Effect of Hydrogen Bonds on the Vibrational Relaxation and

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Effect of Hydrogen-Bond on Vibrational Relaxation and Orientational Relaxation Dynamics of HN and N in Solutions 3

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Chiho Lee, Hyewon Son, and Sungnam Park J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.6b06239 • Publication Date (Web): 18 Aug 2016 Downloaded from http://pubs.acs.org on August 21, 2016

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The Journal of Physical Chemistry

Effect of Hydrogen-Bond on Vibrational Relaxation and Orientational Relaxation Dynamics of HN3 and N3 in Solutions Chiho Lee, Hyewon Son, and Sungnam Park*

Department of Chemistry, Korea University, Seoul 136-701, Korea.

*Author to whom correspondence should be addressed. Email: [email protected]

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Abstract Hydrogen-bonds (H-bonds) play an important role in determining the structures and dynamics of molecular systems. In this work, we investigated the effect of H-bonds on the vibrational population relaxation and orientational relaxation dynamics of HN3 and N3 in methanol (CH3OH) and N, N-dimethyl sulfoxide (DMSO) by using polarization-controlled infrared pump-probe (IR PP) spectroscopy and quantum chemical calculations. Our detailed analysis of experimental and computational results reveals that both vibrational population relaxation and orientational relaxation dynamics of HN3 and N3 in CH3OH and DMSO are substantially dependent on the strength of the H-bonds between a probing solute and its surrounding solvent. Especially, in the case of N3 in CH3OH, the vibrational population relaxation of N3 is found to occur by a direct intermolecular vibrational energy transfer to CH3OH due to a large vibrational coupling constant. The orientational relaxation dynamics of HN3 and N3, which are well fit by a bi-exponential function, are analyzed by the wobbling-in-a-cone model and extended Debye-Stokes-Einstein equation. Depending on the intermolecular interactions, the slow overall orientational relaxation occurs under slip, stick, and superstick boundary conditions. For HN3 and N3 in CH3OH and DMSO, the vibrational population relaxation gets faster but the orientational relaxation gets slower as the H-bond strength is increased. Our current results imply that the H-bonds have significant effects on the vibrational population relaxation and orientational relaxation dynamics of a small solute whose size is comparable to the size of the solvent.

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I. INTRODUCTION In solutions, the intermolecular interactions, such as electrostatic, ion-dipole, dipole-dipole, and hydrogen-bond (H-bond) interactions, have substantial effects on the dynamics of the probing molecule. Such intermolecular interactions are manifest in the peak shift and change in the peak width of vibrational modes in the FTIR spectra.1-5 The vibrational population relaxation and orientational relaxation dynamics of a probing solute are sensitively dependent on the interactions between the probing solute and its surrounding solvent and thus they have been efficiently utilized to measure the effect of the intermolecular interactions on such dynamics.6-15 Especially, the H-bond is one of the most important intra- and intermolecular interactions in determining the structures and dynamics of various H-bonded molecular systems in solutions. In H-bonded solute-solvent systems, the H-bonds can provide an efficient channel for intermolecular vibrational energy transfer to the solvent facilitating the vibrational population relaxation of the vibrationally excited solute. In addition, the rotating solute experiences additional friction by the H-bonds and thus the orientational relaxation gets slower. The dynamics of a small molecule whose size is comparable to or even smaller than that of the surrounding solvent molecules can be more significantly influenced by the H-bonds. It is very interesting to look at the effect of H-bonds on the vibrational population relaxation and orientational relaxation dynamics of small molecules. Hochstrasser and coworkers reported a study of the vibrational and orientational relaxation dynamics of N3, OCN, and SCN in protic (CH3OH and H2O) and aprotic (hexamethyl phosphamide) solvents demonstrating the importance of H-bond interactions in the vibrational and orientational relaxation of the solvated ions in protic solvents.7 Interestingly, the vibrational relaxation and orientational relaxation times of a small probing solute were shown to have an inverse relationship when there is a strong interaction between the solute and its neighboring solvent.7, 13 In other words, stronger interaction between the solute and its surrounding solvent was found to lead to faster 3



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vibrational relaxation and slower orientational relaxation of the solute. More recently, Owrutsky and coworkers studied the vibrational relaxation dynamics of small molecules (hydrazoic and isothiocyanic acids) in protic solvents such as water and methanol to investigate the effects of both solute charge and solvent isotope on the vibrational spectra and dynamics.15 In this work, we studied the effect of H-bonds on vibrational population relaxation and orientational relaxation dynamics of HN3 and N3 in methanol (CH3OH) and N, N-dimethyl sulfoxide (DMSO) by using polarization-controlled IR pump-probe (IR PP) spectroscopy combined with quantum chemical calculations. Azide ion (N3) and azide group (-N3), which have a strong infrared absorption in the 2000 2100 cm-1 region because of the asymmetric stretching vibration of N=N=N, have been extensively used as an IR probe for studying many different molecular systems.4, 16-20 Azide ion (N3) is readily protonated to produce hydrazoic acid (HN3) and its frequency is significantly blue-shifted so that HN3 and N3 are spectrally well-resolved. More recently, HN3/N3 buffers were used to investigate the proton transfer reaction in acid-base equilibria occurring in protic and aprotic solvents.21 In the present work, we have measured the vibrational population decay and orientational anisotropy decay of HN3 and N3 in CH3OH and DMSO because HN3 and N3 make H-bonds with CH3OH and DMSO and their relative H-bond strengths are different. Furthermore, we have obtained H-bond configurations by quantum chemical calculations to estimate the H-bond strength. Our results reveal that the vibrational population relaxation of HN3 and N3 is faster but the orientational relaxation of HN3 and N3 is slower as the H-bond strength is increased. For the vibrational population relaxation of N3 in CH3OH, a direct intermolecular vibrational energy transfer between N3 and CH3OH is found to be important and the corresponding coupling strength is obtained. Detailed analysis of orientational relaxation dynamics are carried out by using the wobbling-in-a-cone model and the extended Debye-Stokes-Einstein equation.

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II. EXPERIMENTAL METHODS A. Sample Preparation and FTIR Spectroscopy Sodium azide (NaN3), methanol (CH3OH), N, N-dimethyl sulfoxide (DMSO) and anhydrous sulfuric acid (H2SO4) were purchased from Sigma-Aldrich and used without further purification. To prepare the sample solutions, NaN3 salt was directly dissolved in CH3OH and DMSO and then anhydrous sulfuric acid was added. Upon addition of anhydrous sulfuric acid, sodium sulfate (Na2SO4) salt was precipitated because of its low solubility. Na2SO4 salt was removed from the solutions by centrifugation. For IR experiments, the sample solutions were housed in a home-made IR cell with two 3 mm thick calcium fluoride (CaF2) windows and the path length was adjusted by using a 12 μm thick Teflon spacer. FTIR spectra of the sample solutions were measured by using a Varian 640-IR spectrometer in the range of 400 4000 cm-1 with a resolution of 1 cm-1 at 22 °C.

B. IR Pump-Probe (IR PP) Spectroscopy Our femtosecond mid-IR laser system and polarization-controlled IR PP experiments were described elsewhere.19, 22-24 Briefly, 800 nm pulses with ~35 fs duration were generated by a Ti:Sapphire oscillator (Tsunami, Spectra-Physics). The generated 800 nm pulses were amplified to ~1.0 mJ per pulse with regenerative amplifier (Spitfire, Spectra-Physics) laser system. The 800 nm pulses were down-converted by optical parametric amplifier (OPA, Spectra-Physics) to generate near-IR pulses at ~1.4 µm (signal) and ~1.9 µm (idler) which were mixed in a 0.5 mm thick AgGaS2 crystal (Type II) producing mid-IR pulses by difference frequency generation. The power spectrum of the mid-IR pulses had a Gaussian envelope with a ~ 250 cm-1 bandwidth (full width at half maximum, FWHM). The chirp of mid-IR pulse was

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properly minimized at the sample position by using CaF2 plates with different thickness. For IR PP experiments, the mid-IR pulse was split into the pump and probe beams with a 9:1 intensity ratio. A motorized linear translational stage, which was placed in the probe beam, was used to control the time-delays between the pump and probe beam. The probe beam after the sample was dispersed through a monochromator onto the 64-element MCT array detector. The IR PP signal S(t) was collected by measuring the transmission of the probe beam through the sample by chopping the pump beam at 500 Hz. For a given delay time t, the IR PP signal was defined by S(t)=[Tpump-on – Tpump-off](t) / Tpump-off =T(t)/T where T is the transmission of the probe beam.19 To separately measure the parallel and perpendicular IR PP signals, S (t ) and

S (t ) , the polarizations of the probe and pump beams were properly adjusted. Before the sample, the pump beam was vertically polarized (0) and the polarization of the probe beam was set to 45 with respect to the polarization of the pump beam. The analyzer polarizer was placed on a rotational stage in the probe beam after the sample and the polarization of the transmitted probe beam was adjusted to 0 or 90 for alternately measuring the parallel and perpendicular IR PP signals, S (t ) and S (t ) .

III. RESULTS AND DISCUSSION A. FTIR Study Figures 1 shows the FTIR spectra measured with HN3/N3 buffers in CH3OH and DMSO. In HN3/N3 buffers, an acid-base equilibrium is established (HN3  H+ + N3). The asymmetric stretching mode of N3 ( vN  ) peaks at 2045 cm-1 in CH3OH and 2000 cm-1 in DMSO, 3

respectively. The asymmetric stretching mode of HN3 ( vHN3 ) is significantly blue-shifted to

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2132 cm-1 in CH3OH and 2126 cm-1 in DMSO, respectively. In CH3OH and DMSO, the vN  3

and vHN3 modes are spectrally well separated, which gives an opportunity to investigate them individually. Close examination of FTIR spectra in Figure 1 reveals some interesting and important features. First, the vN  and vHN3 modes peak at different spectral positions in 3

CH3OH and DMSO, which results from the vibrational solvatochromic shift.25-27 Especially, the peak position of vN  mode in CH3OH is blue-shifted by ~40 cm-1 when compared with 3

that in DMSO. This is because N3 is strongly H-bonded to CH3OH (CH3OHN3) as shown in Figure 2. Second, the peak width of vN  mode is much broader in CH3OH (19.8 cm-1) than 3

DMSO (11.3 cm-1) reflecting a wider distribution of H-bond configurations between N3 and CH3OH. However, the peak width of vHN3 mode is not much different in CH3OH and DMSO (11.6 cm-1 and 13.2 cm-1, respectively). In this case, HN3 is H-bonded to both CH3OH and DMSO and the distribution of H-bond configurations is not substantially different in both solvents. Lastly, the vN  mode is significantly overlapped with the overtone band (2 vCO ) of 3

C-O stretching mode of CH3OH as shown in Figure 1. These spectral features are important in understanding the vibrational population decays of HN3 and N3 in both solvents.

B. Quantum Chemical Calculations To study the H-bond configurations of N3 and HN3 in CH3OH and DMSO, the quantum chemical calculations were carried out using the density functional theory (DFT) method (B3LYP) and a 6-311g++(d, p) basis set implemented in the Gaussian 09 package.28-29 Figure 2 displays the optimized H-bond configurations with one or two solvent molecules and the calculated vibrational frequencies of the vN  and vHN3 modes in the H-bond configurations. 3

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Here, the calculated vibrational frequencies were rescaled by a scaling factor (0.96).30 The IR spectra in Figure 1(C) were calculated. Both N3 and HN3 form H-bonds with CH3OH in Figure 2(A) and 2(B). The average H-bond length between N3 and CH3OH is shorter than that between HN3 and CH3OH. In contrast, HN3 forms H-bonds with DMSO in Figure 2(D) but N3 interacts with DMSO by the ion-dipole interaction in Figure 2(C). The differences in such local H-bond configurations will be used to explain the vibrational population relaxation and orientational relaxation dynamics of N3 and HN3 in CH3OH and DMSO later.

C. IR Pump-Probe Study In IR PP experiments, molecules are vibrationally excited by a strong IR pump pulse and the relaxation of the vibrationally excited molecules is monitored by a time-delayed IR probe pulse. The IR PP signal of a molecular system in solutions decays as a consequence of both vibrational population relaxation and orientational relaxation of the excited molecules. Parallel and perpendicular IR PP signals, S (pr , t ) and S  (pr , t ) , are separately measured in two

different beam polarization configurations. In general, IR PP signal is contributed by the ground-state bleach (GSB,   0  1 ), stimulated emission (SE,   1  0 ), and excitedstate absorption (ESA,   1  2 ). Figure 3 displays the frequency-resolved IR PP signals measured with HN3/N3 buffers in CH3OH and DMSO. In Figure 3, the positive signal in red results from the GSB and SE while the negative signal in blue comes from the ESA. For each IR peak, a pair of the positive and negative signals are measured in IR PP experiments. The frequency difference between the positive and negative IR PP signals corresponds to the vibrational anharmonicity. Both positive (GSB+SE) and negative (ESA) IR PP signals depend on the population of   1 state and thus contain the same dynamic information. The

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vibrational population decay, P(t), and orientational anisotropy decay, r(t), are extracted from S (pr , t ) and S  (pr , t ) at a given probe frequency,1, 31 P(t )  S (t )  2 S  (t )

r (t ) 

(1)

S (t )  S (t )

2  C2 (t ) S (t )  2S (t ) 5

(2)

where C2 (t ) is the orientational correlation function and is represented by the second-order Legendre polynomial of the transition dipole correlation function, C2 (t )  P2 μ(t )  μ(0) . To determine P(t) and r(t) for HN3 and N3 in CH3OH and DMSO, the IR PP signals measured at the peak maxima of vN  and vHN3 peaks were analyzed as indicated as dotted lines in Figure 3

3.

D. Vibrational Population Relaxation Dynamics

Figure 4(A) shows the vibrational population decays, P(t), of vN  and vHN3 in CH3OH and 3

DMSO. Generally, P(t) is described by a first-order kinetic process and is well fit by a single exponential function, P (t )  A exp(t / T1 )

(3)

whereT1 is the vibrational lifetime. The single exponential fit results are summarized in Table 1. The vibrational lifetimes of vN  and vHN3 in CH3OH measured in this work are in 3

excellent agreement with the previously reported values.7, 15, 32 The vibrational lifetime of vN  3

in DMSO (T1=8.7 ps) measured in this work is slightly shorter than the value (T1=10.7 ps) measured by Owrutsky and coworkers.16, 32 In general, the vibrationally excited molecules relax back to the ground state through the intramolecular and intermolecular vibrational relaxation pathways. As shown in Figure 4(A) and Table 1, the vibrational lifetimes of vN  3

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and vHN3 are sensitively dependent on the surrounding solvents (i.e., CH3OH or DMSO) suggesting that the intermolecular vibrational relaxation pathways should play a more critical role in determining the population relaxation rates. The vibrational population relaxation of a solute becomes efficient when the solute’s vibrational modes are spectrally overlapped with the solvent’s vibrational modes. As shown in Figure 1, the vN  mode in CH3OH is 3

significantly overlapped with the overtone band ( 2vCO ) of C-O stretching mode of CH3OH. In addition, the H-bonds appear to have a substantial effect on vibrational population relaxation. As shown in Figure 2, HN3 forms H-bonds with DMSO but N3 does not form H-bonds while both HN3 and N3 form H-bonds with CH3OH. By considering both the spectral overlap and H-bond strength, the vibrational lifetimes of vN  and vHN3 in CH3OH and DMSO can be 3

reasonably well explained. As the average H-bond length is decreased and the spectral overlap is increased, the vibrational lifetime of vN  and vHN3 is found to be shorter as shown in Table 3

1 and Figure 4(A). Especially, the vibrational lifetime of vN  (T1=3.0 ps) in CH3OH is much 3

shorter than that of vHN3 (T1=6.0 ps) due to the stronger H-bond and more spectral overlap. In DMSO, the vibrational lifetime of vHN3 (T1=4.0 ps) is much shorter than that of vN  (T1=8.4 3

ps) because there are relatively strong H-bonds between HN3 and DMSO as shown in Figure 2(D). In the case of N3 in CH3OH, vibrationally excited N3 relaxes back to its ground state by efficiently transferring its vibrational energy to the overtone band ( 2vCO ) of C-O stretching mode of CH3OH as indicated in Figure 4(B).33 The intermolecular vibrational energy transfer (VET) rate ( k N

 3

CH 3 OH

) from vN  to 2vCO can be estimated by comparing the vibrational 3

relaxation rates of vN  in CH3OH and DMSO. By using the vibrational lifetimes of vN  in 3

3

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CH3OH ( T1, CH3OH  3.0 ps ) and DMSO ( T1, DMSO  9.7 ps ), the vibrational relaxation rates of vN  3

in CH3OH and DMSO are calculated by

k N  , DMSO  1 / T1, DMSO  0.10 ps 1 3

and

k N  , CH OH  1 / T1, CH 3OH  0.33 ps 1 , respectively. For this analysis, we use T1, DMSO  9.7 ps 3

3

which is the average value of the vibrational lifetimes of vN  in DMSO (8.7 ps in this work 3

and 10.7 ps by Owrutsky and coworkers16,

32

). By assuming that k N  k N  , DMSO , the 3

3

vibrational relaxation rate of vN  in CH3OH can be approximately written as 3

k N  , CH OH  k N   k N  CH OH 3

3

3

3

(4)

3

 k N  , DMSO  k N  CH OH 3

3

3

Finally, the vibrational energy transfer from vN  to 2vCO is approximately calculated by 3

k N   CH OH  k N  , CH OH  k N  , DMSO  0.23 ps 1 . In this analysis, it is assumed that the vibrational 3

3

3

3

3

relaxation of vN  is insignificantly influenced by the surrounding DMSO molecules but 3

occurs through the intermolecular VET to 2vCO mode in CH3OH. The intermolecular VET from vN  to 2vCO in the H-bonded CH3OHN3 configuration is found to occur with a time 3

constant of 4.5 ps as illustrated in Figure 4(B). For the case of the dephasing mechanism (i.e., V   1 ), the intermolecular VET rate from a donor state (D, vN  ) to an acceptor state (A, 2vCO ) can be theoretically predicted by 3

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k DA 

 D1   A1 2V 2 1  exp( v / k BT ) (vD  vA ) 2  ( D1   A1 ) 2

(5)

where v  vD  vA ,  is the dephasing time, and V is the coupling strength between the two states. As presented in Table 2, all the spectral parameters in Eq. (5) can be extracted from the

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vN  and 2vCO bands in Figure 1(A). The dephasing times (  D1    vD and  A1    vA ) 3

are estimated from the widths of vN  3

and 2vCO bands in the FTIR spectrum and

kDA  k N  CH OH  0.23 ps 1 is calculated above. Therefore, the coupling strength between 3

3

vN  and 2vCO bands is determined to be V  38 cm1 which is relatively large. In the case 3

of N3 in CH3OH, the small frequency difference ( v ) and their large coupling strength (V) make the intermolecular VET very efficient. In the literature, the coupling strength for intermolecular VET is found in the range of 3~10 cm-1 when the vibrational energy difference between donor and acceptor is relatively large (i.e., 40~80 cm-1) and the distance between donor and acceptor is long.34-35 Under this circumstance, the intermolecular VET cannot be very efficient and the coupling strength (V) is relatively small. In the case of H-bonded N3 and CH3OH, the vibrational energy difference between

vN  3

and

2vCO is very small

( v  0.5 cm 1 ) and the distance between N3 and CH3OH is very small because N3 and CH3OH are directly H-bonded. Therefore, the vibrational energy transfer between N3 and CH3OH may occur efficiently like an intramolecular VET resulting in a large coupling strength ( V  38 cm1 ).

E. Orientational Relaxation Dynamics

Figure 5(A) displays the orientational anisotropy decays, r(t), of N3 and HN3 in CH3OH and DMSO. The orientational anisotropy decays in Figure 5 are well fit by a bi-exponential function,

r (t )  a1 exp(t /  or1 )  a2 exp(t /  or2 )

(6)

where  or1   or2 . The fit parameters are summarized in Table 1. The bi-exponential behavior of r(t) for small molecules in solutions has been described by the wobbling-in-a-cone model as

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will be discussed in detail in the next section. In general, the orientational anisotropy decay of a solute is influenced by the friction resulting from the interactions between the solute (N3 and HN3) and its surrounding solvent (CH3OH and DMSO).19 Clearly, the H-bonds (CH3OHN3, CH3OHHN3, and DMSOHN3) and ion-dipole interaction (N3 and DMSO) as shown in Figure 2 are important in understanding the orientational anisotropy decays of N3 and HN3. For example, the long time component (  or2 ) of the orientational anisotropy decay of N3 in CH3OH is almost three times slower than that of HN3. The considerably slow orientational relaxation of N3 in CH3OH arise mainly from the fact that the H-bond between N3 and CH3OH is much stronger than that between HN3 and CH3OH as shown in Figure 2. In DMSO, the orientational anisotropy decay of HN3 is slower than that of N3 because the H-bond between HN3 and DMSO is stronger than the ion-dipole interaction between N3 and DMSO. In the context of a restricted orientational relaxation, the bi-exponential behavior of the orientational anisotropy decay of N3 and HN3 can be analyzed by the wobbling-in-a-cone model.36-38 In this model, two independent orientational diffusion processes are occurring at the same time. The short time component is described as the wobbling motion of a probing molecule undergoing orientational diffusion within a cone of semi-angle c as shown in Figure 5(B). The long time component accounts for the slower overall orientational diffusion without any angular restriction that finally leads to complete orientational randomization of the probing molecules. In the wobbling-in-a-cone model, the orientational correlation function ( C2 (t ) ) is expressed and related to r(t) by 37, 39 C2 (t )  Q 2  (1  Q 2 ) exp(t /  w )  exp(t /  l ) 

5 r (t ) 2

(7)

2 where Q2 is the generalized order parameter (0  Q  1) ,  w and  l is the time constants

for the initial wobbling orientational motion and slower overal diffusive orientational motion,

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respectively. In Eq. (7), Q2 describes the degree of restriction on the wobbling-in-a-cone orientational motion. Q2 = 0 represents unrestricted orientational motion while there is no wobbling-in-a-cone orientational motion when Q2 = 1. In Eq. (7),  w is obtained from the 1 1   or2 ) . l experimentally measured  or1 and  or2 in Eq. (6) using the relation,  w  1/ ( or1

in Eq. (7) is equal to the long time constant (i.e.,

l or2 ) in Eq. (6) and is directly associated

with the orientational diffusion constant, Dl  1/ 6 l , which is obtained from the relation between the decay of the second Legendre polynomial and the orientational diffusion constant. The cone semi-angle ( c ) is determined from the order parameter, Q  [0.5cosc (1  cosc )] . The wobbling-in-a-cone diffusion constant ( Dw ) is calculated by37, 39 Dw 

xw2 (1  xw ) 2 {ln[(1  xw ) / 2]  (1  xw ) / 2}  w (1  Q 2 )[2( xw  1)]

(1  xw )(6  8 xw  xw2  12 xw3  7 xw4 )  24 w (1  Q 2 )

(8)

where xw  cosc . In the limit of c  180 , there is no restriction to the orientational 2 diffusion and Q  0 and Dw  1/ 6 w . Table 3 summarizes the parameters obtained from

the wobbling-in-a-cone model analysis. The wobbling motion of N3 and HN3 occurs on a subpicosecond time scale, and the wobbling time constant (  w ) and cone semi-angle ( c ) of N3 are found to be smaller than those of HN3. On the other hand, the slower overall orientational relaxation (  l ) occurs on a picosecond time scale. Within the framework of the Debye−Stokes−Einstein (DSE) equation, the orientational diffusion of a molecule is sensitively dependent on the solution viscosity which is strongly related to the intermolecular interactions between the probing molecule and its surrounding solvent.

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The orientational relaxation time of a solute in a viscous medium can be theoretically predicted by the extended DSE equation,

 or 

1 VfC  6 Dor kBT

(9)

where kB and T are the Boltzmann constant and temperature, respectively,  is the solution viscosity which is measured by using the Ostwald viscometer, and V is the van der Waals volume of a solute. In Eq. (9), f is the shape factor which accounts for the non-spherical shape of the solute 40 and C is the friction coefficient which represents the coupling between the solute and neighboring solvents.41 Under the stick boundary condition (Cstick=1), it is assumed that there is no relative velocity between the solute molecule and first solvation shell. The stick boundary condition is used when the size of the rotating solute molecule is bigger than that of solvent molecules. On the other hand, when the size of rotating solute molecule is similar or smaller than that of the solvent molecules, the friction coefficient is in the range 0 < Cslip < 1, which represents the slip boundary condition. The shape factor, f, and theoretical slip friction coefficient, Cslip, can be calculated from the tables of Hu and Zwanzig.41  lslip and  lstick for N3 and HN3 in CH3OH and DMSO were calculated from Eq. (9) and compared with the experimentally determined values (  l ) in Table 4. In addition,  l /  lstick was calculated for individual species for quantitative comparison. In the case of N3 in CH3OH, the value of  l /  lstick is 4.1 which means that the orientational relaxation of N3 in CH3OH is four times slower than the value predicted by the DSE equation under the stick boundary condition. Such a large orientational relaxation time is known as a superstick boundary condition in the literature42, which here results from the relatively strong H-bond formed between N3 and CH3OH as shown in Figure 2. The long orientational relaxation time of N3 in CH3OH, which was substantially longer than the

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theoretical orientational time predicted under the stick boundary condition, was reported by Hochstrasser and coworkers and it was attributed to the rotational diffusion of N3 in the Hbonded solvent cage.7 For HN3 in CH3OH,  l /  lstick  1 indicating that the orientational relaxation of HN3 is well described by the stick boundary condition. The orientational relaxation of N3 in DMSO is found to be well represented by the slip boundary condition (  l   lslip ) due to the relatively weak ion-dipole interaction between N3 and DMSO. For HN3 in DMSO,  lslip   l   lstick (i.e., almost halfway between the stick and slip boundary condition). In DMSO, the orientational relaxation of HN3 is twice slower than that of N3 because HN3 interacts strongly with DMSO by the H-bond. The strength of H-bonds is a key factor in determining the orientational relaxation of N3 and HN3 in CH3OH and DMSO.

IV. SUMMARY AND CONCLUDING REMARKS

In this work, we have investigated the effect of H-bonds on the vibrational population relaxation and orientational relaxation dynamics of HN3 and N3 in CH3OH and DMSO by polarization-controlled IR PP spectroscopy and quantum chemical calculations. The vibrational population relaxation of HN3 and N3 in CH3OH and DMSO, which occurs through the intra- and intermolecular relaxation pathways, is sensitively dependent on the spectral overlap and H-bond strength. The vibrational population relaxation of HN3 and N3 in CH3OH and DMSO is faster as the H-bond gets stronger. Especially, the vibrational relaxation of N3 in CH3OH is observed to be fast due to a direct intermolecular VET from N3 to CH3OH which is caused by a large vibrational coupling strength (V=38 cm-1). The bi-exponential behavior of orientational anisotropy is described by the wobbling-in-a-cone model. The extended DebyeStokes-Einstein equation is used to understand the nature of the slow overall orientational

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diffusion under different boundary conditions (slip, stick, and superstick) originating from the strength of the intermolecular interactions. For a small solute molecule whose size is comparable to or even smaller than the surrounding solvent, the local intermolecular interactions such as H-bond, ion-dipole, and dipole-dipole interactions are important in determining its vibrational population relaxation and orientational relaxation dynamics. To fully understand the effect of intermolecular interactions on such dynamics, systematic experimental investigations combined with quantum chemical calculations need to be done in the future.

AUTHOR INFORMATION Corresponding Author

*E-mail [email protected]; Ph +82-2-3290-3144 (S.P.). Notes

The authors declare no competing financial interest.

ACKNOWLEDGEMENTS

This work was supported by the National Research Foundation of Korea (NRF) grants funded by the Korea government (MEST) (Nos. 2013R1A1A2009991 and 20100020209). IR pumpprobe experiments were performed at the Korea Basic Science Institute (KBSI), Seoul Center.

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Table 1. Exponential fit to vibrational population decay, P(t), and orientational anisotropy decay, r(t).

CH3OH

DMSO

T1 (ps)

a1

 or1 (ps)

a2

 or2 (ps)

N3

3.0  0.2

0.05  0.01

0.19  0.02

0.34  0.01

11.0  0.5

HN3

6.0  0.5

0.24  0.01

0.46  0.02

0.12  0.01

3.6  0.1

N3

8.4  0.5

0.11  0.01

0.31  0.02

0.24  0.01

2.7  0.1

HN3

4.0  0.2

0.19  0.01

0.68  0.03

0.16  0.01

6.4  0.1

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Table 2. Parameters for calculating the intermolecular VET rate constant (kDA) and the

coupling strength (V) from vN  (= vD ) to 2vCO (= vA ). 3

kDA (ps-1)

v  vD  vA (cm-1)

 D1 (cm-1)

 A1 (cm-1)

V (cm-1)

0.23

0.5

62.2

128.8

38

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Table 3. Cone semi-angle, c , and orientational diffusion coefficients

CH3OH

DMSO

Q

c (deg.)

 w (ps)

 l (ps)

Dw1 (ps)

Dl1 (ps)

N3

0.85

19

0.19

11.0

6.4

66.0

HN3

0.30

49

0.53

3.63

3.2

21.8

N3

0.60

33

0.35

2.69

4.1

16.1

HN3

0.40

43

0.76

6.43

5.6

38.6

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Table 4. Orientational time constants calculated from the extended DSE equation and the parameters used in the extended DSE equation.

 (cP)a V (Å3)

f

Cslip

 lslip (ps)

 lstick (ps)

 l (ps)

 l /  lstick

N3

0.85

4.7

2.73

0.41

1.1

2.7

11.0

4.1

HN3

0.85

5.5

3.19

0.49

1.8

3.7

3.6

1.0

N3

2.03

4.7

2.73

0.41

2.6

6.4

2.7

0.42

HN3

2.03

5.5

3.19

0.49

4.3

8.7

6.4

0.74

CH3OH

DMSO

a

The solution viscosity, , was measured by the Ostwald viscometer.

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Figure captions Figure 1. FTIR spectra of the asymmetric stretching vibration of N=N=N in HN3/ N3 buffer.

(A) 0.24 M HN3 and 0.12 M N3 in CH3OH and FTIR spectrum of neat CH3OH is compared. (B) 0.30 M HN3 and 0.06 M N3 in DMSO. (C) IR spectra obtained by the quantum chemical calculations. The optimized H-bond configurations are shown in Figure 2(A) and 2(B). In addition, the first overtone band ( 2 CO ) of CO stretching vibration of CH3OH is calculated and compared with  N  and  HN . 3

3

Figure 2. Optimized H-bond configurations of (A) N3 in CH3OH, (B) HN3 in CH3OH, (C) N3

in DMSO, and (D) HN3 in DMSO. The DFT method (B3LYP) with a 6-311g++(d,p) basis set is used. The vibrational frequencies of the asymmetric stretching vibration of N=N=N are calculated in each H-bond configuration and rescaled by a scaling factor (0.96). The H-bonds are indicated by dashed lines. Figure 3. Frequency-resolved IR PP signals, S (pr , t ) and S (pr , t ) , measured with N3

and HN3 in (A) CH3OH and (B) DMSO, respectively. The dotted lines are IR PP signals that were used to obtain vibrational population decay, P(t), and orientational anisotropy decay, r(t) in Figure 4 and 5, respectively. Figure 4. (A) Vibrational population decays, P(t), of N3 and HN3 in CH3OH and DMSO. The

data points were experimentally measured at the =01 transitions. The lines are fit by a single exponential function. (B) Schematic illustration of the intermolecular vibrational energy transfer (VET) from vN  to 2 vCO within the H-bond configuration. 3

Figure 5. (A) Orientational anisotropy decays, r(t), of N3 and HN3 in CH3OH and DMSO.

The data points were experimentally measured at the =01 transitions. The lines are fit by a biexponential function. (B) Schematic illustration of the wobbling orientational diffusion within a cone of semi-angle c . N3 is H-bonded to CH3OH undergoing tethered orientational diffusion at short times within a cone. The transition dipole of N3 is along the molecular axis.

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Figure 1

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Figure 2

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Figure 3

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Figure 4

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Figure 5

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Effect of H-bonds on the vibrational energy relaxation and rotational dynamics of small molecules in liquids. 84x45mm (96 x 96 DPI)


Effect of Hydrogen Bonds on the Vibrational Relaxation and

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