Computational Chemistry

initio calculation (e.g. Section 5.2.3.6.5). This energyEtotalSE, the total internal energy
of the molecule except for zero point vibrational energy, is used to calculate the heat
of formation (enthalpy of formation) of the molecule. Figure6.1will help to make it
clear how this is done. The quantities in Fig.6.1are

1.DH*f298(M), the 298 K heat of formation of the molecule M, i.e. the heat energy
needed to make M from its elements. This is the quantity we want.

2. The atomization energy of M, which is the energy of the atoms minus the energy
   of M. The energy of the atoms isF∑ESE(Ai); the conversion factorFconverts
   ESEðAiÞ, the energy per atom in hartrees, into the same units, kJ mol"^1 or kcal
   mol"^1 , as is used for the experimental heats of formation of the atoms;Fis
   2,625.5 kJ mol"^1 per hartree atom"^1 (or molecule"^1 ). The energy of the mole-
   cule M isFEtotalSE(M), the optimized geometry being used. The same semiempir-
   ical method is used to calculate atomic and molecular energies, both of which
   are negative quantities, the energy of the species relative to electrons and one or
   more atomic cores infinitely separated.ESE(Ai) is purely electronic, since an
   atom has no core–core repulsion (i.e. it has no atoms to separate), while the
   molecular energyEtotalSE (M) includes core–core repulsion.


3. 
   

P

DH*f298(Ai), the sum, over all the atoms A of M, of the experimental 298 K
heats of formation of these atoms.
Equating the two paths from the elements in their standard states at 298 K to
atoms we get

DH*f298ðMÞ¼

X

DH*f298ðÞ"Ai F

X

ESEðÞþAi FEtotalSEðMÞ (6.13)

elements in their

standard states

Σ∆Hf298(Ai)

∆Hf298(M)

molecule M

atoms in their

standard states

atomization energy of M =

FΣESE(Ai)–FESE (M)

total

Fig. 6.1The principle behind the semiempirical calculation of heat of formation (enthalpy of
formation). The molecule is (conceptually) atomized at 298 K; the elements in their standard states
are also used to make these atoms, and to make the molecule M. The heat of formation of M at
298 K follows (with some approximations) from equating the energy needed to generate the atoms
via M to that needed to make them directly from the elements

402 6 Semiempirical Calculations