Solution (source code)

= Solution

The strong band is the \b[$v=0\to1$ vibrational fundamental], and the weaker band near twice its <wavenumber> is the \b[$v=0\to2$ first vibrational overtone]. At room temperature these high-frequency oscillators have overwhelmingly ground-state vibrational populations. In the harmonic-potential, linear-dipole limit the infrared <selection rule> is $\Delta v=\pm1$; <anharmonicity> and nonlinear dipole dependence make the overtone weakly allowed. A $1\to2$ <hot band> would lie near, and slightly below, the fundamental <wavenumber>, rather than near twice it.