NMR studies of ultrafast intramolecular proton tautomerism in crystalline and amorphous N,N′-diphenyl-6-aminofulvene-1-aldimine: Solid-state, kinetic isotope, and tunneling effects

Article abstract of DOI:10.1021/ja801506n

Using solid-state NMR spectroscopy, we have detected and characterized ultrafast intramolecular proton tautomerism in the N-H-N hydrogen bonds of solid N,N′-diphenyl-6-aminofulvene-1-aldimine (I) on the microsecond-to- picosecond time scale. ¹⁵N cross-polarization magic-angle-spinning NMR experiments using ¹H decoupling performed on polycrystalline I-¹⁵N₂ and the related compound N-phenyl-N′-(1,3,4- triazole)-6-aminofulvene-1-aldimine (II) provided information about the thermodynamics of the tautomeric processes. We found that II forms only a single tautomer but that the gas-phase degeneracy of the two tautomers of I is lifted by solid-state interactions. Rate constants, including H/D kinetic isotope effects (KIEs), on the microsecond-to-picosecond time scale were obtained by measuring and analyzing the longitudinal ¹⁵N and ²H relaxation times of I-¹⁵N₂, I-¹⁵N ₂-d₁₀, and I-¹⁵N₂-d₁ over a wide temperature range. In addition to the microcrystalline modification, a novel amorphous modification of I was found and studied. In this modification, proton transfer is much faster than in the crystalline form. For both modifications, we observed large H/D KIEs that were temperature-dependent at high temperatures and temperature-independent at low temperatures. These findings are interpreted in terms of a simple quasiclassical tunneling model proposed by Bell and modified by Limbach. We obtained evidence that a reorganization energy is necessary in order to compress the N-H-N hydrogen bond and achieve a molecular configuration in which the barrier for H transfer is reduced and tunneling or an over-barrier reaction can occur.

Full text of DOI:10.1021/ja801506n

Published on Web 06/14/2008
NMR Studies of Ultrafast Intramolecular Proton Tautomerism
in Crystalline and Amorphous
N,N′-Diphenyl-6-aminofulvene-1-aldimine: Solid-State, Kinetic
Isotope, and Tunneling Effects
Juan Miguel Lopez del Amo,† Uwe Langer,† Vero´nica Torres,† Gerd Buntkowsky,‡
Hans-Martin Vieth,§ Marta Pe´rez-Torralba,| Dion´ısia Sanz,| Rosa Mar´ıa Claramunt,|
Jose´ Elguero, and Hans-Heinrich Limbach*,†
Institut fu¨r Chemie and Biochemie, Takustrasse 3, Freie UniVersita¨t Berlin, D-14195 Berlin,
Germany, Institut fu¨r Experimentalphysik, Arnimallee 14, Freie UniVersita¨t Berlin, D-14195
Berlin, Germany, Institut fu¨r Physikalische Chemie der Friedrich-Schiller UniVersita¨t,
Helmholtzweg 4, D-07743 Jena, Germany, Departamento de Qu´ımica Orga´nica and
Bio-Orga´nica, Facultad de Ciencias, UniVersidad Nacional de Educacio´n a Distancia, Senda del
Rey 9, E-28040 Madrid, Spain, and Centro de Qu´ımica Orga´nica Manuel Lora-Tamayo, CSIC,
Juan de la CierVa 3, E-28006, Madrid, Spain
Received February 28, 2008; E-mail: limbach@chemie.fu-berlin.de
Abstract: Using solid-state NMR spectroscopy, we have detected and characterized ultrafast intramolecular
proton tautomerism in the N-H-N hydrogen bonds of solid N,N′-diphenyl-6-aminofulvene-1-aldimine (I)
on the microsecond-to-picosecond time scale. 15N cross-polarization magic-angle-spinning NMR experiments
using 1H decoupling performed on polycrystalline I-15N2 and the related compound N-phenyl-N′-(1,3,4-
triazole)-6-aminofulvene-1-aldimine (II) provided information about the thermodynamics of the tautomeric
processes. We found that II forms only a single tautomer but that the gas-phase degeneracy of the two
tautomers of I is lifted by solid-state interactions. Rate constants, including H/D kinetic isotope effects (KIEs),
on the microsecond-to-picosecond time scale were obtained by measuring and analyzing the longitudinal
2
15N and H relaxation times of I-15N2, I-15N2-d10, and I-15N2-d1 over a wide temperature range. In addition
to the microcrystalline modification, a novel amorphous modification of I was found and studied. In this
modification, proton transfer is much faster than in the crystalline form. For both modifications, we observed
large H/D KIEs that were temperature-dependent at high temperatures and temperature-independent at
low temperatures. These findings are interpreted in terms of a simple quasiclassical tunneling model
proposed by Bell and modified by Limbach. We obtained evidence that a reorganization energy is necessary
in order to compress the N-H-N hydrogen bond and achieve a molecular configuration in which the barrier
for H transfer is reduced and tunneling or an over-barrier reaction can occur.
Introduction
However, if the H transfer is preceded by fast motions of major
heavy atoms, such as in hydrogen-bond equilibria4 or confor-
Kinetic isotope effects (KIEs) in hydrogen-transfer reactions
generally depend on temperature, a phenomenon which has been
explained by Bigeleisen1 in terms of a combination of Eyring’s
transition-state theory2 and isotope-fractionation theory. This
temperature dependence arises mainly from a difference in the
zero-point energies of the initial and the transition states. As
Bell has shown,3 tunneling through the reaction barrier enhances
KIEs at high temperatures but can lead to temperature-
independent rate constants and KIEs at low temperatures.
mational changes,5 or constitutes an uphill reaction,6,7 temper-
ature-independent KIEs combined with temperature dependence
of the rate constants can be observed. In this case, a minimum
free energy is required in order for “ground state” tunneling
(3) (a) Bell, R. P. The Proton in Chemistry, 2nd ed.; Chapman and HalI:
London, 1973. (b) Bell, R. P. The Tunnel Effect; Chapman and Hall:
London, 1980.
(4) (a) Gerritzen, D.; Limbach, H.-H. J. Am. Chem. Soc. 1984, 106, 869–
879. (b) Limbach, H. H.; Klein, O.; Lo´pez del Amo, J. M.; Elguero,
J. Z. Phys. Chem. 2004, 217, 17–49.
† Institut fu¨r Chemie and Biochemie, Freie Universita¨t Berlin.
‡ Friedrich-Schiller Universita¨t.
(5) Limbach, H.-H.; Lopez, J. M.; Kohen, A. Philos. Trans. R. Soc. London
2006, B361, 1399–1415.
§ Institut fu¨r Experimentalphysik, Freie Universita¨t Berlin.
| Universidad Nacional de Educacio´n a Distancia.
CSIC.
(6) (a) Braun, J.; Schlabach, M.; Wehrle, B.; Ko¨cher, M.; Vogel, E.;
Limbach, H.-H. J. Am. Chem. Soc. 1994, 116, 6593–6604. (b) Braun,
J.; Limbach, H.-H.; Williams, P. G.; Morimoto, H.; Wemmer, D. J. Am.
Chem. Soc. 1996, 118, 7231–7232.
(1) (a) Bigeleisen, J. J. Chem. Phys. 1949, 17, 675–678. (b) Bigeleisen,
J. J. Chem. Phys. 1955, 23, 2264–2267. (c) Melander, L.; Saunders,
W. H. Reaction Rates of Isotopic Molecules; Krieger: Malabar, FL,
1987.
(2) Glasstone, S.; Laidler, J.; Eyring, H. The Theory of Rate Processes;
McGraw-Hill: New York, 1941.
(7) Limbach, H.-H. In Hydrogen Transfer Reactions; Hynes, J. T.,
Klinman, J., Limbach, H.-H., Schowen, R. L. Eds.; Wiley-VCH:
Weinheim, Germany, 2007; Vols. 1&2, Chapter 6, pp 135-221, and
references cited therein.
9
8620 J. AM. CHEM. SOC. 2008, 130, 8620–8632
10.1021/ja801506n CCC: $40.75
2008 American Chemical Society

Studies of Ultrafast Intramolecular Proton Tautomerism
A R T I C L E S
Figure 1. Tautomerism in (a) I and (c) II and X-ray structures of (b) I31and (d) II.27
arising from the heavy-atom reorganization to occur. This term
corresponds to the “work term” in the Marcus theory of electron
transfer.8 Temperature-independent KIEs have been observed
in recent years for a number of hydrogen tunneling reactions
in enzymes.9–12 Arrhenius curves for such H transfers can be
described in terms of quasiclassical tunneling models such as
the Dogonatze-Kusnetzov-Ulstrup model10,13 or in terms of
a modified Bell model.4,5,7 The description of Arrhenius curves
using first principles is more desirable but also much more
difficult.14–16
In order to further develop the theory of H transfer from
kinetic studies, kinetic data over a wide temperature range are
required; these data are difficult to obtain for liquid solutions,
particularly in the case of enzymes in water. In contrast, kinetic
data can be obtained more easily in the case of model systems
in the solid state. Especially important are degenerate or
quasidegenerate reversible systems, which are preferentially
studied using dynamic NMR spectroscopy. Using this method,
some of us have studied model systems involving double, triple,
and quadruple proton transfers,4,5,7,17–19 which are generally
slower and hence more easily studied than single proton
transfers; in addition, a solid-state single proton transfer has
been monitored.20 Traditionally, dynamic NMR spectroscopy
is well-suited for following reactions on the second-to-
microsecond time scale, but the development of solid-state
longitudinal-relaxationNMRtechniquesunderhigh-resolution19,21–23
and/or field-cycling conditions24,25 has extended this regime to
the microsecond-to-nanosecond time scale.
The aim of this paper is to present the results of a combined
solid-state 1H, 2H, and 15N NMR study in which the H/D KIEs
of an ultrafast H transfer in the N-H-N hydrogen bonds of a
model system have been obtained across very large temperature
and dynamic ranges. The model solid is the H chelate N,N′-
diphenyl-6-aminofulvene-1-aldimine (I) (Figure 1a,b). It has
been well-known for a long time that this molecule exhibits a
degenerate proton tautomerism both in the gas phase and in
solution; however, this process could not be followed using any
(17) (a) Aguilar-Parrilla, F.; Scherer, G.; Limbach, H.-H.; Foces-Foces,
M. C.; Cano, F. H.; Smith, J. A. S.; Toiron, C.; Elguero, J. J. Am.
Chem. Soc. 1992, 114, 9657–9659. (b) Aguilar-Parrilla, F.; Limbach,
H.-H.; Foces-Foces, C.; Cano, F. H.; Jagerovic, N.; Elguero, J. J. Org.
Chem. 1995, 60, 1965–1970. (c) Aguilar-Parrilla, F.; Klein, O.;
Elguero, J.; Limbach, H.-H. Ber. Bunsenges. Phys. Chem. 1997, 101,
889–901. (d) Klein, O.; Bonvehi, M. M.; Aguilar-Parrilla, F.; Elguero,
J.; Limbach, H.-H. Isr. J. Chem. 1999, 34, 291–299.
(8) Marcus, R. A. J. Chem. Phys. 1966, 45, 4493–4499.
(9) Knapp, M. J.; Rickert, K.; Klinman, J. P. J. Am. Chem. Soc. 2002,
124, 3865–3874.
(18) Klein, O.; Aguilar-Parrilla, F.; Lopez, J. M.; Jagerovic, N.; Elguero,
J.; Limbach, H.-H. J. Am. Chem. Soc. 2004, 126, 11718–11732.
(19) Lopez, J. M.; Ma¨nnle, F.; Wawer, I.; Buntkowsky, G.; Limbach, H.-
H. Phys. Chem. Chem. Phys. 2007, 9, 4498–4513.
(10) Kohen, A.; Cannio, R.; Bartolucci, S.; Klinman, J. P. Nature 1999,
399, 496–499.
(11) Kohen, A. In Isotope Effects in Chemistry and Biology; Kohen, A.,
Limbach, H.-H. Eds.; Taylor & Francis: Boca Raton, FL, 2006;
Chapter 28, pp 743-765.
(20) (a) Braun, J.; Hasenfratz, C.; Schwesinger, R.; Limbach, H.-H. Angew.
Chem. 1994, 106, 2302–2304. (b) Braun, J.; Hasenfratz, C.; Schwesing-
er, R.; Limbach, H.-H. Angew. Chem., Int. Ed. Engl. 1994, 33, 2215–
2217. (c) Braun, J.; Schwesinger, R.; Williams, P. G.; Morimoto, H.;
Wemmer, D. E.; Limbach, H.-H. J. Am. Chem. Soc. 1996, 118, 11101–
11110.
(12) (a) Basran, J.; Patel, S.; Sutcliffe, M. J.; Scrutton, N. S. J. Biol. Chem.
2001, 276, 6234–6242. (b) Basran, J.; Masgrau, L.; Sutcliffe, M. J.;
Scrutton, N. S. In Isotope Effects in Chemistry and Biology; Kohen,
A., Limbach, H.-H. Eds.; Taylor & Francis: Boca Raton, FL, 2006;
Chapter 25, pp 671-690.
(21) Hoelger, C. G.; Wehrle, B.; Benedict, H.; Limbach, H.-H. J. Phys.
Chem. 1994, 98, 843–851.
(13) (a) Kuznetsov, A. M.; Ulstrup, J. Can. J. Chem. 1999, 77, 1085–
1096. (b) Kuznetsov, A. M.; Ulstrup, J. In Isotope Effects in Chemistry
and Biology; Kohen, A., Limbach, H.-H. Eds.; Taylor & Francis: Boca
Raton, FL, 2006; Chapter 26, pp 691-724.
(22) Langer, U.; Latanowicz, L.; Hoelger, C.; Buntkowsky, G.; Vieth,
H. M.; Limbach, H.-H. Phys. Chem. Chem. Phys. 2001, 3, 1446–
1458.
(23) (a) Limbach, H.-H. In NMR Basic Principles and Progress; Springer-
Verlag: Heidelberg, Germany, 1991; Vol. 23, pp 66-167. (b) Limbach,
H.-H. In AdVances in NMR; Grant, D. M., Harris, R. K. Eds.;
Encyclopedia of Nuclear Magnetic Resonance, Vol. 9; Wiley: Chich-
ester, U.K., 2002; pp 520-531.
(14) Truhlar, D. In Isotope Effects in Chemistry and Biology; Kohen, A.,
Limbach, H.-H. Eds.; Taylor & Francis: Boca Raton, FL, 2006;
Chapter 22, pp. 579-620.
(15) Smedarchina, Z.; Siebrand, W.; Ferna´ndez-Ramos, A. In Isotope Effects
in Chemistry and Biology; Kohen, A., Limbach, H.-H. Eds.; Taylor
& Francis: Boca Raton, FL, 2006; Chapter 20, pp 521-548.
(16) Brackhagen, O.; Scheurer, C.; Meyer, R.; Limbach, H.-H. Ber.
Bunsenges. Phys. Chem. 1998, 102, 303–316.
(24) Xue, Q. A.; Horsewill, A. J.; Johnson, M. R.; Trommsdorff, H. P.
J. Chem. Phys. 2004, 120, 11107–11119.
(25) Brougham, D. F.; Caciuffo, R.; Horsewill, A. J. Nature 1999, 397,
241–243.
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J. AM. CHEM. SOC. VOL. 130, NO. 27, 2008 8621

A R T I C L E S
Lopez del Amo et al.
Table 1. Isotopically Labeled Samples of Crystalline and
Amorphous I and the Measurements in Which They Were Used
sample
crystallinity (%)
NMR method used
I -15N2-c
100
100
100
20
<10
<10
variable-temperature 15N NMR and 15N T1
variable-temperature 2H T1 and 1H T1
variable-temperature 2H T1
I-15N2-d10-c
I-15N2-d1-c
I-15N2-d10-a*
I-15N2-d10-a
I-15N2-d1-a
variable-temperature 15N NMR
variable-temperature 2H T1
variable-temperature 2H T1
Figure 2. Isotopologues of I used in this study.
kinetic method.26 The geometries of the hydrogen bonds of I
and the asymmetrically substituted analog N-phenyl-N′-(1,3,4-
triazole)-6-aminofulvene-1-aldimine (II) (Figure 1c,d) in solu-
tion as well as those of other derivatives have been characterized
by the observation and interpretation of the scalar 15N-H,
H-15N, and 15N-15N couplings across the 15N-H-15N
hydrogen bonds of the 15N-labeled compounds.27–29 The latter
couplings in 6-aminofulvene-1-aldimines have been also ob-
tained recently using solid-state NMR.30 To our knowledge,
NMR studies of the solid-state tautomerism of I have not been
performed to date. Here we show that the proton tautomerism
is also present in the solid state, although the gas-phase
degeneracy is lifted by intermolecular interactions. Using various
relaxation techniques, we determined the H/D KIEs for I over
a very wide temperature range, in which the KIE was observed
to switch from a temperature-dependent to a temperature-
independent regime. In addition to the known crystalline form31
of I, we also observed an amorphous form whose H-transfer
characteristics differ substantially from those of the crystalline
form. Whereas we observed a fast, quasidegenerate H transfer
in I, no dynamics could be detected for II.
crystalline and amorphous forms of I will be detailed. Following
that, the collected kinetic data obtained for the H and D transfers
willbeplottedinArrheniusdiagramsfittedusingtheBell-Limbach
model, and finally, the results of the work will be discussed.
Experimental Section
Sample Preparation. I-15N2 and I-15N2-d10 were prepared using
15N-labeled aniline enriched to 95% with 15N and 15N-labeled
aniline-d5, respectively, as described previously.27 These compounds
were synthesized as described previously,32 using NH415NO3 as
an 15N source. Because of the small amounts of isotopically labeled
I resulting from this synthesis, no further purification was per-
formed, although the liquid 1H NMR spectrum as well as the low-
temperature solid-state 15N NMR spectra showed a small impurity.
Deuteration of I at the mobile proton site was achieved by
dissolving the sample three times in methanol-d1 (Sigma-Aldrich)
and evaporating the solvent under vacuum.
The amorphous form of I was obtained by dissolving a sample
in the minimum possible amount of warm methanol (or methanol-
d1 for I-15N2-d1) and then immediately decreasing the temperature
to -20 °C. After only a few minutes, almost all of the compound
was precipitated. The sample obtained by this procedure had
spectroscopic properties in agreement with an amorphous structure,
as discussed below.
The different samples investigated in this study are characterized
in Table 1. Polycrystalline samples are labeled with “c” and
amorphous samples with “a”. Samples were considered to be
amorphous when the microcrystalline content was less than 10%.
The index “a*” refers to a sample with a crystalline content of
20%. The different grades of crystallinity were calculated on the
basis of 15N NMR line-shape analysis, as discussed below.
NMR Spectroscopy. The 15N CPMAS spectra were recorded
at 9.12 and 30.12 MHz using Bruker CXP 100 and MSL 300 NMR
spectrometers equipped with standard 7 mm and 5 mm Doty
probeheads. We used a normal cross-polarization sequence (which
minimizes ringing artifacts33) with cross polarization times of 3 to
8 ms, 1H 90° pulse widths of 6-10 µs, and recycle delays of 3-10
s. For measurements of the 15N longitudinal relaxation times (T1)
in connection with the CP scheme, a pulse sequence described by
Torchia34 was employed. As a result of phase cycling of the first
proton 90° pulse and the receiver phase, the accumulated magne-
tizations in this experiment cancel at longer mixing times; this
contrasts with the most frequently applied inversion-recovery pulse
sequence, where the equilibrium magnetization approaches maxi-
mum intensity. Between 500 and 2500 scans were accumulated on
average, with a contact time for cross-polarization of 1.5-5.0 ms
and a repetition time of 1-3 s. Low-temperature measurements
were carried out by passing nitrogen gas through a home-built heat
exchanger35 immersed in liquid nitrogen, which allowed temper-
atures as low as 90 K to be achieved while maintaining spinning
speeds between 2 and 2.5 kHz, which are large enough to produce
In particular, we proceeded as follows. Doubly 15N-labeled
I was synthesized, and its high-resolution solid-state 15N NMR
spectra with cross-polarization (CP), 1H decoupling, and magic-
angle spinning (MAS) were obtained. These spectra gave
information about the thermodynamics of the quasidegenerate
H transfer. The measurement of the longitudinal 15N T1
relaxation times provided initial information about the kinetics.
However, as MAS is difficult at low temperatures, we followed
2
the H transfer using H T1 relaxation time measurements of
I-15N2-d10 deuterated on the phenyl rings, as we found that these
deuterons are subject to dipolar relaxation caused by the mobile
proton. 1H T1 relaxation time measurements of I-15N2-d10 were
less informative. The kinetics of the D transfer was followed
by measuring the longitudinal 2H relaxation times of I-15N2-d1
deuterated at the mobile proton site. All three isotopologues of
I are depicted in Figure 2.
This paper is organized as follows. After the Experimental
Section, the thermodynamic and kinetic results observed for the
(26) Mueller-Westerhoff, U. J. Am. Chem. Soc. 1970, 92, 4849.
(27) (a) Claramunt, R. M.; Sanz, D.; Alarco´n, S. H.; Pe´rez-Torralba, M.;
Elguero, J.; Foces-Foces, C.; Pietrzak, M.; Langer, U.; Limbach, H.-
H. Angew. Chem. 2001, 113, 434–437. (b) Claramunt, R. M.; Sanz,
D.; Alarco´n, S. H.; Pe´rez-Torralba, M.; Elguero, J.; Foces-Foces, C.;
Pietrzak, M.; Langer, U.; Limbach, H.-H. Angew. Chem., Int. Ed. 2001,
40, 420–423.
(28) Pietrzak, M.; Limbach, H.-H.; Perez-Torralba, M.; Sanz, D.; Claramunt,
R. M.; Elguero, J. Magn. Reson. Chem. 2001, 39, S100–S108.
(29) Sanz, D.; Pe´rez-Torralba, M.; Alarco´n, S. H.; Claramunt, R. M.; Foces-
Foces, C.; Elguero, J. J. Org. Chem. 2002, 67, 1462–1471.
(30) (a) Brown, S. P.; Perez-Torralba, M.; Sanz, D.; Claramunt, R. M.;
Emsley, L. Chem. Commun. 2002, 1852–1853. (b) Brown, S. P.; Perez-
Torralba, M.; Sanz, D.; Claramunt, R. M.; Emsley, L. J. Am. Chem.
Soc. 2002, 124, 1152–1153.
(32) Otting, H.; Rumpel, L.; Meschede, G.; Scherer, G.; Limbach, H.-H.
Ber. Bunsenges. Phys. Chem. 1986, 90, 1122–1129.
(33) Murphy, P. D. B. J. Magn. Reson. 1986, 70, 307–312.
(34) Torchia, D. J. Magn. Reson. 1978, 30, 613–616.
(35) Kendrick, R. D.; Friedrich, S.; Wehrle, B.; Limbach, H.-H.; Yannoni,
C. S. J. Magn. Reson. 1985, 65, 159–161.
(31) Ammon, H. L.; Mu¨ller-Westerhoff, U. Tetrahedron 1974, 30, 1437–
1443.
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Studies of Ultrafast Intramolecular Proton Tautomerism
A R T I C L E S
Figure 3. Variable-temperature 30.41 MHz 15N CPMAS NMR spectra of polycrystalline (a) I-15N2-c and (b) II-15N5-c.
spectra that are essentially free of rotational sidebands. Chemical
shifts were referenced to external solid 15NH4Cl.
Measurements of the H T1 relaxation times of the deuterated
states was removed as a result of intermolecular interactions in
the solid. The small broad line at 118 ppm observed below 220
K, which was also seen in the H liquid NMR spectrum (not
2
1
samples were performed on a home-built 7 T spectrometer operating
at a Larmor frequency of 46.03 MHz and equipped with a home-
built low-temperature 2H probe. The measurements employed a
saturation-recovery pulse sequence followed by a solid-echo
sequence and recording of the echo. The saturation part involved
a string of 90° pulses (3.6 µs) with nonequal spacing to avoid
formation of undesired echoes. The two 90° pulses of the solid-
echo sequence were spaced by 35 µs. Finally, the echo was Fourier
transformed, allowing the evaluation of T1 for individual lines in
the spectrum.
shown), were assigned to an impurity. All of the chemical shifts
and line separations are summarized in Table S1 in the
Supporting Information.
In contrast, the corresponding spectra of polycrystalline II-
15N5-c (shown in Figure 3b) did not show any dependence on
temperature. The signal assignment proposed is straightforward
and based on liquid-state NMR studies.27
The averaged 15N chemical shifts of I-15N2-c are given by36,37
K12
K12
1
Results
δA )
∆A +
∆B, δB )
∆A +
1 + K12
1 + K12
1 + K12
Variable-Temperature 15N CPMAS Spectroscopy and
Thermodynamics of I. Variable-temperature 15N CPMAS spec-
tra of polycrystalline I-15N2 are shown in Figure 3a. At room
temperature, two lines (at 184 and 167 ppm) were observed,
indicating that the two nitrogen atoms are nonequivalent. When
the temperature was decreased to 126 K, the splitting between
the two lines (now at 207 ppm and 141 ppm) increased. No
coalescence was found anywhere in the temperature range. This
result can be explained by the presence of a slightly asymmetric
double-wellpotentialforprotonmotion,asproposedpreviously.22,36–38
This means that the gas-phase degeneracy of the two tautomeric
1
∆
(1)
B
1 + K12
where K12 represents the equilibrium constant for the proton
tautomerism and δi and ∆i the averaged and intrinsic chemical
shifts of nucleus i. It follows from eq 1 that
1⁄2(δA + δB) ) 1⁄2(∆A + ∆B)
(2)
and that
1 - K12
AB1 + K12
δAB ) ∆
(3)
(36) Limbach, H.-H.; Hennig, J.; Kendrick, R.; Yannoni, C. S. J. Am. Chem.
Soc. 1984, 106, 4059–4060.
where δAB ) δB - δA and ∆AB ) ∆B - ∆A are the averaged
and intrinsic splittings, respectively. The equilibrium constant
can be calculated from eq 3 and the averaged splitting δAB if
(37) Wehrle, B.; Zimmermann, H.; Limbach, H.-H. J. Am. Chem. Soc. 1988,
110, 7014–7024.
(38) Wehrle, B.; Limbach, H.-H. Chem. Phys. 1989, 136, 223–247.
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J. AM. CHEM. SOC. VOL. 130, NO. 27, 2008 8623

A R T I C L E S
Lopez del Amo et al.
Figure 4. (a) Splitting of the two 15N signals of polycrystalline I-15N2-c
as a function of temperature and (b) the corresponding van’t Hoff plot.
the intrinsic splitting ∆AB is known. Since δAB continued to
increase at low temperatures, ∆AB could not be obtained directly.
Therefore, we assumed that the value of ∆A was similar to the
value of 105 ppm found for the imino nitrogen of II-15N5-c.
Using the experimental value of 174 ppm for 1/2(δA + δB), we
then obtained from eq 2 a ∆B value of 245 ppm, i.e., an intrinsic
splitting ∆AB of 140 ppm. In this way, we obtained the
equilibrium constant values listed in Table S2 in the Supporting
Information. They followed the van’t Hoff equation given by
eq 4:
Figure 5. (a) 15N spectra of a I-15N2-a sample measured at room
temperature. Lines A and B correspond to the crystalline phase and broad
lines A* and B* to the amorphous component. (b-d) 15N-{1H} CPMAS
spectra of the same sample at various temperatures, measured 2 months
after the spectrum in (a).
5b-d. At this point, line-shape analysis gave a crystalline
fraction of 20%, indicating a slow rearrangement of the
amorphous form to the more stable crystalline form. The low-
temperature spectra showed that the splitting between the broad
lines of the amorphous form increased in a manner similar to
that of the polycrystalline form.
These results indicate that the hydrogen-bond asymmetry of
the amorphous phase of I consists of a distribution of values
that are on average equal to those observed in the microcrys-
talline sample. Thus, the average reaction enthalpy and entropy
of the amorphous form are similar to those of the polycrystalline
form.
k12
x
∆S12 ∆H12
K12
)
)
2 ) exp(0.3 - 165/T) ) exp
-
(
)
k21 x1
R
RT
(4)
where k12 and k21 represent the forward and reverse rate
constants, respectively, and x1 and x2 the mole fractions of the
two tautomers. This equation yields a reaction enthalpy (∆H12)
of 1.4 ( 0.1 kJ mol-1 and a reaction entropy (∆S12) of 2.49 (
0.05 J mol-1 K-1. The experimental and calculated temperature-
dependent chemical-shift splittings are depicted in Figure 4a
and the van’t Hoff plot in Figure 4b.
15N Longitudinal Relaxation Times of I-15N2-c. The fast
proton tautomerism observed in solid I modulates the 15N-H
dipolar interaction, so in principle, the rate of proton transfer
in I can be obtained by measuring the temperature dependence
of the 15N T1 relaxation time, as shown previously.21 Figure 6
shows a plot of T1 (obtained at 9.12 MHz using a 2.1 T
spectrometer) as a function of reciprocal temperature. The data
are also listed in Table S3 in the Supporting Information. In
contrast to the case for other systems,21,39 the expected minimum
in T1 could not be reached at low temperatures because the H
transfer is very fast. From the slope of the left portion of the
predicted T1 curve, a high-temperature activation energy of only
9 kJ mol-1 was obtained. In this situation, it was not easy to
accurately determine the associated rate constants, as some
The room-temperature 15N CPMAS NMR spectrum of a
sample of amorphous I-15N2-a is shown in Figure 5a. Lines A*
and B* stem from the amorphous form and lines A and B from
a small amount of the polycrystalline form. Within the margin
of error, the positions of A* and B* coincide with those of A
and B, respectively. In contrast, the line widths were much larger
for the amorphous lines. Line-shape analysis was performed
assuming Lorentzian lines, as depicted in Figure 5; the parameter
values employed are assembled in Table S2 in the Supporting
Information. The line broadening can be attributed to a
distribution of local environments in the amorphous solid, giving
rise to a distribution of equilibrium constants in a manner similar
to that found previously for related systems.37
We estimated a crystallinity of 8% for the sample in Figure
5a. However, we noted that the crystalline fraction of the sample
increased with time. After the sample was left for 2 months at
room temperature, we obtained the spectra shown in Figure
(39) Langer, U.; Hoelger, C.; Wehrle, B.; Latanowicz, L.; Vogel, E.;
Limbach, H.-H. J. Phys. Org. Chem. 2000, 13, 23–34.
9
8624 J. AM. CHEM. SOC. VOL. 130, NO. 27, 2008

Studies of Ultrafast Intramolecular Proton Tautomerism
A R T I C L E S
Figure 7. Molecular geometry of I in the vicinity of the hydrogen bond
according to the X-ray crystallographic structure.31
The values of the parameters in eq 5 were evaluated as
follows. Parameters with fixed values included the Larmor
1
frequencies ωI ) 2π × (90.02 MHz) for H and ωS ) 2π ×
(9.082 MHz) for 15N as well as the corresponding gyromagnetic
ratios. The equilibrium constants K12 were calculated for each
temperature using eq 4. The distances in eq 7 correspond to
the short and long distances rNH and rN· · · H illustrated in Figure
6a, which were assumed to be the same in both tautomers. The
jump angle, R, should not be confused with the traditional
N-H-N hydrogen bond angle. Pietrzak et al.28 have proposed
the values rNH ) 1.06 Å and rN · · · H ) 1.74 Å along with a
N-H-N angle of 170° for I; these were derived from the
crystallographic distance rNN ) 2.79 Å31 and from hydrogen-
bond correlations. From these data, the value R ) 5° was
obtained for the jump angle using trigonometric relations.21,39
These parameters led to an RSI value of 0.4 Å-6, which was
kept constant over the whole temperature range.
Figure 6. (a) Change of the hydrogen-bond geometry associated with the
tautomerism of I; R is the jump angle of the dipolar 1H-15N interaction.
(b) 15N longitudinal relaxation times of polycrystalline I-15N2 measured at
2.1 T (9.12 MHz) as a function of reciprocal temperature. The dashed line
was calculated using a simple Arrhenius law (eq 8), while the solid line
was calculated using the rate constants for H tautomerism in crystalline
I-15N2-d10-c obtained using the Bell-Limbach model (see the corresponding
solid line in Figure 13).
In order to calculate the dashed line in Figure 6 using eqs 5
and 6, an Arrhenius law was assumed:
assumptions had to be made. The dashed line in Figure 6 was
calculated as described below.
The master equation for the spin-lattice relaxation rates of
nuclei S caused by fluctuations of the heteronuclear dipolar
interaction with a spin I exchanging between two sites 1 and 2
has been derived previously.24 For solids, this equation depends
on the molecular orientation with respect to the external
magnetic field. However, under MAS conditions in the presence
of a two-state tautomeric equilibrium between two forms 1 and
2, the T1 values are given to a very good approximation by the
isotropic average. For H transfer from and to 15N, the relaxation
rate of the latter can then be expressed as21
k12 ) A exp(-Ea12/RT)
(8)
where Ea12 represents the activation energy of the forward
reaction and A is an effective pre-exponential factor. These
parameters were adjusted to fit the experimental data in Figure
6b to eq 8; we obtained the values Ea12 ) 9 ( 1 kJ mol-1 and
A ) 5 × 1012 s-1. The expected T1 minimum was predicted to
occur at a temperature of 85 K. Unfortunately, our MAS
equipment did not allow us to perform long-time measurements
at this temperature.
In a later stage of our studies, we obtained the solid line in
Figure 6 using the rate constants for H transfer in crystalline
I-15N2-d10 calculated using the Bell-Limbach tunneling model
(described in the Discussion). In fact, a very large flat minimum
is predicted by these data; unfortunately, we could not verify
this because of our experimental limitations.
2
µ0
4K12
SI(1 + K12)2
1
1
30
2
)
γ γ 2p2
I(I + 1)R
×
(4π)
S
I
SI
T
1S
τc
3τc
6τc
+
+
(5)
1 + ωS τc2 1 + (ωI + ωS)2τc2
2
2
2
[
]
1 + (ωI - ωS) τc
2H NMR Spectroscopy and Longitudinal Relaxation of
Static Samples of Ring-Deuterated Polycrystalline and
Amorphous I-15N2-d10. As 2H NMR experiments on static
powdered samples can be performed at cryogenic temperatures,
we wondered whether it would be possible to obtain information
about the H transfer rates in I using this method. This was indeed
the case, as described in this section.
The X-ray structure of I indicates that the distances between
the mobile proton and the nearest aromatic protons are on the
order of only 2.5 Å, as indicated in Figure 7. Therefore, we
anticipated that deuterons at these nearest aromatic sites would
be relaxed by the mobile hydrogen via dipolar interactions,
whereas deuterons at more distant sites should not experience
this kind of relaxation. As it is not possible to deuterate only
the nearest aromatic proton sites, we performed measurements
on the isotopologue in which the aromatic rings are fully
deuterated, assuming that in the case of dipolar relaxation, the
where µ0 is the vacuum permeability, γI and γS are the
gyromagnetic ratios of spins I (hydrogen) and S (nitrogen),
respectively, ωI and ωS are the corresponding Larmor frequen-
cies, and p is Planck’s constant divided by 2π. The inverse of
the correlation time τc for the tautomerism is given by21
1 + K12
K12
1
τc
) k12 + k21
)
k12
(6)
(
)
and the geometric factor RSI resulting from the dipolar interaction
between the two spins is
-3
RSI ) rSI1-6 + rSI2-6 + rSI1
r
-3(1 - 3 cos2 R)
(7)
SI2
where rSI1 and rSI2 represent the distances between spins S and
I in forms 1 and 2, respectively, and R is the jump angle defined
in Figure 6a.
9
J. AM. CHEM. SOC. VOL. 130, NO. 27, 2008 8625

A R T I C L E S
Lopez del Amo et al.
Figure 8. Superimposed experimental and simulated room-temperature 2H
NMR spectra of static samples of I-15N2-d10-c and I-15N2-d10-a measured
at 46.03 MHz (7 T).
Figure 10. Calculated 2H NMR spectra of a powdered sample containing
deuterons exchanging rapidly between two states 1 and 2. The quadrupole
coupling constants qcc(1) and qcc(2) of the two tautomeric states were both
set to a value of 133 kHz. The intrinsic asymmetry factors were set to zero.
The parameters varied were the equilibrium constant for the exchange, K12,
and the jump angle of the deuteron quadrupole coupling tensor, θ. Additional
details about the calculations are provided in the text.
aromatic deuterons.40,41 Such a reduction could arise from small-
angle motions of the phenyl rings or the whole molecule;
however, this question was not studied further.
While the line shapes did not change when the temperature
was decreased, substantial changes in the 2H NMR longitudinal
relaxation times (measured using the saturation-recovery
technique) were observed. Within the margin of error, the
magnetization recovery curves were found to be single
exponentials.
2
The H T1 times obtained for I-15N2-d10-c and I-15N2-d10-a
are included in Table S3 in the Supporting Information and
plotted as a function of reciprocal temperature in Figure 9. A
2H T1 maximum at 250 K was observed for each form, beyond
which the T1 values decreased rapidly with increasing temper-
ature. We attribute this finding to the onset of quadrupole
relaxation caused by ring flips. As the temperature decreased,
the T1 values of the crystalline form decreased, reaching a
minimum of 50 s at 130 K, and then increased again. In contrast,
the values of the amorphous form continued to decrease,
reaching a flat minimum at 50 K.
Figure 9. 2H longitudinal relaxation times T1 for static samples of
crystalline I-15N2-d10-c and amorphous I-15N2-d10-a measured at 7 T, plotted
as functions of reciprocal temperature. The solid lines were calculated as
described in the text.
observed signal should stem entirely from the nearest deuterons.
However, a dipolar relaxation mechanism can be only observed
2
in the absence of quadrupolar H relaxation. We will show
below that in the case of I, such a quadrupolar mechanism is
operative only at high temperatures, as it requires major
molecular motions or ring flips.
In order to analyze the data, we assumed that the relaxation
rate of the quadrupole nucleus S ()2H) is given by a sum of
two terms:
Experimental room-temperature 2H NMR spectra of I-15N2-
d10-c and I-15N2-d10-a (recorded as described in the Experimental
Section, using recycle delays of 10 s) and superimposed
simulated spectra are depicted in Figure 8. From the simulation
of these spectra, quadrupole coupling constant (qcc) values of
171 and 172 kHz and asymmetry factors (η) of 0.08 and 0.07
were obtained for I-15N2-d10-c and I-15N2-d10-a, respectively.
These parameter values indicate that fast phenyl-group flips are
absent; such flips would correspond to 120° jumps in the
quadrupole coupling tensors and lead to typical line-shape
changes as discussed in the next section (see the K12 ) 1, θ )
120° case in Figure 10). The values of qcc are slightly smaller
than the 180-185 kHz values usually observed for immobile
1
T1S
1
TQ1S
1
)
+
(9)
IS
T
1S
where TQ1S represents the quadrupole relaxation mechanism
arising from reorientations of the C6D5 groups (CD reorientation)
IS
2
and T the H dipolar relaxation mechanism caused by the
1S
mobile proton I ()1H) in the hydrogen bond. Since it has been
(40) Gedat, E.; Schreiber, A.; Findenegg, G. H.; Limbach, H.-H.; Bunt-
kowsky, G. J. Phys. Chem. B 2002, 106, 1977–1984.
(41) Parker, W. O., Jr.; Hobley, J.; Malatesta, V. J. Phys. Chem. A 2002,
106, 4028–4031.
9
8626 J. AM. CHEM. SOC. VOL. 130, NO. 27, 2008

Studies of Ultrafast Intramolecular Proton Tautomerism
A R T I C L E S
2
Figure 11. Superimposed experimental and calculated H NMR spectra of static samples of amorphous and crystalline I-15N2-d1 measured at 46.03 MHz
(7 T).
IS
shown21 that the dependence of T on the crystallite orientation
revealed non-Arrhenius behavior that was simulated using the
Bell-Limbach tunneling model, as described in the Discussion.
Finally, the calculated rate constants were reconverted back into
T1 values, yielding the solid lines in the right-hand portion of
Figure 9, which provide excellent fits of the experimental data.
1S
in static powdered samples is small, we assumed that eqs 5–7
2
were also applicable for describing the H relaxation caused
by modulation of the dipolar 1H-2H interaction in the presence
of the proton tautomerism in static samples of I-15N2-d10-c and
I-15N2-d10-a.
2H NMR Spectroscopy and Longitudinal Relaxation of
Crystalline and Amorphous I-15N2-d1. In order to determine H/D
KIEs on the proton tautomerism of I in the crystalline and
As we did not analyze the CD reorientation in more detail,
we expressed the first term in eq 9 using the Arrhenius law
2
amorphous phases, we performed H NMR measurements on
ECD 1
1
1
1
T0
samples deuterated only at the mobile proton sites. In contrast
to the aromatic deuterons, the two-site deuteron tautomerism
)
exp -
-
(10)
TQ1S TQ1S(T0)
(
)
[
]
R
T
2
affects the H NMR line shapes. Spectra calculated using the
giving rise to the solid line on the left-hand side of Figure 9.
We found values of 45 kJ mol-1 and 0.5 s for ECD, the activation
energy for CD reorientation, and T1SQ(298 K), respectively. As
the spectra at room temperature did not indicate fast 180° ring
flips, we assigned this process to a reorientation of the whole
molecule at high temperatures that possibly was coupled to
molecular diffusion processes involving crystal defects. In other
words, the quadrupolar relaxation term dominates only for T >
200 K and can be neglected below this temperature. Moreover,
the values of T1 measured below 200 K were not averaged by
computer program NMR WebLab 4.1.2 written by Spiess et
al.43 are shown in Figure 10. The simulations were performed
using a natural line width W0 given by the expression W0 )
(πT2)-1 ) (0.05sπ)-1 ) 6.37 Hz. It was assumed that both sites
exhibit the same intrinsic axially symmetric quadrupole coupling
tensors: qcc(1) ) qcc(2) ) qcc ) 4qzz/3, where qzz was set to a
value of 100 kHz. Setting K12 ) 0 gave typical Pake doublets,
in which the two maxima are separated by qzz. Increasing K12
to a value of 1 led to line-shape changes that depended on the
value of θ, the jump angle defined at the top of Figure 10. For
θ ) 180°, no changes occurred, but as the angle was decreased,
the two maxima shifted toward each other. For θ ) 90° and
K12 ) 1, qcc was reduced to half the original value, exhibiting
an effective value of zero for the asymmetry factor, η.
Figure 11 displays superimposed experimental and calculated
2H NMR spectra of I-15N2-d1-a and of I-15N2-d1-c obtained at
46.03 MHz. In contrast to the results at lower temperatures,
the signal-to-noise ratio (SNR) of the room temperature
spectrum of I-15N2-d1-a was excellent, as very long measuring
times were possible. However, because the 2H T1 values
decreased as the temperature was decreased, the SNR improved
again. In contrast, the 2H T1 values of I-15N2-d1-c were larger;
moreover, the spectra stemmed from a series of 2H T1 measure-
ments using the saturation-recovery technique, which limited
the total measuring time and hence the SNR.
180° phenyl flips, i.e., they correspond to the relaxation times
IS
1S
T
arising from the modulation of the dipolar interaction
between the mobile H and the nearest aromatic deuterons. This
is plausible because the quadrupole relaxation is not efficient
at low temperatures and spin diffusion among aromatic deu-
terons of static powdered organic solids is poor.42
From an initial data analysis in the neighborhood of the two
T1 minima using eq 5 and assuming simple Arrhenius laws, we
obtained geometrical factors RSI of 0.006 and 0.13 Å-6 for the
crystalline and amorphous samples, respectively. Assuming that
these values would show little dependence on temperature, in
2
the next step we converted the experimental H T1 values into
rate constants k12 using a homemade computer program based
on eqs 4 and 5. The rate constant values obtained in this way
are included in Table S3 in the Supporting Information. These
data were then assembled in an Arrhenius diagram, which
(42) Gan, Z.; Robyr, P.; Ernst, R. R. Chem. Phys. Lett. 1998, 283, 262–
(43) Macho, V.; Brombacher, L.; Spiess, H. W. Appl. Magn. Reson. 2001,
20, 405–432.
268.
9
J. AM. CHEM. SOC. VOL. 130, NO. 27, 2008 8627

A R T I C L E S
Lopez del Amo et al.
solid lines in the right-hand portion of Figure 12, which fit the
experimental data very well.
Discussion
Using 15N solid-state NMR, we have detected fast quaside-
generate tautomerism between two tautomeric states (1 and 2
in Figure 1a) in polycrystalline and amorphous I. In contrast,
no tautomerism was observed for solid II. In the amorphous
form of I, the tautomerism was much faster than in the
crystalline form. The spectra showed that the gas-phase and
solution degeneracy of the tautomerism in I is lifted in the solid
state by intermolecular interactions. From the dependence of
the 15N chemical shifts on temperature, the associated equilib-
rium constants K12 could be obtained. Whereas in the crystalline
form, all of the molecules exhibit the same equilibrium constant
for tautomerism, a distribution of equilibrium constant values
was observed for the amorphous form. Similar environmental
effects on the thermodynamics and kinetics of a solid-state
proton tautomerism have been observed previously for phtha-
locyanine.38 There, the tautomerism was much faster in the ꢀ
form than in the R form. Moreover, a distribution of equilibrium
constant values was observed for an amorphous form.
Figure 12. Longitudinal 2H T1 relaxation times for static samples of
polycrystalline I-15N2-d1-c and amorphous I-15N2-d1-a measured at 46.03
MHz (7 T), plotted as a function of reciprocal temperature. The solid lines
were calculated as described in the text.
Information about the kinetics (including H/D KIEs) of the
ultrafast tautomerism on the microsecond-to-nanosecond time
scale was obtained over a wide temperature range using a
combination of longitudinal 15N and 2H T1 relaxation time
measurements on isotopically labeled I and appropriate data
analyses. In what follows, the results of these measurements
are discussed in detail.
In order to simulate the spectra, the equilibrium constants
were taken from eq 4. The remaining parameter values (qcc
)
120 kHz, η ) 0.2, and θ ) 144°) were optimized and kept
constant for all of the spectra. The agreement between the
simulated and experimental spectra was very satisfactory in the
case of I-15N2-d1-a. For I-15N2-d1-c, the same parameters were
applied, but the fit was less satisfactory. Thus, the poor SNR
did not allow us to elucidate possible changes in qcc, η, or θ in
the crystalline form.
Molecular Geometries in the Crystalline and Amorphous
Phases of I. The crystal structure of I is depicted in Figure 1b.
All of the atoms of the fulvenealdimine skeleton, including the
atoms of the N-H-N hydrogen bond, are located in a single
plane. The N · · ·N distance is rNN ) 2.79 Å.31 The position of
the hydrogen atom cannot be determined by X-ray diffraction,
but on the basis of hydrogen-bond correlations, Pietrzak et al.28
have proposed values of rNH ) 1.06 Å and rN· · · H ) 1.74 Å
along with a N-H-N hydrogen-bond angle of 170°. The phenyl
rings are not located in the molecular plane: the valence-bond
and torsional angles at the amino nitrogen are R1 ) 124.1° and
φ1 ) 7°, while those at the imino nitrogen are R2 ) 121.0° and
φ2 ) 21.6° (Figure 1b). It is obvious that the different geometries
around the two nitrogen atoms, which are fixed by the molecular
environment, contribute to the loss of the gas-phase degeneracy
of the tautomerism of I. A similar phenomenon has been
observed recently for the double proton transfer in bis(arylfor-
mamidine) dimers,19,45 where it was found that having similar
torsional angles at the two nitrogen atoms (φ1 ≈ φ2 ≈ 30°) is
optimal for proton transfer. We note, however, that H transfer
in I is not quenched by the different conformations of the phenyl
rings. Thus, the latter have a smaller effect on the basicity of
the attached nitrogen atoms than chemically different rings, such
as the phenyl and triazole rings in II, which does not exhibit
any sign of tautomerism.
ResultsofT1measurementsperformedusingthesaturation-recovery
technique are given in Table S3 in the Supporting Information
and depicted in Figure 12 as a function of reciprocal temperature.
T1 minima were observed at 220 K for the crystalline form and
120 K for the amorphous form.
To fit these data, we proceeded in a manner similar to that
described above. The master equation for the relaxation of a
deuteron (spin I) in a hydrogen bond can be expressed in the
following form:44
1
T1I
3π2C
10
K12
τc
4τc
1 + 4ωI2τc2
)
+
2
(11)
2
2
(
)
(1 + K12) 1 + ωI τc
The equilibrium constants K12 were taken from eq 4. From an
initial data analysis in the neighborhood of the T1 minimum
using an Arrhenius law for k12, we obtained C values of 2.1 ×
109 and 1.7 × 1010 s-2 for the crystalline and amorphous forms,
respectively. Assuming that these values would show little
dependence on temperature, in the next step we converted the
2
experimental H T1 values into k12 values using a homemade
computer program based on eqs 4 and 11. The rate constants
obtained in this way are included in Table S3 in the Supporting
Information. These data were then assembled in an Arrhenius
diagram. As before, this diagram revealed non-Arrhenius
behavior that was simulated using the Bell-Limbach tunneling
model, as described in the Discussion. Finally, the calculated
rate constants were converted back into T1 values, yielding the
The 15N spectra of the amorphous phase of I shown in Figure
5 indicate a distribution of equilibrium constant values, as
observed previously for amorphous phthalocyanine38 and for a
six-membered N-H-N chelate in polystyrene.37 However, the
average equilibrium constant value is similar to that of the
(44) Medycki, W. R.; Reynhardt, E. C.; Latanowicz, L. Mol. Phys. 1998,
93, 323–328.
(45) Anulewicz, R.; Wawer, I.; Krygowski, T. M.; Ma¨nnle, F.; Limbach,
H.-H. J. Am. Chem. Soc. 1997, 119, 12223–12230.
9
8628 J. AM. CHEM. SOC. VOL. 130, NO. 27, 2008

Studies of Ultrafast Intramolecular Proton Tautomerism
A R T I C L E S
Figure 13. Arrhenius curves for solid-state tautomerism in polycrystalline and amorphous isotopically labeled I. The upper two curves are for the amorphous
form and the lower two curves for the polycrystalline form; in each pair of curves, O and 9 represent data for H and D transfer, respectively. The solid lines
were obtained by fitting the experimental data using the Bell-Limbach tunneling model with the parameter values given in Table 2.
crystalline form, which was also present and whose fraction
slowly increased with time.
KIE. The rate constants and KIEs were even larger for the
amorphous form, where the H and D transfers led to flat minima
at 50 and 120 K, respectively. The observation of these KIEs
does indeed provide evidence that the aforementioned interpre-
Longitudinal Relaxation and H-Transfer Kinetics of I in
the Solid State. In a first attempt, we tried to determine the
inverse correlation times τc-1 ) k12 + k21 and, using the known
values of K12 ) k12/k21, the rate constants k12 for the solid-state
tautomerism of I by measuring 15N T1 values of I-15N2 at 9.12
MHz. At this frequency, these values are governed by modula-
1
tation of a dipolar H-2H relaxation mechanism for the ring-
deuterated phases is correct. Since we could observe the minima,
we were also able to obtain the constants RHD (RSI in eq 5, with
2
S ) H and I ) D) and C (eq 11) from the H T1 values at the
1
tion of the dipolar H-15N interaction induced by the proton
minima. These parameters respectively describe the modulation
of the dipolar coupling tensor of the ring deuterons with the
jumping H and the modulation of the quadrupole coupling tensor
of a jumping D. Assuming these constants to be temperature-
independent, we were able to convert the T1 values into k12
values for H and D transfer (as described above) using the K12
values determined using 15N NMR, which are isotope-
independent.
transfer rather than by the 15N chemical shift anisotropy.21 In
various cases studied previously, where slower proton transfers
were studied, 15N T1 minima were obtained at low temperatures;
these made possible the conversion of 15N T1 values into rate
constant values.19,21,22 In contrast, in the case of I-15N2, the 15
N
T1 values decreased as the temperature was decreased, but a
minimum could not be reached (Figure 6) because the H-transfer
process is too fast.
Not only the values of the rate constants but also the values
of the constants RSI and C were substantially smaller for the
crystalline phases than for the amorphous phases. RSI can be
calculated using eq 7. If it is assumed that the H-D distances
are the same in the two tautomeric forms 1 and 2 (i.e., if rHD1
) rHD2 ≡ rHD), it follows that
Therefore, we probed the H transfer in crystalline and
amorphous I by measuring 2H T1 values of static samples. Only
at high temperatures molecular motions were a source for
2
quadrupole relaxation, leading to similar H T1 values for the
crystalline and amorphous forms that decreased with increasing
temperature (left-hand side of Figure 9), corresponding to an
activation energy of 45 kJ mol-1. However, at lower temper-
atures, the relaxation curves of both phases of I exhibited a
second relaxation mechanism that produced T1 minima. We
attributed these findings to modulation of the dipolar interactions
with ring deuterons located near the mobile H in the N-H-N
hydrogen bond. For comparison, we also measured 2H T1 values
for crystalline and amorphous forms of I that were deuterated
at the hydrogen bond but not at the aromatic rings (Figure 12).
The mobile D was relaxed by a quadrupole relaxation mechanism.
A T1 minimum indicates the presence of a dynamic process
exhibiting an inverse correlation time τc-1 close to the Larmor
frequency of 46 MHz, independent of the operative relaxation
mechanism. For the crystalline form, the minimum caused by
the H transfer was observed at 130 K (Figure 9) and that caused
by the D transfer at 220 K (Figure 12), indicating a large H/D
RHD ) 3rHD-6(1 - cos2 R)
(12)
The factor C can be approximated in a similar way.44 If it is
assumed that the quadrupole coupling tensors qcc are the same
in both tautomeric forms, it follows that
C ) 3qcc2(1 - cos2 θ)
(13)
Thus, the different values of these factors for the crystalline
and the amorphous forms can arise from different values of rHD
and C and/or from different jump angles. In order to obtain
more information about this problem, at least in the case of C,
we performed line-shape analyses of the jumping deuterons
(Figure 11). We observed a quadrupole coupling constant of
qzz ) 3qcc/4 ) 106 kHz for the amorphous forms. In contrast,
we found a smaller coupling constant (90 kHz) for the crystalline
9
J. AM. CHEM. SOC. VOL. 130, NO. 27, 2008 8629

A R T I C L E S
Lopez del Amo et al.
Table 2. Geometric and Kinetic Data and Arrhenius-Curve Simulation Parameters for Solid-State Tautomerism of I and Related Systems
ref
r1 (Å) r2 (Å) q1 (Å) q2 (Å) rNN (Å) kH12,298K (s-1
)
(kH12/kD12)298K Em (kJ mol-1
)
log(A/s-1
)
Ed (kJ mol-1
)
∆m (amu) 2a (Å) ∆ε (kJ mol-1
)
crystalline Ia this work 1.06 1.74 0.34
2.80 2.79
-
9
4
16
-
-
2.1
2.1
10.0
-
12.6
12.6
12.6
-
10.2
5.9
34.3
-
15.1
1
1.5
0
-
3
0.66
0.40
0.87
-
5.2
3.1
6.5
-
amorphous Ib this work 1.08 1.68 0.30
2.76
3.34
-
-
-
-
IIIc
IIIq d
IV
50
50
22
1.03 2.31 0.64
1.33 1.33 0.005 2.66
1.03 1.94 0.45
105
-
2.97 2.97
3 × 109
3.4
12.6
0.17
1.05
a Geometries from ref 28; all other data from this work. b This work; geometries from Figure 14. c Data from refs 7 and 20. d Calculated
transition-state values from refs 7 and 22.
form. This finding indicates that the deuteron in the hydrogen
bond exhibits shorter relaxation times in the amorphous form
than in the crystalline form. This difference must arise from
slightly different H-bond geometries in the two phases. It is
in zero-point energies of the initial and transition states. Another
parameter is the barrier width 2a, which represents the base of
an inverted parabola. Finally, in contrast to the Bell model,
where the tunneling masses of H and D are 1 and 2 amu,
respectively, it is assumed that these masses are given by mH
) 1 + ∆m and mD ) 2 + ∆m, respectively, where ∆m takes
into account small heavy-atom displacements during the tun-
neling process. Effectively, an increase in ∆m decreases the KIE
in the low-temperature regime.
1
then also plausible that the dipolar H-2H relaxation is more
efficient in the amorphous form. It would have been desirable
to obtain further information about the H-bond structures from
these data. However, this would have required extended
theoretical calculations that were beyond the scope of the present
study.
The curve simulation parameters in Table 2 were derived as
follows. We first simulated the Arrhenius curves of the
amorphous form, which gave the better data set. We found that
a common value of A ) 1012.6 s-1 for the pre-exponential factors
of all of the isotopic reactions could well describe all of the
experimental data. Em was determined from the slopes at low
temperatures. Then, Ed and ∆ε were determined from the slopes
of the Arrhenius curves at high temperatures. Finally, ∆m and
2a were adjusted to fit the rate constants and KIEs at low
temperatures. In the case of the crystalline form, the kinetic
data were more scattered and incomplete, especially at low
temperatures. Therefore, as an approximation, we assumed
values of Em and ∆m similar to those in the amorphous form.
In contrast, Em + Ed and ∆ε could be determined from the high-
temperature values; both were significantly larger than in the
amorphous form. This left 2a as the only adjustable parameter
for fitting the non-Arrhenius character of the curves. We had
to use a substantially larger value, which is consistent with a
larger barrier height, Ed.
Simulation of Arrhenius Curves. We finally arrive at the
discussion of the Arrhenius curves for H and D transfers in the
crystalline and amorphous phases of I. The rate constants we
obtained are assembled in the Arrhenius diagram shown in
Figure 13. We observe from this figure that H transfer was
substantially faster in the amorphous form than in the crystalline
form. Also, non-Arrhenius behavior typical of tunneling is
observed. While the KIEs are temperature-dependent at high
temperatures, they are temperature-independent at low temper-
atures for the amorphous form, implying that the Arrhenius
curves should be parallel. The H/D KIE had a value of 4 at 298
K for the amorphous form but seemed to be substantially larger
(9) for the crystalline form. These KIE values are smaller than
the value of 16.5 found for tautomerism of the porphyrin anion20
but similar to the HH/HD KIEs of various double proton
transfers in cyclic dimers of pyrazoles18 and amidines.19
The solid Arrhenius curves were calculated using the Bell
tunneling model3 as modified by Limbach.5,7 This model
provides a first screening of kinetic data for anomalies such as
pre-equilibria, unusual frequency factors, and mismatches of
KIEs at low and high temperatures. Moreover, it provides a
platform for the discussion of different molecular systems and
processes. On the other hand, it does not preclude more in-
depth theoretical analyses that can give definitive answers about
the reaction mechanisms.15
Geometries and Barriers for H Transfer in Intramolecular
N-H-N Hydrogen Bonds. In order to discuss these results in
a wider context, we have included in Table 2 some geometric
and kinetic data for I and related degenerate or near-degenerate
intramolecular N-H-N transfers studied previously, namely,
those in porphyrin anion (III)20 and polycrystalline tetramethyl-
dibenzotetraaza[14]annulene (IV).22
The parameter values used to calculate the solid Arrhenius
curves in Figure 13 are assembled in Table 2. A common pre-
exponential factor of A ) 1012.6 s-1 was used for all of the
processes. Em represents a minimum energy for tunneling to
occur. Its value is isotope-insensitive and determines the slope
of the Arrhenius curve at low temperatures. For a single H
transfer in the absence of pre-equilibria, Em corresponds to a
reorganization energy for compressing the N · · ·N distance. Only
in a compressed configuration can tunneling occur.46 Such a
two-stage process was found for the porphyrin tautomerism by
means of ab initio calculations.47 EHd ≡ Ed represents the intrinsic
barrier for H transfer at the geometry where tunneling becomes
operative. The intrinsic barrier for D transfer is given by EDd )
Ed + ∆ε, where ∆ε is determined primarily by the difference
We also refer to N-H-N hydrogen-bond correlations in
Figure 14a, where the heavy-atom coordinates q2 ) r1 + r2 are
depicted as a function of the proton hydrogen bond coordinates
q1 ) 1/2(r1 - r2). For a linear H bond, q1 represents the distance
of the proton from the H-bond center and q2 the distance
between the heavy atoms. As several papers have shown on
the basis of neutron-diffraction studies, these two coordinates
are correlated.7,48,49 The solid line corresponds to equilibrium
structures as calculated by ab initio methods. The dotted line
includes an empirical correction for quantum zero-point vibra-
tions of the H-bonded proton. We have included data points
for I-IV derived as follows. Data for III were taken from ab
(48) Limbach, H.-H.; Pietrzak, M.; Benedict, H.; Tolstoy, P. M.; Golubev,
N. S.; Denisov, G. S. J. Mol. Struct. 2004, 706, 115–119.
(46) Scherer, G.; Limbach, H.-H. J. Am. Chem. Soc. 1994, 116, 1230–
1239.
(49) Limbach H.-H.; Denisov, G. S.; Golubev, N. S. In Isotope Effects in
Chemistry and Biology; Kohen, A., Limbach, H.-H. Eds.; Taylor &
Francis: Boca Raton, FL, 2006; Chapter 7, pp 193-230.
(47) Maity, D. K.; Bell, R. L.; Truong, T. N. J. Am. Chem. Soc. 2000,
122, 897–906.
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8630 J. AM. CHEM. SOC. VOL. 130, NO. 27, 2008

Studies of Ultrafast Intramolecular Proton Tautomerism
A R T I C L E S
Figure 14. (a) H-bond geometries of various molecular systems containing N-H-N hydrogen bonds. (b) Total barrier heights (Ed + Em) and minimum
energies for tunneling (Em) for the H transfers in the species in (a), as calculated from the Arrhenius curves (see Table 2 and the text).
initio calculations50 and data for IV from the X-ray crystal
structure and dipolar N-D couplings.22,51 The data point for
crystalline I was derived from the crystallographic N · · ·N
distance for a hydrogen-bond angle of 160° derived from ab
initio calculations.27,28 In all cases it was assumed that the
geometric hydrogen-bond correlation is fulfilled. Therefore, all
of the data points are located on the dotted correlation curve.
We have included the ab initio geometry of the porphyrin anion
transition state (IIIq) at q1 ) 0, for which q2 ) 2.66 Å.50 This
value is close to that in the geometry of the strongest symmetric
N-H-N hydrogen bond (2.52 Å) at normal pressures.
The graph of Figure 14a indicates that the minimum-energy
path for a degenerate H transfer in a N-H-N hydrogen bond
must involve an important hydrogen-bond compression, as we
have argued in a number of papers.5,7,23,46,52 Such a compression
does not involve large H/D KIEs and is responsible for the
reorganization energy Em preceding the H transfer, as discussed
above. The compression takes place preferentially along the
correlation line until the system reaches a configuration (at a
given value of q2) where H is transferred from the left to the
right side of the correlation curve, going through the transition
state at q1 ) 0. Here, tunneling and zero-point energy changes
along the minimum-energy path dominate the overall H/D KIEs.
We note that evidence for such a two-stage process has been
found in ab initio calculations of porphyrin.47
The question of whether Em + Ed and Em are related to the
hydrogen-bond geometries of the initial states now arises.
Support for this statement comes from Figure 14b, where the
experimental values of both quantities (solid symbols) are plotted
as a function of q2. Indeed, we found the correlation illustrated
by the dotted line, which was calculated using the expressions
1.5
Ed + Em ) κ(q2 - q2min
)
Em ) 0.22(Ed + Em)
(14)
where q2min ) 2.50 Å and κ ) 58 kJ mol-1 Å-1. It is astonishing
that the reorganization energy Em represents 20% of the total
barrier height Em + Ed. Because of the excellent correlation,
we were tempted to place the experimental values of Em + Ed
and Em for amorphous I (open symbols) on the dotted lines,
from which we estimate that the hydrogen bond in this phase
is somewhat stronger than that in the crystalline form (Table
1), as represented by the open symbols in Figure 14a. Thus, in
comparison with the crystalline form, the smaller barrier and
reorganization energy and the smaller H/D KIEs of the
amorphous form of I are interpreted in terms of a stronger
N-H-N hydrogen bond.
In principle, support for this interpretation could come from
a discussion of the quadrupole coupling constant qzz for the
hydrogen-bonded deuterons. Generally, when a hydrogen bond
is compressed and the deuteron is shifted toward the H-bond
center, the value of qzz decreases. Thus, we observed for IV a
qzz value of 175 kHz,22 whereas the strong H bonds in crystalline
and amorphous I studied here exhibited values of only 95 and
106 kHz, respectively. Thus, the smaller value of qzz for
crystalline I does not support the above interpretation. However,
(50) Vangberg, T.; Ghosh, A. J. Phys. Chem. B 1997, 101, 1496–1497.
(51) Hoelger, C. G.; Limbach, H.-H. J. Phys. Chem. 1994, 98, 11803–
11810.
(52) Benedict, H.; Limbach, H.-H.; Wehlan, M.; Fehlhammer, W. P.;
Golubev, N. S.; Janoschek, R. J. Am. Chem. Soc. 1998, 120, 2939–
2950.
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J. AM. CHEM. SOC. VOL. 130, NO. 27, 2008 8631

A R T I C L E S
Lopez del Amo et al.
general correlations of qzz and asymmetry factors with H-bond
geometries are not presently available, and features other than
the latter could play a role.
are reduced compared with those in crystalline I, although the
H bond might be somewhat stronger in the latter.
Conclusions
Rate constants for the solid-state tautomerism of I, including
H/D KIEs, were followed in this study by NMR relaxometry
on the microsecond-to-picosecond time scale, where the largest
rate constants observed were 1011 s-1. The Arrhenius curves
indicated temperature-dependent isotope effects at high tem-
peratures and temperature-independent ones at low temperatures.
The latter observation is explained by a heavy-atom reorganiza-
tion, namely, a H-bond compression necessary to reach a
configuration in which the barrier height is reduced to such an
extent that tunneling can occur. A smaller heavy-atom reorga-
nization can occur during the H-tunneling process, reducing the
temperature-independent KIEs.
Whereas the tautomerism of porphyrins and the porphyrin
anion, which exhibit large barriers, was almost independent of
the environment,20 we have observed a substantial difference
in that for amorphous and crystalline I, which exhibit quite small
barriers for H transfer in the solid state. This observation can
imply a difficulty for theoretical calculations, as the effects of
different environments must be taken into account when
Arrhenius curves calculated using first principles are to be
compared with experimental ones. Astonishingly, the KIEs
found for I were not much smaller than those found for other
H transfers exhibiting much larger barriers. Furthergoing studies,
e.g., neutron structure determinations and vibrational spectros-
copy experiments as well as theoretical studies, are necessary
in order to obtain more information about the proton tautom-
erism of I.
The discussion of the tunneling parameters ∆m and 2a is more
difficult. These parameters are “soft”, and their physical meaning
is less well-established than those of Em + Ed and Em, which
can easily be established at high and low temperatures from
the slopes of the Arrhenius curves under favorable conditions.
As discussed above, the respective tunneling masses for H and
D are not simply 1 and 2 amu but are increased by an amount
∆m that takes into account heavy-atom motions during the
tunneling process. Clearly, the value of ∆m depends on the
chemical structure. One could speculate that in the case of IV,
which has alternating double and single bonds, ∆m may be
larger than in the aromatic porphyrin anion III. The values of
the barrier widths 2a are on the order expected from the
hydrogen-bond geometries. A direct comparison with crystal
structure data is difficult, as these values refer to the compressed
state in which tunneling can occur and not to the initial states.
Phenyl Group Conformation. Finally, we must discuss the
conformation of the phenyl groups of I. As illustrated in Figure
1, different conformations, in particular, different valence-bond
angles R1 and R2 as well as different torsional angles φ1 and
φ2, lift the degeneracy of the H transfer. In other words, in the
liquid state, the degeneracy of the H transfer requires a
reorganization of the phenyl groups, as discussed recently for
diarylformamidine dimers.19 When the conformations of the
phenyl groups at the amino and imino nitrogens are very
different, only a single tautomeric state can be observed. Thus,
part of the reorganization of the initial states into the compressed
H-bonded state in which tunneling occurs may also involve some
phenyl group reorganization, but it is unlikely that a major
reorganization can be achieved in the solid state with similar
phenyl group conformations at both nitrogen atoms. Neverthe-
less, a different phenyl group reorganization could also con-
tribute to the different kinetic behavior of crystalline and
amorphous I. Thus, it could be the case that the phenyl groups
in the latter exhibit a conformation where both the energy
necessary for H-bond compression and the barrier for H transfer
Acknowledgment. This work was supported by the Deutsche
Forschungsgemeinschaft and the Fonds der Chemischen Industrie,
Frankfurt.
Supporting Information Available: 15N chemical shifts for
I-15N2-c as a function of temperature (Table S1), parameter
values for the line-shape simulations of the spectra shown in
Figure 5 (Table S2), and longitudinal relaxation times and
associated rate constants for H transfer in solid I-15N2 and
partially deuterated isotopologues (Table S3). This material is
available free of charge via the Internet at http://pubs.acs.org.
JA801506N
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8632 J. AM. CHEM. SOC. VOL. 130, NO. 27, 2008