Essentials of Computational Chemistry

382 10 THERMODYNAMIC PROPERTIES
Table 10.4 Predicted 298 K enthalpies of formation (kcal mol −1 ) for hydroxylamine
From
Level of theory Eq. (10.61) Eq. (10.62) Eq. (10.63)
AM1 −32.34 −31.31
HF/cc-pVDZ −12.14 −12.02
HF/cc-pVQZ −8.83 −13.06
B3LYP/aug-cc-pVTZ −12.18 −9.69
MP2/cc-pVQZ −8.61 −12.09
CCSD(T)/cc-pVQZ// −11.56 −10.61
CCSD(T)/cc-pVDZ
BAC-MP4 −12.98 −11.09
G2 −10.60 −11.78 −11.53
G2MP2 −11.46 −11.69 −11.67
G3B3 −10.02 −11.51 −11.53
G3 −9.36 −11.15 −11.28
CBS-Q −10.03 −12.18 −11.16
Statistical a −10.29 ± 0.70 −11.66 ± 0.34 −11.43 ± 0.19
a Average ± standard deviation from G2, G2MP2, G3B3, G3, and CBS-Q.
calculation far exceeds every other entry in the table. Since the G2, G2MP2, G3B3, G3,
and CBS-Q models (all discussed in Chapter 7) are cheaper than CCSD(T)/cc-pVQZ and
moreover designed specifically for the purpose of computing enthalpies of formation, there
is ample reason to focus more closely on their performance.
Rather than attempting to rationalize why any one of these composite levels might
be more or less good than another, let us examine their joint performance. The final
row of Table 10.4 provides the means and standard deviations of the predicted H o
f,298
(H2NOH) values from these levels for Eqs. (10.61) to (10.63). The largest standard
deviation is associated with Eq. (10.61), the next largest with Eq. (10.62), and the smallest,
only 0.19 kcal mol −1 , with Eq. (10.63). This trend is entirely consistent with the above
discussion of the relative quality of the three isodesmic equations, and provides some
quantitative feel for how difficult the accurate computation of an atomization energy really
is. Given this analysis, it appears reasonable to take the average value from the last five
methods and Eq. (10.63) as a best estimate: −11.4 kcal mol −1 . Further support for this
choice comes from considering a different reaction, namely
H2 + H2O2 ⇀↽ 2H2O (10.64)
Note that this is the analog to Eq. (10.62) with hydrogen peroxide replacing hydroxylamine.
In this case, all enthalpies of formation are known experimentally to high accuracy, so the
performance of the various theoretical models may be directly assessed. Applying the same
averaging procedure, one finds that the models predict an enthalpy of formation for H2O2
that is too negative by 0.3 kcal mol −1 . Note that if one assumes that this correction may be
applied to the results from Eq. (10.62) for hydroxylamine, one predicts −11.4 kcal mol −1 ,
in perfect agreement with the uncorrected results from Eq. (10.63).
Note that the average atomization energy prediction differs from −11.4 kcal mol −1 by
only 1.1 kcal mol −1 , which is about the range of accuracy typically quoted for the models