Quantum beats in the recombination fluorescence of radical ion pairs caused by the hyperfine coupling in radical anions

Article abstract of DOI:10.1016/S0009-2614(98)00956-7

The ratios of the radiofluorescence decay curves for n-decane solutions of 1,2,3,4-tetraphenylcyclopenta-1,3-diene and its silicon and germanium analogs (siloles and germoles) in high and zero magnetic fields have an oscillating component caused by singlet-triplet evolution of the pair S⁺/A^-, where S⁺ is the solvent hole and A^- is the radical anion of the acceptor (a compound added). It is shown that the beats are due to the hyperfine couplings (hfc) with either the protons of CH₂, SiH₂ and GeH₂ moieties or chlorine atoms in the GeCl₂ and GeClMe moieties of radical anions. The hfc constants in the anions and spin relaxation times of radical ion pairs were obtained by fitting the experimental curves.

Full text of DOI:10.1016/S0009-2614(98)00956-7

9 October 1998
Ž
.
Chemical Physics Letters 295 1998 230–236
Quantum beats in the recombination fluorescence of radical ion
pairs caused by the hyperfine coupling in radical anions
a
a
b
V.A. Bagryansky , V.I. Borovkov , Yu.N. Molin a,), M.P. Egorov ,
b
O.M. Nefedov
a
Institute of Chemical Kinetics and Combustion, Siberian Branch of the Russian Academy of Sciences, Institutskaya Street 3,
630090 NoÕosibirsk, Russian Federation
N.D. Zelinsky Institute of Organic Chemistry, Russian Academy of Sciences, Leninsky Prospekt 47, 117913 Moscow, Russian Federation
b
Received 28 July 1998
Abstract
The ratios of the radiofluorescence decay curves for n-decane solutions of 1,2,3,4-tetraphenylcyclopenta-1,3-diene and its
Ž
.
silicon and germanium analogs siloles and germoles in high and zero magnetic fields have an oscillating component caused
by singlet–triplet evolution of the pair SqrAy, where Sq is the solvent hole and Ay is the radical anion of the acceptor a
Ž
.
Ž
.
compound added . It is shown that the beats are due to the hyperfine couplings hfc with either the protons of CH2, SiH2
and GeH2 moieties or chlorine atoms in the GeCl2 and GeClMe moieties of radical anions. The hfc constants in the anions
and spin relaxation times of radical ion pairs were obtained by fitting the experimental curves. q 1998 Published by Elsevier
Science B.V. All rights reserved.
1. Introduction
of beats are defined by the differences between the
spin resonance frequencies of the partners of radical
ion pair that can be caused by the difference in their
g factors and hyperfine interactions.
The singlet-correlated radical ion pairs are known
to be formed upon radiolysis of liquid hydrocarbons
w x
containing acceptors of electrons and holes 1 . The
The well-resolved oscillations of the recombina-
tion product yields in the external magnetic field
were detected only in the simplest cases where the
beats were caused either by the difference in g
majority of pairs recombine geminately within a
nanosecond time domain. Before recombination, the
pairs undergo quantum oscillations between singlet
w
x
w x
and triplet states 1,2 , resulting in modulation of the
yield of their recombination product in a particular
spin state. In a high magnetic field, the frequencies
factors of radical ions 3 or by hyperfine couplings
Ž
.
w x
hfc with equivalent protons in radical cations 4 .
The beats were recorded by fluorescence, accompa-
nying the recombination of radical ion pairs from the
singlet state.
In the case of D g beats, the oscillating compo-
nent of the fluorescence decay curve is easily re-
)
Corresponding author. E-mail: molin@ns.kinetics.nsc.su
0009-2614r98r$ - see front matter q 1998 Published by Elsevier Science B.V. All rights reserved.
Ž
.
PII: S0009-2614 98 00956-7

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)
V.A. Bagryansky et al.rChemical Physics Letters 295 1998 230–236
231
vealed through dividing a high field curve by a
reference curve obtained in either a zero or weak
magnetic field where the oscillations are absent. This
approach allowed the use of the D g beats to deter-
mine both the rate constants of the capture of solvent
the hfc beats in these systems will have a simple
pattern in both high and zero magnetic fields and the
oscillations in the curve obtained by division of
fluorescence decay kinetics in high field by that in
zero field will be described by a simple expression.
Moreover, compared to radical cations, a high rate of
radical anion generation can be easily achieved due
to a high diffusion mobility of the primary free
electrons. This allows us to detect the well-resolved
beats and to obtain the hfc constants of the short-lived
radical anions of organosilicon and organogerma-
nium compounds 2–5. The rates of spin relaxation in
the radical ion pairs were estimated from the damp-
ing of the beats.
w x
holes by acceptors 5 and the fraction of spin-corre-
lated radical ion pairs in the tracks of fast electrons
w x
6 .
Unlike D g beats, for the hfc beats it is impossible
to obtain a smooth reference curve. In zero or weak
external magnetic fields the hfc results in a compli-
cated pattern of oscillations, which can be analyti-
cally described for the systems with simple hyperfine
w x
structure only 2 . This hampers the separation and
the analysis of the oscillating component in fluores-
cence decay. In the case of hfc beats from radical
cations another problem arises related to the contra-
dictory requirement on the concentration of a posi-
tive charge acceptor. On the one hand, this concen-
tration should be high enough to provide fast forma-
tion of the desired radical cation. On the other hand,
at a high acceptor concentration the oscillations are
destroyed because of spin dephasing due to ion–
molecular charge transfer.
2. Experimental
The fluorescence decay kinetics were measured
by single photon counting on an X-ray nanosecond
w x
fluorometer 9 . The solution was irradiated with
X-ray pulses from a molybdenum target of ca. 2 ns
duration on a base. The X-ray pulse was generated
w x
Ž
.
We were able to overcome these difficulties 7 by
by an electron gun triggered by a signal 60–80 kHz
Ž .
choosing 1,2,3,4-tetraphenylcyclopenta-1,3-diene 1
of an external generator. This signal was also the
start signal for a time-amplitude converter of the
registration system. The stop signal came from a
photomultiplier tube registering the fluorescence of
the irradiated sample. The width of instrument func-
tion of the apparatus was ca. 3 ns. The accuracy of
the zero time moment, which was identified with the
center of the X-ray pulse, was "0.5 ns. The zero
magnetic field was set to within "1 G. All lu-
minophores used had a fluorescence lifetime shorter
than 1 ns. The fluorescence was recorded without
any light filters.
and its silicon- and germanium-containing analogs
Ž . Ž .
— the phenyl derivatives of silole 2 , germole 3 ,
Ž .
Ž .
dichlorogermole 4 and chloromethylgermole 5 —
as electron acceptors for detection of the hfc beats.
w
x
w x
Tetraphenylcyclopentadiene 1 10 , silole 2 11 ,
w
x
w x
germole 3 12 and dichlorogermole 4 13 were
synthesized according to the published methods.
Chloromethylgermole 5 was obtained by the reaction
of the dilithium salt of 1,2,3,4-tetraphenylbutadiene
w
x Ž
with MeGeCl3 as described in Ref. 13 yield 45%,
.
m.p. 1388C . The solvent n-decane was treated with
In the radical anion of parent compound 1, the hfc
constant with the two equivalent protons of the CH2
group is 25.3 G whereas the couplings with other
KMnO4, shaken with concentrated H2 SO4, washed
with water and dried over Al2O3.
The samples of 10y3 M acceptors solution in
n-decane were degassed by repeated freeze–pump–
w x
protons are small 8 . Therefore one can expect that

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)
232
V.A. Bagryansky et al.rChemical Physics Letters 295 1998 230–236
thaw cycles and sealed in thin-walled quartz cu-
vettes. All experiments were carried out at room
temperature.
not affect the period of the beats. Thus the beats are
caused by hyperfine couplings and the difference in
the g factors of radical ions is not essential.
At an acceptor concentration of 10y3 M, the
Ž
.
capture of the n-decane radical cation hole which is
w x
diffusion controlled 14 , needs approximately 100
3. Results and discussion
Ž
ns, while the electron capture requires 1 ns capture
Ž . Ž .
w x.
Fig. 1 shows the ratios IH t rI0 t of the fluores-
rate constant is ;1012 My1 sy1 14 . Therefore
one can assume that under our conditions the main
contribution to the recombined fluorescence is given
by the SqrAy pairs and the contribution of the
cence kinetics in the external magnetic fields. Hs
3000 G and zero magnetic fields for the 10y3
M
solutions of 1–3 in n-decane. The clearly defined
oscillations of a similar shape but with different
periods were detected for all compounds. A rela-
tively high intensity of the second peak, despite the
damping of oscillations, is the characteristic feature
of the curves. One can note that the first peak
appears somewhat earlier than it could be expected
for the oscillations with a single frequency. The data
on the solutions of germoles 4 and 5 are presented in
Fig. 2. Here the beats are less clearly defined and the
second peak is rather weak. The characteristic fea-
ture of all curves is the damping of the magnetic
field effect with a typical time of ca. 100 ns.
AqrAy pairs is not important S is the n-decane
Ž
.
molecule; A is the acceptor molecule . The shape of
the oscillations is retained when the concentrations
of compounds 1 and 3 were decreased to 10y4 M.
This is an additional argument in support of the
conclusion.
Since the periods and shapes of the oscillations
for the systems studied are different, they should be
caused by hfc in radical anions rather than in n-de-
Ž .y
cane radical cation. In the case of radical anion 1
,
the beats are evidently caused by the dominant split-
w x
ting of the protons of the CH2 group 8 . One can
Measurements in the range of magnetic fields
from 100 to 3000 G for compounds 1 and 3 have
shown that the magnetic field strength variation does
reasonably suggest that in the other compounds stud-
ied, the beats are caused by hfc in similar fragments.
Additional qualitative arguments in support of this
Ž
.
Fig. 1. Ratio of fluorescence decay curves in high 3000 G for 1 and 2 and 1000 G for 3 and zero magnetic fields. The curves are vertically
spaced 0.15 apart for convenience.

(
)
V.A. Bagryansky et al.rChemical Physics Letters 295 1998 230–236
233
Ž
.
Fig. 2. Ratio of the fluorescence decay curves in high Hs3000 G and zero magnetic fields for 4 and 5. The curves are vertically spaced
0.15 apart for convenience.
Ž
.
suggestion follow from the consideration of the spin
dynamics of a radical ion pair neglecting spin relax-
the solvent radical cation hole is a homogeneously
broadened singlet line. Such a spectrum can result
from hole migration over the solvent molecules.
The expression for the probability of finding a
singlet-born pair in the singlet state at high magnetic
Ž
.
ation Fig. 3 . For a radical pair in which one of the
partners has no magnetic nuclei and another has a
hyperfine coupling with two equivalent protons, the
frequency of the singlet–triplet oscillations in a high
magnetic field is equal to a and in zero field is equal
to 1.5a, where a is an hfc constant in the units of
Ž . w
t
x
field WH
1,2 can be generalized using equation
135 in Ref. 15 to take into account electron spin
Ž
.
w x
Ž .
relaxation. For the zero field probability W0 t in the
case of a number of equivalent nuclei it is possible to
divide all the radical pairs into sub-ensembles. Each
sub-ensemble is assumed to have a magnetic nucleus
with one of the possible values of the total spin of all
w x
angular frequency 2 . The calculated ratio of the
singlet populations in high and zero magnetic fields
Ž
.
Fig. 3a has characteristic features which manifest
themselves in the experimental curves shown in Fig.
1. The first peak appears slightly earlier than the
expected one for harmonic oscillations and its inten-
sity is less than that of the second peak. For the
w x
the equivalent nuclei 2 . The evident condition
Ž .
Ž
.
W0 t ™t™` 1r4 was used in the case of zero
field. The relaxation rates were assumed to be inde-
pendent of nuclear spin configuration, both in high
and zero magnetic fields.
splitting on a chlorine nucleus each of 35Cl and 37Cl
Ž
.
isotopes has spin 3r2 all the peaks on the spin
dynamics curve Fig. 3b are equal in intensity.
Ž
.
In terms of these suggestions the probabilities
WH t and W0 t for a pair of compounds 1–3 with
Ž .
EH2 EsC, Si Ge moieties obeys the equations:
Ž .
Ž .
Accordingly, the second peak on the experimental
Ž
.
curves Fig. 2 is less pronounced.
The experimental curves were simulated assuming
1
2 at
Ž .
Ž .
that i radical ions have the same g factors, ii in
the radical anions of compounds 1–3 the hyperfine
coupling with only two equivalent protons is essen-
tial while in the radical anions of dichlorogermol 4
and chloromethylgermole 5 — only that with chlo-
WH t s 1qeyt r T q2e
cos
1
Ž .
ytr T2
1
Ž .
4
2
1
4
1
3at
0
W0 t s
Ž .
q
eyt r T 5q4cos
2
Ž .
12
2
Ž
rine nuclei the difference in hfc constants for the
. Ž .
two isotopes was ignored , iii the ESR spectrum of
for high and zero magnetic fields, respectively.

(
)
234
V.A. Bagryansky et al.rChemical Physics Letters 295 1998 230–236
1
4
1
3at
eyt r T 127q35 cos
0
W0 t s
Ž .
q
420
2
5at
7at
q63 cos
q90 cos
6
Ž .
2
2
y1
Ž
.
Here T1
is the sum of the rates of longitudinal
y1
Ž
.
relaxation and, T2
is the sum of the rates of
transverse relaxation of the radical ions in a pair in a
y1
Ž
.
high magnetic field, and T0
is the sum of the
rates in zero field.
The experimentally observed kinetics of the fluo-
rescence decay is defined as
1
I t AF t u W t q 1yu
7
Ž .
Ž .
Ž .
Ž .
Ž
.
4
Ž .
if fluorescence is considered to be instant. In Eq. 7
Ž .
F t is the rate of recombination of geminate pairs
and u is the fraction of spin-correlated pairs. The
second term in the brackets takes into account the
contribution of the singlet component of non-corre-
lated pairs to the fluorescence. The unknown func-
Ž .
tion F t is excluded if we analyze the ratio
1
IH
I0
t
u WH t q 1yu
Ž .
Ž . 4 Ž
.
.
s
.
8
Ž .
1
t
Ž .
u W0 t q 1yu
Ž .
Ž
4
Fig. 3. The ratio of singlet populations in high and in zero
Ž .
magnetic fields for a singlet born pair:
a for two equivalent
This expression was used to simulate the experimen-
tal curves. The optimization was carried out over
five parameters: a, T0, T1, T2 and u. The solid lines
in Figs. 1 and 2 show the results of simulation
Ž .
nuclei of spin 1r2 for one of the partners; b for one nucleus of
spin 3r2. The pattern is periodically reproduced since spin relax-
ation is neglected.
Ž .
according to expression 8 with the optimal parame-
ters, the values of these parameters are given in
Table 1. The consideration of weak splitting on the
For one nucleus with spin 3r2, the corresponding
Ž
w x.
protons of phenyl groups 1.8 G on six protons 8
has no effect on the simulation results. The introduc-
equations take the forms:
1
at
cos cos at
WH t s 1qeyt r T q2e
ytr T2
1
Ž .
Ž
.
4
2
3
Ž .
Table 1
Parameters of simulation of the curves shown in Figs. 1 and 2
1
4
3
eyt r T 3q5cos 2at
4
Ž .
0
W0 t s
Ž .
q
Ž
.
Compound
a
T0
T1
T2
u
32
Ž .
G
Ž .
ns
Ž .
ns
Ž
.
ns
and for two equivalent nuclei with spin 3r2, we get
1
2
3
4
5
25.0"0.4
15.6"0.3
15.0"0.3
7.0"1
8
10
6
8
7
110
60
120
60
9
0.23
0.1
0.04
0.1
16
17
9
1
2 at
ytr T2
WH t s 1qeyt r T q2e
cos
cos2 at
1
Ž .
Ž
.
4
2
11.4"1
30
12
0.07
5
Ž .

(
)
V.A. Bagryansky et al.rChemical Physics Letters 295 1998 230–236
235
.
tion of non-homogeneous broadening into the spec-
trum of the hole impairs agreement with experiment.
Note that the different parameters define the dif-
ferent features of the curves and therefore are sub-
stantially mutually independent. Thus, the hfc con-
stant a defines the distance between the adjacent
peaks, the long-time decay of the curve depends on
the longitudinal relaxation time T1, the fraction of
spin-correlated pairs mostly determines the peak am-
plitudes and the short time T0 provides a fast curve
rising at the initial time. Statistics of simulations of
various experimental realizations show that the hfc
from singlet pair recombination independent of the
external magnetic field, also contribute to lumines-
cence which results in a decrease of the estimated u
value.
4. Conclusions
The results obtained show the possibilities of the
method of quantum beats for the determination of
hfc constants under conditions where a short lifetime
of the radical anions makes it impossible to study
them by the conventional ESR technique. The method
of quantum beats can be easily generalized to sys-
tems with a greater number of equivalent nuclei
since simulation in this cases is straightforward.
Moreover, one can expect to get otherwise unavail-
able information about the relaxation times of alkane
holes which can be used to estimate the rates of their
migration over the solvent molecules.
Ž
constant is reproduced with the best accuracy see
.
Table 1 whereas the accuracy of the determination
of the other parameters does not exceed several tens
of percent. The hfc values obtained were indepen-
dent of both the acceptor concentration and the
strength of the magnetic field. The relaxation time T1
measured for germole 3 decreased with decreasing
Ž
magnetic field strength T1 is equal to 120, 60, 30
and less then 10 ns at 3000, 1000, 400 and 100 G,
.
respectively .
Acknowledgements
The hfc constant found for the radical anion 1
coincides within the experimental error with that
obtained by ESR spectroscopy in tetrahydrofurane at
This work was financially supported by INTAS
Grant No. 93-1626-EXT , by the Russian Founda-
Ž
.
Ž
w x
203 K 8 . The high value of this constant and small
tion for Basic Research Project Nos. 96-03-33694
splitting of the protons of the phenyl groups show
that the unpaired electron is predominantly localized
in the p-system of cyclopentadienyl ring. One can
suggest that the radical anions of the silicon and
germanium analogs 2–5 have a similar structure. A
detailed quantum-chemical analysis of the electronic
structure of radical anions 1–5 along with the addi-
tional optically detected ESR spectral data will be
.
and 96-03-32836 and by the Russian Ministry of
Ž
Education Grant No. 3H-218-98 in the Field of
.
Fundamental Research .
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w x
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Ž
.
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.
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