MOLECULAR SPECTROSCOPY

SPECTROSCOPY IS THAT BRANCH OF SCIENCE WHICH DEALS WITH THE STUDY OF INTERACTION OF ELECTROMAGNETIC RADIATION WITH MATTER.

ELECTROMAGNETIC RADIATION -THE TERM “ELECTROMAGNETIC RADIATION” REPRESENTS THE RADIANT ENERGY EMITTED FROM ANY SOURCE IN THE FORM OF LIGHT,HEAT ETC.

SOME IMPORTANT CHARACTERSTICS OF THESE ELECTROMAGNETIC RADIATION ARE GIVEN BELOW…THEY HAVE DUAL CHARACTER.THESE WAVES ARE ASSOCIATED WITH ELECTRIC AND MAGNETIC FIELDS.

ALL ELECTROMAGNETIC RADIATIONS TRAVEL WITH THE VELOCITY OF LIGHT.

c=νλ. EACH PHOTON IS A PACKET OF ENERGY WHOSE ENERGY IS GIVEN BY PLANCK’S EQUATION E=hν.WHERE h IS PLANCK’S CONSTANT.

REGION OF ELECTROMAGNETIC SPECTRUM

WHEN THE DIFFERENT TYPES OF ELECTROMAGNETIC RADIATIONS ARE ARRANGED IN ORDER OF THEIR INCREASING WAVELENGTHS OR DECREASING FREQUENCIES, THE COMPLETE ARRANGEMENT IS CALLED ELECTROMAGNETIC SPECTRUM.

REGION OF ELECTROMAGNETIC SPECTRUM

INTRODUCTION TO MOLECULAR SPECTRO SCOPY AND ITS DIFFERENCE FROM ATOMIC

SPECTROSCOPY

• IN CASE OF MOLECULES,WHEN THE ENERGY IS ABSORBED,IT MAY RESULT INTO ROTATION,VIBRATION OR ELECTRONIC TRANSITION.JUST AS ELECTRONIC ENERGY IS QUANTIZED,THE ROTATIONAL AND VIBRATIONAL ENERGIES ARE ALSO QUANTIZED.

• THE ROTATIONAL,VIBRATIONAL AND ELECTRONIC ENERGY LEVELS OF A MOLECULE ARE COLLECTIVELY CALLED MOLECULAR ENERGY LEVELS.THE TRANSITIONS OF ENERGIES CAN TAKE PLACE ONLY BETWEEN THESE LEVELS.THE RESULT IS A MOLECULAR SPECTRUM.

MOLECULAR ENERGY LEVELS

ABSORPTION AND EMISSION SPECTROSCOPY

• THE TRANSITION MAY TAKE PLACE FROM LOWER ENERGY LEVEL TO HIGHER ENERGY LEVEL BY ABSORBING ENERGY.IT IS THEN CALLED ABSORPTION SPECTROSCOPY AND THE RESULT OBTAINED AS A RESULT OF A NUMBER OF SUCH TRANSITIONS IS CALLED ABSORPTION SPECTRUM.

• THE TRANSITION MAY TAKE PLACE FROM HIGHER ENERGY LEVEL TO A LOWER ENERGY LEVEL THEREBY EMITTING THE EXCESS ENERGY AS A PHOTON.IT IS THEN CALLED EMISSION SPECTROSCOPY AND THE RESULT OBTAINED AS A RESULT OF NO. OF SUCH TRANSITIONS IS CALLED EMISSION SPECTRUM.

THE ENERGY OF PHOTON hv EMITTED OR ABSORBED IS GIVEN BY BOHR’S FREQUENCY FORMULA …

TYPES OF MOLECULAR ENERGIES AND BORN-OPPENHEIMER APPROXIMATION

A MOLECULE USUALLY POSSESSES FOUR DIFFERENT TYPES OF ENERGIES. THESE ARE…

• TRANSLATIONAL ENERGY• ROTATIONAL ENERGY• VIBRATIONAL ENERGY• ELECTRONIC ENERGY

• ACCORDING TO BORN-OPPENHEIMER APPROXIMATION,THE TOTAL ENERGY OF A MOLECULE IS THE SUM OF TRANSLATIONAL , ROTATIONAL, VIBRATIONAL AND ELECTRONIC ENERGIES.

E = Et + Er + Ev + Ee

IT IS FOUND THAT THE TRANSLATIONAL ENERGY IS NEGLEGIBLY SMALL.SO

E = Ev + Er + Ee

TYPES OF MOLECULAR SPECTRA

• THE ENERGY ABSORBED FOR ANY TRANSITION IS EQUAL TO THE DIFFERENCE IN THE ENERGIES OF THE TWO LEVELS INVOLVED.IT IS FOUND THAT THESE ENERGIES FOR TRANSITION ARE IN ORDER…

• Et << Er << Ev << Ee

• TRANSLATIONAL ENERGY IS CONSIDERED AS CONTINOUS AND WE DONOT OBSERVE ANY TRANSLATIONAL SPECTRUM.

• PURE ROTATIONAL (MICROWAVE) SPECTRA- THESE SPECTRA ARE OBSERVED IN FAR INFRA-RED REGION OR IN THE MICROWAVE REGION.

• VIBRATIONAL ROTATIONAL SPECTRA- SUCH ENERGIES ARE AVAILABLE IN THE NEAR INFRA-RED REGION.

• ELECTRONIC BAND SPECTRA- FOR A GIVEN ELECTRONIC TRANSITION, A SET OF BANDS OBSERVED.THIS SET OF BANDS IS CALLED A BAND GROUP OR A BAND SYSTEM.THUS WHEREAS ATOMS GIVE LINE SPECTRA, MOLECULES GIVE BAND SPECTRA.THESE SPECTRA ARE OBSERVED IN THE VISIBLE REGION AND ULTRA VIOLET REGION.

REGION OF ELECTROMAGNETIC SPECTRUM AND DIFFERENT TYPES OF MOLECULAR SPECTRA

• RAMAN SPECTRA- THIS IS ALSO A TYPE OF VIBRATIONAL-ROTATIONAL SPECTRUM.IT IS BASED ON SCATTERING OF RADIATION AND NOT ON THE ABSORPTION OF RADIATION BY THE SAMPLE.RAMAN SPECTRA IS OBSERVED IN THE VISIBLE REGION.

• NUCLEAR MAGNETIC RESONANCE(NMR) SPECTRA- THIS TYPE OF SPECTRA ARISES FROM THE TRANSITION BETWEEN THE NUCLEAR SPIN ENERGY LEVELS OF THE MOLECULE WHEN AN EXTERNAL FIELD IS APPLIED ON IT.THE ENERGIES INVOLVED IN THESE TRANSITIONS ARE VERY HIGH WHICH LIE IN THE RADIO FREQUENCY REGIONS.

• ELECTRON SPIN RESONANCE (ESR) SPECTRA-THIS TYPE OF SPECTRUM ARISE FROM THE TRANSITIONS BETWEEN THE ELECTRON SPIN ENERGY LEVELS OF THE MOLECULE WHEN AN EXTERNAL MAGNETIC FIELD IS APPLIED ON IT.

DEGREE OF FREEDOM OF MOTION

•CONSIDER A MOLECULE MADE UP OF N ATOMS.THE ATOMS MAY BE CONSIDERED AS

MASS POINTS.•THE NUMBER OF CO-ORDINATES REQUIRED TO SPECIFY THE POSITION OF ALL THE MASS POINTS i.e. ATOMS IN A MOLECULE IS CALLED

THE NUMBER OF DEGREES OF FREEDOM.•THUS A MOLECULE MADE UP OF N ATOMS HAS

3N DEGREE OF FREEDOM.

WHEN THE THERMAL ENERGY IS ABSORBED BY A MOLECULE,IT IS STORED WITH IN THE MOLECULE IN THE FORM OF :•(1) TRANSLATIONAL MOTION OF THE MOLECULE.•(2) INTERNAL MOVEMENT OF THE ATOMS OF THE MOLECULE, i.e. ROTATIONAL MOTION AND VIBRATIONAL MOTION.

THERE ARE THREE TRANSLATIONAL DEGREE OF FREEDOM.THE REMAINING (3N-3) CO-ORDINATES REPRESENT THE INTERNAL DEGREE OF FREEDOM.•THE INTERNAL DEGREE OF FREEDOM MAY BE SUBDIVIDED INTO-•(1) ROTATIONAL DEGREE OF FREEDOM.•(2) VIBRATIONAL DEGREE OF FREEDOM.

FOR A ROTATIONAL MOTION, THERE ARE 2 DEGREE OF FREEDOM FOR A LINEAR MOLECULE AND 3 FOR A NON LINEAR MOLECULE.

(1). ROTATIONS OF A LINEAR MOLECULE ABOUT TWO MUTUALLY PERPENDICULAR AXES.(2). ROTATIONS OF A NON LINEAR MOLECULE ABOUT THREE MUTUALLY PERPENDICULAR AXES.

•VIBRATIONAL DEGREES OF FREEDOM OF A LINEAR MOLECULE CONTAINING N ATOMS = 3N-5•VIBRATIONAL DEGREES OF FREEDOM OF NON-LINEAR MOLECULE CONTAINING N ATOMS = 3N-6

TRANSLATIONAL ROTATIONAL VIBRATIONAL

FOR LINEAR MOLECULE

3 2 3N-5

FOR NON-LINEAR MOLECULE

3 3 3N-6

FOR A MOLECULE MADE UP OF N ATOMS.TOTAL DEGREE OF FREEDOM = 3NFURTHER SPLIT UP THESE IS AS FOLLOWS:

PURE ROTATIONAL (MICROWAVE) SPECTRA OF DIATOMIC MOLECULES

ENERGY LEVELS OF A RIGID ROTOR-ON THE BASIS OF WAVE MECHANICS, IF DIATOMIC MOLECULE IS CONSIDERED TO BE A RIGID ROTATOR.THEN..

WHERE J IS ROTATIONAL QUANTUM NUMBER THAT CAN HAVE VALUES 0,1,2,3 etc.

------- (1)

I IS THE MOMENT OF INERTIA OF THE MOLECULE ABOUT THE AXIS OF ROTATION, i.e

WHERE m1 AND m2 ARE THE ATOMIC MASSES OF THE TWO ATOMS OF THE DIATOMIC MOLECULES.

PUTTING J = 0, 1, 2, 3 etc. IN EQUATION (1), PATTERN OF THE ROTATIONAL ENERGY LEVELS OBTAINED.THE SPACING BETWEEN THE ENERGY LEVELS INCREASES AS J INCREASES.

ROTATIONAL ENERGY LEVELS OF A DIATOMIC MOLECULE TREATING IT AS A RIGID ROTATOR

ROTATIONAL SELECTION RULES

• ACCORDING TO SELECTION RULES,THE TRANSITION TAKE PLACE ONLY BETWEEN THOSE ROTATIONAL LEVELS FOR WHICH ∆J = ±1

i.e. THE CHANGE IN ROTATIONAL QUANTUM NUMBER IS UNITY.

• THE TRANSITION ∆J = +1 CORRESPONDS TO ABSORPTION.

• THE TRANSITION ∆J = -1 CORRESPONDS TO EMISSION.

ROTATIONAL SPECTRA OF DIATOMIC MOLECULES

THE ALLOWED ROTATIONAL ENERGIES ARE GIVEN BY THE EXPRESSION

AS E = hv

EQUATION (2) BECOMES…

WHERE IS CALLED ROTATIONAL CONSTANT.PUTTING J = 0, 1, 2, 3 etc. IN EQUATION (4) THE WAVE NUMBERS OF THE DIFFERENT ROTATIONAL LEVELS WILL BE…0, 2B, 6B, 12B, 20B, 30B,… AND SO ON.

-------------------- (1)

--------------------(2)

---------------------(3)

--------------------(4)

WHEN A TRANSITION TAKES PLACE FROM A LOWER ROTATIONAL LEVEL WITH ROTATIONAL QUANTUM NUMBER J TO A HIGHER ROTATIONAL LEVEL WITH ROTATIONAL QUANTUM NUMBER J’ ,THE ENERGY ABSORBED WILL BE

GIVEN BY

HENCE IN THE PRESENT CASE J’ = J + 1.

TO EXPRESS IN TERMS OF WAVE NUMBERS…

-------------------(5)

-------------------(6)

------------------(7)

THE WAVE NUMBER OF THE LINES OBTAINED WILL BE 2B, 4B, 6B, 8B, …… AND SO ON.THE VARIOUS LINES IN THE ROTATIONAL SPECTRA WILL BE EQUALLY SPACED.