Fundamentals of Absorption Spectroscopy. Selection Rules

the absorption coefficient a is related to the extinction coefficient k according to  

From the quantum mechanical viewpoint, light absorption occurs when a molecule initially in a state of energy E is excited to an upper state of energy E2 by a photon of energy hPo, thereby satisfying the Planck relation  

This gives a spectral line, at a frequency Pq, the intensity of which is equal to the rate of energy absorption, i.e.  

The energy level of a quantum state if/ is obtained by solving the time-independent Schrodinger equation in the Born-Oppenheimer approximation, where the energy contributions of electronic, vibrational, and rotational motions can be separated  

The energy levels involved in the infrared range are associated with the vibrational energy vib, which for a harmonic oscillator is given by  

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