Overtone

Overtone and Fundamental Band

The infrared spectrum of a molecule results due to the transition between two different vibrational energy levels. The vibrational energy E_vib. = (v + 1/2)h𝜈.
where, v is the number of the vibrational level and can have the values 0,1,2,3,... etc. h is Plank constant and 𝜈 is the vibrational frequency of the band.

The energy difference between the two vibrational energy levels can be written as-
ΔE_vib. = h𝜈.
The transition from ground state (v = 0) to the first excited state (v = 1) is called fundamental band. The energy difference between any two adjacent energy levels either up or down is always same i.e. (h𝜈).

The transition from ground state (v = 0) to the second excited state (v = 2) with the absorption of IR radiation give rise to weak bands, called overtone. Thus the energy difference between two levels can never be equal to h𝜈. If the transition occurs from v = 0 to v = 2 then-
ΔE_vib. = E_vib.(v=2) − E_vib.(v=0)
or, ΔE_vib. = (2 + 1/2)h𝜈 − (0 + 1/2)h𝜈
or, ΔE_vib. = (5/2)h𝜈 − (1/2)h𝜈
or, ΔE_vib. = 2h𝜈
This is the energy of first overtone.

In other words we can say the the transition which does not follow the selection rule (i.e. ΔV = ±1) is called overrtone.
The value of overtone is always greater than that of fundamental bands.
The transition from v = 0 to v = 2 is called first overtone. Similarly, transition from v = 0 to v = 3, 4, 5... are called second, third, fourth ... overtone respectively.

The fundamental transitions, v = ±1, are the most commonly occurring, and the probability of overtones rapid decreases as the number of quanta (Δv = ±n) increases. Based on the harmonic oscillator approximation, the energy of the overtone transition would be n times larger than the energy of the fundamental transition frequency, but the anharmonic oscillator calculations show that the overtones are less than a multiple of the fundamental frequency.

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