1. EXAMPLE THE SPECTRUM OF HCl SHOWS A VERY INTENSE ABSORPTION BAND AT 2886 cm -1 AND A WEAKER BAND AT 5668 cm -1. CALCULATE x e, ṽ o, THE FORCE CONSTANT AND DISSOCIATION CONSTANT. THE INTENSE BAND IS FROM v=0→v=1 AND IT IS THE FUNDAMENTAL BAND HENCE ṽ=(v+½)ṽ o -x e (v+½) 2 ṽ o.

2. POLYATOMIC MOLECULES DEGREES OF FREEDOM: THIS IS THE NUMBER OF INDEPENDENT VARIABLES OR FACTORS THAT MUST BE SPECIFIED IN ORDER TO DEFINE A SYSTEM. THESE FACTORS VARY ACCORDING TO THE TYPE OF SYSTEM. FOR VIBRATIONAL-ROTATIONAL MOTION, THIS CAN BE DESCRIBED BY THE THREE CARTESSIAN COORDINATES, x, y, z. HENCE AN ATOM HAS THREE DEGREES OF FREEDOM IN THE x, y, AND z.

3. DEGREES OF FREEDOM AN ATOM THEREFORE HAS THREE (3) DEGREES OF FREEDOM FOR N ATOMS IN A MOLECULE, THERE WILL BE 3N DEGREES. A DIATOMIC MOLECULE CAN HAVE 3 TRANSLATIONAL DEGREES OF FREEDOM SINCE THE MOLECULE CAN MOVE AND ITS POSITION CAN BE DESCRIBED BY CENTRE OF MASS.

4. DEGREES OF FREEDOM IN A DIATOMIC MOLECULE, ROTATION IS ONLY ON TWO AXES PERPENDICULAR TO THE BOND AXIS. ROTATION HAS ONLY TWO (2) DEGREES OF FREEDOM. THERE IS ONLY VIBRATIONAL DEGREE OF FREEDOM DUE TO OPPOSING MOTION OF TWO ATOMS ASSOCIATED WITH STRTCHING AND COMPRESSION OF THE BOND.

5. DEGREES OF FREEDOM POLYTATOMIC MOLECULES CONTAINING N- ATOMS CAN BE GROUPED INTO TWO-LINEAR AND NON-LINEAR. BOTH GROUPS WILL THE FOLLOWING AS IN TABLE. DEGREES OF FREEDOM LINEARNON-LINEAR TRANSLATION33 ROTATION23 VIBRATION3N-53N-6 TOTAL3N

6. DEGREES OF FREEDOM THE 3N-5 OR 3N-6 ARE THE NORMAL OR FUNDAMENTAL MODES OF VIBRATION WHICH INVOLVE THE INTERNAL MOTION OF ATOMS WHICH MOVE TOGETHER IN PHASE AND WITH THE SAME FREQUENCY BUT DIFFERENT AMPLITUDES AND DIFFERENT DIRECTIONS. DIATOMIC MOLECULE HAS ONLY ONE MODE OF VIBRATION CORRESPONDING TO A STRETCHING MOTION WHILE A NON-LINEAR MOLECULE ABA TYPE TRIATOMIC MOLECULE HAS THREE MODES, TWO FOR STRETCHING MOTION (SYMMETRIC AND ANTI- SYMMETRIC) AND THE OTHER BENDING MOTION.

7. DEGREES OF FREEDOM ILLUSTRATIONS: A B A v1v1 v3v3 v2v2 - + - Symmetric stretch v 1 Anti-symmetric stretch v 3 Bending v 2 Vibrational mode Rotational mode Non-Linear Linear Molecule B A A AA A A AA B B B

8. POLYATOMIC MOLECULES CONTAINING N- ATOMS HAS 3N DEGREES OF FREEDOM OUT WHICH 3N-5 OR 3N-6 DEGREES BELONG TO THE VIBRATIONAL DEGREES DEPENDING ON WHETHER IT IS LINEAR OR NON-LINEAR. THE FREQUENCY OF THESE VIBRATIONS IS GIVEN BY ν=½π(f/µ) ½ OR ṽ=½π(f/µ) ½. THE 3N-5 OR 3N-6 VIBRATIONS MAY INVOLVE CHANGE IN BOND LENGTH OR BOND ANGLE. INFRARED SPECTRUM

9. MOTIONS OF MOLECULES DIFFERNT TYPES OF MOTIONS: (i) STRETCHING-SYMMETRICAL OR ASYMMETRICAL (ii) BENDING (iii)DEFORMATION

10. FACTORS AFFECTING I.R SPECTRUM (i)SPECTRAL RANGE OF INSTRUMENT. SOME INSTRUMENTS HAVE I.R. OF 4000-650 cm-1 BUT FEW UP 200 cm-1. C-H, O-H, N-H ABSORB AT R ABOVE 3000 cm-1. (ii) I.R. ACTIVE AND INACTIVE VIBRATI ONS. LARGER CHANGE IN DIPOLE MOMENT GIVES A HIGHER INTENSITY. e.g. C-O THE DIFFERNCE IN ELECTRONEGAVITY. STRETCHING WILL INCREASE THE DIPOLE MOMENT AND C=O STRETCH WILL INCREASE AN INTENSE BAND IN ACIDS, ALDEHYDES, KETONES ACID CHLORIDES, ESTERS ETC

11. FACTORS AFFECTING I.R SPECTRUM BUT CO 2, AT THE GROUND STATE, NO DIPOLE MOMENT AND THE SYMMETRIC STRETCH WILL PRODUCE NO DIPOLE MOMENT. THE ANTI-SYMMETRIC MODE THE TWO BONDS WILL NOW PRODUCE DIFFERENT BOND LENGTHS AND THEREFORE A DIPOLE MOMENT WILL THEN PRODUCED. O=C=O LINEARNON-LINEAR

12. FACTORS AFFECTING I.R SPECTRUM (iii) NATURE OF SUBSTITUENT. THE MORE ELECTRONEGATIVE THE SUBSTITUENT THE MORE INTENSE THE BAND (iv) DIRECTION OF STRETCHING. SAME DIRECTION PRODUCES GREATER DIPOLE MOMENT WHILE OPPOSITE DIRECTIONS REDUCES THE DIPOLE MOMENT AND HENCE LESS INTENSE.

13. FACTORS COMPLICATE I.R. SPECTRUM (i) OVERTONE AND COMBINATION BANDS:. THESE ARISE WHEN TWO FUNDAMENTAL BANDS ABSORBING AT ṽ 1 AND ṽ 2 ABSORB SIMULTANEOUSLY WITH A RESULTING FREQUENCY APPEARING AT ṽ 1 + ṽ 2. (ii) FERMI RESONANCE: WHEN AN OVERTONE OR COMBINATION BAND HAS THE SAME OR SIMILAR FREQUENCY AS TTHE FUNDAMENTAL BAND, THE TWO BANDS APPEAR SPLIT ON EITHER SIDE OF THE EXPECTED VALUE AND MAY BE OF SIMILAR INTENSITY. THESE ARE CALLED FERMI DOUBLETS.

14. FACTORS COMPLICATE I.R. SPECTRUM (iii) HYDROGEN BONDING AND INTERMOLECULAR INTERACTIONS: SPECTRA OF THE SAME COMPOUND MAY APPEAR DIFFERENT IN DIFFERENT SOLVENTS OR IN GASEOUS OR SOLID PHASES. THIS WILL BE DUE DIFFERENT INTERACTIONS IN DIFFERENT SOLVENTS OR PHASES. THESE INTERACTIONS WILL EITHER SPLIT OR BROADEN THEM.

15. FACTORS COMPLICATE I.R. SPECTRUM (iv) TRANSITIONS IN FINGER PRINT REGION. IN THIS REGION, BENDING AND SKELETAL ARE USUALLY DIFFICULT TO ASSIGN BECAUSE OF STERIC AND ELECTROMETRIC FACTORS.

16. INTERPRETATION OF I.R. SPECTRA THE MOST IMPORTANT APPLICATION OF VIBRATIONAL OR INFRARED SPECTROSCOPY IS FOR THE DETERMINATION OF MOLECULAR STRUCTURE. THIS IS BECAUSE THE STRUCTURE MOLECULES VIBRATE WITHIN THE FREQUENCIES OF INFRARED REGION. FOR STRUCTURE INTERPRETATION, THE I.R. REGION CAN BE DIVIDED INTO FOUR.

17. COMBINATION AND DIFFERENCE BANDS IN A DIATOMIC OR POLYATOMIC MOLECULES THERE ARE OVERTONE BANDS OCCURING AT 2ṽ o, 3ṽ o, 2ṽ 1, 3ṽ 1 etc. HOWEVERR, THE INTENSITY OF THESE BANDS FALL. THERE ARE ALSO OTHER BANDS WHERE WE HAVE ṽ o +ṽ 1, 2ṽ 1 +ṽ 2, ṽ 0 =ṽ o +ṽ 1 +ṽ or ṽ o -ṽ 1. THEFIRST IS A COMBINATION BAND WHILE THE OTHER IS CALLED A DIFFERENCE BAND.

18. INTERPRETATION OF I.R. SPECTRA THESE ARE: (i) 4000 TO 2500 cm -1 WHICH BELONGS TO X-H STRETCHING REGION OF O- H, N-H, AND C-H (ii) 2500 TO 2000 cm -1 WHERE TRIPLE BONDS VIBRATE e.g. C≡N, C≡C. (iii) 2000 TO 1500 cm -1. THIS IS THE DOUBLE BOND REGION e.g. C=C, C=O, C=N, STRETCHING AND N-H BONDING. 1500 TO 600 cm -1. FINGER PRINT REGION.

19. INTERPRETATION OF I.R. SPECTRA DETAILS (i) X-H STRETCHING REGION (4000-2500 cm -1 ). ALL FUNDAMENTAL STRETCHING VIBRATIONS FOR X-H OCCUR IN THIS REGION BUT THE VARIOUS CAN BE DISTINGUISHED; THUS O-H OCCURS AT 3700-3600cm -1 IF NO HYDROGEN BONDING IS PRESENT BUT IT WILL AT LOWER FREQUENCY IF PRESENT. N-H STRETCH OCCURS BETWEEN 3400-3300 cm -1. USUALLY SHARPER THAN O-H STRETCHING VIBRATION. NH 2 -COMPOUNDS SHOW DOUBLET, SECONDARY AMINES SHOW ONE SHARP BAND.

20. INTERPRETATION OF I.R. SPECTRA DETAILS C-H STRETCH. FOR ALIPHATIC COMPOUNDS C- H OCCURS AT 3000-2850 cm -1 AND NORMALLY MODERATELY BROADER THAN HYDROGEN BONDED O-H. CH 3 STRETCH OCCURS AT 2965 AND 2880 cm -1, CH 2 AT 2930 AND 2860 cm -1. OTHER GROUPS WITHIN THE CHAIN CAN INFLUENCE THE ABSORPTION FREQUENCIES. e.g. H-C-O STRETCH FREQUENCY IN ALDEHYDES SPLITS INTO TWO BANDS, 2850 AND 2750 cm -1.

21. INTERPRETATION OF I.R. SPECTRA DETAILS C-H BOND ADJACENT TO DOUBLE BOND OR AROMATIC RING –C-H STRETCHING FREQUENCY INCREASES AND BETWEEN 3100- 3000 cm -1. C-H ADJACENT TO TRIPLE BOND THE BAND APPEARS AS SINGLE, MEDIUM INTENSITY AT 3300 cm -1. C-D STRETCH IS AT 2130 cm -1.

22. INTERPRETATION OF I.R. SPECTRA DETAILS TRIPLE BOND AREA (2500-2000 cm -1 ). THE TRIPLE-BOND STRETCHING ABSORPTION FALLS BECAUSE HIGH FORCE CONSTANT OF THE BONDS. C≡C ABSORBS AT 2300 AND 2050 cm -1 AND NORMALLY WEAK. C≡N ABSORBS BETWEEN 2300 AND 2200 cm -1 WITH MEDIUM INTENSITY.

23. INTERPRETATION OF I.R. SPECTRA DETAILS DOUBLE BOND REGION (2500 T0 1500 cm-1). THE MAIN BONDS ARE C=C AND C=O. C=O STRETCH. OCCURS AROUND 1830-1659 cm-1. IF THERE IS A METAL CARBONYL IT OCCURS AT 2000 cm-1 AND INTENSE. C=C STRETCH OCCURS AT1650 cm-1 AND WEAK IN INTENSITY. N-H BENDING OCCURS AT 1630-1550 cm-1 AND WEAK. THERE IS A STRETCHING VIBRATION AT 3300 cm-1.

24. INTERPRETATION OF I.R. SPECTRA DETAILS SUBSTITUTED BENZENES: OCCURS AT 1630- 1550 cm -1. BANDS ARE NORMALLY WEAK. FINGER PRINT REGION (1500-600 cm -1 ): OBSERVED BANDS DEPENDS ON THE TYPE OF CARBON SKELETON. OSCILLATIONS WILL RESULT FROM PART OF OR THE SKELETON OR ANY ATTACHED FUNCTIONAL GROUP.

25. INTERPRETATION OF I.R. SPECTRA DETAILS C-O STRETCHING HAS INTENSE BAND OBETWEEN 1400-1000 cm -1. AROMATIC RING GIVES TWO SHARP BANDS; 1600 AND 1500 cm -1. SPLITS AT 1600 cm -1. AROMATIC RING AND ALKENES. OUT OF PLANE BENDING BETWEEN 1000 AND 700 cm -1. CH 2 -, cis- AND trans- CAN BE DIFFERENTIATED IN THE REGION. 1,2; 1,3; 1,4; SUBSTITUTED BENZENE RINGS AT 900-700 cm -1. C-Cl OCCURES AROUND 700 cm -1.