Heavy-Atom Tunneling Through Crossing Potential Energy Surfaces: Cyclization of a Triplet 2-Formylarylnitrene to a Singlet 2,1-Benzisoxazole

Article abstract of DOI:10.1002/anie.202006640

Not long ago, the occurrence of quantum mechanical tunneling (QMT) chemistry involving atoms heavier than hydrogen was considered unreasonable. Contributing to the shift of this paradigm, we present here the discovery of a new and distinct heavy-atom QMT

Full text of DOI:10.1002/anie.202006640

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Accepted Article
Title: Heavy-Atom Tunneling Through Crossing Potential Energy
Surfaces: Cyclization of a Triplet 2-Formylarylnitrene to a Singlet
2,1-Benzisoxazole
Authors: Cláudio M. Nunes, Luís Viegas, Samuel Wood, José Roque,
Robert McMahon, and Rui Fausto
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Heavy-Atom Tunneling Through Crossing Potential Energy Surfaces:
Cyclization of a Triplet 2-Formylarylnitrene to a Singlet 2,1-Benzisoxazole
Cláudio M. Nunes,*[a] Luís P. Viegas,*[a] Samuel A. Wood,[b] José P. L. Roque,[a]
[b]
[a]
Robert J. McMahon, and Rui Fausto
[
a]
University of Coimbra, CQC, Department of Chemistry, 3004-535 Coimbra, Portugal
[
b]
Department of Chemistry, University of Wisconsin-Madison, Wisconsin 53706-1322, United States
Abstract: Not long ago, the occurrence of quantum mechanical tunneling (QMT)
chemistry involving atoms heavier than hydrogen was considered unreasonable.
Contributing to the shift of this paradigm, we present here the discovery of a new and
distinct heavy-atom QMT reaction. Triplet syn-2-formyl-3-fluorophenylnitrene, generated
in argon matrices by UV-irradiation of an azide precursor, was found to spontaneously
cyclize to singlet 4-fluoro-2,1-benzisoxazole. Monitoring the transformation by IR
spectroscopy, temperature-independent rate constants (k ~1.4 × 10−3 s  half-life of ~8
min) were measured from 10 to 20 K. Computations estimate rate constants in fair
agreement with experimental values, providing evidence for a mechanism involving heavy-
atom QMT through crossing triplet to singlet potential energy surfaces. Moreover, the
heavy-atom QMT takes place with considerable displacement of the oxygen atom, which
establishes a new limit for the heavier atom involved in a QMT reaction in cryogenic
matrices.
−1
1
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Introduction
The relevance of quantum mechanical tunneling (QMT) to chemistry has been
recognized since the 1930’s, when Bell published his seminal theoretical work
demonstrating the need to consider tunneling in reactions involving the motion of a
[
1]
hydrogen atom or proton. In particular, H-atom QMT is known to play an important role
in many reactions in organic chemistry,[2–4] biochemistry,[5,6] catalysis,[7,8] and interstellar
chemistry.[9,10] The existence of QMT contribution to a chemical reaction is typically
detected indirectly by the observation of nonlinear Arrhenius plots or abnormal kinetic
isotope effects.[2,3] Experimental evidence of QMT has also been obtained using cryogenic
temperatures (e.g., 3−10 K).[11] Under these conditions, thermally activated rates become
−
1
negligible for systems having barriers as low as 1 kcal mol , so that chemical
transformations can only take place by vibrational ground-state QMT. Investigations on
direct observation of QMT in cryogenic conditions have contributed significantly to a better
understanding of the tunneling phenomenon and its role in chemistry.[11] It is now
established that not only can QMT have a profound influence on reaction rates, but it can
also control the selectivity of chemical reactions.[8,12,13]
Because tunneling probability decreases exponentially with the square root of the
moving mass, tunneling of atoms heavier than hydrogen (such as carbon, 12 times heavier)
is predicted to be very unlikely.[14–16] So far only about a dozen examples of direct
experimental observations of heavy-atom QMT reactions in cryogenic conditions have been
reported.[17,18,27–30,19–26] Even fewer cases with clear experimental evidence of heavy-atom
[2]
QMT contribution are known for reactions in solution. The increasing number of recent
reports on experimental and theoretical heavy-atom QMT reactions, however, seems to
suggest that this phenomenon occurs more frequently than had been assumed and can have
significant implications for many chemical reactions.[31–36]
One of the first examples of heavy-atom QMT was described by Buchwalter and
Closs in 1975, regarding the ring-closure of triplet 1,3-cyclopentanediyl 3I to
bicyclopentane II in cryogenic glasses at 1.3 to 20 K (Scheme 1a).[30] Additional evidence
of heavy-atom QMT on the ring-closure of triplet 1,3-diradicals was described later by
3
Dougherty and coworkers for the transformation of triplet 1,3-cyclobutanediyls III to
bicyclobutanes IV in cryogenic matrices at 4 to 20 K (Scheme 1b).[28] Interestingly, in both
2
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cases triplet 1,3-diradicals must undergo intersystem crossing (ISC) to form the singlet
products. However, it is not clear if QMT takes place in the triplet surface, to a geometry
that then undergoes ISC to the singlet surface, or if QMT occurs through crossing surfaces
from triplet to singlet. To the best of our knowledge, the only established case of
heavy-atom QMT through crossing potential energy surfaces was recently reported by Abe,
3
Zeng and coworkers for the rearrangement of triplet nitrene V to isocyanate VI in
cryogenic matrices at 2.8 to 23 K (Scheme 1c).[22]
Scheme 1. Cases of heavy-atom QMT reactions from a triplet ground-state reactant to a
singlet product directly observed at cryogenic temperatures.[22,28,30]
Several H-atom QMT reaction involving a triplet ground-state reactant to a singlet
product are known; mostly H-abstraction in triplet carbenes.[4,37,38] One early example was
reported by McMahon and Chapman, who directly observed the intramolecular [1,4]H-shift
3
from triplet 2-methyl-phenylcarbene VII to singlet o-xylylene VIII in cryogenic matrices
at 4.6 K (Scheme 2a).[39] We discovered in 2016 the first direct evidence of H-atom QMT
in nitrene chemistry, namely the rearrangement of triplet anti-2-formylphenylnitrene
anti- 2′ to singlet imino-ketene 3′ in noble-gas matrices at 10 K (Scheme 2b).[40] It was
3
3
3
proposed that H-atom QMT occurs on the triplet surface from anti- 2′ to 3′, followed by
ISC to the singlet 3′. Indeed, calculations of tunneling probability on the corresponding
triplet surface provided rates in reasonable agreement with the experimental observations.
As far as we know, no clear-cut evidence have been reported for H-atom QMT occurring at
3
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cryogenic temperatures through crossing surfaces from triplet to singlet (instead of H-atom
QMT in a triplet surface succeed by an ISC process).
Scheme 2. Examples of H-atom QMT reactions from a triplet ground-state reactant to a
singlet product directly observed in cryogenic matrices.[39,40]
Following our investigations with arylnitrene 2′, in the current work we demonstrate
that changing the conformation of the aldehyde moiety from anti to syn opens access to a
new heavy-atom QMT reaction (Scheme 3). Arylazide 1, with a fluorine substituent to act
as a hydrogen-bond acceptor for the aldehyde hydrogen atom, was designed as a gateway to
3
3
triplet syn-2-formyl-3-fluorophenynitrene syn- 2. Upon generating syn- 2 in a cryogenic
3
matrix, we discovered that syn- 2 spontaneously cyclizes by heavy-atom QMT to singlet
2
,1-benzisoxazole 4. Non-adiabatic transition state theory (NA-TST) computations, based
on the weak-coupling (WC) formulation, provide evidence for the occurrence of
3
heavy-atom QMT from syn- 2 to 4 through crossing potential energy surfaces (PESs).
Scheme 3. Summary of experimental observations for heavy-atom QMT in the cyclization
3
of triplet syn-2-formyl-3-fluorophenylnitrene syn- 2 to singlet 4-fluoro-2,1-benzisoxazole 4
in an argon matrix at 10 to 20 K.
4
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Results and Discussion
Conformational Analysis. Computations at the CBS-QB3 (complete basis set –
quadratic Becke-3 composite method) level of theory estimate that 2-formylphenylazide 1′
in the gas-phase at room temperature exists essentially in its most stable conformation
aa-1′, with the aldehyde (carbonyl) assuming anti-orientation regarding the azide moiety
(
(
Table 1). Conformer as-1′, with the aldehyde in syn-orientation, is ~2.7 kcal mol1
G298K) higher in energy than aa-1′ and its population is estimated to be no more than
~1%. In agreement with the computed data, the IR spectrum of matrix-isolated 1′ (obtained
from sublimation of 1′ at room temperature) shows only contribution from the aa-1′
conformer (Figure S1 in the Supporting Information (SI)).[40] To obtain a significant
population of the syn-aldehyde conformer in a 2-formylphenylazide derivative, the
stabilization effect of several different substituents acting as a hydrogen-bond acceptor for
the aldehyde hydrogen atom was considered (Table S1). 2-Formyl-3-fluorophenylazide 1
was found to be a promising system. At the CBS-QB3 level of theory, the most stable

1
syn-aldehyde conformer as-1 is only ~0.4 kcal mol higher in energy than the most stable
anti-aldehyde conformer aa-1, and the predicted gas-phase equilibrium population of the
two syn-aldehyde conformers (as-1 and ss-1) is ~45% at room temperature (Table 1).
−
1
Table 1. Relative Gibbs energy at 298.15 K (ΔG298K in kcal mol ) computed at the
B3LYP/6-311+G(2d,p) and CBS-QB3 levels of theory for conformers of 2-formyl-
phenylazide 1′ and 2-formyl-3-fluorophenylazide 1 and their equilibrium populations at
2
98.15 K (Pop298K in %).a
Structure
′, 1
1
R = H , F
Name
aa-1′ | aa-1
0.0 | 0.0
0.0 | 0.0
98 | 55
sa-1′ | sa-1
4.1 | 4.4
3.6 | 3.5
0 | 0
as-1′ | as-1
2.5 | 0.3
2.7 | 0.4
1 | 26
ss-1′ | ss-1
3.4 | 1.3
2.9 | 0.6
1 | 19
ΔG298K (B3LYP)
ΔG298K (CBS-QB3)
Pop298K
a
Equilibrium populations were estimated from Boltzmann distribution based on the ΔG298K value computed at
the CBS-QB3 level of theory. In the names of structures, a stands for anti and s stands for syn, which
corresponds to the orientation of the azide (first letter) and aldehyde (second letter) moieties, relative to one
another.
5
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Matrix-Isolation IR Spectroscopy. 2-Formyl-3-fluorophenylazide 1 was synthesized
using standard procedures as described in detail in the Supporting Information. Monomeric
was isolated in an argon matrix at 15 K by sublimating the sample at room temperature.
1
The IR spectrum of matrix-isolated 1 shows the presence of anti (aa-1) and syn (as-1 and
ss-1) aldehyde conformers in a ratio comparable to the predicted 55:45 ratio (Figures S2
and S3). UV irradiation ( = 320 nm) of 1 led to the formation of several species (Figure
3
3
S4), presumably the corresponding triplet arylnitrenes anti- 2 and syn- 2 and the products
of their chemistry. Irradiation for shorter times and at slightly different wavelengths (e.g.,
2
75 or 308 nm) did not lead to any significant simplification of the photochemistry.
Interestingly, however, we found that one of the photoproducts of 1 spontaneously converts
into another species after the UV-irradiation was stopped and the sample was left in the
dark at 15 K. The IR signatures of these two species were obtained and allowed
identification of the spontaneous cyclization of triplet syn-2-formyl-3-fluorophenylnitrene
3
syn- 2 to singlet 4-fluoro-2,1-benzisoxazole 4 (Figure 1 and Scheme 3).
The experimental IR bands of the consumed and produced species in the reaction
taking place in the dark are well reproduced by the B3LYP/6-311+G(2d,p) computed IR
3
spectra of syn- 2 and 4, respectively (Figure 1). The most characteristic IR bands of triplet
3
1
arylnitrene syn- 2 are observed at 1695, 1517, 1393, 1296, 1035 and ~776 cm ,
corresponding to the vibrational modes computed at 1705 [ν(C=O)], 1519 [ν(CC)ring +
δ(CH)ring], 1394 [δ(OCH)], 1288 [ν(CN)], 1027 [ν(CF) + ν(CC)ring] and 778 [γ(CH)ring
]

1
cm , respectively. Representative IR bands of benzisoxazole 4 are observed at 1666,

1
~
1582, ~1117, 1076, 880 and 786 cm , corresponding to the vibrational modes computed
at 1656 [ν(CC)], 1572 [ν(CC)], 1119 [ν(CO)], 1067 [ν(CF) + δ(Is-ring)], 878 [ν(NO)]

1
3
and 786 [γ(CH)] cm , respectively. Comprehensive assignments of the IR spectra of syn- 2
and 4 are given in Tables S4 and S5.
6
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6
0
0
0
4 : Computed (c)


~




3









2
´
10

~
DarkAr, 15 K (b)


~
1
.2











*
0.0
*














-
1.2
~

3
8
0
0
0

~
syn- 2 : Computed (a)


4












1700
1500
1300
1100
900
700

1
Wavenumber / cm
3
Figure 1. (a) IR spectrum of triplet syn-2-formyl-3-fluorophenylnitrene syn- 2 computed at
the B3LYP/6-311+G(2d,p) level of theory. (b) Experimental difference IR spectrum
showing changes after keeping the sample at 15 K (Ar matrix) in the dark for 40 min,
subsequent to irradiation of 1 at λ = 320 nm (Figure S4). The downward bands are due to
3
consumed species assigned to syn- 2. The upward bands are due to the product assigned to
4
. Asterisk () signals traces of monomeric water. (c) IR spectrum of 4-fluoro-2,1-
benzisoxazole 4 computed at the B3LYP/6-311+G(2d,p) level of theory.
3
Kinetics and Tunneling. The kinetics of spontaneous cyclization of syn- 2 to 4 in an
argon matrix at 15 K were followed by monitoring the intensity changes of the most intense
3
IR bands of syn- 2 to 4 with time (Figure 2). Fitting the experimental data with first-order
3
exponential decay and growth equations, for the consumption of syn- 2 and the production
−
3
−1
of 4, rate constants equal to 1.3 × 10 s were obtained (half-life of 8.7 min). During the
−
1
collection of IR spectra, a cutoff filter above 2200 cm was used to minimize the sample
exposure to the IR spectrometer source light. Possible effects of IR light with frequencies
7
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−
1
below 2200 cm were excluded based on the observation of similar reaction kinetics at the
end of 20 min with a sample held in the complete absence of light (Figure S5). Following
the same procedure, kinetics measurements were also performed for the spontaneous decay
3
−3
−3 −1
of syn- 2 at 10 and 20 K. Rate constants of 1.4 × 10 and 1.5 × 10 s were determined
for the reaction at these temperatures, which correspond to a half-life of ~8 min (Figure
3
S6). Because the cyclization rate of syn- 2 to 4 does not increase upon doubling the
temperature, a thermal over-the-barrier process is ruled out, providing strong evidence for
the occurrence of heavy-atom QMT (Scheme 3).
1.0
0.5
0.0
4
syn-32
0
10
20
30
Time / min
Figure 2. Kinetics of spontaneous rearrangement of triplet syn-2-formyl-3-
3
fluorophenylnitrene syn- 2 to singlet 4-fluoro-2,1-benzisoxazole 4 in an argon matrix at 15
K. Solid () and open () circles represent the time evolution of the amount of syn-32
(consumption) and 4 (production), respectively. The solid and dotted line represent the best
fits obtained using a first-order exponential decay and growth equations, respectively. The
−
3
−1
rate constants obtained were k (15 K) = 1.3 × 10 s (τ1/2 = 8.7 min) for the consumption of
syn- 2 and k′ (15 K) = 1.3 × 10−3 s−1 (τ1/2 = 8.7 min) for the production of 4 (see the
Experimental and Computational Methods section in the SI for more details).
3
Computations. It is interesting to note that the reaction mechanism of heavy-atom
3
3
QMT in the triplet surface, from triplet nitrene syn- 2 to triplet benzisoxazole 4, followed
3
by ISC to the singlet 4, is not feasible because triplet 4 is much higher in energy than
8
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3
−1
3
triplet syn- 2 (> 40 kcal mol ; see Figure 3). Therefore, the cyclization of syn- 2 to 4
should involve heavy-atom QMT through crossing triplet to singlet potential energy
surfaces. Computations at the complete active space self-consistent filed
CASSCF(10,10)/cc-pVDZ level of theory were carried out to search for a minimum-energy
3
crossing point (MECP) between the triplet syn- 2 and singlet 4 surfaces (see Figure 3,
which has been obtained by using just the R(N-O) distance from the intrinsic reaction
coordinate (IRC) data depicted in Figure S7). An MECP was found by starting from a
geometry where the two PESs cross, as a function of R(NO). Its relative energy was
−
1
estimated to be 17.8 kcal mol (ZPE included, which for MECP was calculated using our
own gamread script together with the GLOWfreq code[41]; details are provided in the
−
1
Supporting Information), and the reaction being exothermic by 18.2 kcal mol . To include
dynamical correlation, which is well-known to be critical for reliable kinetics calculations,
single-point energies were subsequently computed at the multireference Møller-Plesset
MRMP(10,10)/cc-pVDZ level of theory. Using this approach, the MECP energy
3
−1
connecting triplet syn- 2 to singlet 4 reduces to 12.1 kcal mol . An identical MECP energy
value was estimated at the density functional theory (DFT) M06-2X/6-311++G(d,p) level
of theory.
60
40
20
0
CASSCF(10,10)/cc-pVDZ
34
MECP
syn-12
syn-32
14
-20
2.7
2.4
2.1
1.8
1.5
R(NO) / Å
Figure 3. IRC path for the cyclization syn-2 → 4 on the singlet (grey) and triplet (black)
surfaces computed at the CASSCF/cc-pVDZ level of theory as a function of the N···O
−
1
3
distance (Å). Energies (kcal mol ) are given relative to the energy of syn- 2. The MECP is
shown in an open circle.
9
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3
Reaction rates for the cyclization of triplet syn- 2 to singlet 4 were computed by
accounting for the different spin multiplicities of the crossing PESs. Two different methods
were employed based on the non-adiabatic-TST time-independent statistical approach:[42–48]
(
i) the Landau-Zener (LZ);[49,50] and (ii) the weak coupling (WC) formulation[51,52] (details
are provided in SI). The calculated LZ rate constants are zero (considering T = 10 or 20 K)
both at the multireference or DFT level. This is expected, since the LZ method neglects
transitions between PESs caused by QMT for energies below the MECP; a thermal over-
the-barrier process at the cryogenic temperatures considered is clearly not accessible. The
calculated WC rate constants are given in Table 2 (see more details in SI and in Table S6).
The WC method accounts for contributions from tunneling below the MECP and from the
classically allowed region above the MECP. Therefore, it is expected to correctly model
heavy-atom QMT through crossing PESs occurring at cryogenic temperatures. The
calculated WC rate constants using the MECP energy computed at the MRMP level of
theory and all additional data taken from the CASSCF computations stay in the range of

1
1
1
6
.9 × 10 s (10 K) to 1.4 s (20 K), which compare fairly well with the experimentally
obtained results and, in particular, demonstrate the achievability of the heavy-atom QMT
mechanism for the investigated chemical transformation. The calculated WC rate constants
using the MECP energy computed at the M06-2X level of theory stay in the range of

2
1
1
.5to3.2 × 10 s , only one order of magnitude higher (faster) than the experimental
results. The WC results unambiguously show that QMT through crossing triplet to singlet
3
PESs is solely responsible for the cyclization of syn- 2 to 4 at cryogenic temperatures.
Table 2. Weak coupling (WC) rate constants calculated for the cyclization of triplet syn-32
to singlet 4.
kc (10 K) / s
6.9 × 101
1.5 × 10 2
1
kc (15 K) / s1
1.1
2.4 × 102
kc (20 K) / s1
1.4
3.2 × 102
Level of theory
MRMP(10,10)/cc-pVDZa

M06-2X/6-311++G(d,p)
aMRMP single point energies on CASSCF(10,10)/cc-pVDZ optimized geometries.
To the best of our knowledge, the WC formulation of non-adiabatic-TST has never
been applied for calculating vibrational ground-state QMT reactions rates, although it has
1
0
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been applied quite successfully to calculate rates of spin-forbidden organic and
organometallic/catalytic reactions.[53–55] In order to further access the robustness and good
performance of the WC method for modeling heavy-atom QMT through crossing PESs at
cryogenic temperatures, rate constants were also calculated for the rearrangement of triplet
3
nitrene V to singlet isocyanate VI reported by Abe and Zeng and coworkers (Scheme
1
c).[22] At the M06-2X/6-311++G(d,p) level of theory, the six calculated rate constants
considering temperatures in the range from 2.8 to 23.0 K) show that reaction occurs only
due to heavy-atom QMT with an impressive agreement with the experimental observations
(

3 1
in cryogenic matrices, essentially sharing the same 10 s order of magnitude (Table S7).
Conclusion
In conclusion, we have presented here the discovery of a new heavy-atom QMT
reaction, which has the distinctive feature of occurring through crossing surfaces from
triplet to singlet. 2-Formy-3-fluorophenylazide 1 was designed to achieve syn-aldehyde
conformational stabilization. The IR spectrum of the room temperature vapor of 1,
quenched in an argon matrix (15 K), confirmed the presence of syn-aldehyde conformers in
a
significant ratio. The conformational tuning opened access to triplet
3
syn-2-formylarylnitrene syn- 2, which was successfully generated in a cryogenic matrix
3
upon UV-irradiation of 1. Triplet nitrene syn- 2 was then found to spontaneously cyclize to
3
singlet 2,1-benzisoxazole 4 in the dark at 15 K. Monitoring the syn- 2 → 4 transformation
−
3 −1
by IR spectroscopy, rate constants of ~1.4 × 10 s (half-life of ~8 min) were measured in
argon matrix at 10, 15 and 20 K, providing clear evidence of heavy-atom QMT. A reaction
mechanism involving heavy-atom QMT on the triplet surface was ruled out since triplet 34
3
is much higher in energy than triplet syn- 2. Computations identified a minimum energy
3
−1
crossing point (MECP) between the triplet syn- 2 and singlet 4 surfaces at ~12 kcal mol ,
an insurmountably large energy requirement for any over-the-barrier process at the
cryogenic temperatures. Non-adiabatic-TST computations, based on the weak-coupling
(WC) formulation, estimate rate constants that display qualitative agreement with
3
experimental measurements, unambiguously demonstrating that cyclization of syn- 2 to 4
at cryogenic temperatures takes place exclusively by heavy-atom QMT through crossing
triplet to singlet PESs.
1
1
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Although carbon-atom QMT is the predominant type of heavy-atom tunneling to be
experimentally observed, oxygen-atom QMT has been hypothesized to contribute to
reactions in atmospheric chemistry and astrochemistry.[56–59] Interestingly, the heavy-atom
3
QMT cyclization of syn- 2 to 4 involves considerable displacement of nitrogen and oxygen
atoms. The direct experimental observation of a heavy-atom QMT reaction with significant
contribution of oxygen-atom displacement represents an important new observation.
Corresponding Author
*
cmnunes@qui.uc.pt (C.M.N); * lpviegas@ci.uc.pt (L.P.V.)
Contributor Roles
C.M.N. conceived the original working hypothesis and performed the matrix isolation
experiments. L.P.V. performed the non-adiabatic-TST computations. S.A.W. performed the
synthetic work. C.M.N., L.P.V. and J.P.L.R. analyzed the data. All authors discussed the
experiments and theoretical results and cowrote the manuscript.
Conflict of Interest
The authors declare no conflict of interest.
Acknowledgements
This work was supported by Project POCI-01-0145-FEDER-028973, funded by FEDER,
via Portugal 2020 - POCI, and by National Funds via the Portuguese Foundation for
Science and Technology (FCT). The Coimbra Chemistry Centre is supported by the FCT
through the projects UIDB/QUI/00313/2020 and UIDP/QUI/00313/2020, co-funded by
COMPETE. C.M.N. acknowledges the FCT for an Auxiliary Researcher grant. L.P.V.
acknowledges the Coimbra Chemistry Centre for the CQC-SER-C2-BPD research grant.
J.P.L.R acknowledges the Project POCI-01-0145-FEDER-028973 for a research grant.
S.A.W. and R.J.M. gratefully acknowledge support from the U.S. National Science
Foundation (CHE-1954270, CHE-1664912).
Keywords: Heavy-atom tunneling, IR spectroscopy, matrix isolation, non-adiabatic
transition state theory, nitrenes
1
2
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