which the standard state is white phosphorus; although red phosphorus is stabler
under normal conditions, these allotropes are apparently somewhat ill-defined). The
specified temperature is usually 298.15 K (about room temperature). The heat of
formation of a compound at room temperature is thus the amount of heat energy
(enthalpy) that must be put into the reaction to make the compound from its
elements in their normal (room temperature and atmospheric pressure) states; it is
the “heat content” or enthalpy of the compound compared to that of the elements.
For example, at 298 K the heat of formation of CH 4 is#74.87 kJ mol#^1 , and the
heat of formation of CF 4 is#933.20 kJ mol#^1 [ 196 ]. To make a mole of CH 4 from
solid graphite (carbon in its standard state at 298 K) and hydrogen gas requires
#74.87 kJ, i.e. 74.87 kJ are given out – the reaction is mildly exothermic. To make a
mole of CF 4 from solid graphite and fluorine gas requires#933.20 kJ, i.e. 933.20 kJ
are given out – the reaction is strongly exothermic. In some sense CF 4 is thermody-
namically much stabler with respect to its elements than is CH 4 with respect to its
elements. Note that the standard heat of formation of anelementis zero, since the
reaction in question is the formation of the element from the element, in the same
state (no reaction). Heat of formation is denotedDH-f or DfH- and heat of
formation at, say, 298 K byDH-f298, “deltaHsub f standard at 298 K”. The delta
indicates that this is a difference (enthalpy of the compound minus enthalpy of the
elements) and the superscript denotes “standard”.
There are extensive tabulations of experimentally-determined heats of forma-
tion, mostly at 298 K. One way to determineDH-f298is from heats of combustion:
burning the compound and the elements and measuring calorimetrically the heat
evolved enables one to calculate the heat of formation by subtraction.DH-f298can
also be obtained by ab initio calculations. This is valuable because (1) it is far easier
Table 5.10 Comparison of speed and ability to handle molecular size for four popular high-
accuracy multistep methods: G3(MP2), CBS-4M, CBS-QB3, and CBS-APNO
Time (h); for less than 1 h: h (min)
Molecule N(heavy)a G3(MP2) CBS-4M CBS-QB3 CBS-APNO
CH3COO# 4 0.05 (3) 0.03 (2) 0.08 (5) 0.5 (30)
CH2FCOO# 5 0.11 (7) 0.05 (3) 0.23 (14) 2.4
CHF2COO# 6 0.22 (13) 0.07 (4) 0.50 (30) Failed
CF3COO# 7 0.17 (10) 0.05 (3) 0.38 (23) Failed
C2F5COO# 10 3.1 0.20 (12) 9 Failed
C3F7COO# 13 12 0.47 (28) Failed?b Failed
C4F9COO# 16 Failed 1 Failed Failed
C5F11COO# 19 Failed 3 Failed Failed
C6F13COO# 22 Failed Failed Failed Failed
The jobs that failed did so because of insufficient diskspace, and this occurred at the first high-level
correlation step. The calculations were done with the G03 program on a computer with the 64-bit
2.66 GHz Intel Core 2 Duo Quad CPU, 4.00 GB RAM, and 900 GB diskspace, running under
Windows VISTA. They reflect the times and size limitations of these methods on a well-equipped
personal computer as of ca. 2009 January. The use of anions here is adventitious, stemming from
another project.
aN(heavy) is the number of heavy (non-hydrogen) atoms.
bThe CCSD(T) energy step was stuck without change for 24 h.
314 5 Ab initio Calculations