Page 115 - Mechanism and Theory in Organic Chemistry

curve more than the left-hand side, and can be accomplished by adding to the
free energy at each point along the curve an increment 6AG0 that increases to the
right. Here the symbol 6 signifies the effect on the quantity AGO of the structural
change.46 The simplest approach is to make the increment increase linearly with
x, that is,

where x is the reaction parameter defined earlier (Figure 2.7), and m is the slope,
positive in the present example. In Figure 2.10 the straight line superimposed on
the reaction coordinate potential curve represents the perturbation 6AG0. If we
place the origin at the vertex of the parabola, it is easy to verify by inspection
that the result of adding the perturbation to the potential energy curve will be to
shift its maximum, and thus the transition state, to the right (dashed curve). A
perturbation with a negative slope, that is, a structural change making motion
from left to right easier, will shift the curve to the left.
It may in some instances be of interest to know how structural changes affect
the position of the transition state on the potential energy surface with respect to
degrees of freedom other than the reaction coordinate. Recall that these other
degrees of freedom correspond to ordinary vibrations. They cut across the surface
perpendicular to the reaction coordinate and are valleys rather than hills. Sup-
pose that we make a change in structure that will make a certain bond, not
corresponding to the one breaking, more difficult to stretch. We show in Figure
2.1 1 the potential surface cut along the stretching degree of freedom, with a
perturbation

where m is positive. Now the perturbed potential (dashed curve) is shifted to the
left. Making the bond more difficult to stretch has changed the structure of the
transition state so that the equilibrium bond distance is shorter.
These arguments are summarized as the reacting bond rules:47
1. For an internal motion of a molecule that corresponds to progress over a
transition state (energy maximum), any change that makes the motion more
difficult will lead to a new molecular geometry at the energy maximum in which
the motion has proceeded farther. Changes that make the motion less difficult
have the opposite effect. (This rule corresponds to the Hammond postulate.)
2. For an internal motion of a molecule that corresponds to a vibration,
any change that tends to force a change in the equilibrium point of the vibration
in a particular direction will do so.
3. Effects on reacting bonds (bonds made or broken in the reaction) are the
most significant; most strongly influenced are reacting bonds nearest the site of
structural change.
These rules will be useful when we wish to analyze reaction paths in terms of
motion along more than one dimension of a potential energy surface. The need
-
48 8 is known as a Lefler-Grunwald oherator, and is used to designate the change in any quantity re-
sulting from a structural change. See J. E. Leffler and E. Grunwald, Rates and Equilibria of Organic
Reactions, Wiley, New York, 1963, p. 26.
47 See note 45, p. 103.