Computational Chemistry

of interest. Among the main tasks of computational chemistry are to determine the
structure and energy of molecules and of thetransitionstatesinvolved in chemical
reactions: our “structures of interest” aremolecules and the transition states linking
them. Consider the reaction

O

O O

transition state

reaction (2.1)

O

O O

isoozone

+

O

• O O

ozone

A priori, it seems reasonable that ozone might have an isomer (call it isoozone)
and that the two could interconvert by a transition state as shown in Reaction (2.1).
We can depict this process on a PES. The potential energyEmust be plotted against
only two geometric parameters, the bond length (we may reasonably assume that
the two O–O bonds of ozone are equivalent, and that these bond lengths remain
equal throughout the reaction) and the O–O–O bond angle. Figure2.7shows the
PES for Reaction (2.1), as calculated by the AM1 semiempirical method (Chapter
6 ; the AM1 method is unsuitable forquantitativetreatment of this problem, but the
potential energy surface shown makes the point), and shows how a 2D slice from

H

O

F

energy

Pmin

q 2 = O F bond length

q 1 = O H bond length

Fig. 2.6 A potential energy surface (PES) for HOF. Here the HOF angle is not shown. This
picture could represent one of two possibilities: the angle might be the same (some constant,
reasonable value) for every calculated point on the surface; this would be an unrelaxed or rigid
PES. Alternatively, for each calculated point the geometry might be that for the best angle
corresponding to the other two parameters, i.e. the geometry for each calculated point might be
fully optimized (Section 2.4); this would be a relaxed PES

14 2 The Concept of the Potential Energy Surface