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Optical resolution of hydrogen tunneling levels in benzoic acid crystals
Journal of Luminescence 40&41 (1988) 203 206 North-Holland, Amsterdam
203
OPTICAL RESOLUTION OF HYDROGEN TUNNELING LEVELS IN BENZOIC ACID CRYSTALS* H.P. Trommsdorff, R.M. Hochetrasser, and M. Pierre Laboratoire de Spectrom~trie Physique, associ~ au C.N.R.S. Universit~ Scientifique, Technologique et M~dicale de Grenoble B.P. 87, 38402 St. Martin d’H~res Cedex, France and Department of Chemistry, University of Pennsylvania, Philadelphia, PA 19104, U.S.A. The tunneling splitting substructure of delocalized proton states of the hydrogen bonds between benzoic acid dimers has been resolved by fluorescence line narrowing techniques, and the rate of relaxation between these levels has been obtained from the dynamics of site selected population gratings. I. INTRODUCTION Carboxylic dimers, linked by two hydrogen bonds, are model systems for the study of the potential function and the dynamics of protons involved in hydrogen bonds.
There exist two
distinct tautomer forms, separated
by a poten—
I1~) — -
—
The two tiall proton low barrier, temperature transfer which interconvert along behaviour the hydrogen of bysuch a concerted systems, bonds. characterized
by the condition that thermally
activated barrier crossing no longer dominates the interconversion interest
process, is of particular
regarding the transition to quantum
transport
by tunneling.
Tunneling tends to
delocalize the protons over the two potential wells.
A condensed phase environment,
other hand, differentiates
on the
the two wells and
tends to localize the protons such that at low temperatures exists.
only the most stable tautomer form
We have shown 1,2 that the optical
spectra of dyes are sensitive structure
to the proton
of the environment and can be used
to access the dynamics of these systems at very low temperatures (see Fig.l).
For
example, measurements of the fluorescence de— cay following site specific excitation yielded
FIGURE 1 Potential function of an acid dimer (filled circles represent protons) coupled to a dye (0 and X represent its ground and electronically excited states).
*This research was supported by a grant from the Division of Materials Research (DMR-85-O774O) and by the United States Army Research Office (Durham). 0022 2313/88/$0350 © Elsevier Science Pubhshers By. (North-Holland Physics Publishing Division)
H.P. Trommsdorff et al.
204
the rate of hydrogen sisted tunneling.
/
Optical resolution of hydrogen tunneling levels
transfer by phonon as-
However, one key quantity,
namely the magnitude of the tunneling matrix element, remained inaccessible
from such
x --~~
experiments.
—
~-~POPULATION -•-.
—
—
-
—
~RANSFER
—
- -
- -
2. TUNNELING LEVEL STRUCTURE In order to have delocalized proton states, it is necessary that the localization energy be comparable or smaller than the tunneling matrix element.
This situation is realized
in thioindigo doped benzoic acid crystals where we found that the asymmetry in the potential function of benzoic acid dimers having a
\ ~ \
~, >
~
.\
/~
/~ --
thioindigo molecule as nearest neighbor is reduced to being smaller than the tunneling splitting.
This near degeneracy is lifted
when thioindigo
FIGURE 2 Fluorescence line narrowing scheme.
is electronically excited.
Optical excitation of the dye causes the system
if the inhomogeneous broadenings
to undergo transitions from a set of delocalized
of the transitions involved in the excitations
onto a set of localized proton levels.
and emission process are correlated
The
absorption spectrum maps the energy spacings
The experimental spectrum is shown in Fig.3.
overlap of the initial (delocalized) and final
The indigo molecule is sandwiched between two
state (localized) wavefunctions.
equivalent benzoic acid dimers so that four
Inhomogeneous
(strain) broadening prevents the resolution of
tunneling levels arise from the two double
the initial distribution of states in conven—
well potentials involved.
tional absorption or emission spectra.
predicted to contain a total of five allowed
Using
The spectrum is
fluorescence line narrowing techniques we have
transitions.
been able to partially resolve the tunneling
in the experiment and the observed linewidth
level substructure (see Fig. 2) 3.
was instrument limited.
The experi
These were only partially resolved
Broadening due to
ment involved narrow band laser excitation of a
incomplete correlations between the inhonioge
localized
neous broadenings was found to be smaller than
proton level.
The ground state level
structure is thereby transferred to the excited
about 0.1 cm l:
state in the sense that, within the inhomoge—
because the levels involved in the excited
neous width of the excited transition, Boltzman
state proton transitions correspond to a polar
weighted population packets are created at
and a nonpolar tautomer configuration.
energies characterized by the ground state
This result suggests that the dominant force
level spacings.
determining the frequency spread in the inhomo—
Tautomerization during the
excited state lifetime of the dye transfers
this is a notable result
geneous distributions is nonlocal, perhaps in
these population packets to the lowest energy
volving a significant correlation length.
localized proton configuration.
magnitude of the tunneling matrix element
The
The
emission back to the delocalized ground state
obtained in these experiments was 0.16 ±0.01
levels is expected to be line narrowed and
cm~ (this value equals one half the tunneling
hence resolves the tunneling substructure
H.P. Trommsdorff et aL
/
Optical resolution of hydrogen tunneling levels
205
holeburning, of the homogeneous linewidth of the transitions at low temperatures when pure 1 dephasing can considered to be negligible. The homogeneous linewidth was found to be
I
the excited state.
~0
The discrepancy in rate,
6larger x 108 than s~,expected was attributed from theto known the finite lifetime of
-~
q)
lifetime of the ground state levels. Recently, a more direct study of ground state dynamics was made using time resolved picosecond transient grating techniques. In the grating experiments, two time coincident laser pulses of equal frequency
/7846 /7847 wavenumber
cm-’
FIGURE 3 Line narrowed emission spectra obtained for thioindigo in benzoic acid: excitation into a vibrational level (top) and the 0-0 transition (bottom) of a higher energy proton configura— tion. The ground state splittings are not seen when a vibrational level is excited because the excitation and subsequent relaxation processes populate the whole inhomogeneous distribution of the emitting state.
splitting of a symmetric dimer).
‘—b
_____________________________________
dT~Tc
The asymmetry
of the double well potential was slightly smaller than this indicating that the protons are delocalized to a very significant degree in
_____________________________________
0
/
2
3 4 5 6 7 8 1/inens
this system at 1.6k. 3. RELAXATION DYNMIICS BETWEEN DELOCALIZED PROTON LEVELS Time resolved fluorescence measurements, as mentioned above, are inadequate to access the relaxation dynamics between these delocalized lPv~is which are associated
with the ground
electronic state of impurity. of the finite
lifetime
One indication
of the ground state
levels was obtained from a determination, by
FIGURE 4 Transient grating measurements in thioindigo doped benzoic acid. The different pump and probe transitions are indicated. Tautomeriza— tion near an excited dye dominates the dynamics in the top curves, while in the bottom only the dynamics between the delocalized proton levels near the ground state impurity contribute to the signal. The peak near t~o reflects a fast process, possibly related to multiphoton excitation of higher electronic states.
206
H.P. Trommsdorff et a!.
/ Optical resolution
of hydrogen tunneling levels
cross in the sample and form an intensity
obtained from the optical holeburning experi—
interference pattern which leads to a
ment mentioned earlier.
spatially periodic excitation of the sample.
these average rates for phonon assisted
The resulting variations in the index of
tunneling between levels separated by a few 1 are of the same order as those tenths of cnr found for transitions between completely
refraction has contributions from both the excited and ground state populations of the dye molecules.
This index grating is probed
It is interesting that
localized states separated by ca. 30 cm~ as
by a time delayed third pulse, and the intensity
occur when the dye is electronically excited
of the diffracted signal which is proportional
and the asymmetry is large.1’2
to the square of the index variations, is
4.
measured as a function of the time delay.
The
SUIII4ARY AND CONCLUSION We have shown here how optical techniques
square root of the signal on a square law de—
can be used to acces the level structure
tector therefore maps out the time evolution
and the dynamics of a condensed phase
of these populations.
tunneling system in the limit of very low
The time evolution arises
because of the occurrence of phonon assisted
temperatures where conventional nuclear
tunneling between localized excited state levels
magnetic resonance and inelastic neutron
and because of the recovery of the ground state
scattering methods become inoperative.
Boltzman distribution which was perturbed by the
results for benzoic acid dimers should be
the pump pulse.
It is the latter process that
we hope to understand through these experiments, Fig. 4 shows the results of transient grating
The
typical for carboxylic acid dimers, because the parameters determined with different probe molecules are fairly insensitive to the nature
experiments on the same system as discussed in
of the probe.
the preceding section.
insensitivity of the rates of relaxation to the
In this plot the expo—
Osie unexpected result is the
nential decay of the excited state population
asymmetry of the double well potential.
of the dye has been subtracted in order to
point certainly deserves further investigation
emphasize the contribution by proton dynamics.
and confirmation.
As indicated earlier, the ground state contains
magnitude of the tunnel splitting, which
four tunneling levels and hence it is necessary
corresponds to a proton oscillation period of
to specify six independent rate constants to
of Ca. 200ps, indicates that the tunneling
completely describe the dynamics.
involves significant
Approximate
symmetry equivalences allow this number to be reduced to three.
Furthermore, the small
structural
relaxation
in addition to proton motion.
The experiments (c) and (d)
in Fig 4.’ each measure a different of these three rates.
combination
It appears as if the
rates might all be quite similar.
When the data
is analyzed on the basis of a single relaxation rate parameter a value of 3.5 x 108 ~ obtained.
This
This value is similar to that
REFERENCES 1. J.M. Clemens, R.M. Hochstrasser, and H.P. Trommsdorff, J. Chem.Phys. 80 (1984) 1744. 2. G.E. Holton, R.M. Hochstrasser, and H.P. Trommsdorff, Chem.Phys. Letters (1986) 44.
131
3. P.M. Hochstrasser, and H.P. Trommsdorff, Chem. Phys. in press.
203
OPTICAL RESOLUTION OF HYDROGEN TUNNELING LEVELS IN BENZOIC ACID CRYSTALS* H.P. Trommsdorff, R.M. Hochetrasser, and M. Pierre Laboratoire de Spectrom~trie Physique, associ~ au C.N.R.S. Universit~ Scientifique, Technologique et M~dicale de Grenoble B.P. 87, 38402 St. Martin d’H~res Cedex, France and Department of Chemistry, University of Pennsylvania, Philadelphia, PA 19104, U.S.A. The tunneling splitting substructure of delocalized proton states of the hydrogen bonds between benzoic acid dimers has been resolved by fluorescence line narrowing techniques, and the rate of relaxation between these levels has been obtained from the dynamics of site selected population gratings. I. INTRODUCTION Carboxylic dimers, linked by two hydrogen bonds, are model systems for the study of the potential function and the dynamics of protons involved in hydrogen bonds.
There exist two
distinct tautomer forms, separated
by a poten—
I1~) — -
—
The two tiall proton low barrier, temperature transfer which interconvert along behaviour the hydrogen of bysuch a concerted systems, bonds. characterized
by the condition that thermally
activated barrier crossing no longer dominates the interconversion interest
process, is of particular
regarding the transition to quantum
transport
by tunneling.
Tunneling tends to
delocalize the protons over the two potential wells.
A condensed phase environment,
other hand, differentiates
on the
the two wells and
tends to localize the protons such that at low temperatures exists.
only the most stable tautomer form
We have shown 1,2 that the optical
spectra of dyes are sensitive structure
to the proton
of the environment and can be used
to access the dynamics of these systems at very low temperatures (see Fig.l).
For
example, measurements of the fluorescence de— cay following site specific excitation yielded
FIGURE 1 Potential function of an acid dimer (filled circles represent protons) coupled to a dye (0 and X represent its ground and electronically excited states).
*This research was supported by a grant from the Division of Materials Research (DMR-85-O774O) and by the United States Army Research Office (Durham). 0022 2313/88/$0350 © Elsevier Science Pubhshers By. (North-Holland Physics Publishing Division)
H.P. Trommsdorff et al.
204
the rate of hydrogen sisted tunneling.
/
Optical resolution of hydrogen tunneling levels
transfer by phonon as-
However, one key quantity,
namely the magnitude of the tunneling matrix element, remained inaccessible
from such
x --~~
experiments.
—
~-~POPULATION -•-.
—
—
-
—
~RANSFER
—
- -
- -
2. TUNNELING LEVEL STRUCTURE In order to have delocalized proton states, it is necessary that the localization energy be comparable or smaller than the tunneling matrix element.
This situation is realized
in thioindigo doped benzoic acid crystals where we found that the asymmetry in the potential function of benzoic acid dimers having a
\ ~ \
~, >
~
.\
/~
/~ --
thioindigo molecule as nearest neighbor is reduced to being smaller than the tunneling splitting.
This near degeneracy is lifted
when thioindigo
FIGURE 2 Fluorescence line narrowing scheme.
is electronically excited.
Optical excitation of the dye causes the system
if the inhomogeneous broadenings
to undergo transitions from a set of delocalized
of the transitions involved in the excitations
onto a set of localized proton levels.
and emission process are correlated
The
absorption spectrum maps the energy spacings
The experimental spectrum is shown in Fig.3.
overlap of the initial (delocalized) and final
The indigo molecule is sandwiched between two
state (localized) wavefunctions.
equivalent benzoic acid dimers so that four
Inhomogeneous
(strain) broadening prevents the resolution of
tunneling levels arise from the two double
the initial distribution of states in conven—
well potentials involved.
tional absorption or emission spectra.
predicted to contain a total of five allowed
Using
The spectrum is
fluorescence line narrowing techniques we have
transitions.
been able to partially resolve the tunneling
in the experiment and the observed linewidth
level substructure (see Fig. 2) 3.
was instrument limited.
The experi
These were only partially resolved
Broadening due to
ment involved narrow band laser excitation of a
incomplete correlations between the inhonioge
localized
neous broadenings was found to be smaller than
proton level.
The ground state level
structure is thereby transferred to the excited
about 0.1 cm l:
state in the sense that, within the inhomoge—
because the levels involved in the excited
neous width of the excited transition, Boltzman
state proton transitions correspond to a polar
weighted population packets are created at
and a nonpolar tautomer configuration.
energies characterized by the ground state
This result suggests that the dominant force
level spacings.
determining the frequency spread in the inhomo—
Tautomerization during the
excited state lifetime of the dye transfers
this is a notable result
geneous distributions is nonlocal, perhaps in
these population packets to the lowest energy
volving a significant correlation length.
localized proton configuration.
magnitude of the tunneling matrix element
The
The
emission back to the delocalized ground state
obtained in these experiments was 0.16 ±0.01
levels is expected to be line narrowed and
cm~ (this value equals one half the tunneling
hence resolves the tunneling substructure
H.P. Trommsdorff et aL
/
Optical resolution of hydrogen tunneling levels
205
holeburning, of the homogeneous linewidth of the transitions at low temperatures when pure 1 dephasing can considered to be negligible. The homogeneous linewidth was found to be
I
the excited state.
~0
The discrepancy in rate,
6larger x 108 than s~,expected was attributed from theto known the finite lifetime of
-~
q)
lifetime of the ground state levels. Recently, a more direct study of ground state dynamics was made using time resolved picosecond transient grating techniques. In the grating experiments, two time coincident laser pulses of equal frequency
/7846 /7847 wavenumber
cm-’
FIGURE 3 Line narrowed emission spectra obtained for thioindigo in benzoic acid: excitation into a vibrational level (top) and the 0-0 transition (bottom) of a higher energy proton configura— tion. The ground state splittings are not seen when a vibrational level is excited because the excitation and subsequent relaxation processes populate the whole inhomogeneous distribution of the emitting state.
splitting of a symmetric dimer).
‘—b
_____________________________________
dT~Tc
The asymmetry
of the double well potential was slightly smaller than this indicating that the protons are delocalized to a very significant degree in
_____________________________________
0
/
2
3 4 5 6 7 8 1/inens
this system at 1.6k. 3. RELAXATION DYNMIICS BETWEEN DELOCALIZED PROTON LEVELS Time resolved fluorescence measurements, as mentioned above, are inadequate to access the relaxation dynamics between these delocalized lPv~is which are associated
with the ground
electronic state of impurity. of the finite
lifetime
One indication
of the ground state
levels was obtained from a determination, by
FIGURE 4 Transient grating measurements in thioindigo doped benzoic acid. The different pump and probe transitions are indicated. Tautomeriza— tion near an excited dye dominates the dynamics in the top curves, while in the bottom only the dynamics between the delocalized proton levels near the ground state impurity contribute to the signal. The peak near t~o reflects a fast process, possibly related to multiphoton excitation of higher electronic states.
206
H.P. Trommsdorff et a!.
/ Optical resolution
of hydrogen tunneling levels
cross in the sample and form an intensity
obtained from the optical holeburning experi—
interference pattern which leads to a
ment mentioned earlier.
spatially periodic excitation of the sample.
these average rates for phonon assisted
The resulting variations in the index of
tunneling between levels separated by a few 1 are of the same order as those tenths of cnr found for transitions between completely
refraction has contributions from both the excited and ground state populations of the dye molecules.
This index grating is probed
It is interesting that
localized states separated by ca. 30 cm~ as
by a time delayed third pulse, and the intensity
occur when the dye is electronically excited
of the diffracted signal which is proportional
and the asymmetry is large.1’2
to the square of the index variations, is
4.
measured as a function of the time delay.
The
SUIII4ARY AND CONCLUSION We have shown here how optical techniques
square root of the signal on a square law de—
can be used to acces the level structure
tector therefore maps out the time evolution
and the dynamics of a condensed phase
of these populations.
tunneling system in the limit of very low
The time evolution arises
because of the occurrence of phonon assisted
temperatures where conventional nuclear
tunneling between localized excited state levels
magnetic resonance and inelastic neutron
and because of the recovery of the ground state
scattering methods become inoperative.
Boltzman distribution which was perturbed by the
results for benzoic acid dimers should be
the pump pulse.
It is the latter process that
we hope to understand through these experiments, Fig. 4 shows the results of transient grating
The
typical for carboxylic acid dimers, because the parameters determined with different probe molecules are fairly insensitive to the nature
experiments on the same system as discussed in
of the probe.
the preceding section.
insensitivity of the rates of relaxation to the
In this plot the expo—
Osie unexpected result is the
nential decay of the excited state population
asymmetry of the double well potential.
of the dye has been subtracted in order to
point certainly deserves further investigation
emphasize the contribution by proton dynamics.
and confirmation.
As indicated earlier, the ground state contains
magnitude of the tunnel splitting, which
four tunneling levels and hence it is necessary
corresponds to a proton oscillation period of
to specify six independent rate constants to
of Ca. 200ps, indicates that the tunneling
completely describe the dynamics.
involves significant
Approximate
symmetry equivalences allow this number to be reduced to three.
Furthermore, the small
structural
relaxation
in addition to proton motion.
The experiments (c) and (d)
in Fig 4.’ each measure a different of these three rates.
combination
It appears as if the
rates might all be quite similar.
When the data
is analyzed on the basis of a single relaxation rate parameter a value of 3.5 x 108 ~ obtained.
This
This value is similar to that
REFERENCES 1. J.M. Clemens, R.M. Hochstrasser, and H.P. Trommsdorff, J. Chem.Phys. 80 (1984) 1744. 2. G.E. Holton, R.M. Hochstrasser, and H.P. Trommsdorff, Chem.Phys. Letters (1986) 44.
131
3. P.M. Hochstrasser, and H.P. Trommsdorff, Chem. Phys. in press.