECULES. THE ELECTRON INTERACTS WITH THE CLOUD WHICH PRODUCES EITHER HIGHER OR LOWER FREQUENCY AND IT IS REFERRED TO AS RAMAN SCATTERING. THE PROCESS CAN BE EXPLAINED BY QUANTUM AND CLASSICAL MECHANICS.

3. RAMAN SPECTROSCOPY CLASSICAL MECHANICAL VIEW POINT: EMPHASIZES ON THE POLARIZABILITY OF A MOLECULE WHEN SUBJECTED TO AN ELECTRIC FIELD. IF THE ELECTRIC FIELD STATIC, IT SUFFERS SOME DISTORTION, WHERE THE POSITVE CHARGES MOVE TOWARDS THE NEGATIVE END OF THE ELECTRIC FIELD WHILE ELECTRONS MOVE TOWARDS THE POSTIVE END.

4. RAMAN SPECTROSCOPY THIS CAUSES A SEPRATION OF CHARGES AND LEADS TO AN INDUCED DIPOLE MOMENT, µ. HENCE THE MOLECULE BECOMES POLARIZED AND CREATES A DIPOLE MOMENT WHICH IS DEPENDENT ON THE MAGNITUDE OF THE APPLIED FIELD E, AND EASE OF DISTORTION. HENCE, µ=αE, α = IS THE POLARIBILITY

5. RAMAN SPECTROSCOPY QUANTUM MECHANICAL VIEW POINT. CONSIDER A QUANTUM OF RADIATION hν ex OF INCIDENT LIGHT STRIKING A MOLECULE. IT CAN BE SCATTERED WITHOUT LOSS OF ENERGY AND THIS SCATTERED LIGHT WILL BE THE SAME FREQUENCY AS THE INCIDENT LIGHT.

6. RAMAN SPECTROSCOPY HENCE THE RALEIGH SCATTERING. BUT IF IT LOSES ENERGY BY TRANSFERRING SOME TO EITHER THE VIBRATIONAL OR ROTATIONAL LEVELS OF THE MOLECULE IN FORM OF QUANTA, IT WILL HAVE A LOWER FREQUENCY GIVEN (ν ex -ν m ).

7. RAMAN SPECTROSCOPY ON THE OTHER HAND IF THE MOLECULE HAPPENS TO BE AT A HIGHER ENERFY LEVEL, ITS COLLISION WITH THE SCATTERED LIGHT WILL LEAD TO THE MOLECULE LOSSING ENERGY TO THE INCIDENT LIGHT WHICH NOW HAS HIGHER ENERGY WITH FREQUENCY; ν ex +ν m. IN THE SPECCTRUM THEREFORE WILL BE THREE LINES WITH FREQUENCIES ν ex, ν ex +ν m, AND ν ex -ν m.

8. RAMAN SPECTROSCOPY THE LINE ν ex -ν m WILL HAVE A LOWER FREQUENCY AND IT IS CALLED STOKES LINE WHILE ν ex +ν m, HAS A HIGHER FREQUENCY AND IT IS CALLED ANTI-STOKES LINE. HENCE THE FREQUENCY OF LIGHT UNDER GOING RAMAN EFFECT WILL FREQUENCY ν=νex±νm AND ARE THEREFORE CALLED RAMAN LINES

9. RAMAN SPECTROSCOPY ELASTIC COLLISIONS WILL NOT SUFFER ANY CHANGE IN FREQUENCY WHILE INELASTICS COLLISIONS WILL RESULT IN LOSS OR GAIN IN ENERGY AND WILL GIVE RISSE RAMAN SCATTERING.

10. RAMAN SPECTROSCOPY FIGURE SHOWING RAMAN LINES. v=1 v=0 v ex vmvm vmvm Elastic interaction Raleigh Scattering Raman scattering Stokes Line ν=ν ex -ν m vv vmvm v ∆v=v ex -v=0 ∆v<0 v-v ex <0 ∆v>0 v-v ex >0 Raman scattering Anti-Stokes line

11. SCHEMATIC RAMAN SPECTRUM v=v ex +v m v=v ex v=v ex -v m λ Raman lines Raleigh line Raman lines ∆ v>0 (anti-Stokes Very weak intensity ∆ v = 0 v>0 (Stokes lines) weak intensity

12. ROTATIONAL RAMAN SPECTRA THE ROTATIONAL ENERGY LEVELS OF LINEAR MOLECULES IS GIVEN AS; E J =BhcJ(J+1)- DJ 2 (J+1) 2 cm -1, (J=0, 1, 2, 3,.........) BUT IN RAMAN SPECTROSCOPY, THE CENTRIFUGAL DISTORTION CONSTANT ‘D’ IS IGNORED. HENCE THE ROTATIONAL ENERGY IS; E J =BhcJ(J+1) (J=0, 1, 2, 3,.........) AND THE SELECTION RULE IS ΔJ=0 OR ±2 ONLY.

13. ROTATIONAL RAMAN SPECTRA USING THE SELECTION RULE OF ΔJ=2 RESULTS INTO AN EQUATION; ΔE=Bhc (4J+6); J=0, 1, 2, 3,...., WHERE J IS THE LOWER ROTATIONAL QUANTUM NUMBER.

14. ROTATIONAL RAMAN SPECTRA CONSIDER TRANSITION FROM J →J+2; ṽ J =E J+1 - E J /hc=2B(J+1) AND THE RAMAN TRANSITION WILL OCCUR AT; ṽ J(RAMAN) =E J+2 -E J /hc= 4B(J+3/2). THE ENERGY SEPARATION IN RAMAN LINES IS 4B. THESE LINES ARE REFERRED TO AS S-BRANCH LINES. FOR ṽ S J→J+2 (STOKES LINE)=ṽ ex -B[(J+2)(J+3)-J(J+1)] ṽ S J→J+2 (STOKES LINE)= ṽ ex -4B(J+3/2); J=0, 1, 2,....

15. ROTATIONAL RAMAN SPECTRA FOR ANTI-STOKES LINES, ΔJ= -2 ṽ S J→J-2 =ṽ ex +B[(J)(J+1)-(J-2)(J-1)] ṽ S J→J-2 =ṽ + 4B (J-1/2); J=2, 3, 4, 5... THESE ARE SCHEMATICALLY ILLUSTRATED BELOW.

16. SCHEMATIC DIAGRAM FOR RAMAN ΔJ=-2ΔJ=+2 J=2→J=0J=0→J=2 J=3→J=1J=1→J=3 J=4→J=2J=2→J=4 J=5→J=3J=3→J=5 J=6→J=4J=4→J=6 J=7→J=5J=5→J=7 J=6→J=8 J=7→J=9

17. SCHEMATIC DIAGRAM FOR RAMAN Raman Lines 7654321076543210 ∆J=-2 ∆J=+2

18. SCHEMATIC DIAGRAM FOR RAMAN Raman lines 6B 4B 30B 26B 22B 18B 14B 10B 6B v ex 6B 10B 14B 18B 22B 26B 30B ANTI-STOKES LINES STOKES LINES WAVELENGTH 4B

19. ROTATIONAL RAMAN SPECTRA THE FREQUENCY OF SEPARATION FOR FIRST STOKES AND ANTI-STOKES LINE ARE 6B WHILE THE REST ARE 4B. HOMONUCLEAR DIATOMIC MOLECULES WITH NO PERMANENT DIPOLE MOMENT CAN BE RAMAN ACTIVE eg CO 2, N 2 O, C 2 H 2 etc SPHERICAL TOPS (CCl 4, CH 4, SiH 4...) WITH ONE VALUE OF MOMENT OF INERTIA FOR WHICH THE POLARIZABILITY CANNOT BE ALTERED ARE NOT RAMAN ACTIVE.

20. ROTATIONAL RAMAN SPECTRA SYMMETRIC TOPS WITH TWO MOMENT OF INERTIA EQUAL HAS THE ROTATIONAL ENERGY GIVEN; E JK (cm -1 )=BJ(J+1)+(A-B)K 2 ; J=0, 1, 2, 3.. AND K= 0, ±1, ±3, ±5... AND B=h/8π 2 I y c AND A=h/8π 2 I x c. K IS A COMPONENT OF ANGULAR MOMENTUM. SELECTION RULE FOR ROTATIONAL RAMAN TRANSITIONS IS; ΔJ=0, ±1, ±2 AND ΔK=0

21. ROTATIONAL RAMAN SPECTRA BASED ON THESE RULES, THE ENERGY DIFFERENCE IN ROTATIONAL RAMAN TRANSITIONS ARE; ΔJ =1ṽ=4B(J+3/2); J=0, 1, 2, 3,.... ΔJ =2ṽ =2B(J+1); J= 2, 3..... WHERE ΔJ=2 TRANSITIONS ARE CALLED S-BRANCH LINES AND ΔJ=1 IDENTIFIED AS R-BRANCH LINES AND COINCIDES WITH EVERY OTHER S- BRANCH.

22. VIBRATIONAL RAMAN SPECTRA AS WITH THE ROTATIONAL, TRANSITIONS WITHIN THE VIBRATIONAL STATES CAN ALSO PRODUCE RAMAN SPECTRA. ALSO A MOLECULE MUST ALSO BE POLARIZABLE BEFORE IT CAN BE ACTIVE. THE OTHER SELECTION RULE FOR RAMAN SCATTERING IS SIMILAR TO PURE VIBRATIONAL STATES i.e. Δv=±1, ±2, ±3... BUT THE INTENSITY OF v=±2, ±3, ±4.... DECREASES VERY FAST AND ONLYΔv= ±1 REMAINS AS THE MAIN INTENSE BAND.

23. VIBRATIONAL RAMAN SPECTRA TWO CONDITIONS THAT ALLOW RAMAN SCATTERING; (i)Δv=±1, IMPLIES TRANSITIONS ARE ONLY POSSIBLE FOR A CHANGE BY ONE UNIT (ii)POLARIZABILITY CHANGES WITH NUCLEAR DISTANCE, CHANGE IN BOND LENGTH DURING VIBRATION.

24. VIBRATIONAL RAMAN SPECTRA RAMAN LINES ARE USUALLY WEAK AND THAT NO OVERTONES ARE OBSERVED. ONLY THE FUNDAMENTAL BAND Δv=±1 IS OBSERVED AND CONSIDERED. THE ENERGY FOR A VIBRATIONAL MODE UNDER GOING A RAMAN SCATTERING IS GIVEN BY; E v =(v+½)hν e, ν e IS THE VIBRATIONAL FREQUENCY AT EQUILIBRIUM.

25. VIBRATIONAL RAMAN SPECTRA FOR A TRANSITION FROM v=0 TO v=1, THE CHANGE IN ENERGY WILL BE; ΔE FUNDAMENTAL = E v=1 - E v=0 =hν e THE CORRESPONDING FUNDAMENTAL FREQUENCY IS; ṽ RAMAN =ṽ ex -ṽ e. FOR Δv=+1, THE FREQUENCY OF THE STOKES LINE ṽ s =ṽ ex - ṽ e AND THE ANTI-STOKES LINE WILL OCCUR AT Δv=-1 AND THE CORRESPONDING FREQUENCY WILL BE AT; ṽ as =ṽ ex + ṽ e

26. VIBRATIONAL RAMAN SPECTRA IN GAS PHASE, EACH VIBRATIONAL TRANSITION WILL CONSIST OF SERIES OF NUMBER OF CLOSELY SPACED ROTATIONAL- VIBRATIONAL LINES. FOR VIBRATIONAL- RAMAN SPECTRUM, THE SET OF ROTATIONAL LINES WITHIN A VIBRATIONAL LEVEL (∆v= ±1) WITH CORRESPONDING SELECTION RULE WITH FF DESIGNATIONS;

27. VIBRATIONAL RAMAN SPECTRA ∆J= +2;S-BRANCH ∆J= 0;Q-BRANCH ∆J= -2;O-BRANCH THUS v=0 TO v=1, TRANSITION IGNORING ANHARMONICITY AND CENTRIFUGAL DISTORTION EFFECTS; E vJ =(v+½)h√ e + BhcJ(J+1)

28. VIBRATIONAL RAMAN SPECTRA THUS v=1,E 1J =3/2h√ e +Bhc J(J+1) FOR v=0,E 0J =½h√ e + Bhc J(J+1) IF v ex IS THE FREQUENCY OF INCIDENT LIGHT TO STUDY RAMAN EFFECT, THEN FOR STOKES LINES, ∆v =+1; ∆J=+2, WHERE J→(S-BRANCH), J=0, 1, 2....... ῡ s =ῡ ex -(ῡ e +6B)STOKES S-BRANCH

29. VIBRATIONAL RAMAN SPECTRA FOR Q-BRANCH, ∆J=0, J→J, AND ῡ s =(ῡ ex -ῡ e ) FOR O-BRANCH, ∆J= -2;J→J-2, J=2, 3, 4... ῡ s =ῡ ex - (ῡ e -6B), CORRESPONDING TO ANTI- STOKES LINES, ∆v=-1 FOR S-BRANCH, ∆J=2; J→J+2; J=0, 1, 2... ῡ s =ῡ ex +ῡ e +6B

30. VIBRATIONAL RAMAN SPECTRA FOR O-BRANCH, ∆J=-2, J→J-2, J=2, 3, 4,.. ῡ s =ῡ ex +ῡ e -6B

31. RAMAN SPECTRA OF POLYATOMIC MOLECULES