Secondary alpha isotope effects on deuterium tunneling in triplet o-methylanthrones: Extraordinary sensitivity to barrier width

Article abstract of DOI:10.1021/ja052487n

The rates of deuterium transfer in the photoenolization of triplet 1,4-dimethyl-10H-anthracen-9-one (1) with varying degrees of deuterium label in their methyl groups (1-d₃, 1-d₂, and 1-d) have been investigated as a function of temperature between 5 and 77 K. Measurable rate constants in the case of 1-d3 and 1-d2 were used to construct Arrhenius plots which illustrate the expected curvature and leveling off of rate constant versus temperature. The difference in tunneling rate constants of 1-d₃ and 1-d₂ yields a tunneling isotope effect, TIE = 2.4, which is attributed to the secondary alpha isotopic substitution. Density functional theory (DFT, B3LYP/6-31G*) calculations were carried out to obtain structural and energetic information for the H(D) transfer along the triplet state zero-point energy levels. The temperature dependence of the rate constants for each isotopologue was simulated with a model that considers the frequency of the C-D stretching mode and the quantum mechanical permeability determined from calculated energy parameters. The model suggests that a difference in barrier width of only 0.015 A between 1-d₃ and 1-d₂ leads to the observed 2-fold difference between tunneling rates. Copyright

Full text of DOI:10.1021/ja052487n

Published on Web 07/02/2005
Secondary Alpha Isotope Effects on Deuterium Tunneling in Triplet
o-Methylanthrones: Extraordinary Sensitivity to Barrier Width
Luis M. Campos, Manoj V. Warrier, Krisztina Peterfy, K. N. Houk,* and Miguel A. Garcia-Garibay*
Department of Chemistry and Biochemistry, UniVersity of California, Los Angeles, California 90095-1569
Received April 27, 2005; E-mail: mgg@chem.ucla.edu
Scheme 1
Quantum mechanical tunneling (QMT) has been invoked in
reactions that occur under cryogenic conditions,1,2 enzymatic
processes involving proton and hydride transfer,3 hydrogen-bonded
networks,4 gas phase,5 and interstellar chemistry.6 In the past few
years, we have analyzed the structural and electronic factors that
affect the rate of photoinduced H-atom tunneling in ortho-methyl
ketones prepared with natural abundance (1a) and trideuterated
methyl groups (1d, Scheme 1).7,8 The reaction9,10 starts by electronic
3
excitation and rapid intersystem crossing to 1 (kISC ∼ 1012 s-1),
followed by a hydrogen atom transfer to form the triplet biradical
32. Excited-state hydrogen transfer (kH(D)) to form 32 competes with
thermal and radiative decay back to the ground state (kTS + kP).
3
Once 2 decays to the singlet state, the enol 2 reverts to 1 by a
proton tunneling mechanism.11
Scheme 2
To measure the rate constant for H(D) transfer (kH(D)), the rate
of disappearance of the triplet ketone (kdec) has been determined
by phosphorescence between 4 and 100 K.7 We consider the rate
of triplet decay (kdec) to be the sum of thermal and radiative rates
(kTS + kP), plus the rate of H(D) transfer (kH(D), eq 1).12
kdec ) kTS + kP + kH(D)
(1)
To obtain kH(D), we assume that kTS and kP are isotope-
independent and may be obtained from a nonreactive compound
with a similar chromophore, such as 3 (kTS + kp ) 5 × 10-2 s-1).7,12
Notably, the rate of H-transfer in 1a is much greater (ca. kH > 106
s-1) than kTS + kP, and no emission is observed. In contrast, rate
measurements for D-transfer in 1d can be carried out easily due to
a much slower reaction. Thus, a QMT mechanism was deduced by
a large tunneling isotope effect (TIE) with a lower limit of ca. kH/
kD > 103 and confirmed by a curved Arrhenius plot of 1d, where
the rate of D-transfer becomes temperature-independent below 30
K, as expected for reactions that occur along zero-point energy
(ZPE) levels.7 Recognizing that the TIEs for 1a and 1d result from
a combination of primary and secondary effects, we decided to
analyze the latter with isotopologues 1b-1d. Assuming a semi-
classical approximation, secondary alpha isotope effects of reactions
that change hybridization from sp3 to sp2 are small and positive.13
The orthogonal vibration that couples more strongly to the reaction
coordinate is a C-H bending mode that changes from ca. 1350
cm-1 in the reactant to ca. 800 cm-1 in the product.13 The ZPE
contribution of the C-H bending mode of the alpha hydrogens on
a vibrationally adiabatic surface and a qualitative depiction of its
effects on the barrier height and width are illustrated in Scheme 2.
From an experimental perspective, alpha secondary TIEs offer an
opportunity to probe the sensitivity of QMT to very subtle changes
in the width and height of the barrier.3
NMR measurements, suggesting that methyl rotation is slow within
the time scale of the QMT reaction.14 As illustrated in Figure 1,
samples of 1b had no detectable emission, and samples of 1c and
1d had relative intensities with values 1c:1d ≈ 1:5. We interpret
these differences in terms of a statistical effect related to the
conformation of the methyl group, which has one C-H bond
opposite and two on the side of the carbonyl group and the
corresponding fraction of conformers predisposed for H- and
D-transfer. Thus, while all three methyl rotamers of 1b have a
hydrogen atom that can be transferred and can deactivate the triplet
state, 1c has only one rotamer with two D-atoms facing the
carbonyl. The emission of 1c is closer to a statistical 33% as
compared to 1d. Arrhenius plots constructed with rates of D-transfer
for 1c and 1d (Figure 1B) show the curvature and plateau
Figure 1. (A) Emission spectra of compounds 1b-d measured in
methylcyclohexane glasses at 10 K. (B) Arrhenius plot of the D-transfer
reactions of 1c and 1d. The rate of reaction from zero-point energy levels
(kZPE), the calculated barrier height (∆Eq), and width (2s) are indicated (the
dotted lines are only qualitative).
Phosphorescence intensities and lifetime measurements of 1b-
1d were carried out as described previously between 100 and 4 K
in methylcyclohexane glasses.7 The phosphorescence spectra of 1b-
2
1d measured between 77 and 5 K confirmed recent solid-state H
9
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J. AM. CHEM. SOC. 2005, 127, 10178-10179
10.1021/ja052487n CCC: $30.25 © 2005 American Chemical Society

C O M M U N I C A T I O N S
and the scaling reduced mass µ (eq 4, µ ) 1 amu). Imaginary
frequency values of -1086 and -1077 cm-1 in 1cq and 1dq result
in barrier widths of 0.968 and 0.983 Å, respectively.
2Vo
µ(2πc|νq|)2
s )
(4)
x
Finally, the calculated kZPE values obtained with eq 2 taking a
frequency factor, cνC-D ≈ 6.5 × 1013 s-1 [kZPE(D2H)calcd ) 1.8 ×
106 s-1 and kZPE(D3)calcd ) 1.2 × 106 s-1] are 2 orders of magnitude
larger than those determined experimentally (kZPE(D2H)exp ) 2.2
× 104 s-1 and kZPE (D3)exp ) 9.3 × 103 s-1). While a calculation
error of ca. 2.3 kcal/mol in the height of the barrier could explain
this discrepancy, an excellent agreement is obtained with known
pre-exponential factors9 of ∼5 × 1011 s-1 for the H-transfer reaction.
A small disagreement between experimental (2.4) and calculated
(1.5) tunneling isotope effects suggests that the one-dimensional
treatment of tunneling accounts only partially for the experimental
observations. However, a simple model based on the effect of
isotopes on ZPE and the shape of the barrier accounts for the
measured results and suggests that a difference of only 0.015 Å in
barrier width leads to 2-fold differences in tunneling rates at very
low temperatures. Studies with higher level calculations and direct
dynamics methods will be reported in due course.
Figure 2. Optimized reactant 31, transition structure TS, and enol 32
(parameters listed, d ) distance, D ) dihedral angle).
Table 1. Energetics for D-Abstraction in the Triplet State: ∆Eq is
the ZPE-Inclusive Barrier Height, ∆Eo is the Zero-Point Inclusive
Energy of Reaction, νq is the Imaginary Frequency of the
Transition State, and ZPE is the Scaled ZPE of the Reactant18
triplet
∆
Eq
∆
Eo
νq
(cm-
ZPE
1
ketone
(kcal/mol)
(kcal/mol)
)
(kcal/mol)
31a
31b
31c
31d
4.5
5.4
5.5
5.6
-4.0
-4.2
-4.1
-4.0
1477i
1088i
1086i
1077i
154.3
150.3
146.4
142.4
characteristic of reactions that occur from ZPE levels.1,15 Tunneling
rates of kZPE(D2H) ) 2.2 × 104 s-1 and kZPE(D3) ) 9.3 × 103 s-1
reveal a positive and relatively large secondary R-TIE of 2.4.
Density functional theory (DFT, B3LYP/6-31G*)16,17 was used
to obtain structure and energetic information along the triplet state
reaction coordinate. The optimized structures for the triplet state
H-transfer reaction are shown in Figure 2 and the ZPE-inclusive18
energetics in Table 1.
Acknowledgment. This work was supported by NSF Grant
CHE0242270. L.M.C. thanks the NSF, Paul & Daisy Soros
Fellowship, and NSF IGERT: MCTP, Grant: DGE-0114443). We
thank Prof. D. Truhlar for valuable comments and advice.
Supporting Information Available: Synthesis of isotopically
labeled anthrones 1b-1d and Cartesian coordinates of the stationary
points. This material is available free of charge via the Internet at http://
pubs.acs.org.
Calculations show that the reaction proceeds with minimal heavy
atom motion. The dihedral angle between the aromatic and CdO
groups (D[Ar-C-O]) change from 178.2 in 31 to 175.3 in the TS
and acquire a slight twist in 32 (D[Ar-C-O] ) 162.7). The
transferring H(D) atom is only 2.38 Å from the carbonyl oxygen
in 31, which is less than the sum of their van der Waals radii (2.72
Å).19 An O-H distance of 1.24 Å in the TS structure is close to
that in the triplet enol 32 (d[O-H] ) 0.97 Å). These results are in
good agreement with a recent literature report.20
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3
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kZPE ) cνC-DPG(EZPE
)
(2)
(3)
PG(EZPE) ) 1/(1 + exp {[2π/(hc |νq|)] (∆Eq)})
Secondary alpha isotopes cause variations in the height of the
barrier (∆Eq) from 5.5 kcal/mol for 1c to 5.6 kcal/mol in 1d.
Changes in the width of the barrier (2s) are estimated from the
assumed parabola, which can be described by the values of νq, Vo,
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