Signatures of Nanoconfinement on the Linear and Nonlinear

Article pubs.acs.org/JPCB

Signatures of Nanoconfinement on the Linear and Nonlinear Vibrational Spectroscopy of a Model Hydrogen-Bonded Complex Dissolved in a Polar Solvent Joseph Tomkins and Gabriel Hanna* Department of Chemistry, University of Alberta, Edmonton, Alberta, Canada T6G 2G2 S Supporting Information *

ABSTRACT: The one-dimensional IR (1D-IR) absorption and IR pump−probe spectra of a hydrogen stretch in a model hydrogen-bonded complex dissolved in a polar solvent confined in spherical hydrophobic cavities of different sizes were simulated using ground-state mixed quantum-classical dynamics. Due to a thorough analysis of key properties of the complex and solvent from equilibrium trajectory data, we were able to gain insight into the microscopic details underlying the spectra. Both the 1D-IR and IR pump−probe spectra manifested the effects of confinement on the relative stabilities of the covalent and ionic forms of the complex through pronounced changes in their peak intensities and numbers. However, in contrast to the 1D-IR spectra, the time-resolved pump−probe spectra were found to be uniquely sensitive to the changes in the molecular dynamics as the cavity size is varied. In particular, it was found that the variations in the time evolutions of the peak intensities in the pump−probe spectra reflect the differences in the solvation dynamics associated with the various forms of the complex in different locations within the cavities. The ability to detect these differences underscores the advantage of using pump−probe spectroscopy for studying nanoconfined systems.

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INTRODUCTION Confinement on nanometer length scales plays an important role in determining the structure and dynamics of many chemical and biological systems of fundamental and technological interest.1−17 Frequently, clusters of atoms or molecules in these systems are forced into contact with various interfaces and, as a result, behave differently near the interface than in the bulk. From water in ion channels, zeolites, membrane proteins, and reverse micelles, to hydrogen-bonded (H-bonded) complexes in nanoconfined solvents, the properties of these systems are intimately correlated with the nature of the confinement. A microscopic picture of how the molecules behave in the presence of their confining framework is required for understanding the macroscopic properties of these systems (e.g., hydrophobicity, hydrophilicity, phase behavior, and chemical reactivity, etc.) and for designing nanomaterials with specific functions by varying the cavity size, geometry, and interface. For example, materials with nanosized pores may be synthesized for use in catalysts, fuel cells, molecular sieves, and sensors. In principle, spectroscopic methods may be used to gain insight into the nature of nanoconfined systems. However, in practice, the spectra may be complicated due to the interactions of the photoactive modes with their environment. Thus, theory and simulation are usually required to interpret the spectra and to gain an in-depth understanding of the underlying structure and dynamics. In particular, linear IR absorption spectroscopy has been used to probe the effects of a confining environment © 2013 American Chemical Society

on the vibrations of a chromophore, but unfortunately limited dynamical information can be extracted.18−22 On the other hand, nonlinear vibrational spectroscopies are capable of revealing detailed dynamical information on a femtosecond time scale since they are sensitive to the fluctuations in a chromophore’s local environment.23−28 However, relatively little attention has been given experimentally to the signatures of confinement on nonlinear vibrational spectra,18,29−37 and, to the best of our knowledge, there have been no computational studies of the nonlinear vibrational spectroscopy of nanoconfined systems. In this article, we study proton-transfer reactions in polar solvents confined in nanosized hydrophobic cavities. Nanoconfined proton transfer represents a class of reactions that is ubiquitous in chemistry and biology and is important in applications to catalysis and fuel cells (see ref 38, and references therein). Both experimental39−45 and theoretical46−49 studies of proton-transfer reactions in nanoconfined systems have been conducted. In general, charge-transfer reactions are strongly coupled to the polar solvents in which they occur and will therefore be strongly affected by confinement. For example, experiments have shown that the proton-transfer rate can decrease significantly upon confinement relative to the bulk.40−42 Most experimental studies have focused on excitedReceived: July 26, 2013 Revised: September 20, 2013 Published: September 30, 2013 13619

dx.doi.org/10.1021/jp407469f | J. Phys. Chem. B 2013, 117, 13619−13630

The Journal of Physical Chemistry B

Article

studied,64−73,76−78,80−87 we only provide a brief description of it (the full details can be found in refs 64, 65, and 71). In this model, the proton is restricted to move along a onedimensional axis that connects the donor (A) and acceptor (B) groups of the complex. The donor, phenol, and acceptor, trimethylamine, are modeled as single particles, and polarizability effects are incorporated by allowing the charges on A and B to explicitly depend on the proton’s position. The potential used to describe the tautomeric equilibrium between the covalent (low dipole moment) and ionic (high dipole moment) forms of the complex (i.e., AH − B ⇌ A− − H+B) is adopted from ref 88. The vibration of the complex is taken into account, and the equilibrium A−B distance is set to 2.7 Å, giving rise to a moderately strong H-bond. The complex is dissolved in a nanocluster of methyl chloride molecules, which are modeled as rigid polar diatomic molecules. The complex− solvent and solvent−solvent interactions are modeled using pairwise Lennard-Jones and Coulombic potentials (the potential parameters can be found in refs 64 and 65). The complex and solvent molecules are confined in a model spherical hydrophobic cavity by applying a confining potential developed by Linse and Halle,89,90 which has been used in several studies for modeling the effects of hydrophobic confinement.46,47,49,91−94 This interaction potential, which is obtained by integrating a Lennard-Jones potential over all points in the cavity exterior, is given by the following 9−3 potential that depends only on the distance of a system particle from the cavity center:90,91

state proton transfer, shedding light on the effects of confinement on the nonequilibrium solvation dynamics on the excited-state electronic surface. However, it is also important to investigate the spectroscopy of ground-state proton-transfer reactions, which can give information about equilibrium and dynamical properties on the ground-state electronic surface. Since linear IR absorption spectroscopy can provide only limited information about the dynamical effects of nanoconfinement, nonlinear vibrational spectroscopies have been used to study ground-state vibrational dynamics in Hbonded complexes.27,50−63 In order to elucidate the signatures of nanoconfinement on ground-state proton-transfer reactions in nonlinear vibrational spectra, we compute both the one-dimensional IR (1D-IR) and IR pump−probe spectra of a proton-transfer mode in a model H-bonded phenol−amine complex64 dissolved in pools of methyl chloride molecules confined in various nanosized spherical hydrophobic cavities. Calculations of the protontransfer rate constant have been carried out for this complex in bulk methyl chloride64−73 and in small unconfined methyl chloride clusters.74,75 In addition, the signatures of solvation and proton-transfer dynamics in these systems have been investigated in simulated 1D-IR, 2D-IR, and IR pump−probe spectra.76−79 It should be noted that a similar model has been studied previously by Thompson and co-workers,46,47,49 but, in contrast to our study, their hydrogen-bonding potential governing the proton-transfer dynamics was different and the O−N bridge length in the complex was constrained. In ref 46, Monte Carlo simulations were used to investigate the distribution of the complex’s position in the cavity and it was found that the proton-transfer reaction involves diffusion of the complex from the cavity wall to the interior of the cavity and vice versa. In ref 47, adiabatic mixed quantum-classical molecular dynamics (MD) simulations of this system were used to investigate the effects of varying the size of the cavity on the ground-state proton-transfer rate constant. The author found that the rate constant increased as the cavity size was increased, which was attributed to an increase in the solvent polarity. In ref 49, 1D-IR spectra of the complex were calculated, but the effects of varying the cavity size on the spectra were not investigated. In this study, we examine the effects of varying the cavity size on the 1D-IR and IR pump−probe spectra. By comparing with the corresponding spectra for the bulk, unconfined version of this system, we are able to identify the spectral signatures of nanoconfinement. In particular, we focus on the ground-state bleach contribution to the IR pump−probe spectra, from which we extract information about the ground-state dynamics of the nanoconfined system. We adopt an adiabatic mixed quantumclassical dynamical approach for computing the spectra, in which the proton is treated quantum mechanically while the remaining degrees of freedom (DOF) are treated classically. The remainder of this paper is organized as follows: The model system is described in section 2. The theoretical and simulation details used for simulating the spectra are outlined in sections 3 and 4, respectively. The results are presented and discussed in section 5. Finally, the main conclusions are summarized in section 6.

u(z ≡ r /R ) = 8πρhc εσ 3[(σ /R )9 F(z , 6) − (σ /R )3 F(z , 3)] (1)

with F(z , 3) = 2/[3(1 − z 2)3 ] F(z , 6) = 2(5 + 45z 2 + 63z4 + 15z 6)/[45(1 − z 2)9 ] (2)

Here, R is the total radius of the cavity (set such that the zerocrossing of the potential yields the desired effective cavity radius, Rcav), r is the distance of the particle from the cavity center, and ρhc = 0.0241 Å−3 is the site density in the cavity exterior. Table 1 summarizes the total and effective cavity radii Table 1. Effective Cavity Radius, Rcav, Total Cavity Radius, R, and the Number of Solvent Molecules Used for the Three Cavity Sizes Studied Rcav (Å)

R (Å)

no. of solvent molecules

10 12 15

11.77 13.78 16.80

28 48 94

and the corresponding number of solvent molecules used in the simulations. The values of ε and σ are taken to be 0.46 kcal/ mol and 2.5 Å, respectively, for all particles in the system.46,91 The model under investigation is similar to that studied in ref 49, but with two main differences: the gas-phase protonic potential and the treatment of the A−B distance. A comparison between the two potentials reveals that both the distance between the covalent and ionic minima and the barrier in going from the covalent well to the ionic well are significantly larger in ref 49. Moreover, the A−B distance is constrained to 2.7 Å in ref 49, whereas in our study it is allowed to vibrate. A flexible

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MODEL The model studied herein is essentially the nanoconfined version of the Azzouz−Borgis model64 for a H-bonded complex in a bulk polar solvent. Since this model has been extensively 13620



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1D-IR Spectra. The 1D-IR spectrum, I(ω), corresponding to the transition between the ground and first-excited states is given by23

A−B coordinate provides a more realistic representation of both the intracomplex interactions and the interactions between the complex and the solvent. Also, it has been shown previously that a flexible A−B coordinate in this model has a significant effect on the dynamics.71,72,85 Thus, while some of our results may be compared qualitatively to those in ref 49, they cannot be compared quantitatively.

I(ω) = Re

■

J (t ) =

(4)

J(t ) = ⟨μ01(t ) μ10 (0) exp[−i

(5)

+ ⟨μ (Q 0) μ (Q 0) μ 10

10

10

− ⟨μ (Q 0) μ (Q 0) μ

(Q t(11,11)) 1

Ppp(ω2 , t1) ≡ Re

(Q t(11,00)) 1

2

10

(Q t(11,11),10 ) 1+ t 2

10

μ

t

dτ ω10(τ )]⟩00 − 01

∫0

t

dτ ω10(τ )]⟩00 − 00

(8)

∫0

∞

dt 2 eiω2t2 Ppp(t 2 , t1)

(9)

where the mixed quantum-classical Liouville expression for the pump−probe signal of a two-state system under weak field conditions is given by78

1

μ

∫0

IR Pump−Probe Spectroscopy. IR pump−probe spectroscopy probes the third-order optical response of a system to two subsequent laser pulses with time delays t1 between the pump and the probe and t2 between the probe and detection. The IR pump−probe spectrum is obtained according to the following Fourier transform with respect to t2:

t + t2

10

∫

where H0(Q,P) = Kbath(P) + E0(Q) and Z0 = ∫ dQ0 ∫ dP0 exp [−βH0(Q,P)] are the classical bath Hamiltonian and partition function that correspond to the ground vibrational state, respectively, and μij(t) = ⟨i;Qt|q̂|j;Qt⟩ and ωij (t) = [Ei(Qt) − Ej (Qt)]/ℏ are the transition dipole moment and transition frequency between vibrational states i and j, respectively. The subscript 00−10 denotes that Qt is propagated classically on the mean potential surface, [E0(Q) + E1(Q)]/2, with the initial conditions {Q0, P0} sampled from exp[−βH0(Q,P)]/Z. Since this involves computationally costly non-equilibrium MD simulations and the effect on the 1D spectrum turns out to be rather small (since J(t) is usually short-lived),77 we simply performed equilibrium MD simulations on the ground-state potential surface and computed

Ppp(t 2 , t1) = ⟨μ10 (Q 0) μ10 (Q 0) μ10 (Q t00) μ10 (Q t00,10 ) exp[ − i ∫t 1 +t 10

1 dQ dP exp[−βH0(Q , P)] μ01(t ) μ10 (0) Z t × exp[−i dτ ω10(τ )]|00 − 01

(7)

where the first term is due to the interactions with the other classical particles and the second term is the Hellmann− Feynman force due to the interaction with the quantum subsystem in state j. The classical equations of motion are then integrated using these forces. It should be noted that in this study the classical DOF are restricted to move on the ground potential energy surface (PES), E0(Q), for the reasons discussed below.

10

(6)

≡ ⟨μ01(t ) μ10 (0) exp[−i

where Ĥ P = K̂ P(p̂) + V̂ C(Q, q̂) is the protonic Hamiltonian, {|j;Q⟩} are the adiabatic protonic states, and {Ej(Q)} are the corresponding adiabatic energies. In adiabatic dynamics, the force acting on a classical particle i is given by

1

dt J(t ) eiωt

∫0

where P ≡ (P1, P2, ..., PN) and Q ≡ (Q1, Q2, ..., QN) are the momenta and coordinates of the N bath particles, q̂ and p̂ are the position and momentum operators of the proton, respectively, Kbath(P) is the kinetic energy of the bath, K̂ P(p̂) is the kinetic energy operator of the proton, and V̂ (Q, q̂) = Vbath(Q) + V̂ C(Q, q̂) is the total potential energy operator, which contains the bath potential, Vbath(Q), and the coupling potential between the proton and the bath, V̂ C(Q, q̂). The vibrational states and energy levels of the proton stretch may then be obtained from the solution of the timeindependent Schrodinger equation for a fixed bath configuration Q:

Fi = −∇i Vbath(Q ) − ⟨j ; Q |∇i VĈ (q ̂, Q )|j ; Q ⟩

∞

where J(t) is the linear optical response function (ORF), which may be given by the mixed quantum-classical Liouville expression:77

THEORETICAL DETAILS Quantum-Classical Adiabatic Dynamics. Due to the mass scale separation between the proton in the complex and the other particles in the model, we adopt a mixed quantumclassical treatment of the system, in which the proton (i.e., subsystem) is treated quantum-mechanically while the remainder of the system (i.e., the A and B groups and the solvent molecules, collectively referred to as the bath) are treated classically. The Hamiltonian of this mixed quantumclassical system is then given by Ĥ (q ̂, p ̂ , Q , P) = Kbath(P) + K̂P(p ̂) + V̂ (Q , q)̂ (3)

ĤP(q ̂, p ̂ , Q )|j ; Q ⟩ = Ej(Q )|j ; Q ⟩

∫0

1

(Q t(11,00),10 ) 1+ t 2

The first term on the right-hand side (RHS) of eq 10 corresponds to the Liouville pathway where the system remains in the ground state during t1, while the second and third terms correspond to the Liouville pathways in which the system hops to the first-excited state (following the interaction with the pump). However, the second (positive) term represents the

dτ ω10(Q t00,10 )]⟩00 − 00 − 10 +τ 1

exp[ − i ∫t

t1+ t 2

1

exp[ − i ∫t

t1+ t 2

1

dτ ω10(Q t(11,11),10 )]⟩00 − 11 − 10 +τ 1

dτ

ω10(Q t(11,00),10 )]⟩00 − (11 → 00) − 10 1+ τ

(10)

contribution of trajectories that remain on the excited-state PES during t1, whereas the third (negative) term represents the contribution of trajectories that relax nonradiatively from the excited- to the ground-state PES during t1. Thus, eq 10 accounts for both radiative and nonradiative nonadiabatic effects. 13621



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Figure 1 shows the ground-state free energy surfaces as a function of the solvent polarization, ΔE, for the three cavity

Since our interest is not to reproduce experimental pump− probe spectra but rather to point out the effects of nanoconfinement on nonlinear spectra, in this study, we focus on the equilibrium solvation dynamics associated with the ionic and covalent tautomers (representing stable species separated by a well-defined barrier only on the ground-state PES72,74), and thereby restrict our computations to the first term on the RHS of eq 10 for the sake of computational efficiency. Computing the second and third terms involves costly nonequilibrium calculations, whereas the first term can be efficiently calculated via equilibrium dynamics after assuming that the dynamics during t2 occurs on the ground-state PES. As in the case of linear response, this is reasonable to assume since the signal along t2 is usually short-lived and therefore the impact of mean surface dynamics on the spectra is rather small. Consequently, we calculate the following:

Figure 1. Ground-state free energy surfaces as a function of the solvent polarization, ΔE, for the Rcav = 10 (red), 12 (green), and 15 Å (blue) cavities.

I Ppp (t 2 , t1) = ⟨μ10 (Q 0) μ10 (Q 0) μ10 (Q t00) μ10 (Q t00,10 ) +t 1

exp[ − i ∫t

t1+ t 2

1

■

dτ

1

sizes. The solvent polarization serves as a convenient reaction coordinate for monitoring the proton-transfer reaction and is defined as

2

ω10(Q t00,10 )]⟩ 1+ τ 00 − 00 − 00 (11)

⎛

ΔE(Q ) =

SIMULATION METHOD Adiabatic mixed quantum-classical MD simulations were performed with a single complex and various numbers of methyl chloride molecules in three model hydrophobic cavities (described in section 2) with Rcav = 10, 12, and 15 Å and a density of 0.8 g/cm3. Table 1 summarizes the effective and total cavity radii and the number of solvent molecules used in this study. Initial configurations were generated by equilibrating the system for 0.1 ns using periodic velocity rescaling to reach a temperature of 260 K. The protonic Hamiltonian matrix was constructed in terms of a basis of 12 quantum harmonic oscillator states, with the first set of 6 states centered at the ionic well of the gas-phase intramolecular potential and the second set of 6 states centered at the covalent well.65,71 The adiabatic states and energies were obtained by diagonalizing this matrix (using the LAPACK DSYGV routine) at each time step. The ground-state adiabatic dynamics was simulated by integrating the classical equations of motion via the velocity Verlet algorithm, using the forces from eq 5, with a time step of 0.5 fs. The SHAKE and RATTLE algorithms were used to constrain the bonds in the methyl chloride solvent. Since the interactions between different cavities are neglected here (i.e., in the limit of infinite dilution), periodic boundary conditions were not employed. An ensemble of 10−16 trajectories of length 0.9 ns were generated for each cavity radius to obtain the reported spectra. The 1D Fourier transforms, required for computing the 1D-IR and IR pump−probe spectra, were carried out numerically via the FFT routine using 512 grid points and a time interval of 0.5 fs. The 512-point time grid was first padded with zeros to generate a 2048-point time grid.

⎞ 1 1 ⎟⎟ − a |Q i − s′| ⎠ ⎝ |Q − s|

∑ zae⎜⎜ i,a

a i

(12)

−19

where zae (e = 1.602 × 10 C) is the charge on atom a in solvent molecule i, and s and s′ denote two positions of the proton within the complex that correspond to the stable covalent and ionic tautomers, respectively. From Figure 1, it can be seen that, as the cavity size decreases, the covalent (ΔE < 0.0134 eC/Å) bath configurations become more stable, while the ionic (ΔE > 0.0134 eC/Å) bath configurations become less stable. More specifically, the covalent state is more stable than the ionic state in the Rcav = 10 Å cavity; both states are roughly equally stable in the Rcav = 12 Å cavity; and the ionic state is more stable than the covalent state in the Rcav = 15 Å cavity. This behavior can be mainly attributed to the inability of a smaller number of solvent molecules to effectively solvate the ionic tautomer and thereby stabilize the system in the ionic state. These results suggest that for Rcav ≈ 12 Å there exists a threshold in the number of solvent molecules beyond which the solvent can effectively stabilize the ionic tautomer. In addition, as the cavity size increases, we see that the widths of the covalent and ionic wells decrease and increase, respectively, while their minima shift to higher ΔE values. This behavior is consistent with the increase in more highly polarized bath configurations as the cavity size is increased. It should be noted that the free energy of the Rcav = 15 Å cavity is similar to that of the bulk.72 In order to correlate the peaks in the IR spectra with the various states of the solvent and complex (i.e., covalent or ionic), we must first examine joint histograms of the fundamental transition frequency, ω01, with both the solvent polarization, ΔE (see Figure 2) and the average proton position, ⟨q⟩ (see Figure 3). The main features to note in Figure 2 are peaks centered at (∼2570 cm−1, ∼0.025 eC/Å) associated with ionic bath configurations (thereby correlating this frequency with the ionic state of the solvent), and peaks centered at (∼2340 cm−1, ∼0.003 eC/Å) associated with covalent bath configurations in the Rcav = 10 and 12 Å cavities (thereby correlating this frequency with the covalent state of the solvent). Both sets of peaks have broad shoulders which extend to low frequencies. In addition, the “covalent″ peak has a smaller (but substantial) shoulder that extends to higher

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RESULTS AND DISCUSSION 1D and 2D Histograms of Various System Properties. By constructing 1D and 2D histograms of various system properties from our trajectory data, we can gain insight into the equilibrium behavior of the system and how these properties are correlated, and, in turn, better understand the details of the 1D-IR and IR pump−probe spectra. This section contains histograms for all cavity radii; i.e., Rcav = 10, 12, and 15 Å. 13622



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Rcav = 10 Å cavity, the covalent tautomer (⟨q⟩ ≈ 0 Å) can also exhibit significantly higher frequencies (i.e., 2500−2800 cm−1) than the ionic tautomer (in any sized cavity) for the reasons discussed below. To gain insight into the preferred positions of the complex within the cavity, we present 1D histograms of RC/Rcav in Figure 4, where RC is the distance from the center of the cavity

Figure 4. Histograms of the distance, RC, between the complex’s center of mass and the cavity center relative to Rcav for the Rcav = 10 (red), 12 (green), and 15 Å (blue) cavities.

Figure 2. Joint histograms of the fundamental transition frequency, ω01, and the solvent polarization, ΔE, for the Rcav = 10, 12, and 15 Å cavities (from top to bottom).

to the center of mass of the complex. As the cavity size increases (i.e., number of solvation shells increases), we see a shift of the RC/Rcav distribution toward the core of the cavity where the complex is more effectively solvated. For Rcav = 10 Å, we identify three regions at approximately 0.75−1 (shoulder), 0.4−0.75 (main peak), and 0.1−0.4 (shoulder); for Rcav = 12 Å, 0.75−1 (shoulder), 0.55−0.75 (shoulder), and 0.1−0.55 (main peak); and for Rcav = 15 Å, 0.75−1 (shoulder), 0.55−0.75 (shoulder), and 0.1−0.55 (main peak). In Figures S1−S3 of the Supporting Information, we present 2D histograms which correlate the complex’s position, RC, with the average proton position, ⟨q⟩, solvent polarization, ΔE, and transition frequency, ω01, respectively. These 2D histograms shed light on the state of the complex/solvent in the aforementioned regions. The region near the cavity wall (i.e., 0.75−1) is inhabited by the covalent tautomer. This is due to the fact that the covalent complex is stabilized near the cavity wall, and in part due to the attractive well in the confining potential near the cavity wall. The central region (i.e., 0.4−0.75) corresponds to a common location in which both forms of the complex reside in different proportions depending on the cavity size. The region near the core (pronounced in the Rcav = 12 and 15 Å cases) is inhabited primarily by the ionic complex, since a larger number of solvent molecules is required to fully solvate solutes with large dipole moments. Such behavior has been previously observed in both unconfined and nanoconfined clusters.46,47,74,95 On the basis of Figure S3 of the Supporting Information, we see that, in the Rcav = 10 Å case, the distribution of transition frequencies, ω01, corresponding to the two peaks is rather sensitive to the complex’s position within the cavity (due to the wide range of solvation environments experienced by the complex), whereas in the Rcav = 12 and 15 Å cases, the distributions are rather independent of the complex’s position (due to the relatively narrow range of solvation environments experienced by the complex).

Figure 3. Joint histograms of the fundamental transition frequency, ω01, and the average proton position, ⟨q⟩, for the Rcav = 10, 12, and 15 Å cavities (from top to bottom).

frequencies. These figures also demonstrate the aforementioned trend in the relative stabilities of the covalent and ionic states in going from Rcav = 10−15 Å (i.e., the gradual disappearance of the feature at ΔE < ΔE⧧). However, an analysis of Figure 3 reveals that the picture is slightly more complicated. For the 13623



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Histograms of the A−B distance, RAB, are presented in Figure S4 of the Supporting Information. As the cavity size decreases, we see an increase in the width of the distribution due to an increased incidence of higher RAB values (and hence an overall increase in the average RAB). From the 2D histograms of RAB with the solvent polarization, ΔE, and the average proton position, ⟨q⟩, in Figures S5 and S6 of the Supporting Information, respectively, we see that this increase in width is associated with the covalent tautomer, which becomes more prevalent as the cavity size decreases and attains higher RAB values (up to ≈2.8 Å). This is due to the fact that the covalent tautomer (which can reside near the cavity wall) is less hindered by the electrostatic interactions with the solvent than the ionic form (which resides near the cavity core). In a larger cavity with more solvent molecules, the ionic form predominates and the average RAB is smaller due to the constricting nature of the electrostatic interactions. Figure 5 shows joint histograms of the transition frequency, ω01, and A−B distance, RAB. From this figure, we can identify

Rcav = 15 Å case), and therefore the transition frequency is sensitive to the RAB fluctuations. However, this is not the case for Rcav = 15 Å, where the electrostatic interactions predominate and thereby preferentially stabilize the ionic form of the complex. Finally, in Figure S7 of the Supporting Information, we present 2D histograms of RC and RAB. We see that as the cavity size decreases, the shapes of the RAB distributions vary more over the range of RC values explored by the complex; i.e., the H-bond strength has a stronger dependence on complex position in smaller cavities, due to interactions of the complex with an increasingly heterogeneous environment. 1D-IR Spectra. Before discussing the 1D-IR spectra, we examine the distribution of fundamental transition frequencies, ω01, for the Rcav = 10, 12, and 15 Å cavities in the upper panel of Figure 6. All three distributions are very broad, with peaks

Figure 5. Joint histograms of the fundamental transition frequency, ω01, and the A−B distance, RAB, for the Rcav = 10, 12, and 15 Å cavities (from top to bottom).

Figure 6. Top panel: Distribution of fundamental transition frequencies, ω01, for the Rcav = 10 (red), 12 (green), and 15 Å (blue) cavities, as obtained from equilibrium MD simulations on the ground-state PES. Bottom panel: 1D-IR spectra of the H-stretch in the A−B complex for the Rcav = 10 (red), 12 (green), and 15 Å (blue) cavities.

two distinct regions across the three cavity sizes: one in which ω01 is strongly dependent on RAB and the other in which ω01 is independent of RAB. In the RAB-dependent region, the frequency increases with increasing RAB, indicative of a weakening H-bond. The relative intensities of these two regions progressively change as the cluster size increases. For Rcav = 10 Å, the frequencies are mainly dependent on RAB; for Rcav = 12 Å, the intensity of the RAB-dependent region decreases, while that of the RAB-independent region increases; and for Rcav = 15 Å, the RAB-independent region dominates. The extent to which the transition frequency depends on RAB is governed by the magnitude of the complex−solvent electrostatic interactions. In the Rcav = 10 and 12 Å cases, these electrostatic interactions are relatively weak (compared to the

centered at ∼2500, ∼2530, and ∼2560 cm−1, respectively, and shoulders stretching down to ∼0 cm−1. We see that the intensity of the peak decreases with cavity size, which is associated with a shift in the complex’s equilibrium from being ionic-dominant to covalent-dominant. The lower panel of Figure 6 contains the 1D-IR spectra of the H-stretch fundamental for the Rcav = 10, 12, and 15 Å cavities. When compared to the distribution of transition frequencies, we see that the spectra are motionally narrowed, as several distinct peaks emerge. Four peaks are observed for all cavity sizes: a minor low-frequency peak at ∼250 cm−1, known 13624



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to be due to bath configurations associated with the transition state of the proton-transfer reaction,76 and three high-frequency peaks (in the range of 1750−2825 cm−1) due to bath configurations associated with the covalent and ionic states of the complex. On the basis of the results of the previous section, the peak at ∼2590 cm−1 in the Rcav = 10 Å case is due to both high- and (mainly) low-polarization bath configurations associated primarily with the complex in its covalent form (see top panels of Figures 2 and 3). As the cavity radius increases from Rcav = 10−15 Å, this peak grows substantially due to an increase in the relative stability of the ionic tautomer in a high-polarization environment over the covalent tautomer in a low-polarization environment. The converse trend is seen in the peak at ∼2280 cm−1, since it is associated primarily with the covalent state. The minor peak at ∼1930 cm−1 is predominantly due to strongly H-bonded covalent complexes situated in the core of the cavity (see Figures 2, 5, and S3 (Supporting Information)) and essentially disappears in going from the Rcav = 10 Å cavity to the Rcav = 15 Å cavity since the incidence of such complexes decreases due to the increase in electrostatic interactions with the solvent. We note that as the cavity size increases, the overall shape of the spectra approaches that of the bulk, unconfined system (see Figure 3 in ref 76). In contrast to the bulk, unconfined system, the covalent tautomer can exhibit higher frequencies than the ionic tautomer in nanoconfined systems. As the cavity radius is decreased from Rcav = 15 Å to Rcav = 10 Å, the proton can approach the A group more closely (as seen by the increase in the maximum ⟨q⟩ in Figure 3) due to the decrease in the complex−solvent electrostatic interactions. This weakens the H-bond, thereby leading to higher transition frequencies. For the Rcav = 10 Å cavity, these higher frequencies occur all throughout the cavity, but the highest ones occur when the complex is near the cavity wall (see Figure S3 of the Supporting Information). As a consequence, we observe a blue-shifting of the of the ∼2590 cm−1 peak by ∼50 cm−1 in the Rcav = 10 Å cavity (relative to the corresponding peaks in the Rcav = 12 and 15 Å cavities). IR Pump−Probe Spectra. Figures 7 and 8 show the ground-state bleach contributions to the IR pump−probe spectra for the Rcav = 10, 12, and 15 Å cavities for 10 pump− probe delays ranging from 0 to 8 ps, computed using eqs 9 and 11. Also included in these plots are the ground-state bleach contributions to the spectra for the bulk, unconfined system.78 As in the case of the 1D-IR spectra, the pump−probe spectra exhibit a four-peak structure, but the intensities of these peaks vary with time in different ways, reflecting the differences in the solvation dynamics associated with the various forms of the complex in its different environments. In Figures 9 −12, we plot the relative intensities (normalized by the peak maxima) of the four peaks for each cavity as a function of the pump−probe delay. In all cases, for a given peak, the intensity relaxation profiles of the nanoconfined systems are different from each other and markedly different from those of the bulk, unconfined system, attesting to the significant effects of nanoconfinement on the solvation dynamics. In contrast, the differences between the Rcav = 15 Å and bulk 1D-IR spectra are not as pronounced. We now discuss the time evolution of the peaks in more detail. For all cavities, we observe a rapid initial decline in the intensity (to varying degrees) of all peaks on a time scale of ∼200−400 fs due to solvation on the ground-state PES. In all cases, this initial decline is followed by an oscillation in the intensity within the first picosecond (except for the highest

Figure 7. Ground-state bleach contributions to the IR pump−probe spectra of the H-stretch in the A−B complex for the Rcav = 10, 12, and 15 Å cavities for pump−probe delays ranging from 0 to 1 ps. Also shown are the corresponding spectra for the bulk, unconfined system.

frequency peaks in the Rcav = 12 and 15 Å cavities), and then followed by a gradual (not necessarily monotonic) relaxation. The period of this oscillation varies from peak to peak and size to size, reflecting the (sub-picosecond) time scale of the solvent rearrangements around the various forms of the complex in its different environments. In the case of the “transition-state″ peak at 230 cm−1, the initial drop is drastic (from 1 to ∼0.12− 0.13) and occurs in ∼200 fs, attesting to the dynamical instability of bath configurations associated with the transition state of the complex in all cavities and in the bulk. The oscillation has a period of ∼400−600 fs and is likely the time scale associated with recrossings of the barrier top at ΔE‡. The relaxation of the intensities over the next 7 ps differs between the nanoconfined and bulk systems. In the case of the nanoconfined systems, the intensities remain relatively constant, while the intensity continues to drop (albeit nonmonotonically) for the bulk system. This suggests that the transition-state solvent fluctuations are more pronounced in the bulk system than in the nanoconfined systems due to the larger number of complex−solvent interactions. In the case of the peak at ∼1930 cm−1, we observe ∼9, ∼16, and ∼19% intensity drops for the Rcav = 10, 12, and 15 Å cavities, respectively, within 375 fs to yield an average initial decay rate of 0.039%/fs. In contrast to the transition-state peak, 13625



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Figure 10. Relative intensities (normalized by the peak maxima) of the 1930 cm−1 peaks in the IR pump−probe spectra of the Rcav = 10 (red), 12 (green), and 15 Å (blue) cavities as a function of the pump−probe delay.

Figure 8. Ground-state bleach contributions to the IR pump−probe spectra of the H-stretch in the A−B complex for the Rcav = 10, 12, and 15 Å cavities for pump−probe delays ranging from 2 to 8 ps. Also shown are the corresponding spectra for the bulk, unconfined system. Figure 11. Relative intensities (normalized by the peak maxima) of the 2280 cm−1 peaks in the IR pump−probe spectra of the Rcav = 10 (red), 12 (green), and 15 Å (blue) cavities as a function of the pump−probe delay. Also shown is the corresponding relative intensity for the bulk, unconfined system.

this peak. The Rcav = 10 and 15 Å configurations are the least and most dynamically stable, respectively, suggesting that the mobility of the solvent molecules surrounding the strongly Hbonded complex in the core of the cavity decreases as the cavity size increases. The oscillation for all three cavity sizes has a period of ∼600 fs. In contrast to the transition-state peak, the intensity does not remain relatively constant after the oscillation, but rather decays. The fact that the intensity does not reach a plateau after 8 ps suggests that the complete equilibration on the ground state takes more time. It should be noted that no comparison to the bulk is made since this peak does not exist in the bulk spectra. In the case of the “covalent″ peak at ∼2280 cm−1, we observe similar intensity drops for the Rcav = 10, 12, and 15 Å cavities (∼27, ∼28, and ∼24%, respectively) within 540 fs to yield an average initial decay rate of 0.049%/fs. In contrast to the peak at ∼1930 cm−1, this drop is somewhat faster, attesting to the relatively lower dynamical stability of the bath configurations

Figure 9. Relative intensities (normalized by the peak maxima) of the 230 cm−1 peaks in the IR pump−probe spectra of the Rcav = 10 (red), 12 (green), and 15 Å (blue) cavities as a function of the pump−probe delay. Also shown is the corresponding relative intensity for the bulk, unconfined system.

this drop is much slower, attesting to the relatively higher dynamical stability of the bath configurations associated with 13626



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covalent states, but the complex may sometimes exist transiently in the ionic state. In such a case, the system is highly unstable, so in order to stabilize it, the complex must reduce its dipole moment via a shift in the protonic charge (taking the complex back to its covalent state). This proton transfer occurs very rapidly (on the time scale of tens of femtoseconds) and is accompanied by a weakening of the Hbond, leading to a blue shift of the frequency.

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CONCLUDING REMARKS In this study, we investigated the effects of varying the degree of confinement on the 1D-IR and IR pump−probe spectroscopy of a H-stretch in a H-bonded complex dissolved in clusters of polar solvent molecules contained in nanosized hydrophobic cavities. As the radius of the cavity is varied (from Rcav = 10 Å to Rcav = 15 Å), we observed significant changes in the spectra, which reflect the shift in the proton-transfer equilibrium and the changes in the underlying dynamics of the complex and solvent. Our main results are as follows: (a) Both the 1D-IR and IR pump−probe spectra reflect the changes in the relative stabilities of the covalent and ionic forms of the complex as the cavity size is varied. (b) Both the 1D-IR and IR pump−probe spectra exhibit a unique peak at ∼1930 cm−1, which does not exist in the bulk spectra. This peak was assigned to strongly H-bonded covalent complexes situated in the core of the cavity. (c) In contrast to the bulk system, the covalent tautomer can exhibit higher frequencies than the ionic tautomer in the Rcav = 10 Å cavity, since the proton can approach the phenol group more closely due to the decrease in the complex−solvent electrostatic interactions. This weakens the H-bond, thereby leading to a blue shift in the ∼2590 cm−1 peak (relative to the corresponding peaks in the Rcav = 12 and 15 Å spectra). (d) As the cavity radius is increased to Rcav = 15 Å, the overall shape of the 1D-IR spectra approaches that of the bulk, unconfined system. (e) For a given cavity size, the intensities of the four peaks in the pump−probe spectrum vary with time in different ways, reflecting the differences in the solvation dynamics associated with the various forms of the complex in its different environments. For a given peak, its intensity relaxation profile varies as the cavity radius is increased from Rcav = 10 Å to the bulk, attesting to the significant effects of nanoconfinement on the solvation dynamics. (f) The highest frequency peak in the pump−probe spectrum of the Rcav = 10 Å cavity blue shifts within the first 200 fs. This is thought to be caused by rapid proton-transfer events within the complex (ionic → covalent) while situated near the cavity wall, leading to a weakening of the H-bond. (g) Although the 1D-IR spectrum of the Rcav = 15 Å case looks fairly similar to that of the bulk, the time-dependent pump−probe spectra reveal significant differences, rendering pump−probe spectroscopy a more sensitive probe for determining the onset of bulk behavior than linear IR absorption spectroscopy. As has been shown in previous studies, nanoconfinement allows one to exercise control over the thermodynamics, kinetics, and mechanisms of chemical reactions by varying the size, geometry, and chemical nature of the confining framework. Our study of a H-bonded complex in nanoconfined clusters of polar molecules has demonstrated how pump− probe spectroscopy in combination with MD simulations can yield deep insight into the effects of varying the properties of

Figure 12. Relative intensities (normalized by the peak maxima) of the 2590 cm−1 peaks in the IR pump−probe spectra of the Rcav = 10 (red), 12 (green), and 15 Å (blue) cavities as a function of the pump−probe delay. Also shown is the corresponding relative intensity for the bulk, unconfined system.

associated with this peak. The oscillation for all three cavity sizes has a period of ∼600 fs. As in the case of the peak at ∼1930 cm−1, the intensity decays after the oscillation. The similarity between the relaxation profiles is a reflection of the fact that the complex−solvent interactions are rather insensitive to cavity size in the case of the covalent tautomer. However, the bulk relaxation profile looks different, exhibiting a fast initial decay and a ∼45% drop in the first picosecond. These differences may be attributed to the wider distribution of solvent environments (around the covalent complex) encountered in the bulk. In contrast to the ∼2280 cm−1 peak, the differences between the relaxation profiles for the peak at ∼2590 cm−1 are more pronounced. We observe intensity drops of ∼23, ∼43, and ∼39% for the Rcav = 10, 12, and 15 Å cavities, respectively, within 590 fs. The relaxation of the Rcav = 10 Å peak is similar to that in the ∼2280 cm−1 case, since both correspond to the covalent state of the complex. The relaxations of the Rcav = 12 and 15 Å peaks are quite similar to the bulk relaxation up to 2 ps, since they all correspond to the ionic state of the complex. These relaxation profiles highlight the differences between the time scales of the short-time solvent reorganization dynamics surrounding the covalent and ionic complexes, with that of the ionic complex being faster due to the larger electrostatic forces present. However, in contrast to the bulk peak, the long-time relaxations are different, with the bulk profile exhibiting an increase due to the tautomerization reaction on this time scale, while the nanoconfined profiles either exhibit a further decrease (in the Rcav = 10 Å case) or remain fairly constant (in the Rcav = 12 and 15 Å cases) on this time scale. As in the case of the 1D-IR spectrum of the 10 Å cavity where we observed a blue shift of the highest frequency peak with respect to the other cavity sizes, here we see that the highest frequency peak for the Rcav = 10 Å cavity blue-shifts from ∼2610 to ∼2640 cm−1 during the first 200 fs (not seen in the larger cavities). On the basis of the top panel of Figure 3, these high frequencies are associated with the complex being near the cavity wall. This ultrafast blue-shifting may therefore be caused by the following scenario: Near the cavity wall, the solvent polarization and the complex are predominantly in their 13627



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(8) Rodriguez, J.; Elola, M. D.; Laria, D. Ionic Liquid Aqueous Solutions Under Nanoconfinement. J. Phys. Chem. C 2012, 116, 5394−5400. (9) Strekalova, E. G.; Mazza, M. G.; Stanley, H. E.; Franzese, G. Hydrophobic Nanoconfinement Suppresses Fluctuations in Supercooled Water. J. Phys.: Condens. Matter 2012, 24, No. 064111. (10) Nielsen, T. K.; Besenbacher, F.; Jensen, T. R. Nanoconfined Hydrides for Energy Storage. Nanoscale 2011, 3, 2086−2098. (11) Fichtner, M. Nanoconfinement Effects in Energy Storage Materials. Phys. Chem. Chem. Phys. 2011, 13, 21186−21195. (12) Nielsen, T. K.; Boesenberg, U.; Gosalawit, R.; Dornheim, M.; Cerenius, Y.; Besenbacher, F.; Jensen, T. R. A Reversible Nanoconfined Chemical Reaction. ACS Nano 2010, 4, 3903−3908. (13) Kim, T.-S.; Dauskardt, R. H. Molecular Mobility under Nanometer Scale Confinement. Nano Lett. 2010, 10, 1955−1959. (14) Kumar, P.; Han, S.; Stanley, H. E. Anomalies of Water and Hydrogen Bond Dynamics in Hydrophobic Nanoconfinement. J. Phys.: Condens. Matter 2009, 21, No. 504108. (15) Rodriguez, J.; Elola, M. D.; Laria, D. Polar Mixtures Under Nanoconfinement. J. Phys. Chem. B 2009, 113, 12744−12749. (16) Giovambattista, N.; Rossky, P. J.; Debenedetti, P. G. Phase Transitions Induced by Nanoconfinement in Liquid Water. Phys. Rev. Lett. 2009, 102, No. 050603. (17) Jonas, A. M.; Hu, Z.; Glinel, K.; Huck, W. T. S. Effect of Nanoconfinement on the Collapse Transition of Responsive Polymer Brushes. Nano Lett. 2008, 8, 3819−3824. (18) Piletic, I. R.; Moilanen, D. E.; Spry, D. B.; Levinger, N. E.; Fayer, M. D. Testing the Core/Shell Model of Nanoconfined Water in Reverse Micelles Using Linear and Nonlinear IR Spectroscopy. J. Phys. Chem. A 2006, 110, 4985−4999. (19) Owrutsky, J. C.; Pomfret, M. B.; Barton, D. J.; Kidwell, D. A. Fourier Transform Infrared Spectroscopy of Azide and Cyanate Ion Pairs in AOT Reverse Micelles. J. Chem. Phys. 2008, 129, No. 024513. (20) Balakrishnan, S.; Javid, N.; Weingaertner, H.; Winter, R. SmallAngle X-ray Scattering and Near-Infrared Vibrational Spectroscopy of Water Confined in Aerosol-OT Reverse Micelles. ChemPhysChem 2008, 9, 2794−2801. (21) Morales, C. M.; Thompson, W. H. Simulations of Infrared Spectra of Nanoconfined Liquids: Acetonitrile Confined in Nanoscale, Hydrophilic Silica Pores. J. Phys. Chem. A 2009, 113, 1922−1933. (22) Sechler, T. D.; DelSole, E. M.; Deak, J. C. Measuring Properties of Interfacial and Bulk Water Regions in a Reverse Micelle with IR spectroscopy: A Volumetric Analysis of the Inhomogeneously Broadened OH band. J. Colloid Interface Sci. 2010, 346, 391−397. (23) Mukamel, S. Principles of Nonlinear Optical Spectroscopy; Oxford: New York, 1995. (24) Jonas, D. M. Two-Dimensional Femtosecond Spectroscopy. Annu. Rev. Phys. Chem. 2003, 54, 425. (25) Khalil, M.; Demirodoven, N.; Tokmakoff, A. Coherent 2D IR Spectroscopy: Molecular Structure and Dynamics in Solution. J. Phys. Chem. A 2003, 107, 5258. (26) Zheng, J.; Kwak, K.; Fayer, M. D. Ultrafast 2D IR Vibrational Echo Spectroscopy. Acc. Chem. Res. 2007, 40, 75. (27) Cho, M. Coherent Two-Dimensional Optical Spectroscopy. Chem. Rev. 2008, 108, 1331. (28) Ogilvie, J. P.; Kubarych, K. J. Multidimensional Electronic and Vibrational Spectroscopy: An Ultrafast Probe of Molecular Relaxation and Reaction Dynamics. Adv. At., Mol., Opt. Phys. 2009, 57, 249. (29) Dokter, A. M.; Woutersen, S.; Bakker, H. J. Anomalous Slowing Down of the Vibrational Relaxation of Liquid Water upon Nanoscale Confinement. Phys. Rev. Lett. 2005, 94, No. 178301. (30) Tan, H.-S.; Piletic, I. R.; Fayer, M. D. Orientational Dynamics of Water Confined on a Nanometer Length Scale in Reverse Micelles. J. Chem. Phys. 2005, 122, No. 174501. (31) Moilanen, D. E.; Levinger, N. E.; Spry, D. B.; Fayer, M. D. Confinement or the Nature of the Interface? Dynamics of Nanoscopic Water. J. Am. Chem. Soc. 2007, 129, 14311−14318. (32) Levinger, N. E.; Swafford, L. A. Ultrafast Dynamics in Reverse Micelles. Annu. Rev. Phys. Chem. 2009, 60, 385.

the confining framework on a chemical reaction of interest. The confinement model employed in this study, although idealized, provides an efficient and useful way for qualitatively investigating trends in system properties and effects on the spectra, rather than resorting to computationally expensive atomistic treatments of the confining cavity. Nevertheless, if quantitative information is desired, a mixed quantum-classical approach (such as the one taken in this study) would be feasible for carrying out fully atomistic simulations of a system and its confining framework. The results of this study are characteristic of a chemical reaction that is strongly coupled to its solvent environment. However, it is worthwhile to investigate the effects of nanoconfinement over a wide range of solute−solvent and solute−cavity couplings. Such computational studies, in which the properties of the system and confining framework are systematically varied, can potentially lead to novel design principles for nanoscale reactors.

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ASSOCIATED CONTENT

S Supporting Information *

Figures showing 1D and 2D histograms of various properties of the system investigated. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by grants from the University of Alberta and the Natural Sciences and Engineering Research Council of Canada (NSERC).

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