To compute an Infrared (IR) spectrum, we need to calculate the vibrational frequencies of the molecule (via second derivatives of energy with respect to nuclear coordinates, or Hessian matrix) as well as the dipole moment derivatives, which determine the infrared absorption intensities.

Vibrational frequencies must always be calculated on a fully optimized geometry at a stationary point. If the system is not at an energy minimum, the Hessian will produce unphysical imaginary frequencies.

In ORCA, you can perform both the geometry optimization and the vibrational frequency calculation in a single run by specifying both Opt and NumFreq (or Freq).

In this example, we calculate the IR spectrum of the isoprene molecule using DFT. Once the calculation finishes, the built-in ORCA utility orca_mapspc extracts the frequencies and intensities to generate the plottable spectrum data.