IR - Spectroscopy Theory, Slides of Organic Chemistry

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IR – spectroscopy Part III

(Theory)

Electromagnetic spectrum

Width and shape of spectral lines

Rotational – vibrational spectrum

Simulation of vibration-rotation line spectrum of carbon monooxide

Line broadening – Doppler effect

Doppler effect

Harmonic oscillator

F = −𝑘𝑞

F = Force acting on the system k = constant strength q = r - r 0 r 0 position at equlibrum r position at the moment

q (t) = Qcos2πνt Q = amplitude ν = frequency

k

Reduced mass

k

μ =

1 1 𝑚 1

1 𝑚 2

=

𝑚 1 𝑚 2 𝑚 1 + 𝑚 2

Bond Energies Reduced mass

CH 3 ―CH 3 368 KJ/mol (12*12)/(12+12) = 6

CH 3 ―H 431 KJ/mol (12*1)/(12+1) = 0.

CD 3 ―D 442 KJ/mol (12*2)/(12+2) = 1.

Quantum harmonic and

anharmonic oscillator

Anharmonic oscillators

𝐸𝑜𝑠𝑐 𝑎𝑛ℎ = ℎ 2 π

𝑘 0 𝑚𝑟𝑒𝑑^ ν^ +^

1 2 −^

ℎ𝑥 2 π

𝑘 0 𝑚𝑟𝑒𝑑^ ν^ +^

1 2

Equation of potential energy of anharmonic oscillator

U(𝑞) =

𝑓 𝑞 𝑞^2

x -anharmonism factor k 0 - constant strength for υ =

Δ𝐸𝑜𝑠𝑐 = 𝐸ν+ 1 − 𝐸ν = 2 ℎπ 𝑚^ 𝑘𝑟𝑒𝑑^01 − 2𝑥(ν + 1 )

Selection rules Δν = +/- 1, +/-2, +/-3, ….

Overtones

γ out of plane Car – H

Overtones or combinational bands

Overtones

Overtone 1783 cm (γ) out of plane C=CH 2 883 cm- 1

Degrees of freedom of molecule

Number of vibrational degree of freedom is (3N – 5) for linear molecule

Translational Energy Molecule also has three translational degrees of freedom

Rotational Energy Two atomic (linear ) molecule has two rotational degrees of freedom

Vibrational Energy Two atomic (linear ) molecule has one vibrational degree of freedom

Degrees of freedom of molecule

Number of vibrational degree of freedom is (3N – 5) for linear molecule

Translational Energy 3N atomic linear molecule also has t hree translational degrees of freedom

Rotational Energy 3N atomic linear molecule has two Rotationa l degrees of freedom

Vibrational Energy Three atomic linear molecule has 4 vibrational degree of freedom