= Raman shift
{c}
{title2=$\Delta\widetilde\nu=\widetilde\nu_0-\widetilde\nu_s$}
The signed <Raman shift> subtracts scattered from incident <spectroscopic wavenumber>:
$$
\Delta\widetilde\nu=\frac{\nu_0-\nu_s}{c}
=\frac{1}{\lambda_0}-\frac{1}{\lambda_s}
=\frac{E_f-E_i}{hc}.
$$
Here $c$ is the <speed of light>, and both <wavelengths> are in <vacuum>. Positive shifts denote <Stokes Raman scattering>; negative shifts denote <Anti-Stokes Raman scattering>. Some plots reverse the horizontal direction or report separate unsigned magnitudes, so check the convention. <Spectroscopic wavenumber> has no $2\pi$ factor, unlike the common angular <wavenumber> $k=2\pi/\lambda$. A shift of $1000\,\mathrm{cm^{-1}}$ means $100000\,\mathrm{m^{-1}}$, not a <frequency> of $1000\,\mathrm{Hz}$.
For a one-quantum change of <molecular vibration> with ordinary <frequency> $\nu_v$, the magnitude is $\widetilde\nu_v=\nu_v/c$. This makes <Raman spectroscopy> attractive: the same molecular <energy> spacing can be read using different visible excitation <wavelengths>. Equal and opposite <Raman shifts> are not equal and opposite changes measured in nanometres, because <wavelength> is the reciprocal of <spectroscopic wavenumber>.
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