Calculating the vibrational spectra of molecules: An introduction for experimentalists with contemporary examples

The theoretical evaluation of vibrational spectra has, in the past, played a crucial role regarding assignment of vibrational spectra, an aspect that might be largely forgotten. This, however, is actually ever so true today, where despite the presence of data bases of spectra (atlas of spectra) there is still a large number of species including, though certainly not exclusively, less stable species which have spectra lacking appropriate interpretation. In recent years the capabilities to calculate vibrational spectra have greatly improved. In this review the basic various approaches are introduced. For practical use, the use of comparatively simple tools including Hartree–Fock level or standard DFT type calculations often already do a very good job at the comparative level. An important recent development includes the observation that differences between experimental and calculated frequencies are largely due to neglect of anharmonicity rather than the theoretical method employed. Methods to include anharmonicity are becoming available for users. The introduction of methods allowing for periodic calculations, involving full 3D molecular structures, lead to new opportunities and final answers to long-standing issues. A number of examples are provided showing where calculated spectra have provided unique added value to experimental work.