Computational Chemistry

A calculation using G2 (for comparison with the atomization method, above)
gives

DHf0-ðCH 3 OHÞ¼ 711 :2kJmol#^1 þDH^0 f0

¼ 711 :2kJmol#^1 þ



# 115 : 53490 #ð# 37 : 78430 þ 2 ð# 1 : 16636 Þ

þ

1

2

ð# 150 : 14821 Þ



h

¼ 711 :2 kJ mol#^1 þ#½Š 115 : 53490 þ 115 : 19113 h

¼ 711 :2 kJ mol#^1 # 0 :34378 h¼ 711 : 2 # 0 : 34378 ' 2625 :5 kJ mol#^1

¼ 711 : 1 # 902 :59 kJ mol#^1 ¼# 191 :4 kJ mol#^1

The value calculated in [ 197 ] by this procedure is#191.3 kJ mol#^1. The
atomization method usually gives somewhat more accurate heats of formation, at
least with the G2-type methods (although for the particular case of methanol with
G2 this is not so), perhaps because these methods were optimized, via the semiem-
pirical terms (Section 5.5.2.2b) to give accurate atomization energies.

Isodesmic Reaction Method

Finally, heats of reaction can be calculated by ab initio methods with the aid of
isodesmic reactions (Section 5.5.2.2a), as indicated in Fig.5.28 (actually, the
scheme in Fig.5.28is not strictly isodesmic – for example, only on one side of
the “isodesmic” equation is there an H–H bond). From this scheme

H

1

C(graphite) + 3H 2 + 2 O 2

CH 4 + H 2 O

CH 3 OH + H 2

∆Eisodesmic

∆Hf0 (CH 3 OH)

∆Hf0 (CH 4 )+∆Hf0 (H 2 O)

• 
  

  –

  
  

Fig. 5.28 The principle behind the ab initio calculation of heat of formation (enthalpy of
formation) using an isodesmic reaction. Methanol and hydrogen are (conceptually) made from
methane and water (other isodesmic reactions could be used); the 0 K enthalpy input for this is the
ab initio energy difference between the products and reactants. Graphite, hydrogen and oxygen are
converted into methane and water and into methanol and hydrogen, with input of the appropriate
heats of formation. The heat of formation of methanol at 0 K follows from equating the heat of
formation of methanol with the sum of the energy inputs for the other two processes. The diagram
is not meant to imply that methanolnecessarilylies above its elements in enthalpy

5.5 Applications of the Ab initio Method 319