- Email: [email protected]
Femtosecond mid-infrared photon echo study of an intramolecular hydrogen bond
12 March 2002
Chemical Physics Letters 354 (2002) 256–263 www.elsevier.com/locate/cplett
Femtosecond mid-infrared photon echo study of an intramolecular hydrogen bond J. Stenger, D. Madsen 1, J. Dreyer, P. Hamm 2, E.T.J. Nibbering, T. Elsaesser
*
Max Born Institut f€ur Nichtlineare Optik und Kurzzeitspektroskopie, Max Born Strasse 2A, D-12489 Berlin, Germany Received 4 January 2002
Abstract The vibrational dephasing dynamics of O–H stretching excitations in a sterically well-defined intramolecular hydrogen bond (H bond) is studied by femtosecond photon echo spectroscopy in the mid-infrared. The O–H stretching vibration of phthalic acid monomethyl ester in inert solution displays a fast decay of phase coherence on a sub-100 fs time scale. Anharmonic coupling of the stretching motion to an underdamped low-frequency mode of the H bond gives rise to oscillations in the transient grating decay and the 3-pulse photon echo peak shift. Spectral diffusion dynamics on longer time scales is absent in such intramolecular H bonds, as opposed to the weaker intermolecular H bonds in water. Ó 2002 Published by Elsevier Science B.V.
1. Introduction Hydrogen bonds determine the structure and dynamics of protic liquids like water as well as of biopolymers like proteins and DNA [1]. The static and dynamical properties of hydrogen bonds are intensively studied using a multitude of spectroscopic techniques, varying from X-ray diffraction, electronic and vibrational spectroscopy, and nuclear magnetic resonance. In particular, it has been shown that steady-state infrared spectroscopy of
*
Corresponding author. Fax: +49-30-6392-1409. E-mail address: [email protected] (T. Elsaesser). 1 Present address: Department of Chemistry, Aarhus University, Langelandsgade 140, 8000 Aarhus C, Denmark. 2 Present address: Physikalisch-Chemisches Institut, Universit€ at Z€ urich, Winterthurer Str. 190, CH-8057 Z€ urich, Switzerland.
the O–H stretching mode has the potential of revealing the strength of the hydrogen bond due to a direct relationship to the red shift of the vibrational frequency of the O–H stretching band [2]. Recently much effort has been put in nonlinear infrared spectroscopy of the dynamical properties of these line shapes using pump-probe and four-wave mixing techniques. From pump-probe studies of the O–H and O–D stretching modes in intermolecular hydrogen bonds of molecular systems such as water, alcohols and acids dynamical information has been obtained on the vibrational lifetimes with typical values in the subpicosecond time range [3– 6], energy redistribution [7–10], energy transfer to neighboring molecules [11], band substructures [12,13] and band shifts due to the dynamical Stokes shift [9,14–17] or due to local heating [18], and orientational dynamics [19,20]. From photon echo and transient hole burning techniques the relative
0009-2614/02/$ - see front matter Ó 2002 Published by Elsevier Science B.V. PII: S 0 0 0 9 - 2 6 1 4 ( 0 2 ) 0 0 1 0 3 - 3
J. Stenger et al. / Chemical Physics Letters 354 (2002) 256–263
magnitude of homogeneous and inhomogeneous contributions to the overall line shape can be determined. Recently, we have shown that the line shape of the O–H stretching mode of HOD in D2 O results from significant contributions from a homogeneous dephasing process with a time constant of 90 fs [21], and an inhomogeneous part that persists on picosecond time scales [22]. The fast dephasing has been explained to be the result of solvent fluctuations that have a major impact due to the strong anharmonicity of the O–H stretching mode. The inhomogeneous part has been ascribed to a distribution in solvent configuration leading to an inhomogeneous contribution to the vibrational transition frequency. The interesting question evolving from the latter work is concerned with the influence of the number of possible geometrical conformations and the dynamical fluctuations associated with that. The objective of the present work is to analyze line broadening contributions for an intramolecular hydrogen bond with a well-defined geometry. We study the dephasing dynamics of the O–H stretching mode of phthalic acid monomethyl ester (PMME-H, inset of Fig. 1), a medium-sized organic molecule which was dissolved in the inert solvent CCl4 . PMME-H forms a medium-strong intramolecular hydrogen bond which is evident from the infrared spectral line shape of the O–H stretching mode (Fig. 1). This absorption band
Fig. 1. O–H stretching band of PMME-H in CCl4 (solid line) and laser spectrum (dashed line). The sharp line at 2950 cm1 is due to the C–H stretching absorption. The molecular structure of PMME-H is also shown.
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exhibits the characteristic strong red shift, strong intensity increase and clearly present substructures, compared to the single resonance of the free hydroxyl-stretch at 3610 cm1 . We have recently performed a pump-probe study [23,24] where we show that the hydroxyl stretching motion of PMME-H and its deuterated analog PMME-D is strongly anharmonically coupled to a 100 cm1 mode which involves an out-of-plane motion of the two units bridged by the hydrogen bond and – thus – modulates the length of the hydrogen bond. The pump-probe study shows that this out-of-plane mode with a dephasing time of approximately 0.5 ps is underdamped. The anharmonically coupled low-frequency mode gives rise to vibrational sidebands of the pure O–H stretching excitation, contributing to the overall line shape of the O–H stretching band. In addition to this feature, there are other broadening mechanisms which are investigated here by photon echo experiments. Anharmonic coupling of the stretching motion to the underdamped low-frequency mode of the H bond gives rise to oscillations in the transient grating decay and the peak shift of 3pulse photon echo signals. Spectral diffusion dynamics on longer time scales is essentially absent in such intramolecular H bonds.
2. Experimental For the photon echo experiment, ultrashort intense mid-infrared pulses were generated by optical parametric amplification. The output pulses of an amplified Ti:sapphire laser system (300 lJ energy per pulse, 90 fs duration, centered at 800 nm) were used to generate a single filament white light continuum, and to amplify this continuum in a KTiOPO4 crystal in two stages (first pass pumped by 3 lJ at 800 nm, second pass pumped by 200 lJ). The resulting idler pulses are tunable between 2700 and 3300 cm1 with respective energies varying between 3 and 5 lJ. In the experiments, the spectrum of the laser pulses was tuned to the maximum of the O–H stretching band of PMME-H (Fig. 1). The 3-pulse photon echo experiment was performed in the so-called box configuration where
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three overlapping beams with wave vectors k1 , k2 and k3 were focused to a spot diameter of 80 lm on the sample. The nonlinear signals were detected in the directions k3 þ k2 k1 and k3 k2 þ k1 . The photon echo signals were measured as a function of the coherence time s, the delay between the two pulses generating the transient grating in the sample, and as a function of the population T , the delay between the second and the third pulse which is diffracted from the sample. The sample consists of PMME-H (phthalic acid monomethyl ester; Aldrich) dissolved in CCl4 (Merck, uvasol) with a concentration of 15 mM, resulting in a maximum vibrational absorbance of about OD ¼ 0.2. The solution is refreshed for every laser shot by use of a flow cell with CaF2
windows separated by 500 lm. Rapid circulation of the sample solution is necessary to avoid accumulation and heating effects.
3. Results Results of the 3-pulse photon echo experiments are presented in Fig. 2. Fig. 2a shows the photon echo signal from PMME-H in CCl4 diffracted into the direction k3 þ k2 k1 as a function of the population time T and of the coherence time s. As a function of T , the signal displays a strong component around T ¼ 0 which decays within the first 300 fs and is followed by a much weaker contribution, extending to picosecond T values. This
Fig. 2. (a) Three-dimensional plot of the photon echo signal from PMME-H in CCl4 , shown on a linear scale as a function of the population time T and the coherence time s. The strong component around zero delay has a relative amplitude of 1 and was truncated in the plot. (b) Contour plot of the results obtained on PMME-H in CCl4 . (c) Contour plot for the signal from the pure solvent CCl4 . Both contour plots are plotted on a logarithmic scale (three orders of magnitude full scale).
J. Stenger et al. / Chemical Physics Letters 354 (2002) 256–263
component is superimposed by oscillations with a period of 330 fs. As a function of the coherence time s, the signal displays a maximum very close to s ¼ 0 for all population times T and a very fast decay which is close to the time resolution of the experiment (Fig. 2b). For comparison, the signal measured with the pure solvent CCl4 is shown in Fig. 2c. One finds a single strong peak at T ¼ 0 which decays within the first 300 fs of T . As a function of s, this signal is centered at s ¼ 0. In Fig. 3, the transient grating scattering (TG) signal, i.e. the signal measured with s ¼ 0, is shown as a function of the population time T . After the initial fast decay, one observes prominent oscillations with a period of 330 fs, superim-
Fig. 3. Transient grating scattering result shown on a linear (a) and a logarithmic scale (b, coherence time s ¼ 0). The 5-level diagram illustrates the complexity of the spectroscopic dynamics. Due to contributions of the O–H stretching vibration in the original ‘cold’ and relaxed ‘hot’ states to the overall signal the transient grating dynamics does not exhibit a single exponential decay.
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posed on a slow decay which extends up to T ¼ 20 ps (Fig. 3b). In addition to the population decay from the v ¼ 1 level of the O–H stretching oscillator which occurs with a time constant of the order of 200 fs [24], there are obviously other contributions to the transient grating dynamics that will be discussed below. In Fig. 4, we plot the photon echo signal as a function of the coherence time s, for T ¼ 0 (solid circles). This trace is equivalent to a 2-pulse photon echo and decays with a time constant of about 30 fs, very close to the instrumental response function as derived from the solvent signal (open circles). At finite values of T , similarly fast decays are observed. We estimated the effect of quantum interference in the echo decay [25,26] by the anharmonically coupled low-frequency mode to be less than 10–20%, leading to an estimated upper limit of 40 fs for the echo decay. The 3-pulse photon echo peak shift (3PEPS [27– 29]) of PMME-H was determined from the 3-pulse photon echo data in Fig. 2. The peak shift represents the shift of the maximum photon echo signal along the coherence time s with respect to delay zero, i.e. the maximum of the instrument response function. In Fig. 5a, the peak shift is plotted as a
Fig. 4. Two-pulse photon echo result of PMME-H in CCl4 (solid circles). The diffracted intensity is plotted on a logarithmic scale as a function of the coherence time s (population time T ¼ 0). The transient indicates the fast initial coherence decay of the O–H stretching mode. Open circles: instrumental response function as measured with the pure solvent CCl4 .
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(a)
(b)
Fig. 5. (a) Three-pulse echo peak shift (3PEPS) of PMME-H in CCl4 , demonstrating the oscillating contribution of the out-ofplane 100 cm1 mode due to anharmonic coupling with the O– H stretching mode. (b) 3PEPS results for HOD=D2 O, measured at the excitation frequencies 3300 cm1 (dashed line) and 3400 cm1 (solid line, for details see [22]). In contrast to PMME-H, spectral diffusion processes on longer time scales are significant.
function of the population time T . We observe an oscillatory behavior of the peak shift displaying a period of about 330 fs, the period of the low-frequency mode coupling to the O–H stretching motion. The peak shift decays to zero with a time constant of about 1 ps. The absolute value of the peak shift of less than 10 fs is distinctly smaller than what has been measured for the O–H stretching vibrations of HDO in D2 O (Fig. 5b) which forms intermolecular hydrogen bonds. Here, the initial 3PEPS signal has a value of 40–60 fs and decays only partly at longer times T .
4. Discussion In the following, we first discuss the contributions of the solute PMME-H and the solvent CCl4
to the photon echo signals. This is followed by an analysis of the transient grating dynamics and of the photon echo peak shift data. The latter are finally compared to recent results on intermolecular hydrogen bonds of HOD in D2 O. In the measurements with the pure solvent CCl4 , we observe a strong signal which is centered around s ¼ 0 and decays very rapidly both as a function of the coherence time s and the population time T (cf. Fig. 2c). This signal occurs exclusively within the temporal overlap of the three pulses and is due to the nonresonant electronic third-order nonlinearity of the solvent and the CaF2 windows of the sample cell. Such nonlinearities display an instantaneous response and – consequently – the transient measured for T ¼ 0 (Fig. 4, open circles) reflects the instrument response function determined by the time envelopes of the pulses. The data in Fig. 4 reveal a slight asymmetry of the pulse envelopes which originates from group velocity dispersion effects in the parametric generation process [30]. In the measurements with PMME-H dissolved in CCl4 , the solvent contributes significantly to the strong signal observed during the temporal overlap of the three pulses (Figs. 2a,c). From the intensity of the signals diffracted from the solution and from the pure solvent, we estimate that about 10% of the main signal peak originate from PMME-H. The 2-pulse photon echo signal (population time T ¼ 0, Fig. 4) of the solution is very close to the instrument response function with a slightly slower decay for positive s. A similarly fast decay is found for finite values of T where the solvent contribution has decayed. We conclude that there is a very fast decay of phase coherence of the O–H stretching excitation with an upper limit of the decay time of approximately 40 fs. It is interesting to note that this decay occurs on a time scale similar to that of the phase relaxation of O–H stretching excitations in HOD=D2 O forming intermolecular hydrogen bonds. On the basis of the present data, it is not possible to decide to what extent the decay of phase coherence in PMME-H reflects a dephasing process in the fast modulation limit, i.e. a purely homogeneous broadening, or a very fast spectral diffusion process within the O–H stretching band.
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The decay of the transient population grating shown in Fig. 3 extends over two orders of magnitude in the population time T and exhibits three components, (i) a fast decay within the first 250 fs, (ii) a slow decay over the time range up to about 20 ps, and (iii) an oscillatory contribution. The lifetime of the v ¼ 1 level of the O–H stretching oscillator of PMME-H has a value of approximately 200 fs, as suggested by recent pump-probe studies [24]. Thus, population relaxation from the v ¼ 1 level may contribute to the initial fast decay, in addition to the solvent signal observed during temporal pulse overlap. The v ¼ 1 population relaxation is due to a nonadiabatic coupling of the v ¼ 1 level to other vibrational states and dissipates the absorbed pump photon energy to other vibrational modes. This dissipation process leads to a ‘hot’ vibrational ground state v ¼ 00 in which the O–H stretching vibration is unexcited but other modes at lower frequencies have accepted the excess energy. The intramolecular hydrogen bond is weakened in this hot ground state, leading to a blue shift of the O–H stretching absorption. On an even slower time scale, the intramolecular excess energy of PMME-H is thermalized and transferred to the surrounding solvent and the molecule returns to its initial ground state v ¼ 0. This relaxation scenario is visualized by the 5-level scheme in the inset of Fig. 3a. The slow decay of the transient grating signal in Fig. 3b reflects the intermolecular thermal relaxation on a time scale of up to 20 ps. This behavior is in very good agreement with recent pump-probe measurements of the nonlinear O–H stretching absorption which show the same slow thermal relaxation [24]. The oscillatory component of the transient grating decay is caused by the anharmonic coupling of the O–H stretching mode to an underdamped low-frequency mode of a 100 cm1 frequency which modulates the length of the hydrogen bond. Wavepacket motion along the lowfrequency coordinate of molecules in the v ¼ 0 state is impulsively excited through a Raman process which occurs within the bandwidth of the mid-infrared pulses and is resonantly enhanced by the O–H stretching absorption. Wavepacket motion in the v ¼ 1 level of the O–H mode is damped very rapidly by the fast v ¼ 1 population decay
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and does not contribute to the oscillations observed here. The 3PEPS reflects inhomogeneous contributions to the line shape of the optical transition which decay by spectral diffusion processes. It has been shown that the 3PEPS decay of vibrational 2and 3-level systems mimics the frequency fluctuation correlation function of the system. Our recent photon echo study of HOD=D2 O demonstrates, however, that this correspondence does not exist for the 5-level scheme involving the hot ground state v ¼ 00 [22] (cf. inset of Fig. 3). The 3PEPS of PMME-H plotted in Fig. 5a shows very small absolute values of the peak shift and an oscillation with a period of 330 fs, corresponding to a vibrational frequency of 100 cm1 . Though the peak shift measured during temporal overlap of the three pulses is influenced by the strong solvent signal (with zero peak shift), the peak shift at population times T > 250 fs is exclusively caused by PMME-H. We conclude from the small absolute value that at those times inhomogeneous broadening of the O–H stretching band is essentially absent. This suggests that for the intramolecular hydrogen bond of PMME-H spectral diffusion does not take place on longer time scales, in sharp contrast to the intermolecular H bonds of HOD in D2 O. In this system, the absolute values of the peak shift are substantially higher for population times up to 20 ps and a delayed maximum of the peak shift occurs for frequencies in the red part of the O–H stretching band (Fig. 5b). As explained in [22], spectral diffusion on time scales much slower than the T1 population relaxation time of the v ¼ 1 state leads to effective additional contributions to the nonlinear signals by the relaxed ‘hot’ ground state. Due to the interference effects between different Liouville space pathways the 3PEPS signal exhibits the delayed increase at the red-edge of the O–H stretching absorption band. If, however, no phase memory persists on this slower time scale, no interference effects between different Liouville space pathways can occur, and consequently no delayed rise of the 3PEPS signal is expected. This happens to be the case for PMME-H in CCl4 . As a consequence, the observed 3PEPS signal mimics more closely the frequency fluctuation correlation func-
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tion despite the fact that for PMME-H we have a 5-level system. Coherent modulations of 3PEPS signals have been observed before for electronic transitions of dye molecules in solution [29,31]. Wavepacket motion due to impulsively excited underdamped intramolecular modes upon ultrafast electronic excitation leads to oscillating contributions of the 3PEPS signals, a consequence of the modulation of the shape of the 3-pulse echo signals due to the formed quantum beats [32]. We report here the first observation of such marked modulations for the 3PEPS signal of a vibrational transition. The occurrence of oscillations in the 3PEPS signal of PMME-H extending up to 1 ps is due to the impulsively excited 100 cm1 out-of-plane mode anharmonically coupled to the O–H stretching mode. Since this coherence persists for times much longer than the v ¼ 1 lifetime, the contribution to the 3PEPS signal originates from wavepacket motion of molecules in the v ¼ 0 ground state.
5. Conclusions We report here the first femtosecond mid-infrared four-wave mixing study of a geometrically well-defined intramolecular hydrogen bond. For the system under study, PMME-H in CCl4 , the absorption line shape broadening mechanisms appears to be dominated by a fast coherence decay on a sub-100 fs time. On the basis of the present data, we cannot discriminate a line broadening mechanism due to fluctuations in the fast modulation limit or with finite correlation times. From the echo peak shift measurements it follows that this fast contribution to the correlation function dominates the line broadening, with spectral diffusion on longer time scales of minor importance. The anharmonically coupled underdamped 100 cm1 out-of-plane mode adds a Franck–Condon progression to the overall line shape. In the light of the present results it will be interesting to decipher the underlying microscopic origin of such a fast decay of the correlation function. One possible reason might be that other intramolecular modes coupled to the O–H stretching mode cause the dephasing. From model
calculations using a Cartesian reaction surface approach it has been found that a bending mode also couples strongly [33], but this mode is only populated at its v ¼ 0 level since its frequency is much higher than kT. The observed overall overdamped behavior can be due to the collective effect of several thermally populated low-frequency modes that have a coupling strength to the O–H stretching mode which is smaller than and even comparable with that of the 100 cm1 out-of-plane mode [24,34]. These lower frequency modes might be underdamped or overdamped, and they might be sensitive to solvent fluctuations, especially those whose frequency is comparable to the intermolecular low-frequency modes of CCl4 . Solvent fluctuations are expected to have an even more pronounced effect than in the case of the weak intermolecular hydrogen bond of HOD=D2 O, since the anharmonicity of the O–H stretching vibration of PMME-H is larger [35]. In order to obtain more insight into the underlying microscopic mechanisms for this ultrarapid dephasing of the O–H stretching mode in an intramolecular hydrogen bond we aim to pursue further studies.
Acknowledgements The mid-infrared spectroscopic activities on hydrogen bonds in the electronic ground state are embedded in the collaborative research center Analysis and Control of Photoinduced Reactions (Sonderforschungsbereich 450 Analyse und Steuerung ultraschneller photoinduzierter Reaktionen), supported by the Deutsche Forschungsgemeinschaft. We cordially thank J. Manz, O. K€ uhn, H. Naundorf and G.K. Paramonov from the Freie Universit€at Berlin for discussions.
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[22] J. Stenger, D. Madsen, P. Hamm, E.T.J. Nibbering, T. Elsaesser, A photon echo peak shift study of liquid water, J. Phys. Chem. A (in press). [23] J. Stenger, D. Madsen, J. Dreyer, E.T.J. Nibbering, P. Hamm, T. Elsaesser, J. Phys. Chem. A 105 (2001) 2929. [24] D. Madsen, J. Stenger, J. Dreyer, P. Hamm, E.T.J. Nibbering, T. Elsaesser, Femtosecond mid-infrared pump-probe study of wave packet motion in a mediumstrong intramolecular hydrogen bond, Bull. Chem. Soc. Jpn (in press). [25] C.J. Bardeen, C.V. Shank, Chem. Phys. Lett. 203 (1993) 535. [26] W.P. de Boeij, M.S. Pshenichnikov, D.A. Wiersma, J. Chem. Phys. 105 (1996) 2953. [27] T. Joo, Y. Jia, J.-Y. Yu, M.J. Lang, G.R. Fleming, J. Chem. Phys. 104 (1996) 6089. [28] W.P. de Boeij, M.S. Pshenichnikov, D.A. Wiersma, Chem. Phys. Lett. 253 (1996) 53. [29] S.A. Passino, Y. Nagasawa, T. Joo, G.R. Fleming, J. Phys. Chem. A 101 (1997) 725. [30] P. Hamm, R.A. Kaindl, J. Stenger, Opt. Lett. 25 (2000) 1798. [31] S.A. Passino, Y. Nagasawa, G.R. Fleming, J. Chem. Phys. 107 (1997) 6094. [32] W.P. de Boeij, M.S. Pshenichnikov, D.A. Wiersma, J. Phys. Chem. 100 (1996) 11806. [33] G.K. Paramonov, H. Naundorf, O. K€ uhn, Eur. Phys. J. D 14 (2001) 205. [34] H. Naundorf, O. K€ uhn, in: A. Douhal, J. Santamaria (Eds.), Femtochemistry and Femtobiology, World Scientific, Singapore, 2002 (to be published). [35] D.W. Oxtoby, D. Levesque, J.J. Weis, J. Chem. Phys. 68 (1978) 5528.
Chemical Physics Letters 354 (2002) 256–263 www.elsevier.com/locate/cplett
Femtosecond mid-infrared photon echo study of an intramolecular hydrogen bond J. Stenger, D. Madsen 1, J. Dreyer, P. Hamm 2, E.T.J. Nibbering, T. Elsaesser
*
Max Born Institut f€ur Nichtlineare Optik und Kurzzeitspektroskopie, Max Born Strasse 2A, D-12489 Berlin, Germany Received 4 January 2002
Abstract The vibrational dephasing dynamics of O–H stretching excitations in a sterically well-defined intramolecular hydrogen bond (H bond) is studied by femtosecond photon echo spectroscopy in the mid-infrared. The O–H stretching vibration of phthalic acid monomethyl ester in inert solution displays a fast decay of phase coherence on a sub-100 fs time scale. Anharmonic coupling of the stretching motion to an underdamped low-frequency mode of the H bond gives rise to oscillations in the transient grating decay and the 3-pulse photon echo peak shift. Spectral diffusion dynamics on longer time scales is absent in such intramolecular H bonds, as opposed to the weaker intermolecular H bonds in water. Ó 2002 Published by Elsevier Science B.V.
1. Introduction Hydrogen bonds determine the structure and dynamics of protic liquids like water as well as of biopolymers like proteins and DNA [1]. The static and dynamical properties of hydrogen bonds are intensively studied using a multitude of spectroscopic techniques, varying from X-ray diffraction, electronic and vibrational spectroscopy, and nuclear magnetic resonance. In particular, it has been shown that steady-state infrared spectroscopy of
*
Corresponding author. Fax: +49-30-6392-1409. E-mail address: [email protected] (T. Elsaesser). 1 Present address: Department of Chemistry, Aarhus University, Langelandsgade 140, 8000 Aarhus C, Denmark. 2 Present address: Physikalisch-Chemisches Institut, Universit€ at Z€ urich, Winterthurer Str. 190, CH-8057 Z€ urich, Switzerland.
the O–H stretching mode has the potential of revealing the strength of the hydrogen bond due to a direct relationship to the red shift of the vibrational frequency of the O–H stretching band [2]. Recently much effort has been put in nonlinear infrared spectroscopy of the dynamical properties of these line shapes using pump-probe and four-wave mixing techniques. From pump-probe studies of the O–H and O–D stretching modes in intermolecular hydrogen bonds of molecular systems such as water, alcohols and acids dynamical information has been obtained on the vibrational lifetimes with typical values in the subpicosecond time range [3– 6], energy redistribution [7–10], energy transfer to neighboring molecules [11], band substructures [12,13] and band shifts due to the dynamical Stokes shift [9,14–17] or due to local heating [18], and orientational dynamics [19,20]. From photon echo and transient hole burning techniques the relative
0009-2614/02/$ - see front matter Ó 2002 Published by Elsevier Science B.V. PII: S 0 0 0 9 - 2 6 1 4 ( 0 2 ) 0 0 1 0 3 - 3
J. Stenger et al. / Chemical Physics Letters 354 (2002) 256–263
magnitude of homogeneous and inhomogeneous contributions to the overall line shape can be determined. Recently, we have shown that the line shape of the O–H stretching mode of HOD in D2 O results from significant contributions from a homogeneous dephasing process with a time constant of 90 fs [21], and an inhomogeneous part that persists on picosecond time scales [22]. The fast dephasing has been explained to be the result of solvent fluctuations that have a major impact due to the strong anharmonicity of the O–H stretching mode. The inhomogeneous part has been ascribed to a distribution in solvent configuration leading to an inhomogeneous contribution to the vibrational transition frequency. The interesting question evolving from the latter work is concerned with the influence of the number of possible geometrical conformations and the dynamical fluctuations associated with that. The objective of the present work is to analyze line broadening contributions for an intramolecular hydrogen bond with a well-defined geometry. We study the dephasing dynamics of the O–H stretching mode of phthalic acid monomethyl ester (PMME-H, inset of Fig. 1), a medium-sized organic molecule which was dissolved in the inert solvent CCl4 . PMME-H forms a medium-strong intramolecular hydrogen bond which is evident from the infrared spectral line shape of the O–H stretching mode (Fig. 1). This absorption band
Fig. 1. O–H stretching band of PMME-H in CCl4 (solid line) and laser spectrum (dashed line). The sharp line at 2950 cm1 is due to the C–H stretching absorption. The molecular structure of PMME-H is also shown.
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exhibits the characteristic strong red shift, strong intensity increase and clearly present substructures, compared to the single resonance of the free hydroxyl-stretch at 3610 cm1 . We have recently performed a pump-probe study [23,24] where we show that the hydroxyl stretching motion of PMME-H and its deuterated analog PMME-D is strongly anharmonically coupled to a 100 cm1 mode which involves an out-of-plane motion of the two units bridged by the hydrogen bond and – thus – modulates the length of the hydrogen bond. The pump-probe study shows that this out-of-plane mode with a dephasing time of approximately 0.5 ps is underdamped. The anharmonically coupled low-frequency mode gives rise to vibrational sidebands of the pure O–H stretching excitation, contributing to the overall line shape of the O–H stretching band. In addition to this feature, there are other broadening mechanisms which are investigated here by photon echo experiments. Anharmonic coupling of the stretching motion to the underdamped low-frequency mode of the H bond gives rise to oscillations in the transient grating decay and the peak shift of 3pulse photon echo signals. Spectral diffusion dynamics on longer time scales is essentially absent in such intramolecular H bonds.
2. Experimental For the photon echo experiment, ultrashort intense mid-infrared pulses were generated by optical parametric amplification. The output pulses of an amplified Ti:sapphire laser system (300 lJ energy per pulse, 90 fs duration, centered at 800 nm) were used to generate a single filament white light continuum, and to amplify this continuum in a KTiOPO4 crystal in two stages (first pass pumped by 3 lJ at 800 nm, second pass pumped by 200 lJ). The resulting idler pulses are tunable between 2700 and 3300 cm1 with respective energies varying between 3 and 5 lJ. In the experiments, the spectrum of the laser pulses was tuned to the maximum of the O–H stretching band of PMME-H (Fig. 1). The 3-pulse photon echo experiment was performed in the so-called box configuration where
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three overlapping beams with wave vectors k1 , k2 and k3 were focused to a spot diameter of 80 lm on the sample. The nonlinear signals were detected in the directions k3 þ k2 k1 and k3 k2 þ k1 . The photon echo signals were measured as a function of the coherence time s, the delay between the two pulses generating the transient grating in the sample, and as a function of the population T , the delay between the second and the third pulse which is diffracted from the sample. The sample consists of PMME-H (phthalic acid monomethyl ester; Aldrich) dissolved in CCl4 (Merck, uvasol) with a concentration of 15 mM, resulting in a maximum vibrational absorbance of about OD ¼ 0.2. The solution is refreshed for every laser shot by use of a flow cell with CaF2
windows separated by 500 lm. Rapid circulation of the sample solution is necessary to avoid accumulation and heating effects.
3. Results Results of the 3-pulse photon echo experiments are presented in Fig. 2. Fig. 2a shows the photon echo signal from PMME-H in CCl4 diffracted into the direction k3 þ k2 k1 as a function of the population time T and of the coherence time s. As a function of T , the signal displays a strong component around T ¼ 0 which decays within the first 300 fs and is followed by a much weaker contribution, extending to picosecond T values. This
Fig. 2. (a) Three-dimensional plot of the photon echo signal from PMME-H in CCl4 , shown on a linear scale as a function of the population time T and the coherence time s. The strong component around zero delay has a relative amplitude of 1 and was truncated in the plot. (b) Contour plot of the results obtained on PMME-H in CCl4 . (c) Contour plot for the signal from the pure solvent CCl4 . Both contour plots are plotted on a logarithmic scale (three orders of magnitude full scale).
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component is superimposed by oscillations with a period of 330 fs. As a function of the coherence time s, the signal displays a maximum very close to s ¼ 0 for all population times T and a very fast decay which is close to the time resolution of the experiment (Fig. 2b). For comparison, the signal measured with the pure solvent CCl4 is shown in Fig. 2c. One finds a single strong peak at T ¼ 0 which decays within the first 300 fs of T . As a function of s, this signal is centered at s ¼ 0. In Fig. 3, the transient grating scattering (TG) signal, i.e. the signal measured with s ¼ 0, is shown as a function of the population time T . After the initial fast decay, one observes prominent oscillations with a period of 330 fs, superim-
Fig. 3. Transient grating scattering result shown on a linear (a) and a logarithmic scale (b, coherence time s ¼ 0). The 5-level diagram illustrates the complexity of the spectroscopic dynamics. Due to contributions of the O–H stretching vibration in the original ‘cold’ and relaxed ‘hot’ states to the overall signal the transient grating dynamics does not exhibit a single exponential decay.
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posed on a slow decay which extends up to T ¼ 20 ps (Fig. 3b). In addition to the population decay from the v ¼ 1 level of the O–H stretching oscillator which occurs with a time constant of the order of 200 fs [24], there are obviously other contributions to the transient grating dynamics that will be discussed below. In Fig. 4, we plot the photon echo signal as a function of the coherence time s, for T ¼ 0 (solid circles). This trace is equivalent to a 2-pulse photon echo and decays with a time constant of about 30 fs, very close to the instrumental response function as derived from the solvent signal (open circles). At finite values of T , similarly fast decays are observed. We estimated the effect of quantum interference in the echo decay [25,26] by the anharmonically coupled low-frequency mode to be less than 10–20%, leading to an estimated upper limit of 40 fs for the echo decay. The 3-pulse photon echo peak shift (3PEPS [27– 29]) of PMME-H was determined from the 3-pulse photon echo data in Fig. 2. The peak shift represents the shift of the maximum photon echo signal along the coherence time s with respect to delay zero, i.e. the maximum of the instrument response function. In Fig. 5a, the peak shift is plotted as a
Fig. 4. Two-pulse photon echo result of PMME-H in CCl4 (solid circles). The diffracted intensity is plotted on a logarithmic scale as a function of the coherence time s (population time T ¼ 0). The transient indicates the fast initial coherence decay of the O–H stretching mode. Open circles: instrumental response function as measured with the pure solvent CCl4 .
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(a)
(b)
Fig. 5. (a) Three-pulse echo peak shift (3PEPS) of PMME-H in CCl4 , demonstrating the oscillating contribution of the out-ofplane 100 cm1 mode due to anharmonic coupling with the O– H stretching mode. (b) 3PEPS results for HOD=D2 O, measured at the excitation frequencies 3300 cm1 (dashed line) and 3400 cm1 (solid line, for details see [22]). In contrast to PMME-H, spectral diffusion processes on longer time scales are significant.
function of the population time T . We observe an oscillatory behavior of the peak shift displaying a period of about 330 fs, the period of the low-frequency mode coupling to the O–H stretching motion. The peak shift decays to zero with a time constant of about 1 ps. The absolute value of the peak shift of less than 10 fs is distinctly smaller than what has been measured for the O–H stretching vibrations of HDO in D2 O (Fig. 5b) which forms intermolecular hydrogen bonds. Here, the initial 3PEPS signal has a value of 40–60 fs and decays only partly at longer times T .
4. Discussion In the following, we first discuss the contributions of the solute PMME-H and the solvent CCl4
to the photon echo signals. This is followed by an analysis of the transient grating dynamics and of the photon echo peak shift data. The latter are finally compared to recent results on intermolecular hydrogen bonds of HOD in D2 O. In the measurements with the pure solvent CCl4 , we observe a strong signal which is centered around s ¼ 0 and decays very rapidly both as a function of the coherence time s and the population time T (cf. Fig. 2c). This signal occurs exclusively within the temporal overlap of the three pulses and is due to the nonresonant electronic third-order nonlinearity of the solvent and the CaF2 windows of the sample cell. Such nonlinearities display an instantaneous response and – consequently – the transient measured for T ¼ 0 (Fig. 4, open circles) reflects the instrument response function determined by the time envelopes of the pulses. The data in Fig. 4 reveal a slight asymmetry of the pulse envelopes which originates from group velocity dispersion effects in the parametric generation process [30]. In the measurements with PMME-H dissolved in CCl4 , the solvent contributes significantly to the strong signal observed during the temporal overlap of the three pulses (Figs. 2a,c). From the intensity of the signals diffracted from the solution and from the pure solvent, we estimate that about 10% of the main signal peak originate from PMME-H. The 2-pulse photon echo signal (population time T ¼ 0, Fig. 4) of the solution is very close to the instrument response function with a slightly slower decay for positive s. A similarly fast decay is found for finite values of T where the solvent contribution has decayed. We conclude that there is a very fast decay of phase coherence of the O–H stretching excitation with an upper limit of the decay time of approximately 40 fs. It is interesting to note that this decay occurs on a time scale similar to that of the phase relaxation of O–H stretching excitations in HOD=D2 O forming intermolecular hydrogen bonds. On the basis of the present data, it is not possible to decide to what extent the decay of phase coherence in PMME-H reflects a dephasing process in the fast modulation limit, i.e. a purely homogeneous broadening, or a very fast spectral diffusion process within the O–H stretching band.
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The decay of the transient population grating shown in Fig. 3 extends over two orders of magnitude in the population time T and exhibits three components, (i) a fast decay within the first 250 fs, (ii) a slow decay over the time range up to about 20 ps, and (iii) an oscillatory contribution. The lifetime of the v ¼ 1 level of the O–H stretching oscillator of PMME-H has a value of approximately 200 fs, as suggested by recent pump-probe studies [24]. Thus, population relaxation from the v ¼ 1 level may contribute to the initial fast decay, in addition to the solvent signal observed during temporal pulse overlap. The v ¼ 1 population relaxation is due to a nonadiabatic coupling of the v ¼ 1 level to other vibrational states and dissipates the absorbed pump photon energy to other vibrational modes. This dissipation process leads to a ‘hot’ vibrational ground state v ¼ 00 in which the O–H stretching vibration is unexcited but other modes at lower frequencies have accepted the excess energy. The intramolecular hydrogen bond is weakened in this hot ground state, leading to a blue shift of the O–H stretching absorption. On an even slower time scale, the intramolecular excess energy of PMME-H is thermalized and transferred to the surrounding solvent and the molecule returns to its initial ground state v ¼ 0. This relaxation scenario is visualized by the 5-level scheme in the inset of Fig. 3a. The slow decay of the transient grating signal in Fig. 3b reflects the intermolecular thermal relaxation on a time scale of up to 20 ps. This behavior is in very good agreement with recent pump-probe measurements of the nonlinear O–H stretching absorption which show the same slow thermal relaxation [24]. The oscillatory component of the transient grating decay is caused by the anharmonic coupling of the O–H stretching mode to an underdamped low-frequency mode of a 100 cm1 frequency which modulates the length of the hydrogen bond. Wavepacket motion along the lowfrequency coordinate of molecules in the v ¼ 0 state is impulsively excited through a Raman process which occurs within the bandwidth of the mid-infrared pulses and is resonantly enhanced by the O–H stretching absorption. Wavepacket motion in the v ¼ 1 level of the O–H mode is damped very rapidly by the fast v ¼ 1 population decay
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and does not contribute to the oscillations observed here. The 3PEPS reflects inhomogeneous contributions to the line shape of the optical transition which decay by spectral diffusion processes. It has been shown that the 3PEPS decay of vibrational 2and 3-level systems mimics the frequency fluctuation correlation function of the system. Our recent photon echo study of HOD=D2 O demonstrates, however, that this correspondence does not exist for the 5-level scheme involving the hot ground state v ¼ 00 [22] (cf. inset of Fig. 3). The 3PEPS of PMME-H plotted in Fig. 5a shows very small absolute values of the peak shift and an oscillation with a period of 330 fs, corresponding to a vibrational frequency of 100 cm1 . Though the peak shift measured during temporal overlap of the three pulses is influenced by the strong solvent signal (with zero peak shift), the peak shift at population times T > 250 fs is exclusively caused by PMME-H. We conclude from the small absolute value that at those times inhomogeneous broadening of the O–H stretching band is essentially absent. This suggests that for the intramolecular hydrogen bond of PMME-H spectral diffusion does not take place on longer time scales, in sharp contrast to the intermolecular H bonds of HOD in D2 O. In this system, the absolute values of the peak shift are substantially higher for population times up to 20 ps and a delayed maximum of the peak shift occurs for frequencies in the red part of the O–H stretching band (Fig. 5b). As explained in [22], spectral diffusion on time scales much slower than the T1 population relaxation time of the v ¼ 1 state leads to effective additional contributions to the nonlinear signals by the relaxed ‘hot’ ground state. Due to the interference effects between different Liouville space pathways the 3PEPS signal exhibits the delayed increase at the red-edge of the O–H stretching absorption band. If, however, no phase memory persists on this slower time scale, no interference effects between different Liouville space pathways can occur, and consequently no delayed rise of the 3PEPS signal is expected. This happens to be the case for PMME-H in CCl4 . As a consequence, the observed 3PEPS signal mimics more closely the frequency fluctuation correlation func-
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tion despite the fact that for PMME-H we have a 5-level system. Coherent modulations of 3PEPS signals have been observed before for electronic transitions of dye molecules in solution [29,31]. Wavepacket motion due to impulsively excited underdamped intramolecular modes upon ultrafast electronic excitation leads to oscillating contributions of the 3PEPS signals, a consequence of the modulation of the shape of the 3-pulse echo signals due to the formed quantum beats [32]. We report here the first observation of such marked modulations for the 3PEPS signal of a vibrational transition. The occurrence of oscillations in the 3PEPS signal of PMME-H extending up to 1 ps is due to the impulsively excited 100 cm1 out-of-plane mode anharmonically coupled to the O–H stretching mode. Since this coherence persists for times much longer than the v ¼ 1 lifetime, the contribution to the 3PEPS signal originates from wavepacket motion of molecules in the v ¼ 0 ground state.
5. Conclusions We report here the first femtosecond mid-infrared four-wave mixing study of a geometrically well-defined intramolecular hydrogen bond. For the system under study, PMME-H in CCl4 , the absorption line shape broadening mechanisms appears to be dominated by a fast coherence decay on a sub-100 fs time. On the basis of the present data, we cannot discriminate a line broadening mechanism due to fluctuations in the fast modulation limit or with finite correlation times. From the echo peak shift measurements it follows that this fast contribution to the correlation function dominates the line broadening, with spectral diffusion on longer time scales of minor importance. The anharmonically coupled underdamped 100 cm1 out-of-plane mode adds a Franck–Condon progression to the overall line shape. In the light of the present results it will be interesting to decipher the underlying microscopic origin of such a fast decay of the correlation function. One possible reason might be that other intramolecular modes coupled to the O–H stretching mode cause the dephasing. From model
calculations using a Cartesian reaction surface approach it has been found that a bending mode also couples strongly [33], but this mode is only populated at its v ¼ 0 level since its frequency is much higher than kT. The observed overall overdamped behavior can be due to the collective effect of several thermally populated low-frequency modes that have a coupling strength to the O–H stretching mode which is smaller than and even comparable with that of the 100 cm1 out-of-plane mode [24,34]. These lower frequency modes might be underdamped or overdamped, and they might be sensitive to solvent fluctuations, especially those whose frequency is comparable to the intermolecular low-frequency modes of CCl4 . Solvent fluctuations are expected to have an even more pronounced effect than in the case of the weak intermolecular hydrogen bond of HOD=D2 O, since the anharmonicity of the O–H stretching vibration of PMME-H is larger [35]. In order to obtain more insight into the underlying microscopic mechanisms for this ultrarapid dephasing of the O–H stretching mode in an intramolecular hydrogen bond we aim to pursue further studies.
Acknowledgements The mid-infrared spectroscopic activities on hydrogen bonds in the electronic ground state are embedded in the collaborative research center Analysis and Control of Photoinduced Reactions (Sonderforschungsbereich 450 Analyse und Steuerung ultraschneller photoinduzierter Reaktionen), supported by the Deutsche Forschungsgemeinschaft. We cordially thank J. Manz, O. K€ uhn, H. Naundorf and G.K. Paramonov from the Freie Universit€at Berlin for discussions.
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