temperature from the free energy of activation, for unimolecular isomerizations.
This regardsDG{as only a weak function ofT, as seems to be the case – see the
above calculation for cyclopropylidene at 77 K. We see that the threshold value of
DG{for observability at room temperature for a species that decays by a unim-
olecular process is predicted to be about 80–90 kJ mol#^1 (t 1 = 2 ¼10 s–9 min),
with a strong dependence onDG{. Experience gives a similar result: in fact the
threshold barrier for observing or isolating a compound at room temperature is
about 100 kJ mol#^1 [ 152 , 153 ].
So far as Eq. (5.197) can deliver them, “quantitatively accurate” reaction rates,
say to within a factor of 2, require activation energies accurate to within about 2 kJ
mol#^1. Nevertheless, the equation does provide a simple way of obtaining service-
ably good rate constants. The (admittedly small) selection of reactions here shows
no bias toward low or high calculated barriers for any of the four methods, and for a
particular kind of reaction it is advisable to choose a method based on a comparison
of methods with experiment results where this information is available.
5.5.2.2e Energies: Concluding Remarks
Foresman and Frisch [ 227 ], in a chapter with very useful data and recommendations
regarding accuracy, show large mean absolute deviations (MAD) and unreservedly
enormous maximum errors for Hartree–Fock calculations and even for MP2 calcu-
lations with reasonably big basis sets; for example:
HF/6–31þG** MAD, 195 kJ mol#^1 (46.7 kcal mol#^1 )
Max. Error, 753 kJ mol#^1 (179.9 kcal mol#^1 )
MP2/6–311þG(2d,p) MAD, 37 kJ mol#^1 (8.9 kcal mol#^1 )
Max. Error, 164 kJ mol#^1 (39.2 kcal mol#^1 )How can this be reconciled with the results shown in this chapter and the modest
levels endorsed by Hehre [ 39 ]? As hinted in reference [ 227 ] (“Don’t Panic!” p. 146,
and “Don’t be overly alarmed, p. 149), the large errors reported are a composite
including some “tough cases” [ 228 ] like atomization energies (e.g.Section 5.4.3.3).
A good feel for the accuracy of various levels of calculation will emerge from
examining the extensive data in Hehre’s book [ 39 ], not losing sight of the fact that
there are cases that yield only to high-accuracy methods (notnecessarilymultistep
methods like those of Section 5.5.2.2b).
For relief and reassurance, Table5.13shows the relative energies of some
isomers calculated at modest levels, namely HF/3–21G(), HF/6–31G, and
MP2/6–31G*. For a reality check, we also see values from G3(MP2) and experi-
ment (experiment: fulvene/benzene, [ 229 / 230 ]; cyclopropane/propene, [ 231 / 231 ];
dimethyl ether/ethanol, [ 232 / 233 ]; methylcyclopentane/cyclohexane, [ 230 / 234 ]).
The energy differences chosen for this illustration are enthalpy differences, because
differences in heats of formation yield these, and heats of formation represent the
most extensive compilations of experimental energy quantities relevant to our
330 5 Ab initio Calculations