This Review brings a new perspective to the study of chemical reactions in compressed fluid media. We begin by reviewing the substantial insight gained from more than 50 years of experimental studies on organic reactions in solution under pressure. These led to a proper estimation of the critical roles of volume of activation (Δ≠V) and reaction volume (ΔV) in understanding pressure effect on rates and equilibria of organic reactions. A recently developed computational method, the XP-PCM (extreme pressure polarizable continuum model) method, capable of carrying out quantum mechanical calculations of reaction pathways of molecules under pressure, is introduced. A case study of the Diels–Alder cycloaddition of cyclopentadiene with ethylene serves, in pedagogical detail, to describe the methodology. We then apply the XP-PCM method to a selection of other pericyclic reactions, including the parent Diels–Alder cycloaddition of butadiene with ethylene, electrocyclic ring-opening of cyclobutene, electrocyclic ring-closing of Z-hexatriene, the [1,5]-H shift in Z-pentadiene, and the Cope rearrangement. These serve as examples of some of the most common combinations of Δ≠V and ΔV. Interesting phenomena such as a shift in a transition state along a reaction coordinate, a switch of rate-determining step, and the possible turning of a transition state into a stable minimum are revealed by the calculations. A reaction volume profile, the change in the volume of the reacting molecules as the reaction proceeds, emerges as being useful.
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