This seems unreasonably big: above, we got 89 and 93 kJ mol#^1 for the benzene
ASA. Yet the equation seems at first sight reasonable: on each side three C¼C, 15
C–C, and 30 C–H bonds. But in fact the numbers of each kind of bond differ at the
hybridization level; for example, the reactants have six sp^2 –sp^2 C–C bonds but the
products have only three of these. Overall, we are converting stronger bonds into
weaker ones, and part of the rise in energy is due to this, rather than to loss of
aromatic stabilization, inflating the supposed ASE. Another example of an ill-
chosen isodesmic-type reaction is given by Slayden and Liebman, where benzene
seems to have an ASE of 269.9 kJ mol#^1 (!) [ 169 ]:
C 6 H 6 þ6CH 4 !3H 2 C¼CH 2 þ3H 3 C#CH 3(Our B3LYP/6–31G* energy/geometry method gives 286 kJ mol#^1 ). This shows
the need to choose isodesmic-type reactions judiciously, and helps to explain the
profusion of methods and terms [ 159 ].
5.5.2.2b Thermodynamics; High-Accuracy Calculations
As the previous discussion suggests (Section 5.5.2.2a), the calculation of good
relative energies is much more challenging than the calculation of good geometries.
Nevertheless, it is now possible to reliably calculate energy differences to within
about)10 kJ mol#^1. An energy difference with an error of)10 kJ mol#^1 is said to
be withinchemical accuracy, although in recent years there has been some ten-
dency to raise the bar to about half this value. The term seems to have been first
used in connection with computational chemistry in 1984 by Moskowitz and
Schmidt (“Can Monte Carlo Methods Achieve Chemical Accuracy?”) [ 174 ] and
was popularized by Pople (biographical footnoteSection 5.3.3) in connection with
the G1 and G2 (see below) methods. Around the time these pioneering high-
accuracy methods were being developed, the term appeared in the title of a review
by Bauschlicher and Langhoff [ 175 ]. An accuracy of about 2 kcal mol#^1 (8.4 kJ
mol#^1 , rounded here to 10 kJ mol#^1 ) was set by Pople and coworkers in 1989 for the
G1 method [ 176 ] as a realistic and chemically useful goal, perhaps because this is
small compared to typical bond energies (roughly 400 kJ mol#^1 ), and comparable
or superior to typical experimental errors. The ab initio energies and methods
needed for results of chemical accuracy are calledhigh-accuracy(or multistep, or
multilevel, or high-accuracy multistep) energies and methods.
As one might expect, high-accuracy energy methods are based on high-level
correlational methods and big basis sets. However, because the straightforward
application of such computational levels would require unreasonable times (be very
“expensive”), the calculations are broken up into several steps, each of which
provides an energy value; summing these gives a final energy close to that which
would be obtained from the more unwieldy one-step calculation. There are two
classes of widely-used high-accuracy energy methods: theGaussian methods,
which originated in the Pople group and derive their names from being first
5.5 Applications of the Ab initio Method 309