Computational Chemistry

(“difference” is defined here as product energy minus reactant energy) governs
the extent to which a reaction has progressed at equilibrium, i.e. the equili-
brium constant, and the energy difference between the transition state and the
reactants (transition state energy minus reactant energy) governs (partially; see
Section 5.5.2.2d) the rate of the reaction, i.e. the rate constant (Fig.5.25). The term
“energy” in chemistry usually means potential energy (often denoted by E),
enthalpyH,orGibbsfreeenergy,G.Thepotentialenergyonacomputed
Born–Oppenheimer surface (the usual “potential energy surface”; Section 2.3)
represents 0 K enthalpy differences without ZPE. Enthalpy differences,DH,and
free energy differences,DG,arerelatedthroughthetemperature-weighted
entropy difference:

DG¼DH#TDS $ð 5 : 179 ¼ 5 : 173 Þ

More detailed discussion of enthalpy, free energy, and entropy are given in
books on thermodynamics, and the relationships between these quantities and
processes at the molecular level are explained in books on statistical mechanics
[ 140 ]; general discussions of these topics are given in physical chemistry texts.
To get an intuitive feel forDHwe can regard it as essentially a measure of the
strengths of the bonds in the products or the transition state, compared to the
strengths of the bonds in the reactants [ 141 ]:

0

4C6+, 8 H+, and (4×6) + (8×1) = 32 electrons,

infinitely separated and at rest

H H

Me Me

ZPE =

304.1 kJ mol–1

0.11582 h

ZPE =

304.7 kJ mol–1

0.11604 h

–155.24291 h –155.24637 h

–155.12709 h –155.13033 h

H Me

Me H

uncorrected ab initio E

ZPE-corrected ab initio E ∆E0Ktotal = –155.12709 – (–155.13033) h

= 0.00324 h = 8.51 kJ mol–1

~ ~

407363.74 kJ mol–1 407372.25 kJ mol–1

Fig. 5.24Absolute and relative ab initio energies, with and without ZPE correction. These are
from HF/3–21G(*)calculations. The calculated reaction energy for the (E) to (Z)(cistotrans)
isomerization is#8.51 kJ mol#^1

298 5 Ab initio Calculations