Essentials of Computational Chemistry

10.6 CASE STUDY: HEAT OF FORMATION OF H2NOH 381
10.6 Case Study: Heat of Formation of H2NOH
Synopsis of Saraf et al. (2003) ‘Theoretical Thermochemistry: ab initio Heat of Formation
for Hydroxylamine’.
Hydroxylamine (H2NOH) is a highly reactive molecule. As such, handling bulk quantities
poses significant safety concerns, and indeed serious accidents occurred in 1999 and 2000
with this molecule in industrial settings. A direct measurement of the 298 K gas-phase
enthalpy of formation of hydroxylamine is not available. Data from the solid phase have
been interpreted to suggest a value of −12.0 ± 2.4 kcal mol −1 , but so large an uncertainty
suggests that theory might prove useful in providing an improved estimate of this quantity,
and this in turn might aid in the design of reaction conditions for reactors containing
hydroxylamine. With that goal in mind, Saraf et al. surveyed a very large number of
different levels of theory, including composite levels, to assess their likely utility for
this task.
We consider here three different reaction protocols for predicting the enthalpy of
formation of H2NOH:
H2NOH ⇀↽ 3H + N + O (10.61)
H2 + H2NOH ⇀↽ NH3 + H2O (10.62)
H2O + H2NOH ⇀↽ NH3 + H2O2
(10.63)
The latter two equations were used by Saraf et al. since the 298 K gas-phase enthalpies of
formation of hydrogen, water, and ammonia are all known to very high accuracy. Thus, the
procedures outlined in Section 10.4.3 may be used to compute the unknown hydroxylamine
enthalpy of formation. As isodesmic equations go, Eq. (10.62) is not particularly good. The
H−H and N−O bonds appearing on the l.h.s. are replaced by new N−H and O−H bonds
on the r.h.s., and there is not much reason to expect these bonds to have similar errors in
computed correlation energies. Eq. (10.63) is an improvement to the extent that the only
major difference in bonding from the l.h.s. to the r.h.s. is the change of an N−O bond to an
O−O bond. As both bonds are heteroatom to heteroatom for first-row atoms, we may expect
a much more favorable cancellation of errors. Saraf et al. did not discuss the atomization
energy, Eq. (10.61), which is in some sense the worst possible isodesmic reaction (perhaps
one should call it the nihildesmic reaction) However, in the limit of perfect accuracy there
is no need for the systematic cancellation of errors that isodesmic reactions are designed
to provide, so we will consider Eq. (10.61) here for comparison.
As can be seen in Table 10.4, AM1 semiempirical theory is poorly suited for this
application. With a polarized valence-double-ζ basis set, HF theory provides surprisingly
good agreement with much higher levels of theory, but this is a case of fortuitous
cancellation of errors, since use of a polarized valence-quadruple-ζ basis set decreases
that agreement. The B3LYP model with a good basis set provides predictions that are not
overall particularly much of an improvement over HF theory. The MP2 level with a large
basis set does better for the more balanced isodesmic equation (10.63), but fares poorly
with Eq. (10.62). Some improvement can be had with CCSD(T), but the cost of such a