ARTICLE pubs.acs.org/JPCB
Unraveling the Correlated Dynamics of the Double Hydrogen Bonds of Nucleic Acid Base Pairs in Solution Yun-an Yan and Oliver K€uhn* Institut f€ur Physik, Universit€at Rostock, D-18051 Rostock, Germany ABSTRACT: Quantum mechanics/molecular mechanics hybrid simulations (CPMD/GROMOS) of nonlinear infrared spectra are performed for a modified adenine-uracil base pair in CDCl3 solution. Employing a mapping between hydrogen bond distances and fundamental as well as overtone transition frequencies on the basis of on-the-fly snapshot potential energy curves, energy gap correlation functions are established. These correlation functions are utilized to determine pump-probe and two-dimensional photon echo spectra. Analysis of the latter yields off-diagonal peaks signifying correlated fluctuations of the N-H 3 3 3 N and N-H 3 3 3 O hydrogen bonds.
’ INTRODUCTION Structural information about biomolecules is encoded in their stationary infrared (IR) spectra.1,2 While linear IR spectroscopy does not provide direct access to the dynamics underlying the line broadening, the various methods of time-resolved nonlinear IR spectroscopy allow one to unravel the time scales of transition frequency fluctuations of stable conformations as well as of chemical reactions involving bond making and breaking.3 Twodimensional (2D) IR spectroscopy which has been pioneered by Mukamel and co-workers4-6 provides a particularly elegant way for scrutinizing not only line broadening mechanisms but also correlated dynamics of coupled vibrations. Within the biomolecular context, coupled carbonyl vibrations and here most notably the amide bands of peptides have received most attention.7-12 Much less work has been devoted to the dynamics of DNA macromolecules,13,14 although a number of pump-probe studies focusing on the hydrogen-bonded NH-stretching range above 3000 cm-1 appeared more recently. For instance, Heyne and coworkers using two-color pump-probe spectroscopy have assigned the hydrogen-bonded NH2 fundamental transition (at 3215 cm-1) that is masked by the water absorption in the linear spectrum.15 Employing polarization dependent pump-probe spectroscopy, Elsaesser et al. concluded that this spectral range also contains the fundamental transition of the hydrogen-bonded thymine NH-stretching fundamental transition.16,17 Further, the vibrational relaxation of the NH2-stretching mode was followed by IR pump/anti-Stokes Raman probe measurements and a mechanism involving first ultrafast energy transfer to the NHstretching vibration and then a 600 fs decay into the NH-bending region has been obtained.18 2D IR spectra were reported only very recently in ref 19. The focus of that work has been on the hydration of DNA oligomers, the simultaneous dynamics of features due to solvating water and DNA building blocks still awaits a detailed analysis. The study of individual base pairs in gas phase20 and solution21 offers direct access to the properties of the intermolecular hydrogen r 2011 American Chemical Society
bonds without the complications added, e.g., by the stacking and backbone interactions present in DNA oligomers. In this way, it may present a first step toward modeling DNA dynamics with the advantage of being able not only to control the conditions provided by the environment (solvent, substitutions) but also to allow for a more accurate theoretical description and the development of approximate simulation protocols. Woutersen and co-worker investigated a substituted adenine-uracil (AU) pair (9-ethyl-8-phenyladenine:1-cyclohexyluracil) in CDCl3 solution using pump-probe spectroscopy and found a decrease of the vibrational relaxation time of the N-H 3 3 3 N hydrogen-bonded NH-stretching vibration by a factor of about 3 as compared with the non-hydrogen-bonded species.21 The observed 340 fs relaxation time is a clear signature of the effect of hydrogen bond mediated anharmonic couplings. Further, analysis of transient spectra revealed a two-step relaxation process with the hydrogen bond acting as an intermediate accepting mode, which subsequently relaxes on a 2.4 ps time scale. This finding has been in accord with related studies of vibrational cooling of nucleobases in aqueous solution following electronic excitation and subsequent internal conversion back to the electronic ground state.22 For the hydrogen-bonded NH2-stretching vibration of the N-H 3 3 3 O hydrogen bond, an analogous behavior can be anticipated. Although this band was not in the focus of ref 21, a similar subpicosecond relaxation is seen in the transient spectrum after excitation with the wing of the pump pulse. Recently, we have developed a quantum mechanics/molecular mechanics (QM/MM) protocol for investigating the dynamics of the stretching vibrations of the hydrogen bonds in solvated base pairs.23,24 Specifically, we have studied the AU system of ref 21 using the CPMD/GROMOS interface as detailed in ref 25. In Special Issue: Shaul Mukamel Festschrift Received: September 7, 2010 Revised: December 20, 2010 Published: February 14, 2011 5254
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ref 24, the correlation between hydrogen bond distances and fundamental stretching transition frequencies was explored to obtain time-dependent transition frequencies entering the expression of the linear absorption spectrum according to line shape theory.26 The distance-frequency correlation itself was established on the basis of solving the vibrational eigenvalue problem for one- and two-dimensional snapshot potentials calculated along the trajectory (see also refs 27 and 28). Although the errors in the absolute band positions have been substantial, the calculated line shapes of the hydrogen-bonded NH-stretching bands were in reasonable agreement with experiment, thus pointing to a meaningful description of the fluctuation dynamics. Furthermore, it has been found that the second order cumulant expansion which is often used for the simulation of spectra26 does give acceptable results for the N-H 3 3 3 N hydrogen bond but not for the N-H 3 3 3 O one. In the present contribution, we will analyze the fluctuation dynamics of the two AU hydrogen bonds by means of nonlinear IR spectroscopy. In the following section, we will present an extension of the model used in ref 24 which includes overtone excitations that are vital for the description of nonlinear spectra. Further, we will briefly review the response function expression for the calculation of spectra beyond the second order cumulant expansion. Subsequently, results on the pump-probe as well as two-dimensional IR spectra will be presented. The latter are discussed in the light of correlated fluctuations of the two hydrogen bonds. A final section summarizes the main results.
’ THEORETICAL MODEL QM/MM Simulation Protocol. The details of the QM/MM setup have been given in ref 24. In brief, all atoms of the AU pair are treated quantum mechanically by Car-Parrinello molecular dynamics (CPMD) using the Becke exchange and Lee-Yang-Parr correlation functional (BLYP) together with a plane wave basis set and Troullier-Martins pseudopotentials with a cutoff of 70 Ry as implemented in the CPMD code.29 The solvent is modeled using the Gromos96 43A1 force field as provided by the GROMOS program package.30 A single AU pair is solved in 100 CDCl3 molecules inside a box having dimensions 30.0 Å 23.5 Å 23.5 Å (density is 0.1 M21). The QM part is placed in a 30.0 Å 15.9 Å 13.2 Å box (cf. Figure 1a). For the starting geometry, a classical solvent equilibration is carried out for 1 ns at 300 K with the solute fixed using the SHAKE algorithm. Subsequently, a QM/MM trajectory is propagated up to 13 ps at 300 K with a NoseHoover chain thermostat by using a time step of 0.048 fs. Assigning the first 1 ps for equilibration of the QM/MM box, a 12 ps production trajectory is available for data analysis. Notice that besides the hydrogen bonds linking the base pair we observed weak hydrogen bonds between the carbonyl groups and the solvent. The average bond lengths have been found to be 3.26 Å (O4-C) and 3.39 Å (O2-C). For selected configurations, snapshot potentials for the motion of the hydrogen atoms within the two hydrogen bonds have been calculated and the respective vibrational eigenvalue problems have been solved. As described in detail in ref 24, the N-H 3 3 3 N bond has been treated in a onedimensional approximation, whereas for the N-H 3 3 3 O bond two-dimensional snapshot potentials have been calculated. This included models which incorporated besides the
Figure 1. (a) Snapshot of the solvated AU pair along the QM/MM trajectory with atom numbering. A few CDCl3 solvent molecules are shown as well. (b) Level scheme of the hydrogen-bonded stretching transitions which have been used in the model. Here, |i, jæ denotes the state with i and j quanta of excitation in the NH-stretching vibration of the N-H 3 3 3 N and N-H 3 3 3 O hydrogen bond, respectively. The average values for the fundamental transitions used in the simulations -1 -1 are ÆωNHN and ÆωNHO 10 æ = 3185 cm 10 æ = 3315 cm . They have been adjusted to reproduce the experimental values as described in ref 24. For -1 the overtone transitions, we have ÆωNHN and ÆωNHO 21 æ = 2955 cm 21 æ = 3100 cm-1 (see text).
N-H 3 3 3 O stretching mode the respective bending coordinate as well as the non-hydrogen-bonded amine NH-stretching mode. Those eigenstates which had the largest overlap with the zero-order N-H 3 3 3 O stretching vibration have been used for further analysis. Notice that we have found that the bending overtone transition as well as the free NH-stretching fundamental transition are well separated from the N-H 3 3 3 O stretching fundamental transition and that the results are almost insensitive to the chosen two-dimensional model. Below, we will use the data obtained for the stretching-bending model only. Further, we note that all those degrees of freedom which are not part of the selected set of modes enter the description according to their actual interaction with the moving hydrogen atoms. This interaction, however, is limited by the assumed adiabatic separation; i.e., nonadiabatic transitions leading to vibrational relaxation cannot be treated within the present approach. Having at hand transition frequencies for different hydrogen bond lengths allowed us to establish an analytical correlation by least-squares 5255
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fitting that was subsequently used to determine frequencies for all points along the trajectory.24 Nonlinear Response Functions. We will adopt an adiabatic model, separating the high-frequency NH-stretching vibrations of the N-H 3 3 3 N and N-H 3 3 3 O hydrogen bonds from the vibrational modes of the environment (classical bath, Q).31,32 A level scheme of the relevant states of the high-frequency oscillators is shown in Figure 1b. The Hamiltonian including the interaction with the laser field, E(t), in dipole and Condon approximation becomes X ðδab Ha ðQ Þ - EðtÞμab Þjaæ Æbj ð1Þ H¼ ab
Here, the summation goes over all states shown in Figure 1b, Ha(Q) is the adiabatic Hamiltonian for state |aæ, and μab are the dipole transition matrix elements which are nonzero only for the indicated transitions. From the on-the-fly calculation, we can obtain the ratio between the transition dipole moment matrix elements of the 0 f 1 and 1 f 2 transitions. We find this ratio to be rather independent of the overall configuration of the solute-solvent system and close to the value for a harmonic oscillator. Trajectory-averaged values that will be used in the simulation of the spectra are μ21/μ10 = 1.48 for the N-H 3 3 3 N hydrogen bond and 1.41 for the N-H 3 3 3 O case. The ratio of μ10 for the two hydrogen bonds is found to be 0.64. A better agreement with experiment, however, is obtained with a value of 0.6 which is used below. The time dependence of the classical bath degrees of freedom translates into time-dependent transition frequencies for the quantum oscillators, i.e., ωab(t) = (Ha(Q(t)) - Hb(Q(t))) (note that we use p = 1). Absorption line shape and nonlinear response depend on the fluctuation of the transition frequencies, i.e., δωab ðtÞ ¼ ωab ðtÞ - Æωab æ
ð2Þ
where Æωabæ is the average value obtained along the trajectory (for numerical values, see caption of Figure 1). For the two transitions between the fundamental and the first overtone state, a linear correlation according to ω21 ¼ Δ þ γω10
ð3Þ
could be obtained from the snapshot potential energy curves (see Figure 2). The value of Δ had to be adjusted to reproduce on average the experimental anharmonicities of 230 cm-1 (NH 3 3 3 N) and 215 cm-1 (N-H 3 3 3 O).21 From the snapshot potentials, one obtains average anharmonicities which are too small by a factor of about 2, thus pointing to the deficiency of the snapshot potential already discussed in ref 24. On the basis of this model, the linear absorption spectrum can be calculated according to26 Z ¥ 1X IðωÞ ¼ jμa0 j2 Re dt exp½iðω - Æωa0 æÞt π a 0 Z t - t = 2T1, a Æexp½i dτδωa0 ðτÞæ ð4Þ 0
Here, we have added a phenomenological damping time T1,a in the spirit of the Bloch model of relaxation.26 Concerning the nonlinear IR spectroscopy, we will discuss two types of experiments. First, pump-probe spectroscopy where the sample interacts with two pulses, E1 and E2, having carrier frequency ω1 and ω2 and being time-delayed by T. Here, the
Figure 2. Frequency correlation between the 1 f 2 and 0 f 1 transitions for (a) the N-H 3 3 3 N and (b) the N-H 3 3 3 O HB. Circles, QM/MM on-the-fly calculations; bullets, experimental results from ref 21; lines, linear regression for the calculated values according to eq 3. The fitted parameters are γ = 1.5986, Δ = -2018.5 cm-1 for the N-H 3 3 3 N hydrogen bond and γ = 1.2436, Δ = -913.6 cm-1 for the N-H 3 3 3 O hydrogen bond.
signal in phase matching direction of the wave vector of the probe pulse k2 is given by26 Z SPP ðω1 , ω2 , TÞ ¼ 2ω2 Re
Z
¥ -¥
dt
Z
¥
0
Z
¥
dt3
dt2 0
¥
dt1 0
fE2 ðt - T - t3 ÞE2 ðt - TÞE1 ðt - t2 ÞE1 ðt - t2 - t1 Þ expðiω2 t3 þ iω1 t1 Þ ½R1 ðt3 , t2 , t1 Þ þ R4 ðt3 , t2 , t1 Þ þ R6 ðt3 , t2 , t1 Þ þ E2 ðt - T - t3 ÞE2 ðt - TÞE1 ðt - t2 ÞE1 ðt - t2 - t1 Þ expðiω2 t3 - iω1 t1 Þ ½R2 ðt3 , t2 , t1 Þ þ R3 ðt3 , t2 , t1 Þ þ R5 ðt3 , t2 , t1 Þg ð5Þ Second, the two-pulse photo echo spectroscopy in the impulsive limit where the signal in rephasing direction kI = k3 þ k2 - k1 is given by the double Fourier transforms for zero waiting time between the second and third pulse Z SI ðω3 , ω1 Þ ¼
Z
¥ -¥
dt3
¥ -¥
dt1 expðiω3 t3 þ iω1 t1 Þ½R2 ðt3 , 0, t1 Þ
þ R3 ðt3 , 0, t1 Þ þ R5 ðt3 , 0, t1 Þ
ð6Þ
For the nonrephasing direction kII = k3 - k2 þ k1, we have Z ¥ Z ¥ dt3 dt1 expðiω3 t3 þ iω1 t1 Þ½R1 ðt3 , 0, t1 Þ SII ðω3 , ω1 Þ ¼ -¥
-¥
þ R4 ðt3 , 0, t1 Þ þ R6 ðt3 , 0, t1 Þ
ð7Þ
All signals depend on the third-order nonlinear response functions Rj (j = 1-8)26 which in the present case are calculated from the average with respect to different time origins for a trajectory with final time Tf 1 Rj ðt3 , t2 , t1 Þ ¼ Tf - t3 - t2 - t1
Z
Tf - t3 - t2 - t1
dt0 R j ðt3 , t2 , t1 , t0 Þ
0
ð8Þ 5256
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straightforwardly by the time average. The response functions for t1 > 1 ps and t3 > 1 ps are set to zero in a smooth way. Concerning population relaxation, we again adopt the phenomenological Bloch model as outlined in ref 26 (see also ref 33). The population relaxation rates for the first excited states have been obtained from the experimental pump-probe spectra; for the overtone states, we assume that the relation for harmonic oscillators holds;34 i.e., these states decay twice as fast as the first excited ones.
’ RESULTS AND DISCUSSION
Figure 3. (a) Linear absorption spectrum in the NH-stretching range of the AU pair according to eq 4 (height of the calculated peak at 3185 cm-1 scaled to experimental value, T1(N-H 3 3 3 N) = 340 fs, T1(N-H 3 3 3 O) = 430 fs) and experimental data from ref 21. (b) Pump-probe spectra according to eq 5 with a pump frequency of 3185 cm-1 as a function of the delay time, T, between pump and probe pulse.
where R j(t3, t2, t1, t0) are the response functions with time origin t0 (assuming that the system is initially in state |0, 0æ) R1 ðt3 ; t2 ; t1 ; t0 Þ ¼
X
μ0d μdc μcb μb0 exp ihωcb it3
b;c;d
Z t þt 1 0 þihωdb it2 - ihωb0 it1 þ i dτδω0d ðτÞ t0 Z t þt þt þt Z t þt þt 2 1 0 3 2 1 0 dτδωdc ðτÞ þ i dτδωcb ðτÞ þi t0 t0 X R2 ðt3 ; t2 ; t1 ; t0 Þ ¼ μ0d μdc μcb μb0 exp ihωcb it3 b;c;d
Z
t2 þt1 þt0
þihωdb it2 þ ihωd0 it1 þ i dτδωdc ðτÞ t0 Z t þt Z t þt þt þt 3 2 1 0 1 0 dτδωcb ðτÞ þ i dτδωb0 ðτÞ þi t0 t0 X μ0d μdc μcb μb0 exp ihωcb it3 R3 ðt3 ; t2 ; t1 ; t0 Þ ¼ b;c;d
Z
t1 þt0
þihωc0 it2 þ ihωd0 it1 þ i dτδωdc ðτÞ t0 Z t þt þt Z t þt þt þt 3 2 1 0 2 1 0 dτδωcb ðτÞ þ i dτδωb0 ðτÞ þi t0 t0 X μ0d μdc μcb μb0 exp - ihωd0 it3 R4 ðt3 ; t2 ; t1 ; t0 Þ ¼ b;c;d
- ihωc0 it2 - ihωb0 it1 þ i Z þi
t2 þt1 þt0
t0
Rj ðt3 ; t2 ; t1 ; t0 Þ ¼
Z
t3 þt2 þt1 þt0
t0
dτδωdc ðτÞ þ i
Z
t1 þt0
t0 / - Rj - 4 ðt3 ; t2 ; t1 ; t0 Þ
dτδω0d ðτÞ dτδωcb ðτÞ j ¼ 5-8
ð9Þ
In the numerical calculation of the nonlinear spectra, the region t1 < 1 ps or t3 < 1 ps for Rj(t3, t2, t1) is determined
Pump-Probe Spectrum. In Figure 3a, we give a comparison between experimental and calculated hydrogen-bonded NHstretching bands. As noted before, the agreement in the line shape is rather reasonable with the line width of the peak originating from the N-H 3 3 3 O hydrogen bond being somewhat underestimated.24 Panel b of Figure 3 shows the pumpprobe spectrum calculated according to eq 5. The pump frequency was taken at the average of the fundamental NHstretching transition of the N-H 3 3 3 N hydrogen bond, and we have employed the impulsive limit. In accord with the experiment, there are two negative bands and one positive band clearly discernible in this spectral region. The two negative bands centered at 3315 and 3185 cm-1 are due to ground-state bleaching and stimulated emission of the NHstretching vibrations of the N-H 3 3 3 O and N-H 3 3 3 N hydrogen bond, respectively. A positive band due to the excited state absorption of the N-H 3 3 3 N hydrogen bond is found around 2950 cm-1, whereas the excited state absorption due to the NH 3 3 3 O hydrogen bond at 3100 cm-1 is masked by the negative bands related to the fundamental transitions (compare also Figure 1b). As mentioned before, the T1 time of the NH-stretching fundamental transitions for the N-H 3 3 3 N hydrogen bond has been adopted from the experiment (340 fs). For the N-H 3 3 3 O case, the relaxation time was fitted to give the decay of the respective peak at 3315 cm-1, which yields a value of 430 fs. Therefore, it is not surprising that the agreement of the decay dynamics with experiment is fairly good. However, one should notice that in the present case of the Bloch model these decays are monoexponential, whereas a second slower component has been observed for the N-H 3 3 3 N hydrogen bond in ref 21. The line width of the dominating negative band is well reproduced (values at T = 0.35 ps are 60 cm-1 (calc.) and 52 cm-1 (exp.)). For the negative band due to the N-H 3 3 3 O hydrogen bond, we find a width of 41 cm-1, but an experimental value cannot be extracted due to the low intensity of the signal and its partial overlap with the main band. The band due to excited state absorption around 2950 cm-1 appears to be somewhat too intense, although a direct comparison with experiment is hampered by insufficient transmission in this spectral range.21 Photon Echo Spectra. While the simulation of the linear and pump-probe spectra mainly served to validate the model, the focus of this contribution is on the dynamical correlations between the bath-induced fluctuations of the two fundamental NH-stretching transitions of the two hydrogen bonds in the base pair. In Figure 4, we present 2D IR photon echo spectra in rephasing, eq 6, and nonrephasing, eq 7, configuration. We can identify six bands which are partly overlapping. Discussing the rephasing signal, SI, the diagonal positive absorption band centered at (ω1 = -3174 cm-1, ω3 = 3178 cm-1) is due to 5257
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Figure 4. Photo echo spectra according to nonrephasing, SII in eq 7, and rephasing, SI in eq 6, direction. Upper and lower panels show the real and imaginary part, respectively, of the signals.
two hydrogen bonds are positively correlated.11,35 This conclusion is supported by the imaginary part of the signal which is shown in the lower panel of Figure 4. On the other hand, the respective cross-peaks in the nonrephasing signal in Figure 4 are oriented along the antidiagonal, thus indicating anticorrelated fluctuations.35 Viewed in terms of two coupled oscillators interacting with a single common heat bath, the two signals in Figure 4 seem to contradict each other. From the point of view of hydrogen bond dynamics, however, this finding merely reflects the fact that in general there are heavy atom vibrational motions which can modulate the two hydrogen bonds in-phase or out-ofphase. The resulting extension/compression of the hydrogen bonds causes an increase/decrease of the transition frequency of the hydrogen’s stretching motion. In the context of proton transfer reactions, such modes are known as promoting and inhibiting vibrations.31 In other words, our results indicate that the two NH-stretching oscillators are coupled to two heat baths. In ref 24, we have shown that the cumulant expansion breaks down for the N-H 3 3 3 O hydrogen bond; thus, an analysis, e.g., in terms of a simple Brownian oscillator model (cf. ref 35), is not possible. Therefore, in order to shed some light into the correlated dynamics of the two hydrogen bonds, we have analyzed the relative velocities of hydrogen bond donor and acceptor atoms, vNN and vNO, in the plane defined by the atoms N3, O4, and N1 (cf. Figure 1a). Introducing the unit vector v (t) = (vNN(t) þ vNO(t))/|(vNN(t) þ vNO(t)| and the orthogonal )
the NH-stretching fundamental transition of the N-H 3 3 3 N hydrogen bond. It contains contributions from ground state bleaching, R3, and stimulated emission, R2, according to eq 9 with b = d. The diagonal peak centered at (ω1 = -3323 cm-1, ω3 = 3322 cm-1) is the respective feature due to the N-H 3 3 3 O hydrogen bond. Both peaks are essentially elongated along the diagonal, thus giving evidence for the inhomogeneity of the hydrogen bond vibrations. Due to the strong anharmonicity of about 200 cm-1, the excited state absorption features are well separated in the spectrum. Specifically, we observe negative absorption bands centered at (ω1 =-3188 cm-1, ω3 =2962 cm-1) and (ω1 = -3340 cm-1, ω3 = 3133 cm-1). They correspond to the transient excited state absorption (R5 with b = d in eq 9 belonging to the N-H 3 3 3 N and N-H 3 3 3 O hydrogen bonds, respectively). Information on the correlated fluctuations of the two hydrogen bonds is contained in the off-diagonal peaks.11,35,36 They are due to ground-state bleaching and stimulated emission and are observed at around (ω1 = -3316 cm-1, ω3 = 3188 cm-1) for |aæ = |0,1æ (N-H 3 3 3 O) and |bæ = |1,0æ (N-H 3 3 3 N) and at around (ω1 = -3186 cm-1, ω3 = 3318 cm-1) for |aæ = |1,0æ and |bæ = |1,0æ. The later feature is better resolved, since it does not overlap with excited state absorptions. This allows for a closer analysis of its shape, which reveals an orientation almost parallel to the diagonal. Thus, on the basis of the rephasing signal alone, one would argue that the NH-stretching frequency fluctuations of the
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)
)
)
complement v^(t) in the above-mentioned plane, one can express the relative velocities of the two hydrogen bonds as vNN(t) = cNN(t)v (t) þ c^(t)v^(t) and vNO(t) = cNO(t)v (t) c^(t)v^(t) (note that we have chosen v^(t) such that c^(t) > 0). Taking the average along the trajectory, we obtain ÆcNN(t)æ = 2.25 10-4, ÆcNO(t)æ = 1.89 10-4, and Æc^(t)æ = 1.34 10-4; i.e., the relative velocities are dominated by components parallel to the unit vector v . More importantly, however, we find that for about 70% of the trajectory the signs of cNN(t) and cNO(t) are the same. According to our definition, this is evidence that the fluctuation dynamics is dominated by an in-phase modulation of the two hydrogen bonds, as suggested by the rephasing signal in Figure 4.
’ SUMMARY We have investigated the fluctuation dynamics of the NHstretching vibrations of the two hydrogen bonds in an AU base pair in CDCl3 using the Car-Parrinello/Gromos QM/MM method for classical trajectory propagation. The dynamics has been analyzed in terms of the IR pump-probe and photon echo spectra. The most important finding concerns the cross-peaks in the rephasing and nonrephasing signals, indicating correlated fluctuations of the two NH-stretching fundamental transitions. Closer analysis revealed that fluctuations are due to both in-phase and out-of-phase motions of the two base pairs with respect to each other, with the in-phase symmetric motion which simultaneously compresses and elongates both hydrogen bonds being dominant along the available trajectory. The model calls for several future extensions, most notably the inclusion of population relaxation beyond the Bloch description, i.e., nonadiabatic effects beyond the present second BornOppenheimer approximation. Here, approaches based on wave function propagations under the action of parametrized reduced Hamiltonians have been suggested (see, e.g., ref 37). Furthermore, the present mapping of transition frequencies based on hydrogen bond lengths could be improved by using an electrostatic mapping as suggested, e.g., in refs 38 and 39. This would render the simulation protocol to become more generally applicable, even though substantial changes are not to be expected for the present system. ’ AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected].
’ ACKNOWLEDGMENT We gratefully acknowledge financial support by the Deutsche Forschungsgemeinschaft (project Ku952/5-1). ’ REFERENCES (1) Jeffrey, G. A.; Saenger, W. Hydrogen Bonding in Biological Structures; Springer: Berlin, 1991. (2) Taillandier, E.; Liquier, J. Methods Enzymol. 1992, 211, 307. (3) Fayer, M. D. Ultrafast Infrared and Raman Spectroscopy; Marcel Dekker: New York, 2001. (4) Tanimura, Y.; Mukamel, S. J. Chem. Phys. 1993, 99, 9496. (5) Mukamel, S. Annu. Rev. Phys. Chem. 2000, 51, 691. (6) Zhuang, W.; Hayashi, T.; Mukamel, S. Angew. Chem., Int. Ed. 2009, 48, 3750. (7) Hamm, P.; Lim, M.; Hochstrasser, R. J. Phys. Chem. B 1998, 102, 6123.
(8) Woutersen, S.; Mu, Y.; Stock, G.; Hamm, P. Proc. Natl. Acad. Sci. U.S.A. 2001, 98, 11254. (9) Zhuang, W.; Abramavicius, D.; Hayashi, T.; Mukamel, S. J. Phys. Chem. B 2006, 110, 3362. (10) Hamm, P.; Helbing, J.; Bredenbeck, J. Annu. Rev. Phys. Chem. 2008, 59, 291. (11) Cho, M. Chem. Rev. 2008, 108, 1331. (12) Cho, M. Two-Dimensional Optical Spectroscopy; CRC Press: Boca Raton, FL, 2009. (13) Krummel, A.; Zanni, M. J. Phys. Chem. B 2006, 110, 13991. (14) Lee, C.; Park, K.-H.; Kim, J.-A.; Hahn, S.; Cho, M. J. Chem. Phys. 2006, 125, 114510. (15) Heyne, K.; Krishnan, G. M.; K€uhn, O. J. Phys. Chem. B 2008, 112, 7909. (16) Dwyer, J. R.; Szyc, y.; Nibbering, E. T. J.; Elsaesser, T. J. Phys. Chem. B 2008, 112, 11194. (17) Szyc, y.; Dwyer, J. R.; Nibbering, E. T.; Elsaesser, T. Chem. Phys. 2009, 357, 36. (18) Kozich, V.; Szyc, y.; Nibbering, E. T. J.; Werncke, W.; Elsaesser, T. Chem. Phys. Lett. 2009, 473, 171. (19) Szyc, y.; Yang, M.; Nibbering, E. T. J.; Elsaesser, T. Angew. Chem., Int. Ed. 2010, 49, 3598. (20) Pl€utzer, C.; H€unig, I.; Kleinermanns, K.; Nir, E.; Vries, M. S. D. ChemPhysChem 2003, 4, 838. (21) Woutersen, S.; Cristalli, G. J. Chem. Phys. 2004, 121, 5381. (22) Pecourt, J.-M. L.; Peon, J.; Kohler, B. J. Am. Chem. Soc. 2001, 123, 10370. (23) Yan, Y.; Krishnan, G. M.; K€uhn, O. Chem. Phys. Lett. 2008, 464, 230. (24) Yan, Y.; K€uhn, O. Phys. Chem. Chem. Phys. 2010, 12, 15695. (25) Laio, A.; VandeVondele, J.; Rothlisberger, U. J. Chem. Phys. 2002, 116, 6941. (26) Mukamel, S. Principles of Nonlinear Optical Spectroscopy; Oxford: New York, 1995. (27) Jezierska, A.; Panek, J. J.; Koll, A.; Mavri, J. J. Chem. Phys. 2007, 126, 205101. (28) Jezierska, A.; Panek, J. J.; Koll, A. ChemPhysChem 2008, 9, 839. (29) CPMD, Copyright IBM Corp. 1990-2006, Copyright MPI f€ur Festk€orperforschung Stuttgart 1997-2001. (30) Scott, W. R. P.; Hunenberger, P. H.; Tironi, I. G.; Mark, A. E.; Billeter, S. R.; Fennen, J.; Torda, A. E.; Huber, T.; Kruger, P.; van Gunsteren, W. F. J. Phys. Chem. A 1999, 103, 3596. (31) Giese, K.; Petkovic0 , M.; Naundorf, H.; K€uhn, O. Phys. Rep. 2006, 430, 211. (32) Bratos, S.; Leicknam, J.-C.; Gallot, G.; Ratajczak, H. In Ultrafast Hydrogen Bond Dynamics and Proton Transfer Processes in the Condensed Phase; Elsaesser, T., Bakker, H. J., Eds.; Kluwer Academic: Dordrecht, The Netherlands, 2002; p 5. (33) Kwac, K.; Cho, M. J. Chem. Phys. 2003, 119, 2256. (34) May, V.; K€uhn, O. Charge and Energy Transfer Dynamics in Molecular Systems, 3rd revised and enlarged ed.; Wiley-VCH: Weinheim, Germany, 2011. (35) Venkatramani, R.; Mukamel, S. J. Chem. Phys. 2002, 117, 11089. (36) Tanimura, Y.; Ishizaki, A. Acc. Chem. Res. 2009, 42, 1270. (37) laCourJansen, T.; Knoester, J. J. Phys. Chem. B 2006, 110, 22910. (38) Hayashi, T.; laCourJansen, T.; Zhuang, W.; Mukamel, S. J. Phys. Chem. A 2005, 109, 64. (39) Auer, B.; Kumar, R.; Schmidt, J. R.; Skinner, J. L. Proc. Natl. Acad. Sci. U.S.A. 2007, 104, 14215.
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