Computational Chemistry

¼½ŠðÞ 711 : 2 þ4 216ðÞþ: 035 246 : 8 kJ mol#^1

##ðÞ 37 : 78430 þ 4 ðÞ## 0 : 50000 74 : 98203

þ#ðފ 115 : 53061 h# 1 : 050 þ 28 ðÞþ: 468

1

2

ðÞ 8 : 680



kJ mol#^1

¼ 1822 :1 kJ mol#^1 ##ðÞ 114 : 76633 h # 115 :53061 h # 22 :33 kJ mol#^1

¼ 1822 :1 kJ mol#^1 # 0 : 76428 ' 2625 :5 kJ mol#^1 # 22 :33 kJ mol#^1

¼ 1822 : 1 # 2006 : 62 # 22 :33 kJ mol#^1 ¼# 206 :8 kJ mol#^1 ;

as obtained above from Eq. (5.192).

Formation Method

An alternative to the atomization method is what has been called the “formation”
method, which is illustrated for methanol in Fig.5.27. This method utilizes a kind of
“pseudo heat of formation”,DHf0^0 , of the compound from atomic carbon and
molecular hydrogen and oxygen (the conventional heat of formation is relative to
graphite and molecular hydrogen and oxygen).
From Fig.5.27

DHf0-ðCH 3 OHÞ¼DH-f0ðCð^3 PÞÞþDH-f0 ð 5 : 194 Þ

where the experimental value ofDH-f0ð^3 CÞis used, and

DHf0-¼DEtotal0KðCH 3 OHÞ#DEtotal0K Cð^3 PÞþ2H 2 þ

1

2

O 2



ð 5 : 195 Þ

H

∆Hf0 (CH 3 OH)

∆H′f0 (CH 3 OH)

∆Hf0(C(^3 P)) CH^3 OH

1

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

1

C( 2

(^3) P) + 2H 2 + O 2

Fig. 5.27 The principle behind the ab initio calculation of heat of formation (enthalpy of
formation) by the formation method. Methanol is (conceptually) formed from atomic carbon
and molecular hydrogen and oxygen; the enthalpy input for this resembles that for the heat of
formation of methanol (hence the name) except that atomic carbon rather than graphite is used.
Graphite is converted to atomic carbon, and the elements in their normal states are also used to
make methanol. The heat of formation of methanol at 0 K follows from equating this quantity to
the heat of atomization of graphite plus the energy needed to make methanol from atomic carbon
and molecular hydrogen and oxygen. The diagram is not meant to imply that methanolnecessarily
lies above its elements in enthalpy

318 5 Ab initio Calculations