Computational Chemistry

not be a stationary point) on another. Thus fluoro- and difluorodiazomethane are HF
minima but are MP2/6–31G transition states [ 91 ]; an attempt to approximate
the MP2/6–31G reaction energy for, say, CHFN 2 !CHF + N 2 , using single-
point MP2/6–31G energies on HF geometries, is misguided if CHFN 2 is a transi-
tion state on the MP2 PES. Nevertheless, because HF optimizations followed by
single-point correlated (MP2 or higher-level) energy calculations are much faster
(“cheaper”) than correlated optimizations, and do usually give improved relative
energies, the method is widely used for large molecules. Figure5.21compares
some MP2 single-point, MP2-optimized, and HF energies; the biggest MP2 single-
point/MP2 optimized difference is 6.9 kJ mol#^1 (HCN reaction energy). The
limited salient experimental information on these reactions, and reaction energies
at 298 K calculated by the accurate G3(MP2) method, is also given [ 92 ]. The
relative energies in Fig.5.21are 0 K enthalpy differences (with raw energy
corrected for ZPE), for uniformity and simplicity, but usually experimental barriers
are given as Arrhenius activation energiesEa, which are simply related to enthalpies
of activationDH{(Eq.5.175), and the extent of a reaction is quantified as an
equilibrium constant which is related (Eq.5.183) to a Gibbs free energy difference
DGreact(Section 5.5.2.1). Free energies of activationDG{can be used to calculate
rate constants (Section 5.5.2.2d) and enthalpies of reactionDHreactare often used
(not theoretically rigorously) as an indication of the extent and even the ease of a
reaction. To give a feel for the quantitative difference in the values of the relative
0 K energies and these five other energy quantities, the calculated values are given
below for the four reactions of Fig.5.21. The 0 K energies are ZPE-corrected MP2/
6–31G energies relative to that of the reactant, and the other energies are at 298 K
(standard room temperature) and are also from MP2/6–31G* calculations and
employ standard ideal-gas statistical thermodynamics algorithms; energy units
are kJ mol#^1.
Ethenol to ethanal
Transition state 0 K relative E¼ 233 Product 0 K relative E¼#71.7
Ea¼DH{þRT¼DH{þ2.48¼234.3

DH{¼231.8

DGreact¼#73.1

DG{¼233.1

DHreact¼#70.9

HNC to HCN

Transition state 0 K relative E¼ 140 Product 0 K relative E¼#87.2

Ea¼DH{þRT¼DH{þ2.48¼142.7

DH{¼140.2

DGreact¼#86.9

DG{¼136.1

DHreact¼#87.8

5.4 Post-Hartree–Fock Calculations: Electron Correlation 267