Computational Chemistry

and cheaper than doing a thermochemical experiment, (2) many compounds have
not been subjected to experimental determination of their heats of formation, and
(3) highly reactive compounds, or valuable compounds available only in very small
quantity cannot be subjected to the required experimental protocol, e.g. combus-
tion. Let’s see howDHf298- can be calculated.

Atomization Method

Suppose we want to calculateDH-f298for methanol. We will calculate the heat of
formation at 0 K (DH-f0) and then correct this to 298 K. Figure5.26shows the
principle behind what has been called the “atomization” method [ 197 ]. Methanol is
(conceptually) atomized at 0 K into carbon, hydrogen and oxygen atoms, in their
ground electronic states. The elements in their normal, unatomized states are also
used to make these atoms, and to make methanol. The heat of formation of
methanol at 0 K follows from equating the energy needed to generate the atoms
from the elements via methanol DHf0-ðÞþCH 3 OH DH-a0ðÞCH 3 OH

)*

to that needed
to make themdirectlyfrom the elements in their normal states:

DHf0-ðCH 3 OHÞþDH-a0ðCH 3 OHÞ¼DH-f0ðCð^3 PÞþ4Hð^2 SÞþOð^3 SÞÞ

i.e.

DH-f0ðCH 3 OHÞ¼DH-f0ðCð^3 PÞþ4Hð^2 SÞþOð^3 SÞÞ#DH-a0ðCH 3 OHÞð 5 : 190 Þ

DH-a0ðCH 3 OHÞis the ab initio atomization energy of methanol, the energy
difference between the atoms and methanol. There are a couple points to note
about this conceptual scheme. We are converting into carbon atoms graphite, a poly-
meric material, so strictly speaking Fig.5.26should shownC(graphite)!nC(^3 P),

H ab initio energy difference

∆Hf0 (C(^3 P) + 4H(^2 S) + O(^3 P))

∆Hf0 (CH 3 OH)

∆Ha0 (CH 3 OH)

CH 3 OH

1

C(graphite) + 2H 2 + 2 O 2

(C(^3 P) + 4H(^2 S) + O(^3 P)

Fig. 5.26 The principle behind the ab initio calculation of heat of formation (enthalpy of
formation) by the atomization method. Methanol is (conceptually) atomized at 0 K into carbon,
hydrogen and oxygen atoms; the elements in their standard states are also used to make these
atoms, and to make methanol. The heat of formation of methanol at 0 K,DH-f0(CH 3 OH),
follows from equating the energy needed to generate the atoms via methanol (DH-f0(CH 3 OH)þ
DH-a0(CH 3 OH)) to that needed to make them directly from the elements in their standard states.
The diagram is not meant to imply that methanolnecessarilylies above its elements in enthalpy

5.5 Applications of the Ab initio Method 315