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the range of the benchmark techniques, at a much lower
computational cost.
The results in Table 2 show that amines are significantly
more prone to aH-abstraction than iso-electronic alcohols.
Indeed, the computed barriers for aH-abstraction from methanol,
ethanol and iso-propanol by CH3OOꢀ were previously calculated
to be 14.0, 11.8 and 10.3 kcal molꢁ1,4 respectively; on average
more than 3 kcal molꢁ1 higher than for the corresponding
amines. This kinetic difference is a direct consequence of the
lower aC–H bond strengths in amines than in alcohols (Fig. 1).
Notice that the correlation between the abstraction barrier and
the aC–H bond (so-called Evans Polanyi correlation) is slightly
curved and levels off for weaker aC–H bonds.
Scheme 2 HO2ꢀ-elimination from
a general a-hydroxy-peroxyl
radical.
previously hypothesized reaction mechanisms.7 Unimolecular
cleavage of the O–O bond in the peroxyl radical is unimportant
in the relevant temperature range, due to the high bond strength.
Computational methods
The C–H bond strength is inversely proportional to the
stability of the radical product. Fig. 2 correlates the H–CH2X
bond strength with the Mulliken spin density on the C-atom in
the ꢀCH2X radical (X = H, SiH3, F, CH3, OH, NH2,
N(H)CH3 in order of decreasing H–CH2X strength). Various
parameters influence the stability of the ꢀCH2X radical,
including (when possible) p-back-donation of 2p-orbitals of
the substituent X into the half-occupied 2p-orbital on the
C-atom,15 in addition to hyperconjugation and s-effects.
Those combined effects cause the C–H bond strength to
decrease in the order CH3F, CH3OH and CH3NH2, despite
the different substituents being iso-electronic and the electro-
negativity decreasing in the order F 4 O 4 N.
All calculations were carried out using the GAUSSIAN09
software package (Revision A.02).8 Geometries of stationary
points (i.e. stable intermediates and transition states) were
initially optimized at the B3LYP-DFT- or QCISD-level.9
Subsequently, the relative energies (corrected for zero-point
energy – ZPE – differences) were quantitatively refined using
various higher levels of theory, such as G3,10 CBS-QB3,11
CBS-APNO12 and G2M13 (see Table 1). ZPE-corrected relative
energies of the stationary points on the Potential Energy Surface
(PES) are reported at 0 K.
a-Pinene oxidation experiments were performed at 80 1C in
a bubble column reactor at 1 atm O2, as described elsewhere.14
Addition of O2 to the a-amino-alkyl radicals is highly
exothermic, with values for DrH ranging from ꢁ27.2 kcal
molꢁ1 (CBS-APNO) to ꢁ32.5 kcal molꢁ1 (G2Mlarge//DFT)
Results and discussion
Formation of a-amino-peroxyl radicals
ꢀ
for the case of CH2NH2, indicating irreversible formation of
Table 2 compares the adiabatic energy barriers for the
aH-abstraction from different types of amines by the CH3OOꢀ
radical. Earlier work showed that for analogous H-abstraction
reactions from alkanes, alcohols and hydroperoxides, the
DFT//DFT results agree within 0.5 kcal molꢁ1 from benchmark
methods like G3, CBS-QB3, and G2M//DFT.4 However, for the
abstraction from amines, the various benchmark levels of theory
clearly deviate more amongst each other (i.e. nearly 2 kcal molꢁ1).
Given that those high levels of theory are computationally rather
demanding, and that they all have their merits and shortcomings,
we prefer to refer to the DFT//DFT results which agree within
the a-amino-peroxyl radical.
ꢀ
Unimolecular HO2 -elimination to imine
Subsequently, the unimolecular decomposition of the a-amino-
peroxyl radicals to the corresponding imine plus HO2ꢀ (Reaction 1
in Scheme 3) is investigated. Similar to the analogous reaction
of a-hydroxyl-peroxyl radicals (Scheme 2), this reaction is
found (via intrinsic reaction coordinate analysis) to proceed
ꢀ
via an H-bonded complex between the imine and HO2 . The
break up of this H-bonded complex does not, however, control
the overall rate. The rate determining step in the mechanism is
the HO2ꢀ-elimination, and mainly involves breaking of the
C–O bond (see Scheme 4).
Tables 3–5 compare ꢀvarious levels of theory for the decomposi-
ꢀ
ꢀ
tion of OOCH2NH2, OOCHCH3NH2, and OOC(CH3)2NH2,
respectively. One observes an excellent agreement (i.e., within
1 kcal molꢁ1) between the CBS-QB3, CBS-APNO and G3
levels of theory. On the other hand, and in contrast to the
situation with a-hydroxyl-peroxyl radicals,5 G2M//DFT gives
slightly different results. It seems unlikely that this deviation
can be (entirely) attributed to a limited CCSD(T)-basis set,
Scheme 3 Competition between the unimolecular HO2ꢀ-elimination
(1) and the bimolecular H-abstraction (2) for a-amino-peroxyl radicals.
Table 1 Summary and details of the levels of theory utilised
Method
Energy calculation
Geometry optimization and ZPE
G2Msmall/DFT E[UCCSD(T)/6-31G(d)] + {E[UMP2/6-311++G(3df,3pd)] ꢁ E[UMP2/6-31G(d)]}
G2Mlarge//DFT E[UCCSD(T)/aug-cc-pVDZ] + {E[UMP2/aug-cc-VTZ] ꢁ E[UMP2/aug-cc-pVDZ]}
UB3LYP/6-311+G(df,pd)
UB3LYP/aug-cc-pVTZ
G2M//QCISD E[UCCSD(T)/6-311G(df,pd)] + {E[UMP2/6-311++G(3df,3pd)] ꢁ E[UMP2/6-311G(df,pd)]} UQCISD/6-311G(d,p)
DFT//DFT
E[UB3LYP/6-311++G(3df,3pd)]
UB3LYP/6-31G(d,p)
c
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Phys. Chem. Chem. Phys., 2012, 14, 11002–11007 11003