EXAMPLE
• THE SPECTRUM OF HCl SHOWS A VERY
INTENSE ABSORPTION BAND AT 2886 cm-1
AND A WEAKER BAND AT 5668 cm-1.
CALCULATE xe, ṽo , 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)ṽo-xe(v+½)2ṽo .
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.
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.
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.
DEGREES OF FREEDOM
• POLYTATOMIC MOLECULES CONTAINING NATOMS CAN BE GROUPED INTO TWO-LINEAR
AND NON-LINEAR.
• BOTH GROUPS WILL THE FOLLOWING AS IN
TABLE. DEGREES OF
LINEAR
NON-LINEAR
FREEDOM
TRANSLATION
3
3
ROTATION
2
3
VIBRATION
3N-5
3N-6
TOTAL
3N
3N
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 ANTISYMMETRIC) AND THE OTHER BENDING MOTION.
DEGREES OF FREEDOM
• ILLUSTRATIONS:
Linear Molecule
A
B
B
Non-Linear
A
v1
A
A
Symmetric stretch v1
B
v3
A
B
A
A
A
Anti-symmetric stretch v3
B
v2
-
+
Bending v2
A
B
A
A
B
A
Vibrational mode
A
A
Rotational mode
INFRARED SPECTRUM
• POLYATOMIC MOLECULES CONTAINING NATOMS 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.
MOTIONS OF MOLECULES
• DIFFERNT TYPES OF MOTIONS:
• (i) STRETCHING-SYMMETRICAL OR
ASYMMETRICAL
• (ii) BENDING
• (iii)DEFORMATION
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
FACTORS AFFECTING I.R SPECTRUM
• BUT CO2, 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 LINEAR
NON-LINEAR
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.
FACTORS COMPLICATE I.R. SPECTRUM
• (i) OVERTONE AND COMBINATION BANDS:.
THESE ARISE WHEN TWO FUNDAMENTAL BANDS
ABSORBING AT ṽ1 AND ṽ2 ABSORB
SIMULTANEOUSLY WITH A RESULTING
FREQUENCY APPEARING AT ṽ1 + ṽ2.
• (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.
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.
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.
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.
COMBINATION AND DIFFERENCE
BANDS
• IN A DIATOMIC OR POLYATOMIC MOLECULES
THERE ARE OVERTONE BANDS OCCURING AT
2ṽo, 3ṽo, 2ṽ1, 3ṽ1 etc . HOWEVERR, THE
INTENSITY OF THESE BANDS FALL.
• THERE ARE ALSO OTHER BANDS WHERE WE
HAVE ṽo+ṽ1, 2ṽ1+ṽ2, ṽ0=ṽo+ṽ1+ṽ or ṽo-ṽ1.
THEFIRST IS A COMBINATION BAND WHILE
THE OTHER IS CALLED A DIFFERENCE BAND.
INTERPRETATION OF I.R. SPECTRA
• THESE ARE: (i) 4000 TO 2500 cm-1 WHICH
BELONGS TO X-H STRETCHING REGION OF OH, 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.
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. NH2-COMPOUNDS SHOW DOUBLET,
SECONDARY AMINES SHOW ONE SHARP BAND.
INTERPRETATION OF I.R. SPECTRA
DETAILS
• C-H STRETCH. FOR ALIPHATIC COMPOUNDS CH OCCURS AT 3000-2850 cm-1 AND NORMALLY
MODERATELY BROADER THAN HYDROGEN
BONDED O-H. CH3 STRETCH OCCURS AT 2965
AND 2880 cm-1, CH2 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.
INTERPRETATION OF I.R. SPECTRA
DETAILS
• C-H BOND ADJACENT TO DOUBLE BOND OR
AROMATIC RING –C-H STRETCHING
FREQUENCY INCREASES AND BETWEEN 31003000 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.
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.
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.
INTERPRETATION OF I.R. SPECTRA
DETAILS
• SUBSTITUTED BENZENES: OCCURS AT 16301550 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.
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.
• CH2-, 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.