Question

How to find intensity of hot band relative to that of fundamental?

Answer 1

The two bands are usually a fundamental vibration and either an overtone or combination band. The wavefunctions for the two resonant vibrations mix according to the harmonic oscillator approximation, and the result is a shift in frequency and a change in intensity in the spectrum.

Answer 2

In molecular vibrational spectroscopy, a hot band is a band centred on a hot transition, which is a transition between two excited vibrational states, i.e. neither is the overall ground state.[1] In infrared or Raman spectroscopy, hot bands refer to those transitions for a particular vibrational modewhich arise from a state containing thermal population of another vibrational mode.[2] For example, for a molecule with 3 normal modes, {\displaystyle \nu _{1}}, {\displaystyle \nu _{2}} and {\displaystyle \nu _{3}}, the transition {\displaystyle 101} ← {\displaystyle 001}, would be a hot band, since the initial state has one quantum of excitation in the {\displaystyle \nu _{3}} mode. Hot bands are distinct from combination bands, which involve simultaneous excitation of multiple normal modes with a single photon, and overtones, which are transitions that involve changing the vibrational quantum number for a normal mode by more than 1.