Past exam of the chemistry A course of the University of Cambridge / 2025 / Paper 1 / A3 / a / iv

A hot band starts from a thermally populated vibrationally excited state, for example $v=1\to 2$. It can satisfy $\Delta v=1$ and need not have a small transition moment, but its lower-state population is reduced by the Boltzmann distribution:It is therefore usually weak at low temperature and grows relative to the fundamental on heating. Anharmonicity shifts its frequency away from the $0\to 1$ transition; in a polyatomic molecule, excitation in another mode can also produce a hot-band sequence.