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Cooperative proton transfer and tunneling in dye doped benzoic acid crystals
11 June 1999
Chemical Physics Letters 306 Ž1999. 124–132
Cooperative proton transfer and tunneling in dye doped benzoic acid crystals Ch. Rambaud, H.P. Trommsdorff
)
Laboratoire de Spectrometrie ´ Physique, UniÕersite´ J. Fourier Grenoble — CNRS (UMR 5588), B.P. 87, 38402 St. Martin d’Heres ` Cx, France Received 6 January 1999; in final form 1 April 1999
Abstract In seleno-indigo doped benzoic acid crystals, the energy level structure of a pair of benzoic acid dimers coupled to the impurity center is characterized by optical spectroscopy and transient hole burning in electric fields. The lowest energy states involve degenerate, polar proton configurations. Proton tunneling lifts this degeneracy. The tunneling matrix element for proton transfer in a benzoic acid dimer equals 6.5 " 1.5 GHz, a value comparable to those found with other guest molecules. Relaxation between the two ground state levels involves the concerted motion of four protons and determines the intensity distribution of the fine structure observed in hole burning. q 1999 Elsevier Science B.V. All rights reserved.
1. Introduction The translational tunneling of protons in the hydrogen bonds of benzoic acid ŽBA. crystals has been the object of extensive experimental and theoretical work w1–12x. Concerted two-proton transfer along the hydrogen bonds of a dimer interconverts the two tautomer structures, denoted L and R in Fig. 1. These two tautomers are equivalent in isolated dimers, but unequivalent in the crystal environment. The energy difference between tautomers is determined by the packing of the molecules in the crystal and is, for a given dimer, also dependent upon the proton position of neighboring dimers. Due to this coupling between proton positions in neighboring dimers, the energy of a pair of two neighboring R tautomers will differ from the energy of two isolated R tautomers in an environment composed of L tautomers. When the coupling dominates the energy difference between tautomers, the phase behavior of the crystals is expected to be affected. NMR measurements under applied pressure indeed suggest such a possibility w13x. Under pressure, the coupling is expected to increase, while the average energy difference between tautomers was shown to decrease. The observation of a discontinuity of the variation, as a function of pressure, of the parameters describing the NMR proton T1 relaxation in pure BA crystals, indicated a subtle phase change. However Raman and structural measurements have not yet been able to substantiate this proposition w14x.
)
Corresponding author. Fax: q33 476514544; e-mail: [email protected]
0009-2614r99r$ - see front matter q 1999 Elsevier Science B.V. All rights reserved. PII: S 0 0 0 9 - 2 6 1 4 Ž 9 9 . 0 0 4 4 7 - 9
Ch. Rambaud, H.P. Trommsdorffr Chemical Physics Letters 306 (1999) 124–132
125
When impurity molecules are introduced into a BA host matrix, dimers in the vicinity of the guest are perturbed and the energy difference between L and R tautomers of these selected dimers is altered. This effect was exploited, when the high resolution low temperature optical spectra of different guest molecules were used to characterize the energy level structure of such isolated dimers in the BA crystal w1–6x. Both coherent and incoherent proton tunneling in these dimers could be characterized. Here, we report the observation and characterization of a complex of two symmetry related dimers sandwiching a guest molecule in which the coupling exceeds the energy difference between tautomer states, so that the lowest energy states of this complex are described by a degenerate pair of
2. Theoretical description of the level structure In symmetry adapted,
yJr'2
0
A i q Ci
yJr'2
0
yJr'2
yJr'2
1 2
y Ci
0
0
0
0
y 21 Ci
0
0 1 2
.
Ž 1.
A i is the energy difference between tautomers neglecting coupling, and Ci is the coupling, which stabilizes the degenerate configurations Ž
1 The vibrational ground state levels corresponding to the L and R tautomers of one dimer are designated by
Ch. Rambaud, H.P. Trommsdorffr Chemical Physics Letters 306 (1999) 124–132
126
Fig. 1. Tautomer exchange of the benzoic acid dimer by concerted two proton transfer.
assumed to be independent of the electronic state of the guest and is, in the present case, small as compared to the energy differences, <2 A i <, < Ci " A i <, so that the Hamiltonian Ž1. is approximately diagonal. When Ci / 0, tunneling removes the degeneracy of the < q :, < y : level pair. In second order of perturbation, the energy of the < q : level with respect to the < y : level at y 12 Ci is d i :
d i s J 2 Cir Ž A2i y Ci2 . . 2
Ž 2.
A 2i y Ci2 .<,
Since J < <Ž perturbations of the < q : wavefunction are very small and are neglected. The resulting level splittings, d i , are at the limit of the resolution of the hole burning experiments. In order to increase the level splitting and to ascertain the assignments, hole burning measurements in applied electric fields were also made. In both the ground and excited electronic states of the system under study, the energy separations between the near degenerate level pair arising from the
d i y 12 Ci
ym i P F
ym i P F
y 12 Ci
.
Ž 3.
The eigenfunctions and eigenvalues of this Hamiltonian are: <1, i : s cos Ž w i . , ysin Ž w i . , <2, i : s sin Ž w i . , cos Ž w i . ,
E1 s E2 s
d i y Ci
q
di
2
< di <
d i y Ci
di
2
y
< di <
(Ž d r2. q Ž m P F .
2
(Ž d r2. q Ž m P F .
2
2
i
i
,
Ž 4. 2
i
i
,
with tanŽ2 w i . s 2 m i P Frd i . The relative intensities of the four electronic transitions, between the level pairs in the ground, g, and excited, e, states of the guest, equal: I1 , 1 s I2, 2 s cos 2 Ž wg y we . ,
I1, 2 s I2, 1 s sin2 Ž wg y we . .
Ž 5.
In the limit of zero and high fields, w f 0 and w f pr4, respectively and the corresponding eigenfunctions are given by the delocalized, Ž< q :, < y :., and localized, Ž
Ch. Rambaud, H.P. Trommsdorffr Chemical Physics Letters 306 (1999) 124–132
127
3. Experimental SI doped BA crystals were grown from the melt by the Bridgman method using extensively zone-refined BA. Single crystal platelets of ca. 1 mm thickness were obtained by cleavage parallel to the Ža,b. plane and all spectra were recorded with light propagating perpendicularly to this plane. Measurements were made with the sample immersed in liquid helium at temperatures between 1.5 and 4.2 K, controlled via the helium vapor pressure. Measurements in electric fields were made by placing the sample between semitransparent, tin oxide coated quartz plates, with fields up to 3 = 10 6 Vrm applied perpendicular to the Ž a,b . plane. Spectra at a resolution of 0.1 cmy1 were recorded using a JY THR 1.5 m monochromator. These measurements were used to determine the temperature dependence of the absorption and to calibrate the line positions for the hole burning experiments. Hole burning experiments were made using a single mode Coherent 599.02 cw dye laser with a linewidth ca. ˚ precision 1 MHz, which could be scanned over 30 GHz. The wavelength of the laser was determined to 0.01 A using a home made wavemeter, and the fringes of a confocal Perot–Fabry interferometer with a free spectral range of 1.5 GHz were recorded simultaneously with the spectra for calibration. Holes with a depth of about 5% were burned close to the center of the inhomogeneously broadened absorption line with a luminous flux of 100 mWrcm2 . The typical optical density at the peak of the absorption line was 0.35 OD. Hole burning spectra were recorded by repetitively scanning the laser over an interval of "15 GHz about the burning frequency at a rate of 120 GHzrs and monitoring the fluorescence of the sample with a suitably filtered photomultiplier. The fluorescence signal was normalized with respect to the intensity of the incident laser, measured with a GaAs photodiode, and was averaged using a microcomputer.
4. Results and discussion As in the case of thioindigo w1,2,5x, SI occupies two different sites in the crystal, corresponding to the two physically acceptable ways in which the guest can substitutionally replace one BA dimer in the host matrix. Fig. 2 shows absorption spectra at 4.2 and 1.6 K in the region of the electronic origin of the so-called blue sites ˚ which were investigated in this work. The lines marked A Ž16982.3 cmy1 ., B Ž16987.4 cmy1 ., around 5885 A, and C Ž17010.0 cmy1 ., are also observed in emission and correspond to the pure electronic transitions of SI in the different proton configurations of the neighboring BA dimers. The inhomogeneous width ŽFWHM. of these lines is about 0.8 cmy1 . At low temperatures only the Ž
128
Ch. Rambaud, H.P. Trommsdorffr Chemical Physics Letters 306 (1999) 124–132
Fig. 2. Absorption spectra in the region of the pure electronic S 0 ™ S1 transition of selenoindigo in a benzoic acid crystal at 4.2 K Žfull line. and at 1.6 K Žbroken line..
longer-lived holes are generated under prolonged irradiation. The width of the holes is strongly temperature dependent and decreases from about 1 GHz at 4.2 K to 50 MHz at 1.5 K. As the population deficit created at the frequency of the burning laser is equilibrated between the two ground state levels involved in the unresolved transitions of line B, side-holes are expected to appear at frequencies of "Ž de y dg . from the central hole. When the hole is burned at the top of the inhomogeneous line profile, the intensity ratio of the integrated hole areas is 1:2:1. These side holes may however be inhomogeneously broadened, because of lack of correlation of the inhomogeneous broadening of the two different transitions w6,16x. Because of this broadening, the peak intensity of side-holes is reduced by the ratio of the widths of the central hole to those of the side-holes. Due to this fact, initial attempts to measure side-holes at the lowest temperatures failed. At a slightly higher temperature of 1.7 K, when the central hole is broadened, a larger population deficit can be created and the detection of side-holes becomes facilitated. Nevertheless, the side-holes could not be fully resolved. The hole profile observed for the transition B only indicated the presence of additional features Žsee Fig. 4 left. as compared to measurements made for lines A and C, where no side-holes are expected and the observed hole profiles are Lorentzian. In order to increase and fully resolve the level splittings, measurements in electric fields were made. Fig. 4 shows the corresponding hole burning spectra. The presence of strongly broadened side-holes is clearly Table 1 Parameters describing the level structure of the complex of a pair of benzoic acid dimers sandwiching the selenoindigo guest
A i ŽGHz. Ci ŽGHz. m ŽD. me y mg s 0.162"0.01 D;
Ground state, i
Excited state, e
17"10 110"10 0.02"0.015
430"20 370"20 0.18"0.015
˚3 a e y a g - 750 A The values of the dipole moment and the polarizability correspond to the projection on an axis perpendicular to the Ž a, b . plane of the benzoic acid.
Ch. Rambaud, H.P. Trommsdorffr Chemical Physics Letters 306 (1999) 124–132
129
Fig. 3. Energy level diagram of the proton configurations in a benzoic acid crystal around a selenoindigo guest molecule in the ground, S 0 , and the excited, S1 , electronic state. The transitions are labeled as in Fig. 2.
observed. Hole profiles were also calculated based on the transition energies and intensities predicted by Eqs. Ž4. and Ž5. and adjusting the values of J, mg and me Žthese two values correspond to the projection of m g and m e on the direction of the applied field, see Table 1.. For intermediate fields, four holes on each side of the central hole are predicted. For comparison with the experimental spectra, the stick spectra were convoluted with a narrow Lorentzian line profile ŽFWHM 0.3–0.4 GHz. for the central hole and broad Gaussian or Lorentzian line profiles ŽFWHM 1–2 GHz. for the side-holes. These fits are shown as continuous lines in Fig. 4. Note that the same values of the parameters, as given in Table 1, were used for fitting all spectra.
Fig. 4. Hole burning spectra of selenoindigo in a benzoic acid crystal at 1.7 K. Left: Observed and fitted hole burning spectra in zero electric field and components of the fit. Right: Hole burning spectra in electric fields at field strengths as indicated, with corresponding fits Žsee text..
130
Ch. Rambaud, H.P. Trommsdorffr Chemical Physics Letters 306 (1999) 124–132
In the initial fitting, using Gaussian line profiles, it was found that the integrated intensity of the side-holes as determined in the fit, had to be reduced by a factor of nearly two in order to reproduce the observed line profiles. Such an intensity deficit of the side holes is possible if the relaxation, distributing the population deficit Žcreated by burning. between levels, is not complete when the side-holes are recorded. Because of the limited lifetime of the holes, a study of the time evolution of the side-holes is not possible, and this observation was tentatively interpreted as indicating a very slow relaxation between the two corresponding levels w15x. When, however, Lorentzian line profiles were used for the side holes, a perfect fit of the spectra could be obtained with the line intensities predicted for a complete relaxation between the two levels. The rate of relaxation between the level pair arising from the Ž
Fig. 5. Hole burning spectra of selenoindigo in a benzoic acid crystal at 1.7 K. Spectra are recorded in applied electric after burning in zero field. Left: spectra at different values of the electric field as indicated. Right: splitting of the main peaks as a function of field strength.
Ch. Rambaud, H.P. Trommsdorffr Chemical Physics Letters 306 (1999) 124–132
131
the hole as a function of field strength is observed, together with the appearance of additional structure at low field strengths. The linewidth at low fields is smaller than that of the side-holes in the preceding experiments and increases significantly at higher fields. A fit of the observed spectra is not shown, as such fits involve too many assumptions and parameters regarding the lineshape functions. However, these measurements immediately give an upper limit for the difference of polarizability, a e y a g , in the two electronic states and yield the value of me y mg with higher precision. These values are quoted in Table 1 and were also used in the determination of the error limits for the values of me and mg .
5. Conclusion The value of the tunneling matrix element, J, associated with the concerted two proton transfer in BA dimers in the crystal, can only be measured if the energy difference between different proton configurations is sufficiently reduced. With the optical spectroscopic methods, this reduction of asymmetry is achieved for selected dimers next to suitable guest molecules, occupying substitutional sites in the BA crystal. The replacement of a BA dimer by a guest molecule disturbs the environment only little, and the present measurements confirm that the value of J does not significantly depend on the nature of the guest and is therefore also characteristic of BA dimers in pure crystals. In previous work, the rate of incoherent tunneling, which scales with J 2, was measured in pure and doped crystals. Assuming that the changes of this rate were entirely due to changes of J, these results implied that J should not vary by more than a factor of about two. The present work indicates that changes of J are in fact smaller and that changes of the rate of incoherent tunneling must in part be due to the changes of the phonon density and phonon coupling constant w4x. The stabilization of the asymmetric proton configurations with respect to the average value of the symmetric configurations equals 5 and 18 K in the ground and excited states of SI, respectively, and similar values have been measured for other guest molecules w1,2x. These values relate to the interaction of protons in two dimers across a guest molecule. The larger excited state value is probably related to the increased polarizability of the guest in the S 1 state. In a pure crystal, such interactions should be of comparable strength, since the smaller distance of between the protons compensates for the smaller polarizability of benzoic acid dimers. These interactions could therefore contribute significantly to the average energy difference between tautomers as derived for example from the population factors determined in different experiments. Recent NMR measurements on oriented single BA crystals of the temperature dependence of the proton dipolar splitting from 10 to 300 K suggest indeed that the average energy difference decreases significantly with increasing temperature and may be dominated by this factor w17x. In this case, the distribution of tautomers in the pure crystal would no longer be at random, a fact that might explain the discrepancies between reported values of the asymmetry w18x.
Acknowledgements We are grateful to A.J. Horsewill for making available to us the unpublished results of Ref. w17x.
References w1x w2x w3x w4x w5x w6x
J.M. Clemens, R.M. Hochstrasser, H.P. Trommsdorff, J. Chem. Phys. 80 Ž1984. 1744. G.R. Holtom, R.M. Hochstrasser, H.P. Trommsdorff, Chem. Phys. Lett. 131 Ž1986. 44. R.M. Hochstrasser, H.P. Trommsdorff, Chem. Phys. 115 Ž1987. 1. J. Skinner, H.P. Trommsdorff, J. Chem. Phys. 89 Ž1988. 897. Ch. Rambaud, A. Oppenlander, M. Pierre, H.P. Trommsdorff, J.C. Vial, Chem. Phys. 136 Ž1989. 335. ¨ A. Oppenlander, Ch. Rambaud, H.P. Trommsdorff, J.C. Vial, Phys. Rev. Lett. 63 Ž1989. 1432. ¨
132 w7x w8x w9x w10x w11x w12x w13x w14x w15x w16x w17x w18x
Ch. Rambaud, H.P. Trommsdorffr Chemical Physics Letters 306 (1999) 124–132 A. Stockli, B.H. Meier, R. Kreis, R. Meyer, R.R. Ernst, J. Chem. Phys. 93 Ž1990. 1502. ¨ R. Meyer, R.R. Ernst, J. Chem. Phys. 93 Ž1990. 5518. A. Heuer, U. Haeberlen, J. Chem. Phys. 95 Ž1991. 4201. C. Scheuer, P. Saalfrank, Chem. Phys. Lett. 245 Ž1995. 201. A.J. Horsewill, A. Ikram, Physika B 226 Ž1996. 202. D.F. Brougham, A.J. Horsewill, R.I. Jenkinson, Chem. Phys. Lett. 272 Ž1997. 69. A.J. Horsewill, P.J. McDonald, D. Vijayaraghavan, J. Chem. Phys. 100 Ž1994. 1889. Unpublished results from this laboratory. H.P. Trommsdorff, Ch. Rambaud, F. Ramaz, H. Port, J.C. Vial, Spectral Holeburning and Luminescence Line Narrowing: Science and Applications, Technical Digest, Vol. 22, Optical Society of America, Washington, DC, 1992, p. 172. M. Johnson, K. Orth, J. Friedrich, H.P. Trommsdorff, J. Chem. Phys. 105 Ž1996. 9762. A.J. Horsewill et al., unpublished results. M.A. Neumann, S. Craciun, A. Corval, M.R. Johnson, A.J. Horsewill, V.A. Benderskii, H.P. Trommsdorff, Ber. Bunsenges. Phys. Chem. 102 Ž1998. 325.
Chemical Physics Letters 306 Ž1999. 124–132
Cooperative proton transfer and tunneling in dye doped benzoic acid crystals Ch. Rambaud, H.P. Trommsdorff
)
Laboratoire de Spectrometrie ´ Physique, UniÕersite´ J. Fourier Grenoble — CNRS (UMR 5588), B.P. 87, 38402 St. Martin d’Heres ` Cx, France Received 6 January 1999; in final form 1 April 1999
Abstract In seleno-indigo doped benzoic acid crystals, the energy level structure of a pair of benzoic acid dimers coupled to the impurity center is characterized by optical spectroscopy and transient hole burning in electric fields. The lowest energy states involve degenerate, polar proton configurations. Proton tunneling lifts this degeneracy. The tunneling matrix element for proton transfer in a benzoic acid dimer equals 6.5 " 1.5 GHz, a value comparable to those found with other guest molecules. Relaxation between the two ground state levels involves the concerted motion of four protons and determines the intensity distribution of the fine structure observed in hole burning. q 1999 Elsevier Science B.V. All rights reserved.
1. Introduction The translational tunneling of protons in the hydrogen bonds of benzoic acid ŽBA. crystals has been the object of extensive experimental and theoretical work w1–12x. Concerted two-proton transfer along the hydrogen bonds of a dimer interconverts the two tautomer structures, denoted L and R in Fig. 1. These two tautomers are equivalent in isolated dimers, but unequivalent in the crystal environment. The energy difference between tautomers is determined by the packing of the molecules in the crystal and is, for a given dimer, also dependent upon the proton position of neighboring dimers. Due to this coupling between proton positions in neighboring dimers, the energy of a pair of two neighboring R tautomers will differ from the energy of two isolated R tautomers in an environment composed of L tautomers. When the coupling dominates the energy difference between tautomers, the phase behavior of the crystals is expected to be affected. NMR measurements under applied pressure indeed suggest such a possibility w13x. Under pressure, the coupling is expected to increase, while the average energy difference between tautomers was shown to decrease. The observation of a discontinuity of the variation, as a function of pressure, of the parameters describing the NMR proton T1 relaxation in pure BA crystals, indicated a subtle phase change. However Raman and structural measurements have not yet been able to substantiate this proposition w14x.
)
Corresponding author. Fax: q33 476514544; e-mail: [email protected]
0009-2614r99r$ - see front matter q 1999 Elsevier Science B.V. All rights reserved. PII: S 0 0 0 9 - 2 6 1 4 Ž 9 9 . 0 0 4 4 7 - 9
Ch. Rambaud, H.P. Trommsdorffr Chemical Physics Letters 306 (1999) 124–132
125
When impurity molecules are introduced into a BA host matrix, dimers in the vicinity of the guest are perturbed and the energy difference between L and R tautomers of these selected dimers is altered. This effect was exploited, when the high resolution low temperature optical spectra of different guest molecules were used to characterize the energy level structure of such isolated dimers in the BA crystal w1–6x. Both coherent and incoherent proton tunneling in these dimers could be characterized. Here, we report the observation and characterization of a complex of two symmetry related dimers sandwiching a guest molecule in which the coupling exceeds the energy difference between tautomer states, so that the lowest energy states of this complex are described by a degenerate pair of
2. Theoretical description of the level structure In symmetry adapted,
yJr'2
0
A i q Ci
yJr'2
0
yJr'2
yJr'2
1 2
y Ci
0
0
0
0
y 21 Ci
0
0 1 2
.
Ž 1.
A i is the energy difference between tautomers neglecting coupling, and Ci is the coupling, which stabilizes the degenerate configurations Ž
1 The vibrational ground state levels corresponding to the L and R tautomers of one dimer are designated by
Ch. Rambaud, H.P. Trommsdorffr Chemical Physics Letters 306 (1999) 124–132
126
Fig. 1. Tautomer exchange of the benzoic acid dimer by concerted two proton transfer.
assumed to be independent of the electronic state of the guest and is, in the present case, small as compared to the energy differences, <2 A i <, < Ci " A i <, so that the Hamiltonian Ž1. is approximately diagonal. When Ci / 0, tunneling removes the degeneracy of the < q :, < y : level pair. In second order of perturbation, the energy of the < q : level with respect to the < y : level at y 12 Ci is d i :
d i s J 2 Cir Ž A2i y Ci2 . . 2
Ž 2.
A 2i y Ci2 .<,
Since J < <Ž perturbations of the < q : wavefunction are very small and are neglected. The resulting level splittings, d i , are at the limit of the resolution of the hole burning experiments. In order to increase the level splitting and to ascertain the assignments, hole burning measurements in applied electric fields were also made. In both the ground and excited electronic states of the system under study, the energy separations between the near degenerate level pair arising from the
d i y 12 Ci
ym i P F
ym i P F
y 12 Ci
.
Ž 3.
The eigenfunctions and eigenvalues of this Hamiltonian are: <1, i : s cos Ž w i . , ysin Ž w i . , <2, i : s sin Ž w i . , cos Ž w i . ,
E1 s E2 s
d i y Ci
q
di
2
< di <
d i y Ci
di
2
y
< di <
(Ž d r2. q Ž m P F .
2
(Ž d r2. q Ž m P F .
2
2
i
i
,
Ž 4. 2
i
i
,
with tanŽ2 w i . s 2 m i P Frd i . The relative intensities of the four electronic transitions, between the level pairs in the ground, g, and excited, e, states of the guest, equal: I1 , 1 s I2, 2 s cos 2 Ž wg y we . ,
I1, 2 s I2, 1 s sin2 Ž wg y we . .
Ž 5.
In the limit of zero and high fields, w f 0 and w f pr4, respectively and the corresponding eigenfunctions are given by the delocalized, Ž< q :, < y :., and localized, Ž
Ch. Rambaud, H.P. Trommsdorffr Chemical Physics Letters 306 (1999) 124–132
127
3. Experimental SI doped BA crystals were grown from the melt by the Bridgman method using extensively zone-refined BA. Single crystal platelets of ca. 1 mm thickness were obtained by cleavage parallel to the Ža,b. plane and all spectra were recorded with light propagating perpendicularly to this plane. Measurements were made with the sample immersed in liquid helium at temperatures between 1.5 and 4.2 K, controlled via the helium vapor pressure. Measurements in electric fields were made by placing the sample between semitransparent, tin oxide coated quartz plates, with fields up to 3 = 10 6 Vrm applied perpendicular to the Ž a,b . plane. Spectra at a resolution of 0.1 cmy1 were recorded using a JY THR 1.5 m monochromator. These measurements were used to determine the temperature dependence of the absorption and to calibrate the line positions for the hole burning experiments. Hole burning experiments were made using a single mode Coherent 599.02 cw dye laser with a linewidth ca. ˚ precision 1 MHz, which could be scanned over 30 GHz. The wavelength of the laser was determined to 0.01 A using a home made wavemeter, and the fringes of a confocal Perot–Fabry interferometer with a free spectral range of 1.5 GHz were recorded simultaneously with the spectra for calibration. Holes with a depth of about 5% were burned close to the center of the inhomogeneously broadened absorption line with a luminous flux of 100 mWrcm2 . The typical optical density at the peak of the absorption line was 0.35 OD. Hole burning spectra were recorded by repetitively scanning the laser over an interval of "15 GHz about the burning frequency at a rate of 120 GHzrs and monitoring the fluorescence of the sample with a suitably filtered photomultiplier. The fluorescence signal was normalized with respect to the intensity of the incident laser, measured with a GaAs photodiode, and was averaged using a microcomputer.
4. Results and discussion As in the case of thioindigo w1,2,5x, SI occupies two different sites in the crystal, corresponding to the two physically acceptable ways in which the guest can substitutionally replace one BA dimer in the host matrix. Fig. 2 shows absorption spectra at 4.2 and 1.6 K in the region of the electronic origin of the so-called blue sites ˚ which were investigated in this work. The lines marked A Ž16982.3 cmy1 ., B Ž16987.4 cmy1 ., around 5885 A, and C Ž17010.0 cmy1 ., are also observed in emission and correspond to the pure electronic transitions of SI in the different proton configurations of the neighboring BA dimers. The inhomogeneous width ŽFWHM. of these lines is about 0.8 cmy1 . At low temperatures only the Ž
128
Ch. Rambaud, H.P. Trommsdorffr Chemical Physics Letters 306 (1999) 124–132
Fig. 2. Absorption spectra in the region of the pure electronic S 0 ™ S1 transition of selenoindigo in a benzoic acid crystal at 4.2 K Žfull line. and at 1.6 K Žbroken line..
longer-lived holes are generated under prolonged irradiation. The width of the holes is strongly temperature dependent and decreases from about 1 GHz at 4.2 K to 50 MHz at 1.5 K. As the population deficit created at the frequency of the burning laser is equilibrated between the two ground state levels involved in the unresolved transitions of line B, side-holes are expected to appear at frequencies of "Ž de y dg . from the central hole. When the hole is burned at the top of the inhomogeneous line profile, the intensity ratio of the integrated hole areas is 1:2:1. These side holes may however be inhomogeneously broadened, because of lack of correlation of the inhomogeneous broadening of the two different transitions w6,16x. Because of this broadening, the peak intensity of side-holes is reduced by the ratio of the widths of the central hole to those of the side-holes. Due to this fact, initial attempts to measure side-holes at the lowest temperatures failed. At a slightly higher temperature of 1.7 K, when the central hole is broadened, a larger population deficit can be created and the detection of side-holes becomes facilitated. Nevertheless, the side-holes could not be fully resolved. The hole profile observed for the transition B only indicated the presence of additional features Žsee Fig. 4 left. as compared to measurements made for lines A and C, where no side-holes are expected and the observed hole profiles are Lorentzian. In order to increase and fully resolve the level splittings, measurements in electric fields were made. Fig. 4 shows the corresponding hole burning spectra. The presence of strongly broadened side-holes is clearly Table 1 Parameters describing the level structure of the complex of a pair of benzoic acid dimers sandwiching the selenoindigo guest
A i ŽGHz. Ci ŽGHz. m ŽD. me y mg s 0.162"0.01 D;
Ground state, i
Excited state, e
17"10 110"10 0.02"0.015
430"20 370"20 0.18"0.015
˚3 a e y a g - 750 A The values of the dipole moment and the polarizability correspond to the projection on an axis perpendicular to the Ž a, b . plane of the benzoic acid.
Ch. Rambaud, H.P. Trommsdorffr Chemical Physics Letters 306 (1999) 124–132
129
Fig. 3. Energy level diagram of the proton configurations in a benzoic acid crystal around a selenoindigo guest molecule in the ground, S 0 , and the excited, S1 , electronic state. The transitions are labeled as in Fig. 2.
observed. Hole profiles were also calculated based on the transition energies and intensities predicted by Eqs. Ž4. and Ž5. and adjusting the values of J, mg and me Žthese two values correspond to the projection of m g and m e on the direction of the applied field, see Table 1.. For intermediate fields, four holes on each side of the central hole are predicted. For comparison with the experimental spectra, the stick spectra were convoluted with a narrow Lorentzian line profile ŽFWHM 0.3–0.4 GHz. for the central hole and broad Gaussian or Lorentzian line profiles ŽFWHM 1–2 GHz. for the side-holes. These fits are shown as continuous lines in Fig. 4. Note that the same values of the parameters, as given in Table 1, were used for fitting all spectra.
Fig. 4. Hole burning spectra of selenoindigo in a benzoic acid crystal at 1.7 K. Left: Observed and fitted hole burning spectra in zero electric field and components of the fit. Right: Hole burning spectra in electric fields at field strengths as indicated, with corresponding fits Žsee text..
130
Ch. Rambaud, H.P. Trommsdorffr Chemical Physics Letters 306 (1999) 124–132
In the initial fitting, using Gaussian line profiles, it was found that the integrated intensity of the side-holes as determined in the fit, had to be reduced by a factor of nearly two in order to reproduce the observed line profiles. Such an intensity deficit of the side holes is possible if the relaxation, distributing the population deficit Žcreated by burning. between levels, is not complete when the side-holes are recorded. Because of the limited lifetime of the holes, a study of the time evolution of the side-holes is not possible, and this observation was tentatively interpreted as indicating a very slow relaxation between the two corresponding levels w15x. When, however, Lorentzian line profiles were used for the side holes, a perfect fit of the spectra could be obtained with the line intensities predicted for a complete relaxation between the two levels. The rate of relaxation between the level pair arising from the Ž
Fig. 5. Hole burning spectra of selenoindigo in a benzoic acid crystal at 1.7 K. Spectra are recorded in applied electric after burning in zero field. Left: spectra at different values of the electric field as indicated. Right: splitting of the main peaks as a function of field strength.
Ch. Rambaud, H.P. Trommsdorffr Chemical Physics Letters 306 (1999) 124–132
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the hole as a function of field strength is observed, together with the appearance of additional structure at low field strengths. The linewidth at low fields is smaller than that of the side-holes in the preceding experiments and increases significantly at higher fields. A fit of the observed spectra is not shown, as such fits involve too many assumptions and parameters regarding the lineshape functions. However, these measurements immediately give an upper limit for the difference of polarizability, a e y a g , in the two electronic states and yield the value of me y mg with higher precision. These values are quoted in Table 1 and were also used in the determination of the error limits for the values of me and mg .
5. Conclusion The value of the tunneling matrix element, J, associated with the concerted two proton transfer in BA dimers in the crystal, can only be measured if the energy difference between different proton configurations is sufficiently reduced. With the optical spectroscopic methods, this reduction of asymmetry is achieved for selected dimers next to suitable guest molecules, occupying substitutional sites in the BA crystal. The replacement of a BA dimer by a guest molecule disturbs the environment only little, and the present measurements confirm that the value of J does not significantly depend on the nature of the guest and is therefore also characteristic of BA dimers in pure crystals. In previous work, the rate of incoherent tunneling, which scales with J 2, was measured in pure and doped crystals. Assuming that the changes of this rate were entirely due to changes of J, these results implied that J should not vary by more than a factor of about two. The present work indicates that changes of J are in fact smaller and that changes of the rate of incoherent tunneling must in part be due to the changes of the phonon density and phonon coupling constant w4x. The stabilization of the asymmetric proton configurations with respect to the average value of the symmetric configurations equals 5 and 18 K in the ground and excited states of SI, respectively, and similar values have been measured for other guest molecules w1,2x. These values relate to the interaction of protons in two dimers across a guest molecule. The larger excited state value is probably related to the increased polarizability of the guest in the S 1 state. In a pure crystal, such interactions should be of comparable strength, since the smaller distance of between the protons compensates for the smaller polarizability of benzoic acid dimers. These interactions could therefore contribute significantly to the average energy difference between tautomers as derived for example from the population factors determined in different experiments. Recent NMR measurements on oriented single BA crystals of the temperature dependence of the proton dipolar splitting from 10 to 300 K suggest indeed that the average energy difference decreases significantly with increasing temperature and may be dominated by this factor w17x. In this case, the distribution of tautomers in the pure crystal would no longer be at random, a fact that might explain the discrepancies between reported values of the asymmetry w18x.
Acknowledgements We are grateful to A.J. Horsewill for making available to us the unpublished results of Ref. w17x.
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