This chapter builds on the methods and techniques outlined in the preceding chapters to illustrate tours of potential energy surfaces (PESs). The comprehensive exploration of a PES with a reasonable degree of accuracy requires enormous computational resources unless efficient exploration techniques as well as appropriate levels of electronic structure calculations are selected.

The exploration of a PES can be highly complex. As an example, for a given set of atoms there may be various isomers, while a chemical compound can have a number of conformers, and there will also be conversion channels between these isomers and conformers. Moreover, chemical structures may decompose or dissociate into smaller chemical species, and in such cases the reverse reaction channels will indicate synthetic reactions. Although many advanced experimental techniques have been developed, it is still very difficult to determine the detailed chemical processes associated with a PES. As an example, mass spectrometric techniques can provide very precise data on the masses of individual compounds and the distribution of various species in a sample. However, these data do not allow the geometrical structures of the chemical species to be determined. In contrast, spectroscopic techniques, such as microwave spectroscopy and electron diffraction, may provide structural information but it is difficult to apply them to unstable structures such as transition states (TSs). Thus, the three-dimensional (3D) behaviors of atoms during chemical processes are, in many cases, still unknown except for a few well-studied cases, such as SN2 and Diels–Alder reactions. Thus, much information related to chemical systems remains to be determined based on the explorations of PESs.