Vibrational-Rotational Spectroscopy

Vibrational-Rotational Spectroscopy Vibrational-Rotational Spectrum of Heteronuclear Diatomic Absorption of mid-infrared light (~300-4000 cm-1): Molecules can change vibrational and rotational states Typically at room temperature, only ground vibrational state populated but several rotational levels may be populated. Treating as harmonic oscillator and rigid rotor: subject to selection rules v = 1 and J = 1. E field = Evib + Erot = = E f Ei = E ( v , J ) E ( v , J ).. v= = v0 ( v + 12 ) + BJ ( J + 1) v0 ( v + 12 ) + BJ ( J + 1) . 2 c . At room temperature, typically v =0 and v = +1: v = v0 + B J ( J + 1) J ( J + 1) . Now, since higher lying rotational levels can be populated, we can have: J = +1 J = J + 1 v = v0 + 2 B ( J + 1) R branch J = 1 J = J 1 v = v0 2 BJ P branch J'=4. J'=3. J'=1. v'=1 J'=0. P branch Q branch J''=3 12B. J''=2 6B. J''=1 2B. v''=0 J''=0 EJ =0. 2B 2B 4B 2B 2B 2B. -6B -4B -2B.

So, the vibrational-rotational spectrum should look like equally spaced lines about ν0 with sidebands peaked at J’’>0. ν 0 • Overall amplitude from vibrational transition dipole moment • Relative amplitude of rotational lines from rotational populations In reality, what we observe in spectra is a bit different. ν 0 ν

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  Precast, Rotational, Vibrational

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