Computational Chemistry

For aminimum

@^2 E

@q^2

> 0 (*2.2)

for allq.
For atransition state

@^2 E

@q^2

> 0 (*2.3)

for allq, except alongthe reaction coordinate, and

@^2 E

@q^2

< 0 (*2.4)

along the reaction coordinate.
The distinction is sometimes made between atransition stateand atransition
structure[ 4 ]. Strictly speaking, a transition state is a thermodynamic concept, the
species an ensemble of which are in a kind of equilibrium with the reactants in
Eyring’s^2 transition-state theory [ 5 ]. Since equilibrium constants are determined by
free energy differences, the transition structure, within the strict use of the term, is a
free energy maximum along the reaction coordinate (in so far as a single species can

minimum

transition state

transition state

region

reaction coordinate

energy

Fig. 2.8 A transition state or saddle point and a minimum. At both the transition state and the
minimum∂E/∂q¼0 for all geometric coordinatesq(along all directions). At the transition state
∂E^2 /∂q^2 <0 forq¼the reaction coordinate and>0 for all otherq(along all other directions). At a
minimum∂E^2 /∂q^2 >0 for allq(along all directions)

(^2) Henry Eyring, American chemist. Born Colonia Juara ́rez, Mexico, 1901. Ph.D. University of
California, Berkeley, 1927. Professor Princeton, University of Utah. Known for his work on the
theory of reaction rates and on potential energy surfaces. Died Salt Lake City, Utah, 1981.
2.2 Stationary Points 17