Considerable attention has been given here to heats (enthalpies) of formation,
because there are extensive tabulations of these, e.g. [ 205 ] and papers on their
calculation appear often in the literature, e.g. [ 201 ]. However, we should remember
that equilibria [ 147 ] are dependent not just on enthalpy differences, but also on the
often-ignored entropy changes, as reflected in free energy differences, and so the
calculation of entropies is also important [ 206 ].
5.5.2.2d Kinetics; Calculating Reaction Rates
Ab initio kinetics calculations are far more challenging than thermodynamics
calculations; in other words, the calculation of rate constants is much more involved
than that of equilibrium constants or quantities like reaction enthalpy, reaction free
energy, and heat of formation, which are related to equilibrium constants. Why is
this so? After all, both rates and equilibria are related to the energy difference
between two species: the rate constant to that between the reactant and transition
state (TS), and the equilibrium constant to that between the reactant and product
(Fig.5.25). Furthermore, the energies of transition states, like those of reactants and
products, can be calculated. The reason for the difference is partly because the
energies of transition states are harder to calculate to high accuracy than are those of
relative minima (“stable species”). Another problem is that the rate does not depend
strictly on the TS/reactant free energy difference (which can often, at sufficiently
high levels, be accurately calculated).
To understand the problem consider a unimolecular reaction
A!BFigure.5.29shows the potential energy surface for two reactions of this type,
A 1 !B 1 and A 2 !B 2. The reactions have identical calculated free energies of
activation. By calculated, we mean here using some computational chemistry
method (e.g. ab initio) and locating a stationary point with no imaginary frequen-
cies, corresponding to A, and an appropriate stationary point with one imaginary
frequency, etc. (Section 2.5), corresponding to B. The “traditional” calculated rate
constant then follows from a standard expression involving from the energy differ-
ence between the TS and reactant (our calculated free energy of activation) and
the partition functions of the two species. However, in the TS region the PES for the
first process is flatter than for the second process – the saddle-shaped portion of the
surface is less steeply-curved for reaction 1 than for reaction 2. If all reacting A
molecules followedexactlythe intrinsic reaction coordinate (IRC; Section 2.2; the
minimum-energy path, MEP) and passed through the calculated TS species, then
we might expect the two reactions to proceed at exactly the same rate, since all A 1
and A 2 molecules would have to surmount identical barriers. However, the IRC is
only an idealization [ 207 ], and molecules passing through the TS region toward
the product frequently stray from this path (dashed lines). Clearly for the reaction
A 1 !B 1 at any finite temperature more molecules (reflected in a Boltzmann
5.5 Applications of the Ab initio Method 323