muonium atom (chemical symbol Mu) is composed of a positive muon as
nucleus with a 1s ground-state electron. As an atom it should reside
in the first box of the Periodic Table, because its Bohr radius and
ionization energy are within 0.5% those of H, D and T. Furthermore,
Mu’s mass is only one ninth the mass of H, and its muon nucleus
lives for a mere 2.2 microseconds, so Mu can be regarded as a
super-light and radioactive isotope of hydrogen. Its comparison with
H is ideal for studying kinetic isotope effects.
The first observation of Mu and studies of its chemical reactivity
were in the gas phase (1). These were followed a few years later by
deductions of its reactions in liquids (2) and then of direct
observation of Mu in water and initial studies of its principal
reactions (3). In this presentation we will discuss only reactions
of Mu in solution --- and almost all are with solutes in water. Most
of these data are at room temperature, but those with variable
temperature have produced activation energies and pre-exponential
factors (4). There already exists an enormous wealth of information
on H-atom reactions in water with which to compare these Mu
reactions (5, 6).
Whereas H is not easy to produce in water nor to observe its
reactions directly on a short timescale, Mu can be directly observed
in any solution at any temperature and any pH --- given (!!) a
source of muons and advanced nuclear physics counting techniques. Mu
is observed through its natural radioactivity decay; but this decay
also has unique spin characteristics which allow much more
reactivity information to be obtained. The muon’s formation and
decay processes violate the parity-invariance principle, which
results in the muons being initially spin polarized then decaying
asymmetrically. Various muon spin polarization techniques are based
on these unique characteristics and have been developed to enable
one to determine the chemical association of the muon at its moment
of decay. Additionally, one can evaluate the actual yield and rate
of disappearance of these states. One of the states directly
observable is the free Mu atom. So its rate of disappearance in the
presence of an added solute can be converted to a chemical rate
constant --- in much the same way that pulse radiolysis, coupled
with spectrophotometry or time-dependent ESR, can directly ‘observe’
H, OH and solvated electrons as they react with solutes (5,7).
The primary technique involved in rate constant measurements of Mu
is that of muon spin rotation (MuSR, here). The actual method of
analysis involves a fitting procedure in which one of the variables
is an exponential decay of the Mu component of the overall muon
signal. The decay constant is interpreted as the pseudo first-order
rate constant for all chemical reactions which convert ‘triplet’ Mu
to ‘singlet’ Mu, or from the free atomic state to a diamagnetic
species or to a free radical (8). Given the presence of a reactive
ingredient at a known concentration, this pseudo Ist order rate
constant can be converted to a real second order rate constant (kM).
In the following Tables these values of kM are given for the
reaction of Mu with the specified solute --- in water at room
temperature (293-298K), unless otherwise indicated. A few reactions
have been studied at other temperatures and in other solvents, as
signified in the Tables.
The Tables report the observed kinetic isotope effect (KIE) of Mu
versus H, given as lighter-over-heavier isotope, kM/kH. Several
different types of KIE’s emerge as a result of studies of Mu vs. H.
The following categories have been delineated (9):
(a) Reactions in which KIE is >1: Due to the lighter isotope
diffusing more rapidly than the heavier isotope.
(b) Reactions in which H reacts faster than Mu: Because the reaction
rate is controlled by the activation barrier --- and this is higher
for Mu than H. [This is contrary to the first-inclinations of many
chemists, who are ingrained with the common premise that the lighter
isotope will react faster. But the reactions of Mu and H involved
here are reactions of free atoms, so the potential energies of the
reactants are essentially equal and it is only the relative energies
of the activated complexes that count. So the higher zero-point
energy of the Mu complex gives it a higher activation barrier and
hence a smaller rate constant than its H analogue.]
(c) Sometimes there are two reaction paths available to the two isotopes
in their reactions towards a particular solute. For instance, in
reaction with acetone, Mu and H can either abstract an H to form HMu
or H2 , or they can add across the C=O double bond to form a
muonated or hydrogenated free radical. When the KIE’s for individual paths are of
the opposite sense (>1 for one path and <1 for the other) then the
overall reaction observed can lead to different paths being
preferred by Mu compared to H, resulting in different reaction
products. The KIE determined from the observation of rates of loss
of Mu and H atoms is thus a composite value. In the case of acetone,
Mu evidently adds faster than it abstracts, while H undergoes the
converse, and the overall observed KIE happens to be >1.
(d) Because of their small masses, quantum mechanical effects are
particularly significant for Mu and H, especially Mu. Thus, for
reaction types with narrow activation barriers, quantum tunneling
undoubtedly plays a role and Mu should win handsomely. On the other
hand, as in (b) above, the zero-point energy quantum mechanical
effect should invariably favour H.
Perhaps 95% of the Mu rate constants have been determined by
observing the loss of ‘triplet’ muonium atoms in the presence of a
solute, as noted above, utilizing Mu’s spin rotation/precession
frequency in external transverse magnetic fields (MuSR). This
process ‘observes’ Mu as it reacts. Thus, in the absence of a
notation to the contrary in the following Tables, the kM reported
will have been determined by MuSR. Occasionally, however, kM has
been evaluated by other techniques. These are also based on the spin
polarization of the muon and its characteristic asymmetric decay,
but they follow Mu indirectly and often have to make assumptions
about the reaction mechanism. One of these involves measuring the
forward-to-backward spin distribution in longitudinal magnetic
fields in the presence of various concentrations of solute at
various magnetic fields. We will refer to this as
mSR in the Tables
to follow. Its values can be used to identify those processes which
can be described as purely electron-spin-exchange interactions in
nature. Such longitudinal field studies subdivide the values of kM
obtained by MuSR into spin-exchange and other reaction types (abstraction,
addition, reduction, combination, etc) when the reactant is
paramagnetic. Another technique which has been used is evaluating
the lifetime of Mu from its linewidth (10). And finally, a value of
kM can sometimes be deduced from measurements of the yield of
muonated free radicals when these are reaction products due to the
presence of various concentrations of an unsaturated solute. Both
high transverse field muon spin rotation (called RSR here) and muon
level-crossing-resonance (LCR or ALCR) techniques have been used in
this regard (11).
The following Tables follow the format of the widely acclaimed
Critical Review of Hydrated Electrons, H Atoms and OH Radicals by
Buxton, Greenstock, Helman and Ross (5). These data were preceded by
earlier reviews and together they give full measure to the extent
and value of such compositories. We hope this compilation will prove
useful to all researchers who are interested in hydrogen atom
reactions or kinetic isotope effects.
References to the Introduction and Notes on
Muonium Data Base
(1) Hughes, V.W., Mc Colm, D.W., Ziock, K., Prepost, R. Phys.
Rev. Letters (1960) 5, 63-5; ibid, Phys. Rev. A (1970) 1, 595.
(2) Brewer, J.H., Crowe, K.M., Gygax, F.N., Johnson, R.F.,
Fleming, D.G., Schenck, A., Phys. Rev. A (1974) 9, 495.
(3) a) Percival, P.W., Fisher, H., Camani, M. Gygax, F.N.,
Ruegg, W., Schenck, A., Schilling, H., Graf, H. Chemical Physics
Letters (1976) 39, 333.
b) Percival, P.W., Roduner, E., Fischer, H. Chemical Physics (1978)
(4) Ng, B.W., Jean, Y.C., Ito, Y., Suzuki, T., Brewer, J.H.,
Fleming, D.G., Walker, D.C. J. Phys. Chem. (1981) 85, 454.
(5) a) Buxton, G.V., Greenstock, C.L., Helman, W.P., Ross,
A.B. J. Phys. Chem. Ref. Data (1988) 17, 513.
b) Web site http://www.rcdc.nd.edu/
(6) Lossack, A.M., Roduner, A.M., Bartels, D.M. Phys. Chem.
Chem. Phys. (2001) 3, 2031.
(7) a) Trifunac, A.D., Bartels, D.M., Werst, D.W. in Pulse
Radiolysis, ed. Y. Tabata, CRC Press, Boca Raton, Fl 1991, p.53.
b) Wybrane zagadnienia chemii radiacyjnej. ed. Kroh,J. PWN,
Warszawa, 1986.(in Polish)
c) Radiation Chemistry –Principles and Applications ed.Farhataziz
VCH Publishers, Inc., 1987
(8) Walker, D.C., Muon and Muonium chemistry. Cambridge
University Press 1983.
(9) Walker, D.C. J. Chem. Soc., Faraday Trans. (1998) 94, 1.
(10) Louwrier, P.W.F., Brinkman, G.A. and Roduner, E.
Hyperfine Interact. (1986) 32, 831.
(11) a) Roduner, E. Progr. React. Kinet. (1986) 14, 1.
b) Roduner, E. Chem. Soc. Rev. (1993) 22, 337.
(12) a) Brewer, J.H. Ph.D. Thesis. (1972) Lawrence Berkeley
Lab., Univ. of California. Berkeley Special Raport LBC-950.
b) Brewer, J.H., Crowe, K.M., Johnson, F.F., Schenck, A. and
Williams, R.W. Phys. Rev. Lett. (1971) 27, 297.
c) Brewer, J.H., Crowe, Gygax, F.N., Fleming, D.G. Phys. Rev. A.
(1973) 8, 77.
(13) a) Firsov, V.G. and Byakov, V.M. Zh. Eksp. Teor. Fiz.
(1964) 47, 1074 or (Engl. transl.) Soviet Physics-JETP (1965) 20,
b) Firsov, V.G., ibid (1965) 48, 1179 or (1966) 21, 786.
By Stefan Karolczak and David Walker
(Lodz and Vancouver)
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