1 Rotational Dynamics of Solutes with Multiple Single Bond Axes

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Rotational Dynamics of Solutes with Multiple Single Bond Axes Studied by Infrared Pump-Probe Spectroscopy Masaki Okuda, Kaoru Ohta, and Keisuke Tominaga J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.7b09939 • Publication Date (Web): 27 Dec 2017 Downloaded from http://pubs.acs.org on December 27, 2017

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The Journal of Physical Chemistry

Rotational Dynamics of Solutes with Multiple Single Bond Axes Studied by Infrared Pump-Probe Spectroscopy

Masaki Okuda1, Kaoru Ohta1, 2, Keisuke Tominaga1, 2*

1

Molecular Photoscience Research Center, Kobe University, Rokkodai-cho 1-1,

Nada, Kobe 657-8501, Japan 2

Graduate School of Science, Kobe University, Rokkodai-cho 1-1, Nada, Kobe

657-8501, Japan

e-mail: [email protected]

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Abstract To investigate the relationship between the structural degrees of freedom around a vibrational probe and the rotational relaxation process of a solute in solution, we studied the anisotropy decays of three different N3-derivatized amino acids in primary alcohol solutions. By performing polarization-controlled IR pump-probe measurements, we reveal that the anisotropy decays of the vibrational probe molecules in 1-alcohol solutions possess two decay components, at sub-picosecond and picosecond time scales. Based on results showing that the fast relaxation component is insensitive to the vibrational probe molecule, we suggest that the anisotropy decay of the N3 group on a sub-picosecond time scale results from a local, small-amplitude fluctuation of the flexible vibrational probe, which does not depend on the details of its molecular structure. On the other hand, the slow relaxation component depends on the solute: with longer alkyl chains attached to the N3 group, the anisotropy decay of the slow component is faster. Consequently, we conclude that the slow relaxation component corresponds to the reorientational motion of the N3 group correlated with other intramolecular rotational motions (e.g., rotational motions of the neighboring alkyl chain). Our experimental results provide important insight into understanding the rotational dynamics of solutes with multiple single bond axes in solution. 2 ACS Paragon Plus Environment

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1. Introduction The conformational dynamics of molecules, such as the local orientational motions of functional groups, play a critical role in chemical processes in the condensed phase. Thus far, ultrafast spectroscopy in the ultraviolet to visible region has been proven to be a powerful technique to provide insight into the cis-trans photoisomerization of organic molecules and biomolecules,1 such as stilbene,2-4 retinal,5-7 and azobenzene.8,9 The cis-trans isomerizations of stilbene and azobenzene have also been examined theoretically using molecular dynamics (MD) simulations.10-17 In addition, recently time-resolved infrared (IR) measurements have been conducted to investigate the structural dynamics of molecules in solutions. Since the transition dipole moments of the vibrational states are localized more in a molecule than those of the electronic states, the information provided by vibrational spectroscopy about the conformational dynamics is complementary to that provided by electronic spectroscopy. Using polarization-controlled IR pump-probe and/or two-dimensional IR measurements, several groups have examined the internal rotational motions of vibrational probes in CHCl318,19 and CCl420 solutions. For molecules with many single covalent bonds, multiple rotational motions around the bond axes are expected if these motions are energetically and 3 ACS Paragon Plus Environment


conformationally allowed. These multiple rotational motions greatly influence the structural dynamics of macromolecules, such as proteins and polymer chains. In particular, “correlations” among different the internal rotational motions play an important role in the structural dynamics of macromolecules in solution. In these cases, two rotational motions around bond axes are correlated when the bond angle around one axis affects the rotational motion around the other axis. However, extensive experimental and theoretical efforts have mainly been used to investigate the rotational dynamics around a particular bond axis in solution. Although several NMR studies have theoretically examined the multiple single bond internal rotational motions of solutes,21-24 NMR spectroscopy does not have sufficient time resolution to observe the ultrafast conformational changes of solutes in solution in real time. As a result, sub-picosecond time-resolved IR spectroscopy is an ideal technique to gain insight into the multiple single bond internal rotational motions of solutes. Using polarization-controlled IR pump-probe spectroscopy, we recently studied the anisotropy decay of the N3 anti-symmetric stretching modes of two different N3-derivatized amino acids (N3-AAs), Boc-3-azide-Ala-OH (N3-Ala, Figure 1(a)) and N-Boc-cis-4-azide-L-proline (N3-Pro, Figure 1(b)), in H2O. N3-Ala and N3-Pro in H2O showed different anisotropy decay behaviors at longer pump-probe delay times: (i) the 4 ACS Paragon Plus Environment

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anisotropy decay of N3-Pro contains a quasi-static component, and (ii) the anisotropy of N3-Ala decays faster than that of N3-Pro.25 Considering the structural differences around the vibrational probe, these results suggested that the internal rotational motion of the methylene group adjacent to the N3 group plays an important role in the anisotropy decay of N3-Ala in H2O. However, due to the fast population decay of the vibrational excited state, it was difficult to conclude whether or not the internal rotational motions of the N3 and the methylene groups of N3-Ala were specifically correlated. In this work, in order to obtain detailed information about the relationship between the observed anisotropy decay and the structural flexibility around the N3 group, we investigated the viscosity- and temperature-dependence of the azide orientational

relaxation

of

three

different

N3-AAs:

N3-Ala,

N3-Pro,

and

N-Boc-6-azide-norleucine (dicyclohexylammonium) salt (N3-Nle, Figure 1(c)). As shown in Figure 1, the structural flexibility around the N3 group differs among these three N3-AAs: while the structural flexibility of N3-Nle is the highest due to the longer alkyl chain, that of N3-Pro is the lowest due to its pyrrolindine ring. Moreover, in order to examine the effect of the ring structure around the N3 group on the observed anisotropy decay, we also studied Boc-4-azide-phenylalanine (N3-Phe, Figure 1(d)), which has a more rigid ring structure. Depending on the molecular structures around the 5 ACS Paragon Plus Environment


N3

group,

we

expected

to

observe

differences

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in

the

viscosity-

and

temperature-dependence of the anisotropy decays of the N3-AAs.

2. Materials and methods Details of the experimental setup for our polarization-controlled IR pump-probe spectroscopy have been provided elsewhere.26 Briefly, mid-IR pulses were generated by pumping the home-built optical parametric amplifier and the successive difference frequency generation on a AgGaS2 crystal with the output from a Ti:sapphire regenerative amplifier (output energy: ~580 μJ/pulse, repetition rate: 1 kHz). The pulse duration of the mid-IR pulses was approximately 100 fs. The bandwidth and pulse energy of the mid-IR pulses were approximately 100 cm-1 and 3 μJ, respectively. The center wavenumber of the mid-IR pulse was set to ~2150 cm-1. The mid-IR pulses were divided into two components (i.e., pump and probe pulses) with a ZnSe wedge window. The probe pulses were detected using liquid N2-cooled 64-channel mercury cadmium telluride (MCT) array detectors after passing through a monochromator. In the polarization-controlled IR pump-probe measurements, isotropic and anisotropic pump-probe signals, N(t) and r(t), are obtained as:

N (t ) =

ΔA// (t ) + 2ΔA⊥ (t ) , 3 6

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(1)

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and r (t ) =

Δ A// (t ) − Δ A⊥ (t ) , Δ A// (t ) + 2 Δ A⊥ (t )

(2)

respectively. Here, the ΔA//(t) and ΔA⊥(t) are the temporal profiles of the IR pump-probe signals under the parallel and perpendicular polarization conditions, respectively, after the vibrational excitation of the N3 anti-symmetric stretching mode by the IR pump pulses. Before the sample, the polarization of the probe pulse was set to 45° with respect to that of the pump pulse by using a wire grid polarizer. After the sample, another polarizer mounted on a motorized rotation mount was used to selectively measure the IR pump-probe signals in the parallel and perpendicular polarizations by setting polarization angles of 0° (for ΔA//(t)) and 90° (for ΔA⊥(t)) with respective to the pump pulses. For solutes, N3-Ala, N3-Pro, N3-Nle, and N3-Phe were purchased from Sigma-Aldrich and used without further purification. For solvents, four primary 1-alcohols (CH3(CH2)nOH, n = 0 − 3) were used. Methanol (MeOH, >99.5%) and ethanol (EtOH, >99.5%) were purchased from Wako Pure Chemical Industries, Ltd. and 1-propanol (1-PrOH, >99.9%) and 1-butanol (1-BtOH, >99.8%) were purchased from Sigma-Aldrich. As a typical aprotic solvent, dimethyl sulfoxide (DMSO) was used for comparison. DMSO was purchased from Sigma-Aldrich. The concentrations of the 7 ACS Paragon Plus Environment


sample solutions were approximately 300 mM. After filtration through disposable membrane filters (diameter size: 0.20 μm, ADVANTEC), the sample solutions were contained in an optical cell with a pair of CaF2 windows. The optical path length was set to 25 μm with a Teflon spacer. The solvent-dependent measurements were conducted at room temperature (293 K). The temperature-dependent measurements were performed from 283 K to 333 K for the 1-BtOH solutions.

3. Results and discussion 3.1. IR absorption spectra Figure 2(a) displays the IR absorption spectra of the N3 anti-symmetric stretching mode of N3-Pro in MeOH and 1-BtOH (see the solvent dependence of the N3-AAs in the 1-alcohol solutions in Figure S1). The peak wavenumber and bandwidth of the IR absorption spectrum in MeOH are 2105.9 cm-1 and 18.3 cm-1, respectively. As shown in Figure S1, the N3 anti-symmetric stretching mode of N3-Pro exhibits a red shift of 2.4 cm-1 going from MeOH to 1-BtOH. Moreover, compared to N3-Pro in H2O,25 the IR absorption spectra in 1-alcohol solutions exhibit red shifts of approximately 10 cm-1, which is the consistent with those reported by Wolfsorndle et al.27 In earlier theoretical works on the solvatochromism of MeN3 in water, Choi et al. 8 ACS Paragon Plus Environment

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showed that the N3 frequency shift is determined by the two competing contributions of

σ-type and π-type HB interactions. These are characterized by the hydrogen bond (HB) angle between the solute and a water molecule, i.e., a σ-type HB interaction causes a blue shift of the N3 frequency while a π-type HB interaction causes a red shift.28 Based on their results, we therefore considered that the σ-type (blue shifting) HB interaction is more important for the N3 frequency shift of N3-Pro in water than in the 1-alcohol solutions, and in MeOH compared to 1-BtOH. Note that, as shown in Figure 2(a), the IR absorption spectra of N3-Pro in the 1-alcohol solutions have higher frequency shoulders. The possible origins of these asymmetric lineshapes include the aggregation of solute molecules29 and the existence of different molecular structures in solution.30 By measuring the IR absorption spectra of N3-Pro in MeOH and 1-BtOH at lower sample concentrations (60 mM, see the concentration dependence of the IR absorption spectra in Figure S2), we confirmed that the spectral lineshape at 300 mM is close to identical that at 60 mM. Consequently, we suggest that the higher frequency shoulders of the IR absorption spectra of N3-Pro in 1-alcohol solutions result not from an aggregation effect but from an inhomogeneous distribution of the conformation of the solute. Figure 2(b) shows the IR absorption spectra of the N3 anti-symmetric stretching 9 ACS Paragon Plus Environment


mode of N3-Pro in 1-BtOH measured at 283 K and 333 K (see the temperature dependence of the N3-AAs in the 1-BtOH in Figure S3). The peak wavenumber and bandwidth of the IR absorption spectrum at 283 K are 2103.0 cm-1 and 18.3 cm-1, respectively. As shown in Figure 2(b), the IR absorption spectrum of N3-Pro in 1-BtOH does not significantly depend on temperature. As the temperature increases, the IR absorption spectrum of N3-Pro exhibits a slight red shift of 1 cm-1 and spectral narrowing by approximately 4 cm-1. The red shift of the absorption band may be due to weakening of the solute-solvent HB strength.31

3.2. Vibrational energy relaxation Figure 3(a) shows the isotropic IR pump-probe signal of the N3 anti-symmetric stretching mode of N3-Pro in MeOH measured at the ν = 0 − 1 vibrational transition. The signal exhibits a sharp peak at around t = 0 ps, which is attributed to the pulse overlapping effect between the pump and probe pulses.32 Therefore, in order to exclude this contribution, the isotropic pump-probe signals after t = 0.2 ps were used for the fitting analyses with a double-exponential function. The results for the other N3-AAs are shown in Figure S4. The obtained time constants for N3-Pro in the 1-alcohol solutions are summarized in Table S1 together with those of the other N3-AAs. These time 10 ACS Paragon Plus Environment

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constants reflect the vibrational energy relaxation (VER) from the v = 1 state. Very recently, Son et al. reported that the VER of the N3 anti-symmetric stretching mode of HN3 in MeOH is characterized by a time constant of 5.6 ps,33 which is longer than those of the N3-AAs in the 1-alcohol solutions summarized in Table S1. When the vibrational mode of a polyatomic molecule is excited, the excited population relaxes to the thermally equilibrated state not only via direct relaxation to the ground state but also via intramolecular vibrational redistribution (IVR) to the other vibrational modes.34 Since the number of intramolecular vibrational modes in the N3-AAs is greater than in HN3, various IVR processes are expected to enhance the VER rates of the N3 anti-symmetric mode of N3-AAs in the 1-alcohol solutions. As listed in Table S1, the VERs of N3-AAs exhibit weak dependence on the 1-alcohol solvents. Therefore, we can consider the double-exponential decay of the vibrational lifetime to result from efficient IVR processes, which compete with direct relaxation to the ground state. Theoretical studies using MD simulations will provide detailed information on the vibrational relaxation processes of the N3-AAs in the 1-alcohol solutions. Figure 3(b) displays the isotropic IR pump-probe signal of N3-Pro in 1-BtOH measured at 283 K. The IR pump-probe signal can also be reproduced by a double-exponential function. The temperature dependences of the VER time constants 11 ACS Paragon Plus Environment


of N3-Pro in 1-BtOH are summarized in Table S1, together with those of the other N3-AAs. Theoretical studies of the VER of solutes in solutions suggest that the VER is enhanced due to an increase in the number of energy-accepting modes at higher temperatures.35-38 For example, experimental studies by the Fayer group have revealed that the VERs of W(CO)6 and Cr(CO)6 in CCl4 increase with increasing temperature.39,40 However, as shown in Figure S5, the VERs of the N3-AAs do not show clear temperature dependences. As mentioned above, the VERs of the N3-AAs in the 1-alcohol solutions are controlled by IVR processes. Within the framework of the Fermi Golden Rule, the VER rate is determined by several factors, such as the coupling strength with the energy-accepting modes and the vibrational density of states of the accepting modes, which are generally independent of temperature. Consequently, the VERs of the N3-AAs in 1-BtOH are insensitive to temperature.

3.3. Solvent- and temperature-dependent anisotropy decays Figures 4 and 5 display the solvent- and temperature-dependence of the anisotropy decays of the N3 anti-symmetric stretching mode of the N3-AAs, respectively. Considering the overlapping effect of the pump and probe pulses and the short vibrational lifetimes compared to the anisotropy decays, we used the anisotropic IR 12 ACS Paragon Plus Environment

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pump-probe signals from t = 0.2 – 7 ps for the fitting analyses, using a double-exponential function (the validity of the functional form will be discussed below):

f (t) = A1 exp(− t /τR1) + A2 exp(− t /τR2 )

(3)

where τR1 < τR2. The obtained fitting parameters (i.e., Ai and τRi) are summarized in Table S2. The solvent- and temperature-dependence of the anisotropy decays of the other N3-AAs are also shown in Table S2. As shown in Table S2, we found that the anisotropies of the N3-AAs in the 1-alcohol solutions decay with sub-picosecond (minor component, A1 and τR1) and picosecond (major component, A2 and τR2) time constants. Figures 6 and 7 display the relaxation times τR1 and τR2 of the N3-AAs as a function of the viscosity of the 1-alcohol solvents (η) and of the viscosity over temperature (η/T), respectively. In our previous work, the anisotropy decays of N3-Ala and N3-Pro in H2O did not contain sub-picosecond components.25 This is partly due to a smaller contribution of the fast decay component to the anisotropy decay in H2O. Since the fast anisotropy decays of the N3-AAs likely show strong dependence on the friction from neighboring solvents (see Figure 6), theoretical studies are necessary to investigate to what extent solute-solvent interactions (e.g., HB and collision) affect the fast orientational relaxation dynamics of the N3 group in the 1-alcohol solutions. Hereafter, 13 ACS Paragon Plus Environment


we will discuss interpretations of the experimentally observed anisotropy decays of the N3-AAs in the 1-alcohol solutions. In protic solvents, it is well known that a solute with hydrogen-bonding sites, such as the oxygen atom of a carbonyl group, can form HB complexes with solvents. In previous studies, Hirai et al. suggested that 9-fluorenone in 1-octanol forms HB complexes with one and two alcohol molecules.41 Therefore, the N3-AAs may also form specific HB complexes between the N3 group and 1-alcohol molecules. In this case, the two relaxation times τR1 and τR2 are most likely related to the rotational dynamics of different species, that is, hydrogen-bonded and non-hydrogen-bonded N3-AAs. However, even in the aprotic solvent DMSO, the anisotropy decays of N3-Ala and N3-Nle (see Figure S6) are characterized by fast and slow time constants: 0.80 ps and 15.3 ps for N3-Ala, and 0.81 ps and 8.1 ps for N3-Nle. Because of the low solubility of N3-Pro in DMSO, the anisotropy decay of N3-Pro in DMSO cannot be measured accurately. Consequently, we suggest that the fast and slow anisotropy decays of the N3 group result from different types of molecular motions rather than the rotational relaxations of different HB complexes in the 1-alcohol solutions. As mentioned in Section 3.1, the asymmetric lineshapes of the IR absorption spectra of the N3-AAs in the 1-alcohol solutions result from the inhomogeneous 14 ACS Paragon Plus Environment

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conformational distribution of the vibrational probe molecules. Therefore, we can consider that the central part of the bleach/stimulated emission spectra from the major conformer overlaps with the red side of the transient absorption spectra from the minor one. A small contribution from the minor conformer may influence the temporal evolution of the observed anisotropy decay. However, as shown in Figure S7, the anisotropy decays of the N3-AAs in MeOH do not significantly depend on the probe wavenumber. Similar tendencies were observed for the other 1-alcohol solutions. In particular, even in the blue side of the bleach/stimulated emission spectra, where the contribution of the transient absorption spectra from the minor conformer is greater, the temporal profile of the anisotropy decay is similar to that at the peak position of the bleach/stimulated emission spectra. Therefore, we can consider the anisotropy decay of the minor conformer to be similar to that of the major one and thus signal overlapping effects, such as signal cancellation, do not significantly affect the decay features of the derived anisotropy decays of the N3-AAs in the 1-alcohol solutions. It should be noted that it is difficult to evaluate the wavenumber dependence of the initial values of the anisotropy decay because of the non-resonant IR pump-probe signal from the 1-alcohol solvent, observed at around the time origin (approximately −0.2 ps < t < 0.2 ps, data not shown). 15 ACS Paragon Plus Environment


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In previous studies, non-exponential behaviors have been frequently observed for the anisotropy decays in solutions. These decay behaviors are often discussed in terms of the “wobbling-in-a-cone” model. 42-44 One of the examples is the anisotropy decays of a small linear anion in a room temperature ionic liquid and AOT reversed micelles.45 Tamimi and Fayer reported that the anisotropy of SeCN− in the room temperature ionic liquid can be characterized by a triple-exponential with an initial inertial drop, which reflects independent orientational diffusive motions. Following their study, we considered the following function to describe the contribution of internal rotational relaxation as well as the whole rotation of the molecule (see the derivation of Eq. (4) in the Supplemental Information):

[

(

)

]

r(t) = r0 P2 exp(− t /τ slow) + 1 − P2 exp(− t /τ fast ) exp(− t /τ M ) .

(4)

τfast and τslow are the rotational correlation times for the fast and slow restricted orientational motions, respectively. τM is the rotational correlation time for a complete orientational randomization process due to the whole molecular rotation. r0 is the initial value of the observed anisotropy: r0 = r(0). P is the order parameter related to the semi-angle of the wobbling cone (θ), which is defined as:

1 P = cosθ (1 + cosθ ) . 2


(5)

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In our cases, we can neglect the contribution of the overall reorientations of the N3-AAs to their anisotropy decays in the 1-alcohol solutions based on the following reasons. Lee et al. have reported that the reorientational motion of N3− in MeOH occurs with a time constant of 12.7 ps.46 As discussed below, the Stokes-Einstein-Debye (SED) theory predicts a longer rotational relaxation time constant for a solute with a larger hydrodynamic volume. However, we found that the anisotropies of the N3-AAs with larger molecular volumes in the 1-alcohol solutions show faster decays than that of N3− in MeOH (see Figure 4 and Figure 5(A) in Ref. 46). Therefore, Eq. (4) can be modified to be:

[

(

)

]

r (t ) = r0 P 2 exp(− t / τ slow ) + 1 − P 2 exp(− t / τ fast ) .

(6)

It should be noted that, obviously, the rotational relaxation of the whole molecule is necessary for complete randomization of the anisotropy. However, the contribution of these slow dynamics cannot be accurately determined because of the short vibrational lifetimes of the N3-AAs in the 1-alcohol solutions (see Table S1). Finally, we obtained the double-exponential fitting function given in Eq. (3) by rewriting the parameters in Eq. (6) as: A1 = r0(1 − P2), A2 = r0P2, τR1 = τfast, and τR2 = τslow. First, we discuss the interpretation of the fast decay component characterized by A1 and τR1. According to the wobbling-in-a-cone model, the rotational motion of the 17 ACS Paragon Plus Environment


N3 group around the CN bond axis is expected to occur within a given cone. By performing geometry optimizations of the N3-AAs in the gas phase with Gaussian 09 at the B3LYP/6-311++G(3df,2pd) level,47 we found that the cone semi-angles related to their N3 rotational motions are approximately 60°-62.0° for N3-Ala, 63.1° for N3-Pro, and 63.0° for N3-Nle. Therefore, if the fast anisotropy decay corresponds to the wobbling motion of the N3 group in the cone, the amplitude of the fast component A1 should take a value of approximately 0.25 (substitute r0 ≈ 0.30 and P2 ≈ 0.14 into A1 = r0(1 − P2)). However, based on the result that the A1 values determined by the fitting analyses with Eq. (3) are mostly ~0.1 (see Table S2), we suggest that this fast decay component does not simply reflect the rotational motion of the N3 group around the CN bond axis. In principle, the anisotropy decay of a transition dipole moment in a solution r(t) has a theoretical maximum value of 0.4 at t = 0. However, if the transition dipole moment undergoes ultrafast inertial motions, the value of the experimentally determined r(t = 0) becomes less than 0.4 because of a finite experimental time resolution.48 In this work, by extrapolating the fitting curves in Figures 4 and 5 to t = 0 ps, we found that the initial values of the anisotropy decays of the N3-AAs in the 1-alcohol solutions range from 0.31 to 0.37. Therefore, these results indicate that the ultrafast orientational 18 ACS Paragon Plus Environment

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randomization related to the inertial motion of the N3 group is completed within our experimental time resolution (i.e., ~100 fs). Moreover, in addition to the inertial motion of the N3 group, the vibrational probe can undergo orientational randomization induced by the other internal rotational motions. We suggest that a local, small-amplitude fluctuation of the flexible molecular structure may lead to the fast anisotropy decay of the N3 group on the sub-picosecond time scale. Since the amplitude and time scale of the fast decay component in the anisotropy is similar among all the vibrational probe molecules (see A1 and τR1 in Table S2), this small-amplitude rotational motion does not depend on the details of the molecular structure. Here, it should be noted that, if the local rotation results from an inertial motion, the fast anisotropy decay of the N3 group can be expressed by a Gaussian function and no viscosity- and temperature-dependence should be observed. However, the fast anisotropy decay of the N3-AAs in the 1-alcohol solutions can be fitted by an exponential function and, as shown in Figures 6(a) and 7(a), the fast relaxation times τR1 obtained from the fitting analyses exhibit both viscosityand viscosity-temperature-dependences (hereafter, simply temperature-dependence). Therefore, in order to obtain detailed information about the molecular origin of this fast decay component, it is necessary to theoretically investigate the anisotropy decays of the N3-AAs in the 1-alcohol solutions with molecular dynamics simulations. 19 ACS Paragon Plus Environment


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Next, we discuss the interpretation of the slow decay component, characterized by A2 and τR2. As shown in Figures 6(b) and 7(b), the viscosity- and temperature-dependence of τR2 of the N3-AAs differs from those of τR1. These results indicate that the molecular structure around the N3 group is important for its slow rotational motion in the 1-alcohol solutions: as the structural flexibility around a vibrational probe becomes higher, the anisotropy decays on a shorter time scale, which is qualitatively in good agreement with our recent results in H2O.25 We also examined the anisotropy decays of N3-Phe in the 1-alcohol solutions (see the results in the Supporting Information). As mentioned in the Introduction, N3-Phe has its vibrational probe adjacent to a benzene ring, which is more rigid than the pyrrolindine ring of N3-Pro. Therefore, based on the results that the τR2 time constants of N3-Pro are smaller than those of N3-Phe (see Table S2), the anisotropy decay of the N3 group of N3-Pro can be considered to be induced by the structural dynamics of the pyrrolindine ring (e.g., a flip-flop motion) and/or the other internal rotational motions. According to the SED theory, the reorientational relaxation time constant of a solute in solution (τR) can be described as: τR =

Veffη C k BT

(7)

where kB and T are the Boltzmann constant and the temperature, respectively. Veff is the 20 ACS Paragon Plus Environment

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effective hydrodynamic volume of the solute in solution and η is the viscosity of solution. C is the friction coefficient between the solute and neighboring solvents.49 Under the stick boundary condition, where the size of the solute is much larger than that of the solvent, the friction coefficient C is unity. On the other hand, under the slip boundary condition, where the solute has comparable or smaller volume to that of the solvent, C ranges between 0 and 1. By using Eq. (7) and the viscosity- and temperature-dependence of the rotational relaxation time τR, we can evaluate the effective hydrodynamic volume Veff of the rotating molecule in the solution. However, owing to the lack of the knowledge on the friction coefficient for the N3-AAs in each 1-alcohol solution, only the temperature-dependence of τR2 of the N3-AAs in 1-BtOH was analyzed using the SED theory. From the linear fitting analyses for the temperature-dependence of τR2, the ratios of Veff of the N3 group in 1-BtOH are obtained as Veff, N3-Ala : Veff, N3-Pro : Veff, N3-Nle = 0.59 : 1 : 0.46, where the ratio for N3-Pro is normalized to unity. Here, we assume that the friction coefficient C is identical for the three probes in 1-BtOH. This result indicates that the effective hydrodynamic volume of the N3 group in 1-BtOH decreases when its nearby structural flexibility increases. To discuss the relationship between the reorientational motions of the N3 group and its adjacent alkyl chain, we define two dihedral angles φ(t) and θ(t) (see the 21 ACS Paragon Plus Environment


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definitions in Figure 8(a)) and introduce the generic rotational time correlation function of the N3 group in 1-BtOH (C2(T)) (see the derivation of Eq. (8) in the Supplemental Information): C2 (t ) ∝ exp(− t / τ M )

 exp[ia θ (t ) − ib θ (0)]exp[ia φ (t ) − ib φ (0)] 1

1

2

2

−2≤a1 ,a2 ≤2 −2≤b1 ,b2 ≤2

= exp(− t / τ M )

  dθdφdθ dφ 0

−2≤a1 ,a2 ≤2 −2≤b1 ,b2 ≤2

0

exp[ia1θ + ia2φ ]G(θ , φ , t | θ 0 , φ0 ,0)

(8)

× exp[− ib1θ 0 − ib2φ0 ] peq (θ 0 , φ0 )

where τM is the reorientational time constant of the whole molecule and peq(θ0, φ0) is the orientational distribution in thermal equilibrium. Green’s function G(θ, φ, t|θ0, φ0, 0) corresponds to the conditional probability distribution that the dihedral angles at θ0 and

φ0 at t = 0 take the value of φ and θ at time t. Technically, the time-dependence of G(θ, φ, t|θ0, φ0, 0) can be determined by the following rotational diffusion equation in the presence of a potential created by surrounding molecules:50  ∂ 2 G 1 ∂G = Dθ  2 + k BT ∂t  ∂θ

 ∂ 2 G  ∂ 2V 1 ∂V ∂G   G D + + +   2 φ 2 k θ θ ∂ ∂ θ φ ∂ ∂   BT   

 ∂ 2V ∂V ∂G     2 G+ ∂φ ∂φ    ∂φ

(9)

where Dθ and Dφ are the rotational diffusion constants associated with the internal rotations of the N3 group and its adjacent alkyl chain, respectively. V(θ, φ) is the potential energy for the two reorientational motions created by the surrounding molecules. Since realistic parameters for Eq. (9) are not available, we here give a qualitative view for two limiting cases as schematically shown in Figure 8. If either the 22 ACS Paragon Plus Environment

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landscape of V(θ, φ) is almost flat (see Figure 8(b)) or the maximum value of V(θ, φ) is lower than the thermal energy of kBT, the conditional probability distribution G(θ, φ, t|θ0,

φ0, 0) undergoes a random walk on this energy surface (blue arrows in Figure 8(b)); that is, the two internal rotational motions of the N3 group and its neighboring alkyl chain are uncorrelated. Therefore, in the case of an uncorrelated reorientational motion, the effective hydrodynamic volume of the N3 group is expected to become larger with a longer alkyl chain. Moreover, the decay behavior of the anisotropy on the picosecond time scale will depend on the number of the alkyl rotational motions, which contribute to the anisotropy decay of the N3 group. On the other hand, if V(θ, φ) is assumed to possess a characteristic landscape, as depicted in Figure 8(c), the conditional probability distribution G(θ, φ, t|θ0, φ0, 0) does not diffuse freely but progresses along a specific pathway, searching for the lowest energy barrier (pink arrow in Figure 8(c)), that is, the two internal rotational motions of the N3 group and its neighboring alkyl chain are correlated. In this case, the problem is reduced to a quasi-one-dimensional problem. Since the kinetics should be described by one-dimensional dynamics, the slow anisotropy decay may be characterized by one characteristic time constant on a picosecond time scale. Moreover, by recalling the bicycle-pedal mechanism related to the cis-trans photoisomerization of polyenes,1,51 this 23 ACS Paragon Plus Environment


kind of correlated reorientational motion is expected to provide a smaller effective hydrodynamic volume for the N3 group. Therefore, based on the results that show that the effective hydrodynamic volume of the N3 group decreases with increasing structural flexibility around the N3 group and that the anisotropy decays of N3-Ala and N3-Nle contain one picosecond decay component, the reorientational motion of the N3 group in 1-BtOH can be considered to be correlated to those of its nearby alkyl chain. Before finishing this section, we should emphasize that it is important to investigate to what extent the rotational dynamics of a solute with multiple single bond axes are correlated to solvent motions. So far, several theoretical studies have examined the structural dynamics of solutes from the viewpoint of thermodynamics with free energy potential surfaces.52-54 However, for a solution, the solvation structure can be expected to evolve with time in accordance with the structural changes of a solute. The solute feels not only time-averaged but also time-dependent interactions from the surrounding solvents, that is, V(θ, φ) in Eq. (9) should be time-dependent. Moreover, time-dependent interactions influence the kinetics of the structural isomerization of the solute. Therefore, insight into the dynamical correlation between the solute and solvent motions is important for understanding the structural dynamics of macromolecules, such as proteins and polymer chains, in solution. Theoretical studies with MD simulations 24 ACS Paragon Plus Environment

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will provide valuable information on this question.

4. Conclusion In this work, in order to gain insight into the relationship between the experimentally observed anisotropy decay and the structural flexibility around the vibrational probe, we performed polarization-controlled IR pump-probe measurements for three different N3-AAs (i.e., N3-Ala, N3-Pro, and N3-Nle) in the primary 1-alcohol solutions. From the IR pump-probe measurements, we found that the anisotropy decays of N3-AAs contain the three decay components, which are related to inertial motion (< 100 fs), fast (sub-picosecond time scale) and slow reorientational motions (picosecond time scale). The solvent- and temperature-dependence of the fast relaxation time τR1 are almost identical among the three N3-AAs. Based on the wobbling-in-a-cone model, we assigned the fast decay component to the local reorientation of the N3 group induced by ultrafast structural dynamics of the other parts of the molecule. On the other hand, the solvent- and temperature-dependence of the slow relaxation time τR2 depend on the solute. Therefore, we suggest that this slow relaxation component corresponds to the internal reorientation of the N3 group coupled to the other intramolecular rotational motions. Based on the SED theory, we estimated the effective 25 ACS Paragon Plus Environment


hydrodynamic volumes of the N3 groups of the N3-AAs in 1-BtOH from the temperature-dependence of τR2, which shows a smaller effective hydrodynamic volume with increasing structural flexibility around the N3 group. These experimental results clearly show that the structural flexibility around a vibrational probe plays a key role in the internal rotational motion of the vibrational probe. Moreover, we briefly discuss a qualitative picture of the internal rotational motions of the N3 group and its neighboring alkyl chain. We suggest that the reorientational motion of the N3 group in 1-BtOH is correlated with that of its nearby alkyl chain.

Acknowledgments Theoretical calculations were performed using the Research Center for Computational Science, Okazaki, Japan. This work was partially supported by Grant-in-Aids for Scientific Research on the Priority Area Molecular Science for Supra Functional Systems (JP20050019) and on JSPS Research Fellow (JP16J05643) from the Ministry of Education, Culture, Sports, Science, and Technology (MEXT) of Japan.

Supporting Information IR absorption spectra of the N3-AAs in primary 1-alcohol solutions, IR absorption 26 ACS Paragon Plus Environment

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spectra of the N3-AAs in MeOH and 1-BtOH at low and high sample concentrations, temperature-dependent IR absorption spectra of the N3-AAs in 1-BtOH solution, solvent- and temperature-dependent vibrational energy relaxation of the N3-AAs in primary 1-alcohol solutions, anisotropy decays of N3-Ala and N3-Nle in DMSO solution, wavenumber-dependent anisotropy decays of the N3-AAs in MeOH solution, extension of the wobbling-in-a-cone orientational correlation function to multiple-restricted angular motion, anisotropy decays of N3-Phe in primary 1-alcohol solutions, derivation of the generic rotational time correlation function for solutes with multiple single bond axes in solution, and fitting parameters obtained for vibrational energy relaxations and anisotropy decays of the N3-AAs in primary 1-alcohol solutions. This information is available free of charge via the Internet at http://pubs.acs.org

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or 1-butanol at several temperatures. J. Chem. Thermodynamics, 2009, 41, 1432-1438.

Figure Captions Figure 1. Molecular structures of (a) Boc-3-azide-Ala-OH (dicyclohexylammonium) salt

and

(b)

N-Boc-cis-4-azide-L-proline

N-Boc-6-azide-norleucine

(dicyclohexylammonium)

(dicyclohexylammonium)

salt,

salt,

and

(c) (d)

Boc-4-azide-phenylalanine. Boc represents the tert-butoxycarbonyl group.

Figure 2. (a) IR absorption spectra of the N3 anti-symmetric stretching mode of N3-Pro in MeOH (red) and 1-BtOH (blue) measured at 293 K. (b) IR absorption spectra of the N3 anti-symmetric stretching mode of N3-Pro in 1-BtOH measured at 283 K (blue) and 333 K (red).

Figure 3. Temporal profiles of the isotropic IR pump-probe signals taken from the peak wavenumber of the ν = 0 − 1 vibrational transition of N3-Pro (a) in MeOH measured at 293 K and (b) in 1-BtOH measured at 283 K. The light blue lines represent the fitting results to double exponential functions.


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Figure 4. Temporal profiles of solvent-dependent anisotropy decays taken from the peak wavenumber of the ν = 0 − 1 vibrational transition of (a) N3-Ala, (b) N3-Pro, and (c) N3-Nle measured at 293 K. MeOH (red), EtOH (green), 1-PrOH (light-blue), and 1-BtOH (blue). Closed circles are the experimental results. The solid lines represent the fitting results to double exponential functions given by Eq. (3).

Figure 5. Temporal profiles of temperature-dependent anisotropy decays taken from the peak wavenumber of the ν = 0 − 1 vibrational transition of (a) N3-Ala, (b) N3-Pro, and (c) N3-Nle measured in 1-BtOH. Closed circles are the experimental results. The solid lines represent the fitting results to double exponential functions given by Eq. (3).

Figure 6. Plot of the (a) τR1 and (b) τR2 of N3-Ala (red, ●), N3-Pro (blue, ■), and N3-Nle (green, ▲) as a function of the viscosity of the 1-alcohol solvents (η). The viscosity of each 1-alcohol solvent at 293.15 K is as follows: ηMeOH = 0.611 mPa･s55, ηEtOH = 1.1617 mPa･s55, η1-PrOH = 2.4104 mPa･s55, and η1-BtOH = 3.0100 mPa･s56.

Figure 7 Plot of the (a) τR1 and (b) τR2 of N3-Ala (red, ●), N3-Pro (blue, ■), and N3-Nle (green, ▲) as a function of the viscosity over the temperature (η /T). The 37 ACS Paragon Plus Environment


temperature-dependence of the viscosity of 1-BtOH is as follows:56 η1-BtOH,

Page 38 of 50

283 K

=

3.8794 mPa･s, η1-BtOH, 293 K = 3.0100 mPa･s, η1-BtOH, 303 K = 2.3147 mPa･s, η1-BtOH, 313 K = 1.8476 mPa･s, η1-BtOH, 323 K = 1.4952 mPa･s, and η1-BtOH, 333 K = 1.2435 mPa･s.

Figure 8. Schematic illustration of the two-dimensional potential energy surfaces for the reorientational motions of N3-Ala and N3-Nle, (a) mapped along the two dihedral angles φ (red) and θ (green). (b) Low barrier case and (c) high barrier case. Blue and pink lines represent possible pathways on the energy surfaces with respect to reorientational motions around φ and θ (see Section 3.3).


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Figures and Tables

Figure 1.


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Figure 2.



Figure 3.


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Figure 4.



Figure 5.


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Figure 6.



Figure 7


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Figure 8.


The Journal of Physical Chemistry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46

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Table 1. Solvent- and temperature-dependence of the parameters that characterize the vibrational energy relaxation and the anisotropy decay of N3-Pro in primary 1-alcohols. Vibrational Energy Relaxation(a)

Anisotropy Decay

Solvent

A1

τ10 / ps

A2

τ20 / ps

A1

τR1 / ps

A2

τR2 / ps

MeOH

−0.35±0.03

0.7

−0.54±0.03

2.3

0.10±0.01

0.2±0.1

0.26±0.01

6.3±0.1

EtOH

−0.30±0.01

0.6

−0.63±0.02

2.2

0.09±0.01

0.4±0.1

0.25±0.01

8.3±0.3

1-PrOH

−0.29±0.02

0.6

−0.60±0.02

2.3

0.10±0.01

0.5±0.1

0.23±0.01

12.2±1

−0.36±0.01

0.5

−0.58±0.02

2.5

0.07±0.01

0.7±0.1

0.24±0.01

20.3±1.9

1-BtOH (283 K)


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Table 1. (continued). 1-BtOH −0.41±0.02

0.7

−0.52±0.02

2.7

0.07±0.01

0.6±0.1

0.24±0.01

16.1±0.8

−0.41±0.02

0.5

−0.55±0.02

2.5

0.07±0.01

0.5±0.1

0.24±0.01

12.9±0.6

−0.43±0.02

0.6

−0.53±0.02

2.6

0.09±0.01

0.4±0.1

0.24±0.01

10.0±0.4

−0.47±0.02

0.6

−0.48±0.02

2.8

0.11±0.01

0.3±0.1

0.24±0.01

8.8±0.3

−0.47±0.02

0.6

−0.46±0.02

2.7

0.12±0.02

0.3±0.1

0.24±0.01

7.2±0.3

(293 K) 1-BtOH (303 K) 1-BtOH (313 K) 1-BtOH (323 K) 1-BtOH (333 K) (a) Ai and τi0: amplitude and time constant of the ith component in the fitting function A1exp(−t/τ10) + A2exp(−t/τ20). The uncertainties of time constants τ10 and τ20 are approximately 0.1.



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1 Rotational Dynamics of Solutes with Multiple Single Bond Axes

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