Deprotonation Dynamics of N,N

Jun 15, 2009 - The protonation/deprotonation dynamics of N,N-dimethylacetamide (DMAA) in hydrochloric acid has been studied with a Raman band shape ...
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Ultrafast Protonation/Deprotonation Dynamics of N,N-Dimethylacetamide in Hydrochloric Acid As Studied by Raman Band Shape Analysis† Daisuke Watanabe and Hiro-o Hamaguchi* Department of Chemistry, School of Science, The UniVersity of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan ReceiVed: February 18, 2009; ReVised Manuscript ReceiVed: April 30, 2009

The protonation/deprotonation dynamics of N,N-dimethylacetamide (DMAA) in hydrochloric acid has been studied with a Raman band shape analysis based on the two-state dynamic exchange model. The observed Raman band shape changes of the symmetric and antisymmetric CC/CN stretch modes with acid concentration have been successfully interpreted in terms of the ultrafast dynamic exchange between DMAA and its protonated form DMAAH+. It is confirmed that the protonation takes place on the oxygen atom rather than on the nitrogen atom. Quantitative information on the exchange dynamics between DMAA and DMAAH+ has been obtained from the curve fitting of the observed band shapes. The protonation process follows the first-order kinetics with a rate constant of k1 ) (10.1 ( 0.2) × 1010 s-1 M-1, which is slightly larger than the value expected for a simple diffusion-controlled reaction and which can be explained in terms of the proton transfer through the hydrogen-bonding network. The mean lifetime of the protonated form DMAAH+ is strongly dependent on the acid concentration; it is several picoseconds in concentration lower than 0.5 mol dm-1 but is prolonged to a few tens of picoseconds in concentrations higher than 2 mol dm-1. It is also shown that the static equilibrium model, which corresponds to the slow exchange limit, fails to explain the observed band shape changes with acid concentration and that they can be explained if and only if the effect of ultrafast exchange is taken into account. Introduction Molecular-level understanding of thermal chemical reactions in solution is one of the central issues of contemporary physical chemistry. Though macroscopic reaction rates can be easily determined by various titration methods, the elementary dynamics involved in these reactions are difficult to access experimentally. Even state-of-the-art ultrafast time-resolved spectroscopies cannot trace these dynamics, because thermal reactions cannot be initiated by light. Application of time-resolved spectroscopies requires synchronized initiation of reactions for a large number of molecules involved in the sample ensemble.1 They are suitable for studying ultrafast dynamics involved in photochemical reactions but not for those in thermal reactions, which are statistical from their nature. As a consequence, our understanding of thermal reactions is much less advanced than that of photochemical reactions. We are yet to elucidate when and how thermal reactions in solution are initiated, how fast and which route they proceed, and when and how they are terminated. Our group has been making efforts to understand ultrafast dynamics of thermal chemical reactions using a frequencydomain approach based on the analysis of Raman band shapes. In particular, we have been using the two-state dynamic exchange model to derive quantitative dynamical information on short-lived reaction intermediates involved in thermal reactions. The approach was first used for trans-stilbene in the first-excited singlet (S1) state, a well-known intermediate of the photochemical trans to cis isomerization reaction.2-5 Subpicosecond exchange dynamics between the S1 state and a nearby polarized †

Part of the “Hiroshi Masuhara Festschrift”. * Tel: +81-3-5841-4329. Fax: +81-3-3818-4621. E-mail: hhama@ chem.s.u-tokyo.ac.jp.

state (most probably with a zwitterionic structure) was elucidated through the analysis of the solvent dependence of the CdC stretch Raman band shape. A clear linear relationship has been found between the rate of hopping from the S1 state and the rate of isomerization, strongly suggesting that ultrafast exchange is involved in the process of isomerization. The approach was next used for studying the ion association dynamics of the sulfate ions in aqueous solutions.6 It has been shown that the mean time between associations is a few picoseconds and that the mean lifetime of the associated form is several hundred femtoseconds. The acid-catalyzed dehydration reaction of tertbutanol was studied most recently.7 Highly dynamic nature of the tert-butyl carbocation has been elucidated; in 1 mol dm-3 sulfuric acid, it is generated in time scales of 10 ps, and is annihilated with lifetimes of about 500 fs. In the present paper, the protonation reaction of N,Ndimethylacetamide (DMAA) in hydrochloric acid is studied. Protonation is definitely one of the most fundamental chemical reactions. It is involved in almost all the acid/base-catalyzed reactions. In particular, protonation to amides has been studied extensively.8-15 Amides have two different protonation sites, that is, the oxygen atom and the nitrogen atom. The Oprotonation is the predominant process and plays crucial roles in many organic reactions such as hydrolysis. The N-protonation causes the proton exchange of amides and plays significant roles in biochemistry.8,11-14 The proton exchange rate of peptide bonds, which are secondary amides, gives useful information on the conformation of proteins. Thus, the N-protonation dynamics of amides has been studied extensively by NMR.9-13 On the other hand, the dynamics of the O-protonation process has been much less studied, though it is highly important from the standpoint of understanding chemical reactions. The ultrafast

10.1021/jp9014993 CCC: $40.75  2009 American Chemical Society Published on Web 06/15/2009

Protonation/Deprotonation Dynamics of DMAA SCHEME 1: Two-State Exchange Model for the Protonation/Deprotonation Dynamics of DMAA

O-protonation dynamics fall in the time regime of picosecond, which is out of the reach of the NMR studies. Here, we study DMAA in place of N-methylacetamide (NMAA), which is the most popular prototype amide, for the following two reasons. First, NMAA forms stable hydrogenbonded clusters through a positively charged proton on the nitrogen atom. As a result, all Raman bands are inhomogeneously broadened because of the coexistence of monomers, dimers and higher aggregates.16 This inhomogeneity makes the band shape analysis prohibitively difficult. For DMAA, we have no evidence of aggregation in hydrochloric acid. Second, the existence of the metastable cis isomer of NMAA also causes a difficulty. It is known that the C-N bond rotates in acidic environments to cause isomerization to the cis form. There exist no geometrical isomers for DMAA. Thus, we believe that DMAA is the most suitable for investigating amide protonation/ deprotonation dynamics with a Raman band shape analysis. Experimental Section Spontaneous Raman scattering (90° scattering) was measured using the 514.5 nm emission line of an Ar+ laser (Spectra Physics: Stabilite2017). Laser power at the sample point was about 100 mW. A triple polychromator with a subtractive dispersive filter (SPEX: Triplemate 1877) was used with a liquid-nitrogen-cooled charge-coupled device (Princeton Instruments: Spec-10 400B LN). The wavenumber resolution was 4.4 cm-1 for the symmetric CC/CN stretch and 4.3 cm-1 for the antisymmetric CC/CN stretch band, respectively. Gaussian functions with these full widths were used as the slit functions for the band shape analysis. The polarization measurements were carried out using a film polarizer as an analyzer. A polarization scrambler was placed in front of the entrance slit. The isotropic component of Raman scattering was calculated as I| - (4/3)I⊥, where I| represents the observed parallel component and I⊥ the perpendicular component of Raman scattering, respectively. In the present study, we analyze the isotropic component of the Raman spectra, which is free from the effect of rotational diffusion, and hence we can discuss the band shape that is determined solely by vibrational dephasing. All the chemicals were obtained commercially and used as received. The concentration of DMAA was 1.1 mol dm-3 for all measurements.

J. Phys. Chem. C, Vol. 113, No. 27, 2009 11663 frequencies ω, the amplitudes a, and the intrinsic dephasing rates Γ are defined separately for the two Raman bands examined (symmetric and antisymmetric CC/CN stretch band), but the protonation rate W1 and the deprotonation rate W2 are taken to be common to them. It is natural to consider that the changes of the two bands have the same origin of protonation/ deprotonation dynamics. The vibrational correlation function under this model is given as follows:17

1 (a1 a2 ) W1 + W2 iω1 - W1 - Γ1 W2 W2 0 a1 exp t W1 iω2 - W2 - Γ2 0 W1 a2 (1)

φ(t) )

[(

)( )

) ](

The theoretical band shape (isotropic part of the Raman band) that should be observed under this dynamics is given by the Fourier transform of the correlation function (1). The Fourier transformation can be carried out analytically and the band is given as

[

1 (a1 a2 ) W1 + W2 i(ω - ω1) + W1 + Γ1 -W2 -W1 i(ω - ω2) + W2 + Γ2 W2 0 a1 0 W1 a2

I(ω) ) Re

(

(

) )( )]

-1

(2)

The inverse matrix in (2) is obtained analytically and the band shape can be expressed in the explicit form given below. I(ω) ) W1W2(a2δω1 - a1δω2)2 + a22Γ2W1δω12 + a12Γ1W2δω22 + Ξ{a12Γ2W2 + a22Γ1W1 + (a1W2 + a2W1)2} π(W1 + W2)[(δω1δω2 - Ξ)2 + {δω1(Γ2 + W2) + δω2(Γ1 + W1)}2]

(3) Here, the following symbols are used for simplicity: δω1 ) ω - ω1, δω2 ) ω - ω2, and Ξ ) Γ1Γ2 + Γ1W2 + Γ2W1. The band shape (3) is based on the stochastic theory formulated originally by Kubo and Anderson.18,19 Many researchers have subsequently developed derived band shape formulas based on this Kubo-Anderson theory and proved their usefulness.20-31 Results and Discussion

Theorical Basis To analyze the observed Raman band shapes quantitatively, the protonation/deprotonation dynamics of DMAA is modeled with a two-state dynamic exchange scheme as shown in Scheme 1. This exchange scheme is similar to that we used in our previous papers2-7 but is more general. The vibrational amplitude a and the intrinsic dephasing rate Γ are now defined independently for each state. The amplitude corresponds to the norm of the isotropic component of the Raman scattering tensor, and the intrinsic dephasing to the bandwidth that is observed in the absence of the exchange dynamics. Note that the

The observed changes of the Raman spectra (isotropic components) of DMAA in different concentrations of hydrochloric acid are given in Figure 1. The symmetric CC/ CN stretch band (left) and the antisymmetric CC/CN stretch band (right) are shown. These spectra are normalized so that the area of the symmetric stretch bands change linearly with the acid concentration. In the neutral solution without acid, the effect of protonation can be neglected. Therefore, the values of ω1, a1, and Γ1 can be determined readily from the peak position, the amplitude, and the bandwidth obtained with the fitting of the observed

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Watanabe and Hamaguchi

Figure 1. Raman spectral changes of DMAA with the concentration of hydrochloric acid: the symmetric CC/CN stretch band (left); the antisymmetric CC/CN stretch band (right).

Figure 2. Raman spectral changes with the concentration of hydrochloric acid for three vibrational bands ascribed solely to DMAA: CN stretch + methyl rock (left); NC antisymmetric stretch (middle); CO double bond stretch (right).

Figure 3. Fitting results for the observed bands of DMAA; the symmetric CC/CN stretch band (left) and the antisymmetric CC/CN stretch band (right): (O) observed band shape; (solid line) fitted theoretical band shape.

spectrum in the neutral solution. Since the observed band shape is the convolution of the real band shape with a slit function, the fitting has been conducted with a Voigt function whose Gaussian component corresponds to the experimentally determined slit function. As a result of the fitting analysis, the following values have been obtained: ω1 ) 745.43 ( 0.05 cm-1, a1 ) 11.5 ( 0.1, and Γ1 ) 3.27 ( 0.05 cm-1 for the symmetric CC/CN stretch and ω1 ) 965.7 ( 0.1 cm-1, a1 ) 3.30 ( 0.05, and Γ1 ) 3.5 ( 0.1 cm-1 for the antisymmetric. The same logic is applicable for the opposite limit. Figure 2 shows the changes of three other Raman bands with the acid concentration. These bands are all ascribed to unprotonated DMAA; CN stretch + methyl rock, NC antisymmetric stretch, and CO double bond stretch, respectively. As seen from Figure 2, they are not detectable at [HCl] ) 4.5 M. This fact indicates that the equilibrium of the reaction shifts to the protonated side almost completely and that a great majority of molecules exist as DMAAH+ at this concentration. Therefore, the spectrum at [HCl] ) 4.5 M is very close to that of DMAAH+, providing us with highly reliable initial values of ω2, a2, and Γ2. With these

initial values of ω2, a2, and Γ2 together with the prefixed values of ω1, a1, and Γ1, we can easily optimize the rate parameters W1 and W2 to reproduce the band shape changes in Figure 1. The fitting results are shown in Figure 3. The theoretical formula for the two-state exchange (2) reproduces the observed band shape changes very well for both of the two bands simultaneously. It is noteworthy that the changes of the two different bands are explained with the common rate parameters W1 and W2. The optimized values of the parameters are as follows: ω2 ) 743.9 ( 0.2 cm-1, a2 ) 10.3 ( 0.2, Γ2 ) 4.5 ( 0.3 cm-1 for the symmetric stretch mode, and ω2 ) 957.4 ( 0.2 cm-1, a2 ) 2.82 ( 0.05, Γ2 ) 5.1 ( 0.3 cm-1 for the antisymmetric stretch mode. The concentration dependence of the optimized rate parameters is shown in Figure 4 (left). We can see that the protonation rate W1 increases linearly with increasing acid concentration, indicating that the protonation reaction obeys the first-order reaction kinetics. Assuming the complete dissociation of hydrochloric acid, the rate constant k1 is obtained as k1 ) (10.1 ( 0.2) × 1010 s-1 M-1, giving the formation rate of DMAAH+

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Figure 4. Acid-concentration dependence of the optimized rate parameters (left) and the characteristic times of the reaction (right).

as k1[H+][DMAA]. This rate constant is slightly larger than that expected for a simple diffusion-controlled reaction. It will be explained from the hydrogen-bonding network involving DMAA and the proton transfer through it. In addition to the direct protonation by a neighboring proton, extra protonation caused by a distant proton can take place through the hydrogen-bonding network without the necessity of thermal diffusion. This effect will be most likely to increase the protonation rate, though the detailed mechanism is left to be elucidated in a future study. On the contrary, the value of W2 decreases with increasing acid concentration. This result indicates that the deprotonation process is not controlled by spontaneous proton release but that it requires a proton-accepting water molecule. Assuming that the concentration of free water molecule is 50 M in the neutral DMAA solution, the rate constant k2 is calculated to be k2 ) 4.6 × 109 s-1 M-1, with the deprotonation rate expressed as k2[DMAAH+][H2O]. This value is less than a half of that of the protonation reaction. Nevertheless, deprotonation occurs faster than protonation because of the high concentration of water. From the two rate parameters, the characteristic times of the reaction, T1 and T2, are calculated as T1 ) (2πcW1)-1 and T2 ) (2πcW2)-1, where c is the light speed. The calculated values are plotted in Figure 4 (right). The value of T1 represents the mean time interval of the protonation reaction, and T2 is the mean lifetime of the protonated form. From the figure, we can see that the protonation occurs in a few tens of picosecond time in dilute acids and that it occurs much more frequently in a few picoseconds in higher acid concentrations. The lifetime of the protonated form is as short as several picoseconds in dilute acids but it is prolonged to a few tens of picosecond in concentrated acid solutions. For the two-state dynamic exchange model to hold, the protonated from DMAAH+ must come back exclusively to DMAA without any side reactions. We first confirm that the protonation occurs on the oxygen atom and not on the nitrogen atom8,11-14 and then consider the possibility of side reactions. Figure 5 compares the Raman spectrum (isotropic component) obtained at [H+] ) 4.5 M with the calculated spectra for the O-protonated and N-protonated forms. The calculation was carried out with Gaussian03 at the B3LYP/6-311+G** level.32 It is obvious that the observed spectrum, which must be very close to that of DMAAH+ as already discussed, is explainable only with the O-protonation model. Two chemical processes are conceivable subsequent to the protonation on the oxygen atom, internal rotation and hydrolysis. The protonation on the oxygen atom makes the CN bond order larger and increases the barrier height for the internal rotation. Therefore, we can safely neglect the effect of the CN bond rotation. We also checked the effect of hydrolysis. Strong Raman bands of the hydrolysis products, dimethylamine and acetic acid, appeared several days after the sample preparation. In the present

Figure 5. Raman spectrum observed at [H+] ) 4.5 M (top) and the calculated Raman spectra for the O-protonated form (middle) and the N-protonated form (bottom) of DMAAH+.

Figure 6. Comparison of the dynamic and static approaches for analyzing the antisymmetric stretch band of DMAA: (O) observed band shape; (solid line) fitting result based on the static model; (dotted line) fitting result based on the dynamic exchange model.

experiments, however, the Raman spectra were measured immediately after the sample preparation, and no signals due to the products were observed during the experiments. Therefore, the effect of hydrolysis is also safely neglected in the present analysis. No significant side reactions proceed from the protonated form DMAAH+. Although we have good grounds to apply the two-state dynamic exchange model for the band shape analysis of DMAA, we still need to check how the ordinary two-state static equilibrium model could possibly account for the observed band shape changes. Within the framework of the dynamic exchange model, the two-state static equilibrium corresponds to the slow exchange limit, where the reaction is so slow that the effect of the dynamics can be totally neglected. Under the assumption of static equilibrium, the changes of the observed band shape

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must be reproduced by the linear combinations of the two limiting spectral components. One limiting component, which corresponds to DMAA, is obtained as the spectrum of the neutral solution. The other component can be taken as the spectrum at [H+] ) 4.5 M, which is very close to the spectrum of DMAAH+ as already discussed. We have tried to fit the observed band shape changes as linear combinations of these two spectral components. In this fitting analysis, we fix the peak positions and the bandwidths of each component and adjust the population ratio only. We use the same population ratio for the symmetric and the antisymmetric stretch mode, as it should be. The fitting result for the antisymmetric CC/CN stretch band is shown in Figure 6. The static approach obviously fails to reproduce the experimental band shape changes, highlighting the excellent agreement obtained with the dynamic exchange model. This fact indicates that the usual spectral analysis using band division is not good enough and that the exchange dynamics must be considered when we interpret the observed band shape changes in Figure 1. Conclusion The ultrafast dynamics of the protonation/deprotonation reaction of N,N-dimethylacetamide (DMAA) has been elucidated on the basis of the two-state dynamic exchange model. The changes of the two different Raman bands (the symmetric CC/ CN stretch and the antisymmetric CC/CN stretch modes) with acid concentration have been explained simultaneously in terms of the common rate parameters, to provide quantitative information on the protonation/deprotonation dynamics of DMAA in hydrochloric acid. In dilute acids ([H+] < 1 M), the protonation occurs once in a few tens of picosecond and the mean lifetime of the protonated form is several picoseconds. The protonation time is shortened to a few picoseconds in higher acid concentrations ([H+] > 4 M) and, concomitantly, the lifetime of the protonated from is prolonged to a few tens of picoseconds. We can say that “the equilibrium of the reaction shifts to the protonated form DMAAH+” with increasing acid concentration. Note, however, that this shift should not be regarded as a static equilibrium shift. The protonation/deprotonation reaction of DMAA in hydrochloric acid is highly dynamical, having mean reaction times and mean lifetimes comparable with one another. The Raman band shape analysis based on the dynamic exchange model has shed a new light on this fundamental process in aqueous solution. References and Notes (1) Hamaguchi, H.; Gustafson, T. L. Annu. ReV. Phys. Chem. 1994, 45, 593–622, and references therein. (2) Hamaguchi, H. Acta Phys. Pol., A 1999, 95, 37–48. (3) Hamaguchi, H.; Iwata, K. Chem. Phys. Lett. 1993, 208, 465–470.

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