Computational Chemistry

5.5.2.2 Energies: Calculating Quantities Relevant to Thermodynamics
and to Kinetics

5.5.2.2a Thermodynamics; “Direct” Methods; Isodesmic Reactions

Here we are concerned with the relative energies of species other than transition states.
Such molecules are sometimes called “stable species”, even if they are not at all stable
in the usual sense, to distinguish them from transition states, which exist only for an
instant on the way from reactants to products. A “stable species”, in contrast, sits in a
potential energy well and survives at least a few molecular vibrations (>ca. 10#^13 s).
The very useful book byHehre [ 39 ] contains a wealth of information on computational
and experimental results concerning thermodynamic quantities.
The ab initio reaction energy that is most commonly calculated is simply the
difference in ZPE-corrected energies,DEtotal0K, which is the reaction enthalpy change
at 0 K (Eq.5.181). This provides an easily-obtained indication of whether a reaction
is likely to be exothermic or endothermic, or of the relative stabilities of isomers.
Table5.9illustrates this procedure. The results are only semiquantitatively correct,
and the HF/6–31G* method is not necessarily better here than the HF/3–21G for
such “direct” (simple subtraction) energies. In fact, it has been documented by

Table 5.9 Reaction energies and relative energies of isomers (HF/3–21G()andHF/6–31G)
Reactants,E, h Products,E, h Reaction energy, or relative energy of
isomers
Calculated, h/ kJ mol#^1 Exp, kJ
mol#^1
H 2 + Cl 2 2HCl #915.94846#(#915.86949) # 192
#1.11234 + (#914.75715)
¼#915.86949

2(#457.97423)

¼#915.94846

¼#0.07897/# 207

#1.11625 + (#918.91145)
¼#920.02770

2(#460.05272)

¼#920.10544

#920.10544 – (#920.02770)
¼#0.07774/# 204
2H 2 +O 2 2H 2 O #151.12838 – (#150.99008) # 523
2(#1.11234) + (#148.76540)
¼#150.99008

2(#75.56419)¼

#151.12838

¼#0.13830/# 363

2(#1.11625) + (#149.61336)
¼#151.84586

2(#75.98778)¼

#151.97556

#151.97556 – (#151.84586)
¼#0.12970/# 341
Trans-2-butene Cis-2-butene #155.12768 – (#155.13032) 4.6
#155.13032 #155.12768 ¼0.00264/6.93
#155.99472 #155.99196 #155.99196 – (#155.99472)
¼0.00276/7.2
HCN HNC #92.32215 – (#92.33570) 60.7
#92.33570 #92.32215 ¼0.01355/35.6
#92.85721 #92.83828 #92.83828 – (#92.85721)
¼0.01893/49.7
The energies in hartrees are ab initio energies including ZPE. The calculations on O 2 are UHF, on
triplet O 2. Calculations are by the author, experimental energies are from reference [ 39 ],
Tables 2–13 and 2–14.

5.5 Applications of the Ab initio Method 303