Proton tunneling in molecular solids

JOURNAL

OF

LUMINESCENCE ELSEVIER

Journal of Luminescence 66&67 (1996) 146-151

Proton tunneling in molecular solids M. Neumanna, M. Johnsonb, L. von Lauea, H.P. Trommsdorff”,” ’ Lahoratoire de Spectromke

Physique, Universitt! Joseph Fourier-Grenoble I, B.P. 87, F-38402 St. Martin d’H&-es Cedex, France bInstitut Laue-Langevin, BP 165, 38042 Grenoble, France

Abstract Low-temperature optical spectroscopy of guest-host molecular crystal systems gives direct access to proton tunneling processes. Examples include the photo-induced creation and evolution of “proton defects”, as well as translational tunneling along hydrogen bonds and rotational tunneling of methyl groups. The first observation of the effect of rotational tunneling on conventional absorption spectra is reported for y-picoline single crystals.

1. Introduction

Quantum mechanical tunneling is associated with the delocalization of the wave function of a particle beyond the classically allowed regions of the potential energy surface. Tunneling phenomena are characterized by the tunneling matrix element J which depends exponentially on the mass m of the particle and on the properties (width w and height H) of the energy barriers separating allowed regions of the potential function. For one-dimensional potentials the following relation holds: In(J) CC - wm. In symmetric double-well potentials, tunneling delocalizes the particle over both wells and leads to a splitting of the degenerate energy levels corresponding (in the absence of tunneling) to wave functions localized in one or the other well (“coherent” tunneling). The splitting of the energy levels then equals the tunneling matrix element J, which can in this case be measured directly. When the potential wells are inequivalent, the particle localizes in one or the other well and tunneling is manifested by the escape of the particle *Correspondingauthor.

from a metastable well even when its energy is lower than the height of the potential barrier defining the well (“incoherent” tunneling). This rate of escape k is proportional to J*. The observation and quantitative characterization of tunneling phenomena makes it possible to assess classically forbidden regions of potential energy surfaces, which are inaccessible by conventional spectroscopic methods. The optical spectra of guest molecules in a host matrix at low temperatures are sensitive to the local environment. Information about the structure as well as subtle changes of the environment of the guest molecule is obtained by monitoring these spectra. We have, in recent years, exploited these possibilities to follow and to characterize proton tunneling processes in doped molecular crystals. The displacement of a proton is one of the simplest and most ubiquitous nuclear rearrangements [ 11. Usually, such proton motions do not involve a large structural relaxation of the heavier nuclei and can therefore occur readily by tunneling in rigid low-temperature solids. There are a number of unique possibilities in the study of these processes offered by optical spectroscopy as compared to

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other techniques. One of the most important is the possibility to alter suddenly internuclear potentials by promoting the molecule to an excited electronic state. This allows us to populate non-equilibrium nuclear states at arbitrarily low temperatures and to follow the relaxation in the absence of thermal excitations. Using these methods we have investigated in low temperature solids, both coherent and incoherent proton tunneling processes corresponding to proton displacements along hydrogen bonds [2], in photochemical proton transfer reactions [3], and in the rotation of methyl groups [4].

2. Proton translations along hydrogen bonds The inner tautomerization of the symmetric benzoic acid dimers occurs by a concerted transfer of the two acid protons along the two hydrogen bonds that link the dimer. Benzoic acid dimers are the only system in which both the rate of incoherent tunneling at low temperatures and, independently, the coherent tunneling splitting were determined [2]. Considerable concerted effort. combining optical spectroscopy as described above with studies by IR, Raman, NMR [5], inelastic and quasi-elastic neutron scattering [6] as well as structural studies is therefore concentrated on this material. The present work addresses the issues of the proper description of the reaction surface and the influence of the environment on this multidimensional potential energy surface. A proper modeling of this surface, which allows computational evaluations of the proton transfer rate and of the tunneling splitting in hydrogen bonds, must incorporate the relaxation of the molecular skeleton, that is, the coupling of the proton motion with motions of the heavier nuclei. The calculation of tunneling processes in multidimensional potential energy surfaces is a task that can be tackled for a limited number of dimensions only, so that a reduction of the reaction surface to the essential degrees of freedom is required. Calculations for formic acid dimers yield a tunneling splitting [7] that is smaller by nearly two orders of magnitude as compared to the value measured in benzoic acid [2]. In view of the similar structure of the car-

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boxylic acid dimer ring in the two compounds, this large discrepancy is likely to be due to the omission of relevant skeleton modes. The participation of skeleton modes can be assessed by measuring tunneling in isotopically labeled (‘*O, ’ 3C) compounds. First measurements by NMR as well as by optical spectroscopy indicate a reduction by about 20% of the tunneling rate in the “0 compound demonstrating the importance of the heavy atoms in the reaction coordinate [S]. A direct measurement of the tunneling matrix element, via hole burning and a quantitative analysis of the data, are underway. The effect of the solid state environment is to lift the energy degeneracy of the otherwise equivalent tautomers. The energy bias between tautomers of a given dimer in the crystal (ca. 50 cm- ‘) is not only determined by the crystal packing, but is also dependent on the tautomer state of neighbouring dimers, so that tautomer states of different dimers are coupled. The magnitude of the coupling of two dimers sandwiching a guest molecule is obtained from the observed energy level structure and lies in the range l-8 cm-‘. In the pure crystal the direct coupling of two dimers is conceivably larger. If this coupling exceeds the energy bias imposed by the crystal packing, a collective ordering of the acid protons in the crystal is expected (3-D Ising model). NMR measurements under high hydrostatic pressure ( > kbar) indicate a strong reduction of the average energy bias and the onset of a phase change [S]. Further structural and spectral studies under higher pressure are therefore undertaken to confirm this phenomenon.

3. Photo-induced, reversible proton transfer reactions, between a dye and the host matrix

The observation of temperature-independent reaction rates and of large deuteration effects is generally taken as an indication of tunneling in proton and hydrogen atom transfer reactions [l]. In lowtemperature solids, these reactions displace protons from their original position so that the absorption spectrum of the dye is modified and spectral hole burning can be observed. Only a few examples of such reactions in well-defined guest-host crystal

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systems have been reported. Pentacene in benzoic acid crystals is the model system most extensively characterized by optical spectroscopy [3]. The following reaction mechanism was established by measurements on crystals with selectively deuterated guest and host molecules. In the optically excited singlet state (lifetime 20 ns), pentacene abstracts a proton from the matrix. The reaction is reversible and the pentacene-proton complex dissociates rapidly (on a time scale < ms). The proton does not always return directly to its original position in the matrix, but may occupy different, metastable positions from which it returns on longer time scales (l-lo4 s) to the stable position. Due to this proton displacement, the pentacene molecule finds itself in an altered environment, its optical transitions are shifted, and new lines are observed in the spectrum (“defect sites”). The proton displacements can thus be monitored by following the temporal evolution of these spectral lines. The ensemble of these defect sites represents a disordered solid and exhibits many of the characteristics observed for glasses doped with dye molecules: The shift of spectral lines due to the proton displacements covers a spectral range of about + 150 cm-‘. Spontaneous and light-induced spectral diffusion processes are observed and reflect the evolution of the proton displacements. In contrast to a glass, however, the distribution of defect sites and transition energies is discrete, and the ensemble of defect sites anneals, so that the “ordered” doped crystal with only one stable substitution site is finally recovered. As in a glass, the rates of recovery and their variation as a function of temperature cover a wide range. Because of the discrete nature of the distribution it becomes possible to measure properties for individual sites (spectral position, lifetime, thermal stability, local crystal field) and to establish correlations between these properties. Recent measurements have shown that the different sites have very different thermal stabilities ranging from less than 20 K to more than 80 K. No clear correlations between the spectral position, low temperature lifetime, and the thermal stability could be found. The temperature stability was found to be correlated and the low-temperature lifetime somewhat anticorrelated with the local crystal field. The possibility to establish such correlations for indi-

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vidual sites exists in glasses only via single molecule spectroscopy. Even with this technique it is not possible to measure deuteration effects for individual sites which relate to the width and heights of barriers over which protons are displaced. An interesting result, obtained via measurements in electric fields, is the identification of sites where two protons are displaced symmetrically about the pentacene molecule so that the inversion symmetry of the site remains preserved.

4. Ridged body rotations of CH3 groups The potential function governing the rotational motion of a CH3 group in a solid is strictly threefold symmetric with three equivalent minima. This symmetry is not broken by any conceivable distortion of the environment and the localization of the -CH3 rotor in one of the potential wells is impossible. -CH3 rotations are thus characterized by coherent tunneling and a tunneling splitting, that depends critically on the shape and the height of the energy barriers separating different potential minima. Rotational tunneling provides a very sensitive probe of this potential function, which has intra- as well as intermolecular contributions. The measurement of tunneling splittings, subsequent to controlled geometry changes, offers a severe test of force field models. Optical spectroscopy of rotational tunneling systems provides rich, novel information that is complementary to established inelastic neutron scattering (INS) and NMR techniques. In particular, the tunneling behavior in electronically excited states becomes accessible and relaxation processes can be followed in a very direct fashion. Di-methyl-s-tetrazine (DMST) has been studied in different host matrices [4,9]: In the isolated molecule the rotation of the -CH3 groups is nearly free and the small hindering potential as well as the geometry in the electronic ground and in the first excited singlet state are known. Tunneling splittings are dominated by intermolecular contributions to the hindering potential and depend strongly on the host matrix. Geometry changes, upon electronic excitation, lead to a change of the tunneling splitting, which is measured directly as a line splitting of the corresponding transitions. In addition to

M. Neumann et al. J Journal of Luminescence

the tunneling splitting, dominated by the energy barriers, optical spectra give access to the change of the equilibrium position of the -CH3 rotor and the frequency of the rotational oscillation in both electronic states, which is determined by the shape of the classically allowed region of the potential. Other ways to alter intermolecular distances are the application of pressure or the complete or partial deuteration of the methyl rotor or of the matrix. All of these have been combined with optical measurements. The unprecedented detailed information relating to the potential energy function obtained in these experiments provides a severe test for the validity and the parameters of atom-atom potentials used to describe this function. The relaxation between tunneling levels involves a change of the total spin of the methyl protons (“nuclear spin conversion”) and is a very slow process. Optical methods were shown to be ideally suited to measure the rate of this process over many orders of magnitude (l-10’ s) making it possible to identify different contributions to the relaxation [4]. Under applied pressure, the rate was found to decrease significantly, a result that is in line with an increase of height of the potential barriers under pressure. At 3.3 K the relaxation process is dominated by an Orbach process with an activation energy of EA = 20.3 cm- ‘. This activation energy equals the lowest energy librational excitation of the methyl group as observed in the fluorescence spectrum [4]. The relaxation data under applied pressure can be quantitatively analyzed by assuming that the activation energy (in cm- ‘) increases with pressure (P, in kbar) as: E,(P) = 20.3 (1 + 0.0956P) [lo]. Fluorescence measurements under applied pressure are underway in order to verify if the librational mode shows the expected frequency increase. Since the line splittings resulting from rotational tunneling are usually quite small, hole burning techniques were required in all experiments discussed above to uncover this information in the inhomogeneously broadened optical spectra. Very recent experiments in pure crystals of y-picoline (4-methyl-pyridine) have for the first time demonstrated dramatic changes related to rotational tunneling in conventional absorption spectra. The choice of this molecule was made because y-pico-

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line has been extensively investigated by INS and NMR [ll, 131 and shows one of the largest tunneling splittings: 4.17 cm- ‘. This value is only slightly smaller than the energy difference between the two lowest levels (5.28 cm-‘, i.e. the rotational constant) of a free CH, rotor. The line splitting of electronic transitions equals the difference in tunneling splitting between the ground and electronically excited state and this difference is thus expected to be largest in a molecule like y-picoline. The -CH3 rotation of isolated y-picoline is nearly free, while in the crystal the weak hindering potential has dominant contributions which depend on the relative orientation of different methyl groups. The description of such an ensemble of coupled methyl rotors and the quantitative understanding of the transitions observed in INS is complex and is the object of recent theoretical work [ll, 121. Different approaches, starting from the excitations of an infinite chain of coupled rotors on the one hand [ 1l] and exact numerical quantum mechanical calculations for a small ( < 4) number of coupled rotors on the other [12], have been used. This issue of the coupling between -CH3 groups was an additional incentive to study y-picoline by optical spectroscopy, and to investigate the interplay of the coupling of electronic and rotational excitations. Fig. 1 shows the evolution of the polarized absorption spectrum of a single crystal of extensively purified y-picoline as a function of time at 2.1 K subsequent to cooling the sample in 3 min from 20 to 2.1 K. At 20 K the lowest energy tunneling levels (associated with different nuclear spins) are nearly equally populated. Spin conversion times in y-picoline have been measured by neutron transmission and increase rapidly, when the temperature is lowered, from 6 min at 14 K and to about 10 h at 2.4 K [ 133. The population distribution between different spin species corresponding to a temperature of 20 K is, therefore, conserved immediately after the rapid cooling of the sample to 2.1 K, and thermal equilibrium is attained only after long waiting times. The evolution of the spectrum over 13 h exhibits this process and is discussed below. It is possible to approach the equilibrium at low temperatures faster by cooling the sample more slowly in finding a compromise between the less favorable thermal equilibrium at intermediate temperatures

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h c In C al -0

66& 67 (I 996) 146- 151

2

m .u 2 0 o 35680

35690

35700 wavenum

Fig. 1. Polarized absorption 3 min. from 20 K to 2.1 K.

spectra

of a y-picoline

35710

35720

ber (cm-‘)

single crystal

and the shorter relaxation times. More fully relaxed spectra show a further increase of the intensity of the high energy peak at 35706.8 cm- ’ at the expense of the low energy peak at 35703.8 cm- ‘. The electronic spectra of crystalline y-picoline have not been reported previously. Based on the intensity and in analogy with the spectral assignments made for the parent pyridine compound in vapor phase, the absorption around 3.5700 cm- ’ is assigned to the pure electronic transition involving a ‘nx* excited state. As electronic exchange interactions are known to be very small for singlet nrc* excitations ( < cm- ‘) and the resolution of our spectra due to energy disorder is less than about 2 cm- i, we neglect possible exciton spittings due to the presence of four molecules in the unit cell and consider the excited state to be essentially localized on one molecule. The observed spectra as well as their general evolution as a function of waiting time can be understood as follows. The two lines that emerge after long waiting times are assigned to transitions from the two lowest energy tunneling levels. The splitting between tunneling levels of y-picoline in the crystal is thus reduced by an amount d = 3 cm-‘, from 4.17 cm-’ in the ground state to 1.2 cm-’ in the electronically excited state. A reduction of the tunneling splitting is expected as the molecule expands in the excited state and, as a con-

at 2.1 K as a function

of time subsequent

to cooling

the sample

in

sequence, the potential barriers hindering the methyl rotation increase. The tunneling splitting of molecules near an excited molecule is similarly reduced albeit by a smaller amount, 6. Immediately after cooling the sample, the population of the lowest tunneling levels is nearly equal and the average excitation energy of an ensemble of molecules is located at - (d + N6)/2 with respect to the transition energy of a sample in which all molecules are in the lowest tunneling level. N is the number of neighboring molecules for which the tunneling splitting is reduced. When N is large, the width of the frequency distribution is given by 6J%ln% Within this crude picture the values of N and 6 can be evaluated from the observed frequency shift of 9 cm-’ and line width of 6cm-’ as N = 9-10 molecules and 6 = 1.5 cm-‘. This simple evaluation neglects the coupling between -CHJ rotors and differences in the value of 6 for different neighboring molecules. The analysis does give a reasonable estimate of average values and supports the proposition of coupled methyl groups in y-picoline. A full analysis of the observations must also take into account the electronic coupling. As the order increases after long waiting times at sufficiently low temperatures, the delocalization of the electronic excitation (exciton splitting) may eventually be observed if it is not limited by other inhomogenieties of the crystal. From the temporal evolution of the

M. Neumann et al. /Journal of Luminescence 66& 67 (I 996) 146 151

spectra, the spin conversion time can also be estimated to be longer than 26 h at 2.1 K. This value is larger than the value of ca. 14 h obtained by an extrapolation to lower temperatures of previous measurements limited to 2.4 K. The differences could be due to differences in the purity of the samples and reflect the contribution of intermolecular spin exchange processes to the relaxation in the unpurified sample used in the neutron transmission measurements. Optical measurements in isotopically mixed crystals might be best suited to expose this phenomenon which has recently been theoretically investigated [14]. For example, in a crystal of perproto- in ringdeutero-y-picoline the methyl group dynamics is virtually unchanged in the electronic ground state, while the selective optical excitation of the perproto molecule is possible and allows us to pump and to monitor the population of tunneling levels locally. 5. Conclusion The few examples discussed here of different proton tunneling processes demonstrate the wealth of information that can be obtained by optical spectroscopic methods. Even though many requirements must be met by the guest-host system to exploit fully the power of these methods, the indepth study of some model systems by optical techniques provides benchmarks for the proper modeling of tunneling phenomena. Acknowledgements Many colleagues, cited in the references, have contributed to the this work, which is supported by a research grant under the EC HCM (CT940466) program. References [l]

V.A. Benderskii, D.E. Makarov Dynamics at Low Temperatures

and C.A. Wight, Chemical (Wiley, New York, 1994).

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