Dispersed Three-Pulse Infrared Photon Echoes of Nitrous Oxide in

Article pubs.acs.org/JPCB

Dispersed Three-Pulse Infrared Photon Echoes of Nitrous Oxide in Water and Octanol J. T. Shattuck,† J. R. Schneck,† L. R. Chieffo,† S. Erramilli,‡ and L. D. Ziegler*,† †

Department of Chemistry and the Photonics Center, Boston University, 590 Commonwealth Avenue, Boston, Massachusetts 02215, United States ‡ Department of Physics and Department of Biomedical Engineering and the Photonics Center, Boston University, 590 Commonwealth Avenue, Boston, Massachusetts 02215, United States S Supporting Information *

ABSTRACT: Dispersed IR three-pulse photon echoes due to the antisymmetric (ν3) stretch mode of N2O dissolved in H2O and 1-octanol at room temperature are reported and analyzed. The experimentally determined transition frequency−frequency correlation function (FFCF) in these two solvents is explained in terms of inertial solvent contributions, hydrogen bond network fluctuations, and, for octanol, the motions of the alkyl chains. The H2O hydrogen bond fluctuations result in 1.5 ps FFCF decay, in agreement with relaxation rates determined from photon echo based measurements of other aqueous solutions including salt solutions. In octanol, hydrogen bond fluctuations decay on a slower time scale of 3.3 ps and alkyl chain motions result in an inhomogeneous broadening contribution to the ν3 absorption spectrum that decays on a 35 ps time scale. Rotational reorientation of N2O is nearly 3 times faster in octanol as compared to water. Although the vibrational ν3 N2O absorption line shapes in water and octanol are similar, the line widths result from different coherence loss mechanisms. A hot band contribution in the N2O in octanol solution is found to have a significant effect on the echo spectrum due to its correspondingly stronger transition moment than that of the fundamental transition. The dephasing dynamics of the N2O ν3 stretch mode is of interest as a probe in ultrafast studies of complex or nanoconfined systems with both hydrophobic and hydrophilic regions such as phospholipids, nucleic acids, and proteins. These results demonstrate the value of the N2O molecule to act as a reporter of equilibrium fluctuations in such complex systems particularly due to its solubility characteristics and long vibrational lifetime.

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INTRODUCTION Biological macromolecular structures such as proteins, nucleic acids, and lipids possess regions of both hydrophobic and hydrophilic character that are central to the biological activity of these molecular systems. Finding and exploiting molecular probes that can simultaneously report on the structure and dynamics of such distinct domain types can be valuable measures of molecular level structure−function relationships in these biological systems. Vibrational energy relaxation (VER) measurements of the ν3 asymmetric stretching mode (∼2230 cm−1) of nitrous oxide (N2O) dissolved in water, octanol, and lipid bilayers have been reported and shown to be a useful measure in particular of changes in the structure of water molecules surrounding zwitterionic phospholipid head groups.1,2 Distinct ν3 lifetimes (T1) were observed for N2O solvated in the acyl tail, interfacial water, and bulk water regions of hydrated DOPC (dioleoylphosphatidylcholine) bilayers. The ν3 lifetime of the interfacial N2O population varied from 43 ps at 10% hydration to 19 ps at 33% hydration, the excess water point.2 This effect is attributed to changes in the solvent density of intermolecular states resonant with the ν3 band (∼2230 cm−1) © 2013 American Chemical Society

resulting from oriented interfacial water molecules near the lipid phosphate groups at the interlamellar bilayer region.3 In contrast, the N2O ν3 v = 1 level lifetime was 51 ps in DOPC acyl chain regions and 9 ps for N2O in bulk water pools formed at high hydration levels. The observed partitioning of N2O into the aqueous phase and acyl chain regions of lipid membranes is consistent with molecular dynamics simulations of N2O−lipid− water systems.4 Thus, the N2O VER rate appears to be an experimentally convenient tool for reporting on the structure and dynamics of interfacial water in lipids and, potentially, in other biological or nanoconfined systems. This paper reports on the solvation dynamics of the ν3 transition of N2O in water and octanol determined by frequency dispersed three-pulse IR photon echoes (3PPE). The vibrational dephasing dynamics of this reporter molecule are a measure of Special Issue: Michael D. Fayer Festschrift Received: July 3, 2013 Revised: August 7, 2013 Published: August 13, 2013 15774

dx.doi.org/10.1021/jp4065533 | J. Phys. Chem. B 2013, 117, 15774−15785

The Journal of Physical Chemistry B

Article

the ultrafast fluctuation dynamics in these two contrasting hydrophilic and largely hydrophobic solvent environments. Octanol has often been used as a model molecular system for characterizing lipid properties.5−7 While our vibrational lifetime results, described further below, support a view of octanol as simply a bulk hydrophobic or “oily” homogeneous medium, it has also been viewed as a structural analogue for phospholipids owing to its hydroxyl “head group” and nonpolar hydrocarbon tail. Multicomponent contributions to the decay of vibrational echo signals may offer greater sensitivity to these various structural regions than seen in VER studies. Just as our earlier studies of the VER dynamics of this N2O mode in water and octanol provided a basis for understanding N2O lifetime effects in lipid bilayers,2 these 3PPE studies of N2O in these neat model solvents will provide a basis for characterizing and understanding the nature of the observed responses reported in subsequent vibrational echo studies of this probe reporter molecule (N2O) in more complex biological systems such as hydrated lipids, proteins, and nucleic acids. Several properties of N2O and its asymmetric stretching ν3 mode make it an attractive vibrational “reporter” of local solvation effects in biological systems. The weak dipole moment (0.16 D) of N2O8 allows both polar and nonpolar regions of a material to be probed in a single experiment. In particular, the N2O octanol/water partition coefficient is 2.5 at ambient temperatures.9 It is a small neutral solute, and hence potentially less perturbing than larger electronic chromophores or ionic species employed as probes of inherent structures of solvents or biological systems. The ν3 mode has a large extinction coefficient (∼1.5 × 103 M−1 cm−1 in water), and its frequency (2215−2235 cm−1) is in a spectral region that is removed from absorptions due to most protein, nucleic acid, lipid, or strong solvent bands (vide inf ra). The gas phase N2O ν3 frequency (2224 cm−1) is redshifted in nonpolar environments and blue-shifted in aqueous solutions. 10 This force constant change can be readily rationalized in terms of N2O’s ground electronic resonance structures. The N2O ν3 v = 1 lifetime, 52 ± 1 ps, and fundamental transition frequency in octanol are identical to that seen for N2O in the acyl chain region of hydrated lipids (51 ± 2 ps).1,2 Thus, these different solvation environments can be separated both by their average ν3 vibrational frequencies as well as by their different relaxation rates as determined by IR based spectroscopic measurements. Furthermore, the N2O ν3 lifetimes in both water and octanol (∼10−50 ps) provide a large dynamic time range for solvent fluctuation studies via vibrational echo techniques. As a contrast, the isoelectronic triatomic, N3−, has an asymmetric stretch (v = 1) lifetime of ∼0.8 (2.3) ps in H2O (D2O).11,12 The longer T1 of N2O is advantageous in order to probe slower components of solvation responses. For example, water residence times up to ∼100 ps in biological systems may be probed via ultrafast N2O vibrational techniques.13,14 Finally, we note that understanding the molecular details of solvation for N2O, a common general anesthetic,15,16 in different bath types could be useful for learning about the molecular-level mechanism of general anesthetic action. The partitioning of N2O between octanol and water is the standard benchmark used to assess anesthetic potency.16 Both lipid membrane and protein-based models of anesthetic action have been previously proposed for N2O.15,17−19 The linear absorption spectrum of the N2O ν3 fundamental band centered at 2230 cm−1 in water and 2218 cm−1 in octanol is shown in Figure 1. The corresponding linewidths (fwhh) are 10 and 13 cm−1, respectively. The inset of Figure 1 shows the N2O

Figure 1. Normalized linear absorption spectrum of the N2O ν3 asymmetric stretching band in octanol (2218 cm−1) and H2O (2230 cm−1) with the water background signal subtracted. The absorption spectrum of ∼100 mM in H2O showing the overlapping bend−libration water band is displayed in the inset. The small feature at ∼2202 cm−1 in the octanol spectrum is due to an asymmetric stretch originating from the thermally populated N2O bend (ν2) level.61

ν3 absorption in a H2O solution (∼0.1 M N2O) overlapping the broad water bend−libration combination band absorption. This weak solvent feature has a peak extinction coefficient of ∼3 M−1 cm−1 at 2130 cm−1 and a fwhh of ∼300 cm−1. The N2O ν3 lifetime is 52 ps in octanol and 9 ps in H2O at room temperature. Thus, although the absorption line width is only 30% different in these two solvents, the rate of VER following excitation of the ν3 fundamental, which can depend on a number of local bath factors, differs by nearly a factor of 6.1,2 This lifetime difference and the corresponding solvent dependent vibrational transition frequency at least suggest that mechanisms of N2O ν3 coherence loss may be different as well in these two local molecular environments as borne out by the results reported here. Vibrational photon echo analysis allows the mechanisms of the total dephasing of the resonant oscillator’s coherence to be determined. Thus, all the molecular processes contributing to the shape of the linear absorption spectrumspectral diffusion, inhomogeneous broadening, rotational diffusion, and lifetime effectsare delineated by this technique in conjunction with pump−probe measurements. Photon echo signal analysis provides a more direct measure of a solvent’s structure and dynamics than T1 measurements because the time scales of solvent equilibrium fluctuations and characteristic motions are explicitly revealed by the photon echo signal decays. Vibrational lifetimes are generally only implicitly dependent on the structure and dynamics of the bath surrounding a solute in solution. The analysis of three-pulse photon echo (3PPE) data can be accomplished via either so-called peak shift measurements or global photon echo fitting procedures.12,20 In the former, the time difference between the peaks of phase matched rephasing and nonrephasing signals yield an approximation of the transition frequency−frequency correlation function (FFCF). The FFCF is the key experimentally determined quantity in photon echo experiments.20,21 In the global echo fitting procedure, the entire two-dimensional time dependence of the observed photon echo signal is fit as a function of the parameters determining the FFCF. The FFCF, determined by either photon echo data analysis methodology, is a direct probe of the equilibrium structural fluctuations of a solution, at least as they couple to the vibrational potential of the resonant probe solute mode. The FFCF generally reveals multiple fluctuation components in liquid 15775



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Table 1. Results of Global Fitting Analysis for Dispersed 3PPE Response due to Fundamental Resonance of the N2O ν3 Mode in Octanol and Watera N2O/octanol N2O/H2O a

Δ1 (ps−1)

τ1 (ps)

Δ2 (ps−1)

τ2 (ps)

Δ3 (ps−1)

τ3 (ps)

T1 (ps)

D (ps−1)

T2* (ps) (Δ12 τ1)−1

1.0 2.0

0.23 0.16

0.16 0.62

3.3 1.5

0.56

35

52 9

0.62 0.22

4.3 1.6

Lifetimes (T1) and rotational diffusion constants (D) have been determined independently.1,2

spectrum which overlaps the N2O ν3 vibrational absorption. (See inset in Figure 1.) The sample cell was loaded with the liquid solvent and pressurized to 1 atm of pure N2O for octanol and to 10 atm of N2O for water in order to bring the peak absorption of the dissolved N2O ν3 band to be in the range of ∼0.2−0.5 OD in the solutions. The different pressures are needed to account for differences in path length and N2O solubility in each of the two solvents. The sealed samples were allowed to equilibrate for at least 12 h before data acquisition. Dispersed Three-Pulse Vibrational Photon Echo Measurements. Approximately 3 W of the output power from a Legend Elite Duo (Coherent Inc.) titanium sapphire regeneratively amplified laser system, which nominally produces 35 fs, 800 nm pulses at a 1kHz repetition rate, is directed into a Topaz (Light Conversion) optical parametric amplifier (OPA). The OPA output at ∼1300 and ∼1800 nm is used to generate the difference frequency pulse centered at ∼4500 nm (∼2200 cm−1) in a 500 μm AgGaS2 (Altechna) crystal. Varying thicknesses of CaF2 and germanium windows are inserted in the beamline to compensate for chirp in the IR output pulse at the sample.28 Following 1:2 beam expansion, the ultrafast IR pulse is divided into three beams of nearly equal energy with relative timings between each pair of pulses (τ and T) set by computer controlled translation stages (Melles Griot) with mounted gold retroreflectors. The relative polarizations of the incident pulses are controlled by a combination of grid polarizers and 1/2-wave plates. The three incident ∼1.5 μJ/pulse, 90 fs pulses are focused to a 90 μm diameter spot at the sample by an off-axis parabolic mirror ( f = 100 mm). An identical parabolic mirror after the sample collimates these transmitted beams and the signal beams. The 3PPE signals in the two phase matched directions and are monitored with liquid nitrogen cooled HgCdTe detectors. The −k1 + k2 + k3 or α-direction is dispersed by a 100 mm monochromator equipped with a 150 grooves/mm grating blazed at 4.5 μm onto a 32-channel array detector (Infrared Associates) and results in 2 cm−1 spectral resolution. The βdirection phased matched signal, k1 − k2 + k3, related by time reversal to the α signal, is detected on a single element detector in a spectrally integrated fashion and used to determine the experimental τ = 0 time, i.e., when the k1 and k2 pulses are temporally overlapped. Rotational Anisotropy Measurements. Rotational anisotropy, R(t), measurements were carried out in a standard twobeam pump probe configuration with the polarization of the probe pulse beam oriented parallel and then perpendicular to the pump. Relative pump and probe polarization directions were controlled by 1/2-wave plate (Altchna) and grid polarizers placed both before and after the sample. Best-fitted exponential decays to the observed R(t) given by the pump−probe response integrated over the entire width of the dispersed signal determine the rotational diffusion constant, D, and are listed in Table 1.

solutions. Probably the greatest utility of this approach is that it provides a measure of the fluctuation components that describe the dephasing of the vibrational coherence for time scales much longer than the vibrational coherence decay time determined by the lifetime of the vibrational level. While vibrational coherence times are typically on the order of a picosecond, vibrational lifetimes may be as long as 50 ps for some condensed phase oscillators, thus extending determination of equilibrium fluctuation dynamics out to 100 ps in favorable systems. Small ions, e.g., N3−, SCN−, OCN−, or small highly polar molecules or molecular groups (water, nitrile, or azide groups) have typically served as probes of solvent fluctuations via vibrational photon echo techniques. Thus, 3PPE studies carried out with N2O offer a contrast to these solutes due to the weak dipole character of this reporter molecule. In particular, solvation results of aqueous solutions can be compared to those shown here for the aqueous N2O solution. For this 3PPE homodyne technique, the delay between the first two pulses is the coherence time and the interval between the second and third pulses is called the population time.20 The photon echo spectrum as a function of coherence time for a given population time is the measurement technique employed for the vibrational photon echo observation reported here. Several frequency dispersed vibrational 3PPE studies have been previously carried out.22−27 As discussed in greater detail below, the frequency selected vibrational echo measurements were necessary here to avoid solvent interference effects in the integrated photon echo signal. Furthermore, analysis of frequency dispersed 3PPE signals offers significant simplification of the 3PPE data analysis. Fewer density matrix pathway histories are required for modeling the frequency selected echo response effectively reducing the resonant vibrational system to a two-level description as compared to a three-level system and thus simplifying the required analysis. The dispersed echo analysis also avoids interferences between 0−1 and 1−2 vibrational resonances to the integrated echo signal. Although not the focus of this report, the dispersed 3PPE analysis has the potential to provide more molecular information by allowing comparison of the dynamics of the 0−1 and 1−2 coherence loss mechanisms. The results described here show that despite the relatively modest difference in absorption line shape N2O should be an effective probe of equilibrium fluctuations over a large temporal range in complex molecular systems characterized by regions of distinct polarity differences and allow ultrafast solvation studies in a wide range of solvent environments as well.

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EXPERIMENTAL SECTION Sample Preparation. N2O solutions were prepared in a variable path length stainless steel cell designed for pressurized samples. The solvents of interest here, octanol and water, were sandwiched between two 2 mm thick CaF2 windows separated by 100 and 25 μm thick Teflon spacers, respectively. A thinner optical path length was preferable for the N2O water solution in order to minimize photon echo signal contributions from the water bend−libration combination band region of the water 15776



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THREE-PULSE VIBRATIONAL PHOTON ECHO THEORY SUMMARY The vibrational 3PPE signal is generated by the optically induced third order polarization, P(3)(t), given by a convolution of the corresponding material response functions for the relevant pulse interaction histories and the three incident vibrationally resonant laser pulses characterized by electric field amplitudes E1, E2, and E3:12,20,21 (3)

P (τ , T , t ) ∝

∫0

∞

dt 3

∫0

∞

dt 2

∫0

∞

lifetimes of the v = 1 and v = 2 vibrational levels. For the harmonic approximation often invoked in the preliminary analysis of vibrational photon echo responses, μ12 ≈ (2)1/2μ01 and 2T1′ = T1.12,20,31 The effects of orientational relaxation dynamics of the transition dipoles on the 3PPE signal are modeled by O(t1, t2, t3) in eq 2:12,20,32,33 O(t1 , t 2 , t3) =

dt1(∑ R i(t1 , t 2 , t3))

× E3(t − t3)E2(t + T − t3 − t 2) (1)

R(t1, t2, t3) is the third order response function generating the signal fields in the two photon echo phase matched directions, kα,β = ∓k1 ± k2 + k3, where ki (i = 1, 2, 3) corresponds to the wavevectors of the three incident pulses. τ and T, referred to as the coherence and population times, respectively, correspond to the delay between the first and second pulses, E1 and E2, and the second and third pulses, E2 and E3, respectively. As has been well characterized previously,20,29 eight distinct density matrix time evolution pathways contribute to vibrational 3PPE phase matched signal directions, kα,β, in general. The relevant response functions are given by20,29,30

g (t ) =

∫0

t

dτ ′

∫0

τ′

dτ″C(τ″)

where

C(t ) = ⟨δω10(t )δω10(0)⟩

(4)

C(t) is the transition frequency−frequency correlation function (FFCF) and the key quantity determined by three-pulse photon echo studies.21 It is the central dynamical function for the description of solvation and spectroscopic line shapes in condensed phase systems. We assume here that the δω10(t) and δω21(t) frequency fluctuations are strictly correlated. In the usual Kubo treatment,20,21,35 C(t) is given by

R1 = R 2 ∝ μ10 4 e−iω01(t3− t1)O(t1 , t 2 , t3) × exp[− (t1 + 2t 2 + t3)/2T1] exp(−g (t1) + g (t 2) − g (t3) − g (t1 + t 2) − g (t 2 + t3) + g (t1 + t 2 + t3))

n

C(t ) = ⟨δω10(t )δω10(0)⟩ =

∑ Δi 2e−t /τ

i

i=1 2

2 iΔt3 −iω01(t3− t1)

R3 ∝ −μ10 μ21 e e O(t1 , t 2 , t3) ′ × exp[−(T1 + T1′)t3/2TT − (t 2 + t1/2)/T1] 1 1 × exp(−g (t1) + g (t 2) − g (t3) − g (t1 + t 2) − g (t 2 + t3) + g (t1 + t 2 + t3))

(5)

The sum is over all the distinct degrees of freedom of the bath that couple to the excitation energy, Δi (ps−1) corresponds to the instantaneous distribution of transition frequencies (Gaussian fwhh (cm−1) = Δi (ps−1)/0.113), and τi is the single exponential time scale characterizing the system’s memory loss of the initial transition frequency resulting from fluctuations of the ith degree of freedom. The corresponding total line shape function is thus

R 4 = R 5 ∝ μ10 4 e−iω01(t3+ t1)O(t1 , t 2 , t3) × exp[− (t1 + 2t 2 + t3)/2T1] exp(−g (t1) − g (t 2) − g (t3) + g (t1 + t 2) + g (t 2 + t3) − g (t1 + t 2 + t3)) 2

(3)

where D is the rotational diffusion coefficient which can be independently determined by pump−probe anisotropy decay measurements.34 The pure dephasing dynamics of the resonant vibrational transition are given by g(t), the line shape function. Treating the transition frequency fluctuations as a Gaussian random process, a cumulant expansion approach for g(t) yields35

i

× E1(t + T + τ − t3 − t 2 − t1)

1⎛ 4 −6Dt2⎞ −2D(t1+ t3) ⎜1 + ⎟e e ⎝ ⎠ 9 5

g (t ) =

∑ gi(t ), i

2 iΔt3 −iω01(t3+ t1)

R 6 ∝ −μ10 μ21 e e O(t1 , t 2 , t3) ′ × exp[−(T1 + T1′)t3/2TT − (t 2 + t1/2)/T1] 1 1 × exp(−g (t1) − g (t 2) − g (t3) + g (t1 + t 2) + g (t 2 + t3) − g (t1 + t 2 + t3))

where gi(t ) = Δi 2 τi[t 2/τi − (1 − exp(−t /τi))]

(6)

for the ith component contributing to the FFCF. When the three incident pulses are not temporally overlapped and E1, E2, E3 is the enforced sequential field temporal interaction history, only pathways R1, R2, and R3 contribute to the echo signal in the kα direction. As evident in eq 2, density matrix pathways R1 and R2 generate echo signal polarization at the fundamental frequency, ω10, whereas pathway R3 generates echo signal polarization at the anharmonicity shifted frequency, ω10 − Δ(ω21). The observed homodyne detected integrated 3PPE signal as a function of coherence time (τ) for a given population delay (T) is given by

R 7 ∝ μ10 2 μ212 eiΔt3e−iω01(t3+ 2t2 + t1)eiΔt2O(t1 , t 2 , t3) × exp[− (t1 + t3)/2T1 − t 2/2T1′] × exp(+g (t1) − g (t 2) + g (t3) − g (t1 + t 2) − g (t 2 + t3) − g (t1 + t 2 + t3)) R 8 ∝ −μ10 2 μ212 eiΔt3e−iω01(t3+ 2t2 + t1)eiΔ(t2 + t3)O(t1 , t 2 , t3) × exp[− (T1 + T1′)t3/2TT 1 1′ − t1/2T1′] × exp(+g (t1) − g (t 2) + g (t3) − g (t1 + t 2) − g (t 2 + t3) − g (t1 + t 2 + t3))

S(τ , T ) ∝ (2)

∫0

∞

|P(3)(τ , T , t )|2 dt

(7)

The frequency dispersed 3PPE signal is related to a Fourier transform of the signal polarization:

μ10 and μ12 are the magnitudes of the transition dipole moments corresponding to the v = 0 ↔ v = 1 and v = 1 ↔ v = 2 transitions centered, respectively, at ω10 and ω21, Δ is the anharmonicity of the first overtone level (Δ = ω10 − ω21), and T1 and T1′ are

S(τ , T , ω) ∝ | 15777

∫0

∞

dtP(3)(τ , T , t )eiωt |2

(8)



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transition frequency distribution is evident in Figure 2 for the N2O ν3 transition in both solvents. The peak shift or echo signal maximum is at τ = ∼110 and ∼180 fs at T = 0 in octanol and water, respectively. As shown below, this reflects the stronger coupling (Δi) between N2O and H2O than with octanol. In initial attempts to determine the transition frequency correlation function, measurements were made of the frequency integrated 3PPE peak shift in the α and β phase matched directions for N2O water and octanol solutions as a function of the population time, as has been previously described in other homodyne detected IR photon echo studies.12,20,31 Experimentally, this peak shift is the value of τ corresponding to the maximum in the frequency selected 3PPE signal relative to τ = 0. τ = 0 is found as 1/2 the time interval separating the maxima of the α and β signals, reverse temporal mirror images of each other, for each population time (T) and provides a very precise (±1 fs) determination of τ = 0. This T dependent peak shift is often taken as a measure of the FFCF for both vibrational and electronic ultrafast echo studies. The integrated echo signals in the two (α, β) phase matched directions as a function of τ for three population times (T) are shown in Figure 3 for both N2O solvent solutions. At T = 5 ps, the peak shift has decayed to 50 fs and has fully disappeared only by ∼110 ps, indicating some long-lived inhomogeneity in the N2O/octanol system (vide inf ra). However, for the aqueous N2O solution, a large pulse width limited signal component (i.e., signal feature vanishes for τ > pulse width) that exhibited no peak shift, but whose intensity was

Within the framework of this line shape analysis, the corresponding linear absorption spectrum is given by33 Iabs(ω) ∝ Re

∫0

∞

dt e−i(ω10 − ω)t DCF(t )

DCF(t ) = e−g(t )e−t /2T1e−2Dt

where (9)

DCF(t) is the time dependent part of the dipole correlation function.

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RESULTS AND DISCUSSION Frequency Dispersed and Integrated 3PPE Data. The dispersed 3PPE signals in the α direction due to 90 fs pulses resonant with the N2O ν3 mode in octanol and H2O at a near zero population time are shown in Figure 2. The echo

Figure 2. The dispersed three-pulse photon echo signals due to 90 fs pulses resonant with the ν3 mode of N2O in octanol and H2O for a population time of 0 (T = 0) are displayed in the upper and lower panels, respectively. Echo polarization contributions due to 0−1 and 1−2 resonances are clearly resolved in the dispersed aqueous N2O solution echo signals and less distinctly evident in the corresponding N2O in octanol ν3 echo signal.

polarizations generated at the 0 → 1 and 1 → 2 ν3 resonances at 2230 and 2212 cm−1 are clearly evident in the aqueous N2O solution signal. In contrast, only the ν3 0 → 1 resonant 3PPE signal component at 2218 cm−1 is clearly evident for the N2O in octanol solution. The contribution to the 3PPE response to the red side of this peak corresponding to the echo intensity at the 1 → 2 transition cannot be fully resolved and appears relatively weaker in the octanol solvent than in H2O. The origin of this effect will be discussed below. The characteristic vibrational echo peak shift resulting from incomplete memory loss of the initial

Figure 3. Integrated three-pulse photon echo signals due to resonance with the N2O ν3 mode in H2O and octanol for both phase matched α (blue) and β (red) directions for three different population times. The peak shift between the maximum of these two time reversal symmetry related signals is evident. The peak shift disappears on a much faster time scale for the water solution than for N2O in octanol. 15778



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Figure 4. N2O ν3 0−1 resonant frequency selected three-pulse photon echo signals as a function of coherence (τ) and population (T) times for the octanol solution. Only signal frequencies due to the 0−1 resonance in the range from 2215 to 2225 cm−1 were used to construct this echo response.

is resonant with the relatively narrow (∼10 cm−1) 0 → 1 or 1 → 2 ν3 resonances. As a further check on this strategy for eliminating this large unwanted solvent contribution, no noticeable signal above the noise level could be observed in the dispersed neat water sample for this same narrow range of selected frequencies. Similarly, only 3PPE signals in the signal frequency range from 2214 to 2228 cm−1, corresponding to signal polarization resonant with the 0 → 1 transition of N2O in octanol, were used to construct the echo responses for this octanol solution. The coherence time (τ) dependence of the 0−1 frequency selected echo signals as a function of population time (T) in the kα = −k1 + k2 + k3 direction are shown in Figure 4 for the N2O in the octanol solution. Precise (±1 fs) τ = 0 determination is given by the simultaneous measurement of the integrated signal in the kβ direction. The ability to eliminate contributions to the integrated vibrational echo response generated by ultrafast pulses resulting from the 1 → 2 transition of the vibrator of interest, other solute modes, combination bands, as well as modes of other species in a mixture, by frequency selection has been previously noted and exploited in other dispersed vibrational echo studies.22−26,38 Frequency selection has also been used to separate different density matrix pathway contributions to P(3) ultrafast signals in addition to vibrational photon echoes, such as OHD impulsive stimulated Raman or pump−probe spectroscopy, in order to isolate, or in some cases amplify, specific molecular responses contributing to the total signal intensity.39−41 For the 3PPE data of interest here, in addition to eliminating the background contribution of water in the aqueous N2O solution, and avoiding the potential for observing nonexponential decay character in the spectral pulse width integrated 3PPE responses,26 analysis of the frequency selected 0 → 1 resonant echo polarization signal is reduced to a simple two-level treatment of photon echo responses. As long as the selected signal frequency components have minimal contribution from the anharmonically red-shifted 1 → 2 resonance, this excited state absorption source of echo polarization can be neglected. Thus, calculated responses including only density matrix histories R1 and R2 are required for these corresponding frequency selected vibrational echo signals in the kα direction (τ, T > 0). Frequency−Frequency Correlation Function Determination. For an initial estimate of the FFCF, C(t), we fit the integrated three-pulse photon echo peak shift to the minimum number of exponential decay components required to achieve a

constant for at least hundreds of picoseconds, was detected in the integrated signals in both phase matched directions (see Figure S1, Supporting Information). When this feature was subtracted from the integrated 3PPE signals, peak shift relaxation was found to occur on a very different time scale in H2O than in octanol. As seen in Figure 3, the peak shift for the ν3 N2O in H2O photon echo which was larger than that of the octanol solution at T = 0 is nearly 0 by T = 2 ps. Unfortunately, this autocorrelation-like additional signal component compromised the accuracy of the peak shift measurements for the aqueous N2O solution particularly at short times. In order to determine the origin of this polarization component in the 3PPE phase matched directions, we found that this same feature was observed in the corresponding three-pulse dependent, homodyne integrated signals from neat H2O alone. Thus, we attribute this signal component to the phase matched transient grating signal in the echo directions due to the long-lived (∼ms) bleach response seen in the pump−probe signal of neat H2O excited at these same IR excitation wavelengths.36 The entire spectral width of the 90 fs incident pulse centered at 2230 cm−1 is resonant with the weak (εpeak ∼3 M−1 cm−1) but broad (∼300 cm−1 fwhm) bend− libration combination band of H2O (see inset in Figure 1) found in this region of the H2O spectrum. In addition, an underlying water absorption continuum due to higher order overtones and combinations of low frequency modes and evident throughout the water IR spectrum spans the entire pulse spectral range as well.36 The same T independent, pulse width limited feature was reported in integrated 3PPE studies of the azide ion in an aqueous protein environment excited at similar IR frequencies.37 Thus, in order to eliminate this interfering broad water signal in this study, we analyze only the 0 → 1 resonant portion of the dispersed echo response as a function of τ and T. The N2O ν3 0 → 1 resonant 3PPE contribution peaked at 2230 cm −1 in water is clearly evident in the dispersed 3PPE signal (Figure 2), and thus, dispersed homodyne intensities in the range from ∼2225 to ∼2238 cm−1 only were summed and used to construct the τ and T dependent N2O/water solution echo responses analyzed here. No evidence of the overlapping H2O transient grating response, characterized by the pulse width limited τ dependence and T independence, was observed in the 0 → 1 frequency selected 3PPE signals in water. Effective discrimination against this overlapping and interfering solvent component was achieved because the water response was generated at all ultrafast pulse frequencies (∼400 cm−1), whereas the 3PPE signal polarization 15779



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satisfactory fit (eq 5). The water solution echo data had the water interference term removed as described above. The temporal peaks of the echo responses were determined by fitting a Gaussian to the top 20% of the α and β signals to minimize peak shift determination errors at short population times where the echo signal is most significantly asymmetric with respect to τ.42 Use of the first moment, M1, of the echo signals in each direction to experimentally determine the 3PPE peak shift42 showed no significant difference in the time scales found by Gaussian fitting the peak shift directly. Best fits to the population time (T) dependence of the N2O ν3 peak shift identified double exponential decays for each solution: 3.3 and 35 ps for octanol and 0.16 and 1.5 ps for H2O. Thus, these results already reveal that solvation dynamics in these two solutions are significantly different. However, global fitting of all the echo decays for each population time has been shown to produce more accurate FFCF results in particular with respect to short time components and fluctuation amplitudes (Δi), although nearly identical fluctuation time scales (τi) are found via both approaches.12,33 Consequently, we used the integrated 3PPE peak shift Δi and τi values as initial guesses for the global fitting procedure for the frequency selected, τ dependent echo signals (Figure 4) for each population time (T). Excellent global fits to the observed 0−1 resonant frequency selected echo decays of the ν3 N2O transition in H2O and octanol were obtained. Representative frequency selected echo signal decays for each solvent at two different population times and corresponding best fits are shown in Figure 5. The global fits to the data were modeled by a calculated echo signal derived from the R1 and R2

third order response functions (eq 2) for all experimental τ and T values, and the constraint of simultaneously fitting the linear absorption line shape (eq 9). T10 (and T21 by virtue of the harmonic approximation), D, and the ν3 anharmonicity values required for the fitting procedure are known from previous pump−probe results1,2 and orientational anisotropy measurements reported here (Table 1) for the N2O ν3 transition in each solvent. The resulting absorption spectra fits are shown in Figure 6. (Hot band contribution at 2202 cm−1 in N2O octanol solution will be discussed further below.)

Figure 6. Resulting best fits to the linear absorption spectra of the N2O ν3 mode in octanol and H2O. The small feature at ∼2202 cm−1 is due to the transition to the ν2 + ν3 combination band originating in the thermally populated ν2 bending level (588 cm−1).

Thus, this global echo time dependence and absorption line shape nonlinear least-squares fitting analysis yields the 3PPE experimentally determined N2O ν3 FFCF transition energy for each of the two solvents. The resulting best-fit determined N2O in H2O ν3 FFCF is C W(t ) = (2.0 ps−1)2 e−t /0.16ps + (0.62 ps−1)2 e−t /1.5ps (10)

The corresponding FFCF for N2O in octanol is found to be CO(t ) = (1.0 ps−1)2 e−t /0.23ps + (0.16 ps−1)2 e−t /3.3ps + (0.56 ps−1)2 e−t /35ps

(11)

All spectral line shape parameters, including the amplitudes (Δi) and decay time constants (τi), are also summarized in Table 1. These two correlation functions are plotted in Figure 7. This figure highlights the similarities and differences between the fluctuation dynamics reported by the N2O ν3 mode for these two solvents. Although the solvation reponses at the shortest times (≤250 fs) are similar, significant differences are seen at the intermediate and longer time scales. As evident in Figure 7, the H2O solvation response is essentially over by 3 ps, whereas, in contrast, the response in octanol is evident out to ∼120 ps. Two exponential decay components, τ1 = 0.16 ps and τ2 = 1.5 ps, are needed to fit the solvation response for the ν3 mode in water (eq 5). The shortest decay component (Δ1, τ1) is close to the homogeneous or motionally narrowing limit, Δ1τ1 < 1.35 This short time transition energy correlation decay is generally attributed to rapid inertial solvent motions and has been found to be a ubiquitous solvent response component in all previous vibrational photon echo studies.12,20,22,27,29,43−45 The pure dephasing time associated with this fluctuation component in water (T2* = 1/Δ12τ1) is 1.6 ps. For this nearly homogeneous

Figure 5. Comparison of results of global best fits to observed 0−1 frequency selected 3PPE signals for two different population times for N2O in octanol and H2O. Global fits to the data were achieved by constraining the global procedure to simultaneously fit the absorption spectrum. 15780



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description of the fastest solvation response. These components for the N2O ν3 mode in octanol vary over 2 orders of magnitude in time scale. The fastest octanol fluctuation component results from a process that is close to the homogeneous limit (Δ1τ1 < 1), as found for N2O in H2O, and corresponds to a pure dephasing time of 4.3 ps. The slower T*2 for N2O in octanol than water (1.6 ps) is primarily due the smaller determined coupling strength (Δ1) in the alkyl alcohol than water and may be rationalized by the anticipated weaker dipole−dipole interaction in this solvent than water. Relaxation times very similar to the 3PPE based τ2 and τ3 have been reported from the analysis of previous spectroscopic studies of pure octanol. The intermediate (τ2) 3.3 ps decay CO(t) component determined here is in the spectral diffusion regime, Δ2τ2 ∼ 1, just as seen for the corresponding picosecond process in the H2O FFCF (Table 1). This relaxation component is also of the same time scale as the 4.5 and 4.1 ps decays reported from the analysis of 3PPEs of OCN− and SCN− in methanol.43 Furthermore, dielectric relaxation measurements of octanol display reorientational relaxation processes which decay with a 3.2 and 38.7 ps (±10%) exponential time constant in the subnanosecond response regime.53 These decay constants are in quantitative agreement with the results reported here for N2O vibrational solvation in octanol (Table 1). Additionally, exponential decays of 3.8 and 3.5 ps have been previously identified in the Fourier transformed spontaneous dispersed Rayleigh scattering spectrum and the direct time domain OKE measurements of octanol at 298 K, respectively.54 These values are nearly identical to the τ2 3.3 ps decay indentified in the FFCF for N2O in octanol. The slower time scale τ3 component corresponds to a fluctuation that is best described as an inhomogeneous contribution to the absorption line width of the ν3 N2O transition in octanol, i.e., Δ3τ3 ≫ 1. As analogously assigned for N2O in H2O and all previous vibrational echo studies, the most rapid CO(t) fluctuation component, τ1 = 230 fs, is assigned to inertial motions in octanol. It is also noted that a large amplitude ∼200 fs decay component is found in the time domain OKE response and in the Fourier transformed depolarized quasi-elastic light scattering spectrum of pure octanol, where collision-induced effects are cited as the origin of these rapid reorientational motions in this pure liquid.54 The τ2 decay times identified in the vibrational 3PPE analysis of OCN− and SCN− in methanol, 4.1 and 4.5 ps, are attributed to the fluctuations of the hydrogen bonding network in these alcohols.43,44 This fluctuation rate is about 3 times slower than the analogously identified hydrogen bonding fluctuations of aqueous solvents (Table 2) as noted above. Simulation studies report that small ion reorientation times in methanol are about 3 times longer than those in water.55 Thus, due to the similarity of this time scale in previous experimental and calculation studies, the 3.3 ps τ2 decay in CO(t) is attributed as well to fluctuations of the hydrogen bonding interactions in liquid octanol structures at room temperature. A range of hydrogen bonded network structures, including polymeric chains, four-, five-, and six-membered rings, and some more densely packed aggregates, are found in MD simulations of pure octanol.56 The τ2 time scale has also been attributed to reorientational motions of OH groups in the octanol simulation study and in the dielectric relaxation studies, albeit with monomer structures in mind before the recent generation of experimental hydrogen bonding dynamics studies in water were carried out.53,56

Figure 7. Plots of the frequency−frequency correlation functions (FFCF) for the N2O ν3 resonance in octanol and H2O determined by this vibrational 3PPE analysis. The inset shows just the first 5 ps of these FFCFs.

dephasing component, the uncertainty in Δ1 and τ1 is typically greater than that for the corresponding T*2 decay time given the pulse duration of the pulses used in these experiments (90 fs). The lack of accuracy with respect to the shortest FFCF time scale components, Δ1 and τ1, makes more detailed comparison with other vibrational echo results difficult; however, we note that the homogeneous dephasing rate (T2*) corresponding to this component for N2O in H2O, 1.6 ps, is in the range of that reported for the negatively charged azide ion: 1.8 ps in D2O and 0.8 ps in H2O.12,43 Furthermore, as might be expected, the coupling strength, Δ1, for the N3− solute in water is greater than that reported here for N2O in water. The second, slower CW(t) 1.5 ps decay process is in the spectral diffusion regime where Δ2τ2 ∼ 1. A fluctuation component in the 1.2−1.5 ps time scale has been observed in all other vibrational transition energy correlation functions found for aqueous solutions of small molecules (see Table 2) and is Table 2. Rapid (T2*), Intermediate, or Slow FFDF Decays (τ2) and Static (Δo) Component

N3−/H2O N3−/D2O SCN−/D2O HOD/H2O HOD/D2O N2O/H2O

vibrational frequency

T2* (ps) (Δ12 τ1)−1

τ2 (ps)

Δ0 (ps−1)

T1 (ps)

ref

2048 2043 2065 2510 3400 2230

0.8 1.8 0.7 ∼0.2

1.2 1.3 1.3 1.4 1.4 1.5

0.2 0.3 0 0 0 0

0.8 2.3 18.3 1.45 0.7 9

45 12 27 46 51 this work

1.6

attributed to the hydrogen bond breaking and formation motions of the water network.12,46−52 This decay component is a consistent dynamical feature of liquid water both as captured by experiments and theory. As has been noted previously, it is also a time scale that is virtually independent of deuterium substitution (see Table 2, for example), further supporting the description of this degree of freedom as largely translational as compared to rotational in origin. Although two components were sufficient to fit the N2O in octanol peak shift data, three fluctuation components, τ1 = 0.23 ps, τ2 = 3.3 ps, and τ1 = 35 ps (eq 11 and Table 1), are required to fit the corresponding frequency selected echo responses via the global fitting analysis described above constrained to simultaneously fit the linear spectrum, thus providing a better 15781



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We attribute the 35 ps inhomogeneously broadened FFCF component to motions of the alky chain regions of octanol. Dielectric relaxation studies interpret this reorientational component to rotation of monomers or octanols hydrogen bonded in clusters at one end.53 The dielectric relaxation measurements reported for other molecules tend to support this interpretation for this response component. For example, the τ3 relaxation times of n-alcohols are similar to those for the alkyl bromide molecules of comparable size and increases with the chain length as seen for this component of the alkyl bromides.57 On the other hand, the τ2 time depends very little on the length of the n-alcohol hydrocarbon chain in dielectric measurements.53 This observation further supports, along with the 4.1 and 4.5 ps FFCF times for ions in methanol,43,44,58 the interpretation of τ2 as representing fluctuations of the hydrogen bonding moiety. Similarly, simulations support the interpretation of the 35 ps time scale as resulting from whole alkyl chain reorientational motion.56 Comparison of N2O and Azide Aqueous Solution Responses. Comparison of the FFCF of N2O and N3− in aqueous solution as determined by vibrational photon echoes studies is interesting given the similar electronic and nuclear sizes of these reporter solutes. The azide charge is the significant difference and alters the consequent solvent−solute interaction range and strength. We take the presence of the countercation to be negligible at experimental salt concentrations. However, as already discussed above, the water hydrogen bonding network fluctuation time scale attributed to the 1.5 ps FFCF decay for N2O in H2O is essentially equal to that found for the FFCF of azide in both H2O (1.2 ps) and D2O (1.3 ps).12,43 The short time inertial fluctuation time scales are also not very different. Perhaps the most substantive difference between the aqueous FFCFs determined by these two probe molecules is the static contribution found for the aqueous azide solution (Table 2). No such contribution is found for the uncharged N2O solute probe. This relatively small amplitude static component may be attributable to more tightly bound first solvation shell water molecules giving rise to an inhomogeneous static contribution on the measurement time scale of 3−5 ps. Such solvation shell structures would be absent in solutions of the weakly polar N2O solute. Results for 3PPE of the larger monovalent SCN− anion in water do not reveal a long-lived static component for the FFCF which appears consistent with this effect arising from small ionfirst solvation shell effects. Further simulation studies contrasting solvation for these simple solutes in water solution could further help identify this small ion related FFCF component. Three-Pulse Photon Echo Spectral Analysis. As a further test of this analysis of the dispersed 3PPE signals from these two N2O solutions, the FFCFs determined by the global fitting of the τ and T dependence of the echo responses were used to calculate the observed echo signal spectra (eq 8). These spectra correspond to vertical slices across the echo responses shown in Figure 2, for a given τ and T. Pathways R1, R2, and R3 were required for these calculated echo spectra. The anharmonicity is the only fitting parameter (aside from an overall scaling parameter) when a single v = 0 → v = 1 ν3 vibrational resonance is assumed; all relevant frequency correlation functions are taken to be identical, and harmonic approximations are maintained (μ21 ≈ (2)1/2μ10 and T1′ ≈ 0.5T1). As seen in Figure 8 (upper panel), the calculated echo spectrum of the water solution nicely matches the observed τ = 150 fs, T = 200 fs spectrum for an anharmonicity of 15 cm−1 within the S/N of these observations. In particular, the relative intensities of the 0−1 and 1−2

Figure 8. Comparison of observed and calculated echo spectra. The echo spectrum corresponding to the ν3 mode resonance of N2O in H2O (upper panel) corresponds to T = 0.2 ps and τ = ∼0. The corresponding echo spectrum for N2O in octanol is given for T = 1 ps and τ = ∼0. Excellent agreement between the calculated and experimental spectra is found.

resonance are nearly equal apart from the pulse spectral effects (pulse centered at 2230 cm−1). For delta function pulses, these two polarization components should be of equal magnitude under these harmonic assumptions. The excellent agreement between the observed and calculated echo spectrum is consistent with the line broadening model given by the experimentally determined FFCF for N2O in water. In contrast, the 1−2 ν3 resonance at ∼2200 cm−1 in the corresponding observed echo spectrum of N2O in octanol at τ = 100 fs and T = 1 ps appears to be ∼30% of the intensity of the 0− 1 resonance, as seen in the lower panel of Figure 8. Inclusion of the thermally populated ν2 bend mode to the ν2 + ν3 combination level10 hot band transition as a resonant source of echo polarization is found to fully account for this diminished 1−2 echo spectrum feature originating from N2O molecules in the ground vibrational state (v1 = 0, v2 = 0, v3 = 0). Although, the initial population of the 589 cm−1 ν2 mode is only 6% at 293 K, best fits to the linear absorption spectrum (Figure 1) determine that the transition moment for this hot band excited from the v2 = 1 level is ∼1.7 times larger than the ν3 excitation originating in the cold bending level (v2 = 0). Interestingly, excitation of the bend has only a small effect on the observed stretching frequency (16 cm−1 red shift, Figure 1) but has a profound effect on the transition dipole of N2O in octanol. Since the resonant third order polarization contribution to the signal amplitude is 15782



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proportional to μ4 (eq 2), this weakly populated hot band level can have a rather noticeable effect on the homodyne echo signal in the 1−2 resonance region due to this bend stretch anharmonicity, at least in octanol. When the 70% larger transition moment determined by the linear spectrum is used together with the line shape parameters given by the above analysis (i.e., FFCF, T1, and D for N2O in octanol), an excellent fit to the observed echo spectrum in octanol is obtained, as seen in Figure 8 (lower panel). The ν3 anhamonicity, i.e., (ω10 − ω21), for N2O is found to be 13 cm−1 from this spectral fitting procedure. The 1−2 band appears reduced in this spectrum because the overlapping 0−1 and 1−2 polarization contributions are of opposite sign (eq 2).22 In water solutions, the effect of the anharmonicity resulting from this bending level on the ν3 transition moment is much smaller (feature at ∼2212 cm −1 in Figure 6) and thus makes a near negligible contribution to the echo spectrum and signal. Origins of N2O ν3 Absorption Line Widths in H2O and Octanol. The various temporal contributions to the ν 3 absorption line shape of N2O in H2O and octanol are plotted in Figure 9. The solid black line in each panel is proportional to

the DCF decay time for the aqueous solution (see Figure 9). Vibrational dephasing due to hydrogen bond fluctuations, although clearly evident in the echo signals, contributes very little to the DCF decay of the N2O ν3 mode in octanol. Interestingly, the inhomogeneous effects (g3(t)) of the slowly (35 ps) relaxing alkyl chains make a more significant contribution to this DCF decay than the pure dephasing effects of the solvent inertial motions, although both of the effects are slower than the rotational diffusion contribution to the ν3 N2O DFC decay in the octanol solution. Lifetime effects have virtually no influence on the observed absorption line widths in either solvent but of course are crucial to allowing the longer lived FFCF components to be accurately identified. Finally, we note here that the relative rotational diffusion constants, D, determined by pump−probe anisotropy measurement, of N2O in H2O and octanol (Table 1) do not follow the relative bulk hydrodynamic viscosity values (ηoctanol = 7.45 cP and ηwater = 0.89 cP at 298 K), as predicted by the classical Debye−Stokes−Einstein relationship.59 We attribute the slower reorientational dynamics of N2O in water (strongly dipolar solvent) than in octanol (weak dipolar solvent) to the different solute solvent interactions in each of these two solutions. In part, this is evidenced by the 12 cm−1 red shift observed for the N2O ν3 fundamental on going from water to octanol. Further evidence of different solute−solvent interactions is given by the consistently smaller coupling strengths for the FFCF components for N2O in octanol than water found here (Table 1). Deviations from ideal DSE behavior in octanol solutions have been previously reported.60 However, further theoretical and simulation studies regarding the short rotational diffusion time scale observed for N2O in octanol are of interest in subsequent work.

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CONCLUSION Vibrational three-pulse photon echoes using the ν3 antisymmetric stretching mode of N2O as a probe are successful in determining the different equilibrium fluctuations in H2O and octanol at room temperature at least as they couple to the ν3 vibrational force field. The N2O ν3 absorption linewidths differ by only 30% in these two solvents; however, the dominant mechanism of vibrational coherence loss is different in these two solvents for this transition. Rotational diffusion dominates the observed line width in octanol with a much smaller contribution from the slowly relaxing alkyl chain interactions. The ν3 line width in H2O predominantly results from the combination of inertial motion, rotational diffusion, and hydrogen bond network dynamics. While both solutions exhibit a homogeneous dephasing contribution due to inertial motions of the solvents, the 3PPEs of N2O in H2O reveal a 1.5 ps decay attributed to fluctuations of the hydrogen bonding network. This is a robust component in aqueous solutions and appears independent of deuterium substitution in the solvent (Table 2). The FFCF for N2O in octanol exhibits decay times assigned to hydrogen bonding fluctuations for the structures present in the octanol liquid (3.3 ps) and the motions of the alkyl chains (35 ps). The results presented here highlight the value that N2O offers as a reporter of solvent fluctuations via photon echo based ultrafast methodologies. As demonstrated here, due to its small dipole, N2O has the ability to dissolve in both hydrophobic and hydrophilic environments, which allows it to be used as a probe of solvent dynamics in complex systems, such as lipid membranes, solvated proteins, and DNA. This is an obvious limitation for small charged solutes. Furthermore, the relatively long vibrational lifetime of this oscillator allows the observation

Figure 9. All the sources contributing to the dipole correlation function for the ν3 linear absorption spectrum are plotted for N2O in H2O and octanol. The Fourier transform of the total decay function is the calculated absorption band shown in Figure 6 (except for the small hot band contribution). The pure dephasing effects included here result from the analysis of the vibrational photon echo signals.

the 0 → 1 transition dipole correlation function (DCF). The 1/e decay time is ∼30% slower for the water than the octanol N2O solution, which is consistent with the observed (Figures 1 and 6) relative FTIR ν3 linewidths, 10 cm−1 (H2O) and 13 cm−1 (octanol). However, the origin of this absorption width is very different in the two solvents. The very rapid rotational diffusion largely dominates all the contributions to the overall DCF decay for N 2 O in octanol. By contrast, the most important contributions to the spectral line width for N2O in water are the dephasing attributable to inertial solvent motions (g1(t)) and rotational diffusion relaxation. The hydrogen bond fluctuations of the water network (g2(t)) also have some significant effect on 15783



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of fluctuations over a wide dynamic range of time scales, as seen here for octanol. On the basis of the results of the dynamics of model solvents revealed by this 3PPE study, a subsequent step will be the use of N2O to report on the fluctuation dynamics in more complex biological environments which possess hydrophobic and hydropholic regions via heterodyne detected ultrafast 2DIR measurements. The photon echo results reported here indicate that N2O should be an effective probe of femtosecond to picosecond motions in biological structures such as proteins, DNA, and lipids and their local regions of hydration owing to their distinct dynamical time scales and expected N2O frequency shifts. The successful use of this N2O probe in 2DIR measurements of heterogeneous media such as these biological systems will probably be dependent on the ability to spectrally as well as temporally resolve N2O’s responses in these different polar and nonpolar regions. While octanol itself is often used as a model system for phospholipids, it is interesting to note that both the hydroxyl “head group” and the alkyl chain of octanol contribute to the FFCF with fluctuation time scales that differ by an order of magnitude (3.3 and 35 ps). By contrast, VER studies for the ν3 mode in octanol see only a single exponential time scale characteristic of hydrocarbon environments.1 This observation alone underscores the sensitivity of the 3PPE technique to the structure and dynamics of complex systems compared to T1 measurements. As discussed previously,20,43,45,58 these results additionally highlight that 3PPE measurements reveal inherent fluctuation time scales of their bath environments given the robustness, for example, of intermediate τ2 decay times attributed to hydrogen bonding network fluctuation times in water. The decays reported here for this weak dipole solute (N2O) are essentially identical to those found in aqueous solutions of ions (N3−) and more polar solutes (HOD). Furthermore, fluid relaxation times found directly by the vibrational photon echo technique are found here to be in very close agreement with other methodologies for measuring responses in this frequency regime such as dielectric relaxation techniques and electronically nonresonant time domain Raman or quasi-elastic scattering approaches. These complementary experimental approaches can be exploited, especially when combined with atomistic simulation and temperature studies, to more conclusively determine the nature of these responses and a better understanding of their relative amplitudes to the total response for each of these techniques.

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REFERENCES

(1) Chieffo, L. R.; Amsden, J. J.; Shattuck, J. T.; Hong, M. K.; Ziegler, L. D.; Erramilli, S. Vibrational Infrared Lifetime of the Anesthetic Nitrous Oxide Gas in Solution. Biophys. Rev. Lett. 2006, 1, 309−316. (2) Chieffo, L. R.; Shattuck, J. T.; Pinnick, E.; Amsden, J. J.; Hong, M. K.; Wang, F.; Erramilli, S.; Ziegler, L. D. Nitrous Oxide Vibrational Energy Relaxation Is a Probe of Interfacial Water in Lipid Bilayers. J. Phys. Chem. B 2008, 112, 12776−12782. (3) Pinnick, E. R.; Erramilli, S.; Wang, F. Computational Investigations of Lipid Hydration Water of La POPC at Three Hydration Levels. Mol. Phys. 2010, 108, 2027−2036. (4) Pinnick, E. R.; Erramilli, S.; Wang, F. The Potential of Mean Force of Nitrous Oxide in a 1,2-Dimyristoylophosphatidylcholine Lipid Bilayer. Chem. Phys. Lett. 2010, 489, 96−98. (5) MacCallum, J. L.; Bennett, W. F. D.; Tieleman, D. P. Distribution of Amino Acids in a Lipid Bilayer from Computer Simulations. Biophys. J. 2008, 94, 3393−3404. (6) Marrink, S. J.; Risselada, H. J.; Yefimov, S.; Tieleman, D. P.; de Vries, A. H. The MARTINI Force Field: Coarse Grained Model for Biomolecular Simulations. J. Phys. Chem. B 2007, 111, 7812−7824. (7) Smith, R. N.; Hansch, C.; Ames, M. M. Selection of a Reference Partitioning System for Drug Design Work. J. Pharm. Sci. 1975, 64, 599−606. (8) Shulman, R. G.; Dailey, B. P.; Townes, C. H. Molecular Dipole Moments and Stark Effects. III. Dipole Moment Determinations. Phys. Rev. 1950, 78, 145−148. (9) Kaliszan, R.; Markuszewski, M. Ç . Brain/Blood Distribution Described by a Combination of Partition Coefficient and Molecular Mass. Int. J. Pharm. 1996, 145, 9−16. (10) Gorga, J. C.; Hazzard, J. H.; Caughey, W. S. Determination of Anesthetic Molecule Environments by Infrared Spectroscopy: I. Effects of Solvating Molecule Structure on Nitrous Oxide Spectra. Arch. Biochem. Biophys. 1985, 240, 734−746. (11) Zhong, Q.; Baronavski, A. P.; Owrutsky, J. C. Vibrational Energy Relaxation of Aqueous Azide Ion Confined in Reverse Micelles. J. Chem. Phys. 2003, 118, 7074−7080. (12) Hamm, P.; Lim, M.; Hochstrasser, R. M. Non-Markovian Dynamics of the Vibrations of Ions in Water from Femtosecond Infrared Three-Pulse Photon Echoes. Phys. Rev. Lett. 1998, 81, 5326−5329. (13) Brunne, R. M.; Liepinsh, E.; Otting, G.; Wüthrich, K.; van Gunsteren, W. F. Hydration of Proteins: A Comparison of Experimental Residence Times of Water Molecules Solvating the Bovine Pancreatic Trypsin Inhibitor with Theoretical Model Calculations. J. Mol. Biol. 1993, 231, 1040−1048. (14) Makarov, V. A.; Andrews, B. K.; Smith, P. E.; Pettitt, B. M. Residence Times of Water Molecules in the Hydration Sites of Myoglobin. Biophys. J. 2000, 79, 2966−2974. (15) Janoff, A. S.; Miller, K. W. In Biological Membranes; Chapman, D., Ed.; Academic Press: London, 1982; pp 417−476. (16) Urban, B. W.; Bleckwenn, M.; Barann, M. Interactions of Anesthetics with Their Targets: Non-Specific, Specific or Both? Pharmacol. Ther. 2006, 111, 729−770. (17) Franks, N. P.; Lieb, W. R. Molecular Mechanisms of General Anaesthesia. Nature 1982, 300, 487−493. (18) Franks, N. P.; Lieb, W. R. Molecular and Cellular Mechanisms of General Anaesthesia. Nature 1994, 367, 607−614. (19) Jevtovic-Todorovic, V.; Todorovic, S. M.; Mennerick, S.; Powell, S.; Dikranian, K.; Benshoff, N.; Zorumski, C. F.; Olney, J. W. Nitrous Oxide (Laughing Gas) Is an NMDA Antagonist, Neuroprotectant and Neurotoxin. Nat. Med. 1998, 4, 460−463. (20) Hamm, P.; Hochstrasser, R. M. In Ultrafast Infrared and Raman Spectroscopy; Fayer, M. D., Ed.; Marcel Dekker, Inc.: New York, 2001; pp 273−348. (21) Mukamel, S. Nonlinear Optical Spectroscopy; Oxford University Press: Oxford, U.K., 1995. (22) Asplund, M. C.; Lim, M.; Hochstrasser, R. M. Spectrally Resolved Three Pulse Photon Echoes in the Vibrational Infrared. Chem. Phys. Lett. 2000, 323, 269−277.

ASSOCIATED CONTENT

S Supporting Information *

Figure containing normalized integrated echoes of N2O in water showing the ubiquitous nature of the resonant background signal due to the underlying bend−libration combination band and continuum modes of water at two different population times. This material is available free of charge via the Internet at http:// pubs.acs.org.

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AUTHOR INFORMATION

Notes

The authors declare no competing financial interest.

ACKNOWLEDGMENTS This material is based upon work supported by the National Science Foundation under CHE-1152797. The support of the Boston University Photonics Center is gratefully acknowledged as well. 15784



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(23) Xu, Q.-H.; Thompson, D. E.; Merchant, K. A.; Fayer, M. D. Separation of Contributions to the Third-Order Signal: Ultrafast Frequency-Selected Vibrational Echo Experiments on a Metalloporphyrin-CO. Chem. Phys. Lett. 2002, 355, 139−146. (24) Thompson, D. E.; Merchant, K. A.; Fayer, M. D. TwoDimensional Ultrafast Infrared Vibrational Echo Studies of Solute− Solvent Interactions and Dynamics. J. Chem. Phys. 2001, 115, 317−330. (25) Ha, J.-H.; Lee, K.-K.; Park, K.-H.; Choi, J.-H.; Jeon, S.-J.; Cho, M. Integrated and Dispersed Photon Echo Studies of Nitrile Stretching Vibration of 4-Cyanophenol in Methanol. J. Chem. Phys. 2009, 130, 204509−204509. (26) Merchant, K. A.; Xu, Q.-H.; Thompson, D. E.; Fayer, M. D. Frequency Selected Ultrafast Infrared Vibrational Echo Studies of Liquids, Glasses, and Proteins. J. Phys. Chem. A 2002, 106, 8839−8849. (27) Ohta, K.; Maekawa, H.; Tominaga, K. Vibrational Population Relaxation and Dephasing Dynamics of Fe(CN)64- in D2O with ThirdOrder Nonlinear Infrared Spectroscopy. J. Phys. Chem. A 2004, 108, 1333−1341. (28) Demirdoven, N.; Khalil, M.; Golonza, O.; Tokmakoff, A. Dispersion Compensation with Optical Materials for Compression of Intense Sub-100-fs Mid-Infrared Pulses. Opt. Lett. 2002, 27, 433. (29) Ohta, K.; Tominaga, K. Dynamical Interactions between Solute and Solvent Studied by Three-Pulse Photon Echo Method. Bull. Chem. Soc. Jpn. 2005, 78, 1581−1594. (30) Hamm, P.; Lim, M.; Hochstrasser, R. M. Vibrational Relaxation and Dephasing of Small Molecules Strongly Interacting with Water. Springer Ser. Chem. Phys. 1998, 63, 514−516. (31) Lim, M.; Hamm, P.; Hochstrasser, R. M. Protein Fluctuations Are Sensed by Stimulated Infrared Echoes of the Vibrations of Carbon Monoxide and Azide Probes. Proc. Natl. Acad. Sci. U.S.A. 1998, 95, 15315−15320. (32) Tokmakoff, A.; Fayer, M. D. Homogeneous Vibrational Dynamics and Inhomogeneous Broadening in Glass-Forming Liquids: Infrared Photon Echo Experiments from Room Temperature to 10 K. J. Chem. Phys. 1995, 103, 2810−2826. (33) Lim, M.; Hochstrasser, R. M. Unusual Vibrational Dynamics of the Acetic Acid Dimer. J. Chem. Phys. 2001, 115, 7629−7643. (34) Graener, H.; Seifert, G.; Laubereau, A. Direct Observation of Rotational Relaxation Times by Time-Resolved Infrared Spectroscopy. Chem. Phys. Lett. 1990, 172, 435−439. (35) Kubo, R. A Stochastic Theory of Line Shape and Relaxation; Oliver & Boyd: Edinburgh, Scotland, 1962. (36) Chieffo, L.; Shattuck, J.; Amsden, J.; Erramilli, S.; Ziegler, L. D. Ultrafast Vibrational Relaxation Following Librational Combination Band Excitation in H2O. Chem. Phys. 2007, 341, 71−80. (37) Bandaria, J. N.; Dutta, S.; Hill, S. E.; Kohen, A.; Cheatum, C. M. Fast Enzyme Dynamics at the Active Site of Formate Dehydrogenase. J. Am. Chem. Soc. 2007, 130, 22−23. (38) Merchant, K. A.; Thompson, D. E.; Xu, Q.-H.; Williams, R. B.; Loring, R. F.; Fayer, M. D. Myoglobin-CO Conformational Substate Dynamics: 2D Vibrational Echoes and MD Simulations. Biophys. J. 2002, 82, 3277−3288. (39) Constantine, S.; Zhou, Y.; Morais, J.; Ziegler, L. D. Dispersed Optical Heterodyne Detected Birefringence and Dichroism of Transparent Liquids. J. Phys. Chem. A 1997, 101, 5456−5462. (40) Zhou, Y.; Constantine, S.; Harrel, S.; Ziegler, L. D. The Probe Frequency Dependence of Nonresonant Femtosecond Pump−Probe Nuclear Responses: Undercutting Vibrational Inhomogeneities. J. Chem. Phys. 1999, 110, 5893−5905. (41) Rosca, F.; Kumar, A. T. N.; Ye, X.; Sjodin, T.; Demidov, A. A.; Champion, P. M. Investigations of Coherent Vibrational Oscillations in Myoglobin. J. Phys. Chem. A 2000, 104, 4280−4290. (42) Joo, T.; Jia, Y.; Yu, J.-Y.; Lang, M. J.; Fleming, G. R. Third-Order Nonlinear Time Domain Probes of Solvation Dynamics. J. Chem. Phys. 1996, 104, 6089−6108. (43) Ohta, K.; Tayama, J.; Saito, S.; Tominaga, K. Vibrational Frequency Fluctuation of Ions in Aqueous Solutions Studied by ThreePulse Infrared Photon Echo Method. Acc. Chem. Res. 2012, 45, 1982− 1991.

(44) Ohta, K.; Maekawa, H.; Saito, S.; Tominaga, K. Probing the Spectral Diffusion of Vibrational Transitions of OCN- and SCN- in Methanol by Three-Pulse Infrared Photon Echo Spectroscopy. J. Phys. Chem. A 2003, 107, 5643−5649. (45) Maekawa, H.; Ohta, K.; Tominaga, K. Vibrational Dynamics in Liquids Studied by Non-Linear Infrared Spectroscopy. Res. Chem. Intermed. 2005, 31, 703−716. (46) Asbury, J. B.; Steinel, T.; Kwak, K.; Corcelli, S. A.; Lawrence, C. P.; Skinner, J. L.; Fayer, M. D. Dynamics of Water Probed with Vibrational Echo Correlation Spectroscopy. J. Chem. Phys. 2004, 121, 12431− 12446. (47) Lawrence, C. P.; Skinner, J. L. Vibrational Spectroscopy of HOD in Liquid D[sub 2]O. III. Spectral Diffusion, and Hydrogen-Bonding and Rotational Dynamics. J. Chem. Phys. 2003, 118, 264−272. (48) Moller, K. B.; Rey, R.; Hynes, J. T. Hydrogen Bond Dynamics in Water and Ultrafast Infrared Spectroscopy: A Theoretical Study. J. Phys. Chem. A 2004, 108, 1275−1289. (49) Steinel, T.; Asbury, J. B.; Zheng, J.; Fayer, M. D. Watching Hydrogen Bonds Break: A Transient Absorption Study of Water. J. Phys. Chem. A 2004, 108, 10957−10964. (50) Fecko, C. J.; Eaves, J. D.; Loparo, J. J.; Tokmakoff, A.; Geissler, P. L. Ultrafast Hydrogen-Bond Dynamics in the Infrared Spectroscopy of Water. Science 2003, 301, 1698−1702. (51) Fecko, C. J.; Loparo, J. J.; Roberts, S. T.; Tokmakoff, A. Local Hydrogen Bonding Dynamics and Collective Reorganization in Water: Ultrafast Infrared Spectroscopy of HOD/D2O. J. Chem. Phys. 2005, 122, 054506-18. (52) Stenger, J.; Madsen, D.; Hamm, P.; Nibbering, E. T. J.; Elsaesser, T. A Photon Echo Peak Shift Study of Liquid Water. J. Phys. Chem. A 2002, 106, 2341−2350. (53) Garg, S. K.; Smyth, C. P. Microwave Absorption and Molecular Structure in Liquids. LXII. The Three Dielectric Dispersion Regions of the Normal Primary Alcohols1. J. Phys. Chem. 1965, 69, 1294−1301. (54) Paolantoni, M.; Sassi, P.; Morresi, A.; Cataliotti, R. S. Reorientational Dynamics in a Liquid Organized System: Brillouin and Depolarized Rayleigh Scattering Experiments in 1-Octanol. Mol. Phys. 2001, 99, 1493−1502. (55) Ferrario, M.; Klein, M. L.; McDonald, I. R. Dynamical Behavior of the Azide Ion in Protic Solvents. Chem. Phys. Lett. 1993, 213, 537−540. (56) DeBolt, S. E.; Kollman, P. A. Investigation of Structure, Dynamics, and Solvation in 1-Octanol and Its Water-Saturated Solution: Molecular Dynamics and Free-Energy Perturbation Studies. J. Am. Chem. Soc. 1995, 117, 5316−5340. (57) Hennelly, E. J.; Heston, J. W. M.; Smyth, C. P. Microwave Absorption and Molecular Structure in Liquids. III. Dielectric Relaxation and Structure in Organic Halides. J. Am. Chem. Soc. 1948, 70, 4102−4111. (58) Ohta, K.; Tayama, J.; Tominaga, K. Ultrafast Vibrational Dynamics of SCN- and N3- in Polar Solvents Studied by Nonlinear Infrared Spectroscopy. Phys. Chem. Chem. Phys. 2012, 14, 10455− 10465. (59) Jose, P. P.; Chakrabarti, D.; Bagchi, B. Complete Breakdown of the Debye Model of Rotational Relaxation near the Isotropic-Nematic Phase Boundary: Effects of Intermolecular Correlations in Orientational Dynamics. Phys. Rev. E 2006, 73, 031705. (60) Courtney, S. H.; Kim, S. K.; Canonica, S.; Fleming, G. R. Rotational Diffusion of Stilbene in Alkane and Alcohol Solutions. J. Chem. Soc., Faraday Trans. 2 1986, 82, 2065−2072. (61) Herzberg, G. Infrared and Raman Spectroscopy; Van Ostrand: 1950.

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Dispersed Three-Pulse Infrared Photon Echoes of Nitrous Oxide in

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