energy–distance graph for that motion is the force constant for the vibration (i.e. the
second derivative of the energy with respect to the motion; the first derivative of
energy with respect to motion is the force). Along that direction the PES is a
plateau. There are thus three ways in which a structure can be a stationary point,
i.e. rest on a flat spot on the PES: it can reside at a relative minimum, where the
surface curves up in all directions, at a saddle point, where the surface curves
downward in one or more directions, or at a point where along one direction the
surface does not curve at all (is a plateau).
The third situation could correspond to a “structure” in which an optimization
algorithm, in its zeal to find a stationary point (where all first derivatives are zero)
moves two molecules significantly beyond their van der Waals separation:
geometryenergyvan der Waals
separationPES essentially flat along
direction of this geometry changeThe vibrational mode corresponding to altering the separation of the molecules
is ca. 0 cm#^1 ; the internal modes of each molecule, bond stretch, bend, and torsional
modes, are of course nonzero.
Chapter 2, Harder Questions, Answers
Q8
The ZPE of many molecules is greater than the energy needed to break a bond; e.g.
the ZPE of hexane is about 530 kJ mol#^1 , while the strength of a C–C or a C–H
bond is only about 400–530 kJ mol#^1. Why then do such molecules not spontane-
ously decompose?
They do not spontaneously decompose because the ZPE is not concentrated in
just one or a few bonds. An exotic structure could indeed run the risk of decom-
posing by such concentration of its vibrational energies. A candidate for this is the
transition state (which is calculated to be nonplanar) for inversion of methane.
Incidentally, this would correspond to racemization if four different hydrogens
could be attached to a carbon; unfortunately^4 H has a halflife of only 10#^22 s [1].
600 Answers