Molecular Dynamics Simulations of Hydrogen Bond Dynamics and Far

Article pubs.acs.org/JPCC

Molecular Dynamics Simulations of Hydrogen Bond Dynamics and Far-Infrared Spectra of Hydration Water Molecules around the Mixed Monolayer-Protected Au Nanoparticle Zhen Yang,* Yunzhi Li, Guobing Zhou, Xiangshu Chen,* Duanjian Tao, and Na Hu College of Chemistry and Chemical Engineering, Jiangxi Inorganic Membrane Materials Engineering Research Center, Jiangxi Normal University, Nanchang 330022, People’s Republic of China S Supporting Information *

ABSTRACT: Molecular dynamics simulations have been performed to systematically investigate the structure and dynamics properties, hydrogen bond (HB) dynamics, and farinfrared (far-IR) spectra of hydration water molecules around the mixed monolayer-protected Au nanoparticles (MPANs) with different ligand compositions and length. Our simulation results demonstrate that the translational and rotational motions of hydration water molecules in the proximity of charged terminal NH3+ and COO− groups are suppressed significantly with respect to the bulk water. Compared to the bulk water, meanwhile, longer structural relaxation times of hydration H2O−H2O HBs indicate enhanced strength of H 2 O−H 2 O HBs at the interface of mixed MPANs. Accordingly, these hydration water molecules around the charged terminal groups can exhibit a considerable blue-shift in farIR spectra for all ligand compositions and length studied here. A series of detailed HB analyses manifest that above restricted behavior of hydration water molecules can be attributed to the stronger H2O−NH3+ and H2O−COO− HBs and the corresponding structural relaxation times are much greater than those of hydration H2O−H2O HBs. Furthermore, we find that increasing ligand length can affect much the morphology of self-assemble monolayers in water owing to enhanced hydrophobic interactions between alkane chains and water molecules and favor the translational mobility of hydration water molecules owing to weaken electrostatic interactions. Unlike the translational motions, our comparison results among different ligand lengths clearly confirm that the rotational relaxation of hydration water molecules should be dominated by the local and directional HBs at the interfaces, rather than the previous explanation of the ratio between hydrophobic/hydrophilic exposed regions. More importantly, our simulations reveal at a molecular level that the ligand composition has a little influence on the structure, dynamics, HBs, and far-IR spectra of hydration water molecules around the mixed MPANs mainly due to the comparable strength between H2O−NH3+ and H2O−COO− HBs.

1. INTRODUCTION In the past decades, monolayer-protected metal nanoparticles have received much attention due to their potential applications in biosensing,1−4 imaging,4−7 drug delivery,7−12 and molecular recognition.13−16 More recently, the mixed monolayerprotected Au nanoparticles (MPANs) whose self-assemble monolayers (SAMs) are composed of two different ligand species and an Au core12,17−35 have exhibited superior properties in comparison with the monoligand counterparts, since more desired properties of mixed MPANs can be achieved not only by varying the size of Au core and ligand length but also by changing the composition and relative position of mixed ligands.14,28−30 Furthermore, the unique properties of mixed MPANs are not simply additive sometimes owing to the synergistic effect of two ligand types in the SAMs.14,17 Therefore, a comprehensive understanding of their physical and chemical properties is significantly favorable to design and synthesis of various MPANs with tailored © 2015 American Chemical Society

properties. One of the most crucial properties is the structure and dynamics of hydrogen bond (HB) network in the hydration layer of mixed MPANs, which play an important role in determining the interfacial properties of functionalized nanomaterials. As pointed out by Schatz,36 experimental observations of the objects on a nanoscale are often fraught with enormous difficulty. Therefore, different experimental characterizations may result in different arguments since the thicknesses of hydration layers are around 1 nm.37 Alternatively, molecular dynamics (MD) simulations can provide a direct and deep insight into the relevant HB structure and dynamics in the hydration layer at a molecular level.38−42 For example, earlier MD simulations have shown that only about 2−3 HBs per Received: July 10, 2014 Revised: January 10, 2015 Published: January 13, 2015 1768

DOI: 10.1021/jp506875m J. Phys. Chem. C 2015, 119, 1768−1781

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The Journal of Physical Chemistry C

hydration water molecules, and their relationship with the hydration HB network have also been investigated and discussed in detail. This paper is organized as follows. In section 2, we present the description of initial configuration setup, potential model, details of MD simulations, and density functional theory (DFT) calculations. Then, the calculation results are shown and discussed in section 3. Finally, we offer a few general conclusions and remarks in section 4.

water molecule can be formed at the MPAN interface when the SAMs consist of the hydrophobic alkylthiols.38 Recent MD simulations have further revealed that the carboxyl, hydroxyl, and amine terminal groups can form stronger HBs with the interfacial water molecules in the hydration layer so that the HB strength between interfacial water molecules also becomes weaker.39 On the contrary, the enhanced HBs between water molecules have been found in the hydration layer of charged MPAN,42 since the cationic amine terminal groups and counterions can form a stable ion wall which significantly restricts the escape of interfacial water molecules from the hydration layer.42 Nevertheless, most of previous MD simulations only focused on the structure and dynamics of interfacial HBs around the homoligand MPANs rather than the mixed MPANs. For the mixed MPANs, current MD simulations mainly concerned the packing morphologies of mixed SAMs on the surface of nanoparticles.43−47 For example, Glotzer and coworkers43,44 have studied the nanoscale morphologies of two immiscible ligands on the surface of nanoparticle by using atomic and mesoscale simulations. They revealed that the gain of conformational entropy of the longer or bulkier ligands on nanoparticle should be responsible for the stripelike morphologies observed from experimental STM image25,28 since such morphologies can result in a lower free energy than the complete demixing.43 Subsequently, they further confirmed that the formation of stripe morphologies depends on the geometry differences between mixed ligands rather than their chemical compositions.44 More recently, a series of MD simulations of Alexander-Katz and co-workers47 showed that the particle sizes as well as the choice of relative ligand length have significant effects on the surface properties of mixed MPANs, while three striped, mixed, and random packing morphologies exhibit similar behavior due to the fluctuations of mixed ligands. Compared to the detailed investigation of surface packing morphologies, however, the relevant knowledge of structure and dynamics of HBs in the hydration layer remained rudimentary for the mixed MPANs. Additionally, infrared (IR) spectroscopy is always one of most valuable analysis tools to extensively investigate the structure and dynamics of hydration water molecules at different interfaces.21,48−50 The previous experimental21,27,51 and theoretical studies38,48,49,52−59 have confirmed that the unique HB vibration modes between water molecules, originating from the attractive interaction between the HB donor and the HB acceptor, are generally located in the far-IR region.48,55−57 Such vibrational signatures provide a direct insight into the dynamics of HB formation and breaking. Therefore, a molecular-level interpretation of HB vibrational modes of hydration water molecules around the mixed MPAN is also helpful for experimentally understanding the relevant HB dynamics in the hydration layer. To shed light on above these issues, a series of classical MD simulations have been carried out here to investigate the HB dynamics and far-IR spectra of hydration water molecules around the mixed MPAN [Au 140 (SH(CH 2 ) n (NH 3 + ) x (COO−)1−x)62] (n = 12 and 6, x = 0.25, 0.50, and 0.75) with Na+ (or Cl−) counterions in aqueous environment, as described by the recent experiments of Grzybowski and co-workers.26 In this work, we mainly focus on how the presence of mixed MPANs with different ligand compositions and length affects the interfacial HB properties and relevant far-IR spectra by comparison with the bulk water. Meanwhile, the orientation distribution of SAMs, the translation and rotation dynamics of

2. SIMULATION METHOD 2.1. Initial Configuration Setup. On the basis of the recent experiments of Grzybowski and co-workers,26 we constructed six mixed MPAN systems [Au 1 4 0 (SH(CH2)n(NH3+)x(COO−)1−x)62] (n = 12 and 6, x = 0.25, 0.50, and 0.75), with Na+ (or Cl−) counterions in aqueous environment. For convenience, the mixed MPAN systems with long ligands [SH(CH2)12(NH3+)x(COO−)1−x] and short ligands [SH(CH2)6(NH3+)x(COO−)1−x] were denoted as the C12 and C6 systems, respectively. Similarly to our previous work,42,60 62 hexanethiols were adhered to the Au140 core surface. Then, the decanethiols were generated by the extension of the ligand chains with the CH2 group one by one. To prevent the entanglement of ligand chains, an additional MD simulation was run for 2 × 104 steps for the isolated MPAN after each new group was added. Finally, the corresponding mixed C12 and C6MPANs were produced through adding the NH3+ and COO− terminal groups into hexanethiols and decanethiols, respectively. When x = 0.25, 0.50, and 0.75, the number of NH3+ groups is 16, 31, and 46, respectively. Accordingly, the number of COO− groups is 46, 31, and 16, respectively. To obtain the low-lying mixed MPANs, 1 × 105 relative positions of NH3+ and COO− terminal groups for each mixed MPAN were randomly generated as the initial structure. Then, a low storage Broyden−Fletcher−Goldfarb−Shanno nonlinear optimization was used to minimize these isolated MPANs without solvent, where the Au core was treated as rigid. For each composition, the structure with the lowest optimized energy was chosen as our initial configuration of mixed MPAN. It should be noted that the obtained mixed MPANs display the NH3+ and COO− terminal groups distributed in a mixing manner due to the attractive and repulsive electrostatic interaction, as shown in Figure S1 of the Supporting Information. Next, the mixed MPAN was accommodated into a cubic simulation box (110 × 110 × 110 Å3) which was filled with bulk water molecules. Each water molecule overlapping the mixed MPAN was removed when its center of mass separating from the nearest atom of the MPAN is less than 5.0 Å. Then, a canonical MD simulation with a small time step of 0.1 fs was performed for 1 × 105 steps to relax this system. Finally, Na+ (or Cl−) counterions were randomly added to maintain the electrical neutrality of mixed MPAN systems except for x = 0.5. Therefore, six simulation systems for next NPT MD simulations contain a mixed MPAN, 31 500 water molecules, and Na+ (or Cl−) counterions for x = 0.25 (or 0.75). 2.2. Potential Model. In this work, the united-atom OPLS force field61 was used for the charged ligands and Na+ (or Cl−) counterions, where each CH2 group of the ligands was represented as one pseudoatom while the polar NH3+ and COO− groups were treated as the all-atom model to maintain more detailed information at the interface of mixed MPANs. Meanwhile, the water molecules were represented by using the TIP3P model,62 which is compatible with the united-atom 1769


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Figure 1. Radial density distributions of water molecules, two charged terminal groups (i.e., NH3+ and COO− groups), and Na+ (or Cl−) counterions around the mixed MPAN for the C12 systems: (a) x = 0.25, (b) x = 0.50, and (c) x = 0.75, and the C6 systems: (d) x = 0.25, (e) x = 0.50, and (f) x = 0.75. For clarity, the insets show details of charged groups and counterions at the interface.

OPLS force field. However, it should be noted that the TIP3P model often fails to quantificationally reproduce the dynamics properties of water, such as translational and rotational motions.63 The Au−SH interaction was approximated by a nonbonded m−n short-range potential64,65 U (r ) =

E0 ⎡ ⎛ r0 ⎞n ⎛ r0 ⎞m⎤ ⎢m⎜⎝ ⎟⎠ − n⎜⎝ ⎟⎠ ⎥ n − m⎣ r r ⎦

boundary conditions were used in all three directions. The Newton’s equations of motion were integrated by using the velocity−Verlet algorithm with a time step of 2 fs. The cutoff distance of nonbonded interactions except for the Au−SH interaction was set to 12 Å, and the long-range electrostatic interactions were calculated by using the particle-mesh Ewald (PME) method.66 The NPT MD simulation was run for 15 ns duration, where the first 5 ns was for equilibration and the next 10 ns with the trajectories stored every 50 fs for data analysis. After equilibration, the dimensions of simulation box are about 99.96 × 99.96 × 99.96 Å3 for three C12 systems and 99.20 × 99.20 × 99.20 Å3 for three C6 systems. On the other hand, two additional NPT MD simulations following the last equilibration configuration were run to calculate the continuous HB dynamics and far-IR spectra, respectively. One NPT MD simulation was run for 500 ps with the trajectories stored every 5 fs, which is short enough for the continuous HB dynamics. The other simulation was run for 100 ps with a smaller time step of 0.5 fs and the velocity trajectories stored every 0.5 fs, which is necessary for calculating the relevant vibrational spectra. 2.4. DFT Calculations. To obtain the binding energies (Ebinding) of hydration water molecules and terminal NH3+ and COO− groups, a series of independent DFT calculations at the B3LYP/6-311+G(d,p) level were performed for the complexes of one water molecule and one terminal group, i.e., SH-

(1)

where E0 = 38.6 kJ mol−1, m = 4, n = 8, r0 = 2.9 Å, and the cutoff distance was set to be 6.2 Å. For the reason for computational economy, the bond length of water molecules was fixed through the RATTLE algorithm during simulation. The nonbonded interactions were described by the combination of electrostatic and Lennard−Jones (L−J) interactions. It should be noted that the L−J parameters of Au atoms were derived from the previous work, which can reproduce satisfactorily the adsorption energies of water molecules at the Au surface.65 Finally, all L−J parameters and partial atomic charges used in this work were summarized and are listed in Table S1 of the Supporting Information. 2.3. MD Simulation Details. For each mixed MPAN system, MD simulation was carried out in isothermal−isobaric ensemble (NPT) with the temperature of 298.0 K and the pressure of 1.0 atm. The Nosé−Hoover method was applied for maintaining the constant temperature, and the periodic 1770


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The Journal of Physical Chemistry C (CH2)12NH3+−H2O and SH(CH2)12COO−−H2O. Meanwhile, the Ebinding value of H2O−H2O interaction was also calculated for comparison. Full geometry optimizations were performed for these complexes, and then the binding energies of these optimized geometries were calculated with the correction of basis set superposition error (BSSE) at the same level. All DFT calculations in this work were performed with the GAUSSIAN 09 program.67

3. RESULTS AND DISCUSSION 3.1. Structure and Dynamics of Hydration Water Molecules. Based on our MD simulations, the radial density distributions of water molecules, two charged terminal groups (i.e., the NH3+ and COO− groups), and Na+ (or Cl−) counterions around the mixed MPAN for different ligand compositions and length are first presented in Figure 1. For the mixed C12 MPANs, we can see clearly from Figure 1a−c that both the terminal groups of ligands spread approximately from 15 to 30 Å with the maximum density peak of about 22 Å after simulation equilibration, and the Na+ (or Cl−) counterions also prefer to assemble in the vicinity of the terminal groups due to the strong electrostatic interactions. Similar density peaks can be also observed at around 17 Å for the C6 systems, as shown in Figure 1d−f. Furthermore, the density distributions of water molecules are found to be zero around 11.5 Å for all mixed MPANs, suggesting that water molecules cannot access the Au core owning to the steric hindrance of mixed SAM on the nanoparticle surface. However, all density profiles of water molecules for the C12 systems (see Figure 1a−c) have almost no peak near the outmost region of SAMs (around from 25 to 30 Å) while there are obviously main density peaks (around from 16 to 21 Å) for the C6 systems (see Figure 1d−f), suggesting that such absence of water density peaks in the hydration can be related to the ligand length of mixed SAMs. Similar phenomena can be also observed in the monoligand MPAN with dodecanethiol ligands65 while one or more pronounced density peaks can be only found in the shorter monoligand systems of neutral39,40 and charged MPAN.42 A time-averaged normalized angle distribution g(θ)60,68 is also constructed here to elucidate the orientation distribution of ligands on the Au core. The orientation angle θ between two different ligand chains is defined as the angle between the linking vectors from the SH group to the terminal group. As shown in Figure 2a−c, the mixed C12 MPANs (especially for the composition of x = 0.5) in water exhibit two main peaks in the angle distribution, indicating two large ligand bundles on the core surface. However, the C12 MPANs in vacuum almost display one broad peak near 90°, corresponding to the spherical and uniform distribution of ligand chains on the core surface, as shown in Figure S2a−c of the Supporting Information. On the other hand, the comparisons between Figure 2 and Figure S2 show that the mixed C6MPANs in water and in a vacuum present similar angle distribution only with one broad peak. The difference in the SAM morphology between the C12 and C6MPANs in water can be attributed to the presence of hydrophobic interaction of alkane chains in water. For the C12 systems, the distribution of two ligand bundles in water can decrease obviously the contact area of alkane long chains and water molecules so that the hydrophobic interaction from the ligands becomes weaker. To better analyze the unique properties of hydration water molecules around the mixed C12 MPAN, the radical SAM extension region (i.e., the radial distance with respect to the

Figure 2. Normalized angle distribution g(θ) between passivating chains on the mixed C12 [(a) x = 0.25, (b) x = 0.50, and (c) x = 0.75] and C6 [(d) x = 0.25, (e) x = 0.50, and (f) x = 0.75] MPANs in water. The insets show the corresponding final snapshots. For clarity, the water molecules as well as Na+ (or Cl−) counterions have been removed.

center of Au core is less than 30 Å) is divided into two subregions: one subregion (denoted as region 1) is the radial distance within 5 Å with respect to the C atom (terminal COO− group) or the N atom (terminal NH3+ group), and the other subregion (region 2) is the remaining region, as shown in Figure S3 of Supporting Information. However, it should be noted that the properties of hydration water molecules in region 1 are only investigated for the C6 systems in this work because of poor statistics resulting from several water molecules merely located in region 2 of the C6 systems. As shown in Figure 3, the translational motions of hydration water molecules are described by the mean-square displacement (MSD). Then, their isotropic diffusion coefficients Di can be specified using Einstein’s relation69 ⟨[ri(t ) − ri(0)]2 ⟩ (2) t →∞ 6t 2 where ⟨[ri(t) − ri(0)] ⟩ is the MSD of water molecules in region i at a certain time of t. It should be emphasized that to determine one water molecule locates in region i or not is that the molecule is only in this region at time 0 and time t. The diffusion coefficients Di of hydration water molecules are listed in Table 1. For comparison, the MSD curve and Di of bulk water are also given in Figure 3 and Table 1, respectively. In region 1 of C12 systems, we can see clearly from Figure 3a that the MSD curves of hydration water molecules for different ligand compositions almost display identical variation patterns, suggesting that the translational motions of hydration water molecules are rather insensitive to the ligand composition. However, their MSD data increase more slowly with time than that of bulk water. Accordingly, the diffusion coefficients Di of water molecules in region 1 of C12 systems are in the range between 1.66 × 10−5 and 1.71 × 10−5 cm2/s at three different ligand compositions, which are only one-third of the bulk Di = lim

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hydration water molecules far away from the terminal groups of SAMs (i.e., in region 2) move more rapidly. As shown in Figure 3c, we can find that the hydration water molecules exhibit slower translational motions in region 1 of the C6 systems compared to those in region 1 of the C12 systems, and their diffusion coefficients Di further decrease into the range between 0.72 × 10−5 and 0.77 × 10−5 cm2/s. In other words, decreasing the ligand length disfavors the translational mobility of hydration water molecules in region 1 owing to stronger electrostatic interaction from the charged terminal groups and counterions (i.e., higher charge densities in region 1 of the C6 systems compared to those of the C12 systems, as shown in the inset of Figure 1). In addition, we can see from Figure 3b that the slope change of MSD curves is up to about 20 ps so that some molecules initially in region 2 can leave this region. To estimate this effect, we calculate additional MSD curves in region 2 of the C12 systems, where to determine one water molecule locates in region 2 or not is that the molecule continuously locates in this region from time 0 to time t. The comparison details are shown in Figure S4 of the Supporting Information. On the other hand, the rotational motions of hydration water molecules are also studied through the time correlation function (TCF), where the orientation of each water molecule is represented by four different unit vectors, including OH, HH, dipole (μ), and normal (⊥ = rOH1 × rOH2) vectors, respectively. Then, the corresponding TCF Cαrl(t) of hydration water molecules can be calculated as70−72 Crlα(t ) =

Table 1. Diffusion Coefficient Di, Structural Relaxation Time HB τHB C , and Average lifetime τS of H2O−H2O HBs in Regions 1 and 2 of the C12 Systems and Region 1 of the C6 Systems as Well as the Corresponding Bulk Values compositions

Di (10−5 cm2/s)

τHB C (ps)

τHB S (ps)

region 1 (C12)

x = 0.25 x = 0.50 x = 0.75 x = 0.25 x = 0.50 x = 0.75 x = 0.25 x = 0.50 x = 0.75 bulk values

1.68 1.66 1.71 3.66 3.65 3.65 0.76 0.77 0.72 5.47

5.0 5.0 4.8 3.8 3.8 3.7 5.0 4.9 4.9 2.9

0.315 0.325 0.317 0.295 0.294 0.292 0.302 0.316 0.311 0.290

region 2 (C12)

region 1 (C6)

bulk

⎞ α α u ( t ) u (0) ∑ j j ⎟⎟ ⎠ j=1 Ni

(3)

where Pl is the lth rank Legendre polynomial (l = 1 and 2) and uαj (t) is the unit vector of the jth water molecule at time t, which points along the α-axis in the molecular reference frame. Ni is the number of water molecules that are in the region i at time 0 and time t, and the angular bracket means that the ensemble averaging is taken over all tagged water molecules at different reference initial times. As shown in Figure 4, all Cαrl(t) curves (l = 2) of hydration water molecules in region 1 of the C12 systems decay much slower than the bulk curve, which are obviously nonexponential functions and cannot be described by a single-exponential law. Similar rotational behavior of water molecules has been also observed at the surface of monoligand MPANs39,40,42 and proteins.37,53,56 Therefore, the corresponding rotational relaxation times ταl of hydration water molecules are calculated by fitting the Cαrl(t) decay curves through three weighed exponentials, which is expressed as53,73,74

Figure 3. Time dependence of MSD of water molecules around the mixed MPAN: (a) region 1 and (b) region 2 of the C12 system and (c) region 1 of the C6 system. For comparison, the MSD for the bulk water is also shown.

subregions

⎛ 1 Pl ⎜⎜ N ⎝ i

Crlα(t ) = A exp( −t /τa) + B exp(−t /τb) + C exp(−t /τc) (4)

and then τlα = Aτa + Bτb + Cτc

(5)

where A, B, and C are the fitting parameters and A + B + C = 1; τa, τb, and τc are the time constants. We can find from Table 2 that all τα2 values of hydration water molecules in region 1 of the C12 systems are at least 3 times larger than the corresponding bulk values, which are consistent with the results of Figure 4. HH For example, the bulk τHH 2 value is only 0.73 ps, while the τ2 values in region 1 are 3.55, 3.65, and 3.19 ps for the ligand compositions x = 0.25, 0.50, and 0.75, respectively. In addition,

diffusion coefficient of 5.47 × 10−5 cm2/s. By comparison with region 1, the diffusion coefficients Di of hydration water molecules in region 2 of C12 systems are in the range between 3.65 × 10−5 and 3.66 × 10−5 cm2/s, indicating that these 1772


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Figure 4. Four TCFs for the rotational dynamics of water molecules in region 1of the C12 systems: (a) OH, (b) HH, (c) dipole, and (d) normal (⊥ = rOH1 × rOH2) vectors. For comparison, the corresponding results for the bulk water are also shown. Here the rotational TCFs are constructed using the second-order Legendre polynomial.

dominated by both the local HBs and the electrostatic interaction at the interface, the rotational motions of water molecules only require their neighboring HB rearrangements rather than the position change of themselves. In other words, the rotational motions of hydration water molecules are dominated by the local and directional HBs at the interface of mixed MPANs and not affected much by the electrostatic interaction. Therefore, the ligand length has a little influence on the rotational motions of hydration water molecules because of the same number of terminal NH3+ and COO− groups (forming strong HBs with hydration water molecules, as discussed in section 3.2) between the C12 and C6 systems, although the C6 systems exhibit a lower ratio between hydrophobic/hydrophilic exposed regions compared to the C12 systems. However, in the previous work, Marchi and coworkers75 have found that the rotational relaxation of hydration water molecules near the micelle consisting of the C12E6 surfactants is obviously slower than that of bulk water, while that near the micelle consisting of the lauryl dimethyl amino oxide (LDAO) surfactants is much closer than the bulk value. Then, they attributed this difference to the ratio between hydrophobic/hydrophilic exposed regions at the interfaces of C12E6 and LDAO micelles.75 In fact, our simulation results confirm that this difference should be attributed to more HBs formed by hydration water molecules with the C12E6 micelle compared to the LDAO micelle, rather than the previous explanation of the ratio between hydrophobic/hydrophilic exposed regions.75 Such unique translational and rotational motions of hydration water molecules in regions 1 of the C12 and C6 systems can be attributed to the strong interactions between hydration water molecules and terminal NH3+ and COO− groups of ligands. Then, two corresponding binding energies between one water molecule and one terminal group have been determined from the DFT calculations, as shown in Figure 6.

Table 2. Four Types of Rotational Relaxation Times of Water Molecules in Regions 1 and 2 of the C12 Systems and Region 1 of the C6 Systems as Well as the Corresponding Bulk Valuesa l=2

compositions

τOH 2 (ps)

τHH (ps) 2

τμ2 (ps)

τ⊥2 (ps)

region 1 (C12)

x = 0.25 x = 0.50 x = 0.75 x = 0.25 x = 0.50 x = 0.75 x = 0.25 x = 0.50 x = 0.75 bulk values

2.75 2.88 2.12 0.78 0.76 0.74 2.62 2.40 2.01 0.69

3.55 3.65 3.19 0.83 0.81 0.79 3.25 3.14 3.05 0.73

3.27 3.46 3.76 0.79 0.78 0.77 2.87 2.80 2.93 0.68

3.24 3.28 2.41 0.59 0.56 0.53 2.94 2.45 2.21 0.50

region 2 (C12)

region 1 (C6)

bulk a

Here the rotational TCFs are constructed using the second-order Legendre polynomial.

the τOH 2 values are the least compared to other three rotational relaxation times in region 1 of the C12 systems while the τ⊥2 value is the least among the bulk values, suggesting that the hydration water molecules form the strong HBs with the terminal NH3+ and COO− groups. However, in region 2 of the C12 systems (see Figure 5 and Table 2), all Cαrl(t) curves of hydration water molecules are almost identical to the bulk curves, and their τα2 values are slightly more than the bulk values. By comparison, we can see from Table 2 that the τα2 values of hydration water molecules in region 1 of the C6 systems are slightly less than those of the C12 systems, which is significantly different from the comparison in translational motions between the C6 and the C12 systems. The corresponding Cαrl(t) curves of the C6 systems are shown in Figures S7 and S8 of the Supporting Information. Unlike the translational motions 1773


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Figure 5. Four TCFs for the rotational dynamics of water molecules in region 2 of C12 systems: (a) OH, (b) HH, (c) dipole, and (d) normal (⊥ = rOH1 × rOH2) vectors. For comparison, the corresponding results for the bulk water are also shown. Here the rotational TCFs are constructed using the second-order Legendre polynomial.

of hydration water molecules are independent of the ligand composition, as shown in Figures 3−5. 3.2. HB Dynamics in the Hydration Layer. In our mixed MPAN systems, there are three major types of intermolecular HBs with water molecules in the hydration layer, i.e., H2O− NH3+, H2O−COO−, and H2O−H2O HBs. It is well-known that the breaking and forming processes of HBs in the hydration layer play an important role in determining the functionality of proteins and MPANs.37,42 The relevant HB dynamics can be characterized by both the continuous SHB(t) and intermittent CHB(t) TCFs, which are defined as the following expressions:76−78

SHB(t ) =

⟨h(0)H(t )⟩ ⟨h(0)h(0)⟩

(6)

⟨h(0)h(t )⟩ ⟨h(0)h(0)⟩

(7)

and Figure 6. Optimized structures and Ebinding at the B3LYP/6311+G(d,p) level for the (a) H2O−H2O, (b) SH(CH2)12NH3+− H2O, and (c) SH(CH2)12COO−−H2O interactions.

C HB(t ) =

where the variable H(t) is unity when the tagged HB pair at a certain region is continuously kept from time 0 to time t, and zero otherwise. On the other hand, the population variable of h(t) is unity when a particular HB pair at a certain region exists at time t, and zero otherwise. Hence, the continuous function provides a more accurate HB lifetime than the intermittent function, while the intermittent function allows the reformation of broken HBs in the interval of time t so that it can provide much information on the structural relaxation of HBs.37,56 In other words, the relaxation time of SHB(t) is usually called the average lifetime of HBs (τHB S ) while the relaxation time of CHB(t) describes the structural relaxation time of HBs (τHB C ). Similarly to the calculation of rotational relaxation times τR, we also employ the three weighted exponentials (see eqs 4 and 5) to obtain the corresponding τHB and τHB S C values. It

The calculated Ebinding values for SH(CH2)12NH3+−H2O and SH(CH2)12COO−−H2O interactions are −16.69 and −18.43 kcal mol−1, respectively, which are more than 3 times larger than the Ebinding value of H2O−H2O interaction (−5.03 kcal mol−1). Such strong interaction between hydration water molecules and terminal groups leads to that the diffusion coefficients of hydration water molecules in region 1 are onethird of the bulk value (see Table 1) and their rotational relaxation times ταl are more than 3 times larger than the corresponding bulk values (see Table 2). In addition, we find that the Ebinding value of SH(CH2)12NH3+−H2O interaction is close to that of SH(CH2)12COO−−H2O interaction, which results in that both the translational and the rotational motions 1774


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presents that the CHB(t) curves of hydration water molecules in both regions 1 and 2 of the C12 systems decay slower than the bulk curve, suggesting enhanced H2O−H2O HBs around the mixed MPANs. Accordingly, we can see from Table 1 that the calculated τHB C values in regions 1 and 2 of the C12 systems are larger than the bulk value by more than 60% and 25%, respectively. It should be emphasized that the CHB(t) allows for long sojourns after the HB breaking so that the hydration water molecules around the terminal groups of ligands can re-form HBs with its neighboring water molecules during the sojourn time. Similar phenomena can be observed for the C6 systems, as shown in Figure 7c. The comparisons in τHB C between the C6 and C12 systems indicate that the hydration H2O−H2O HBs are not affected much by the ligand length (see Table 1). As shown in Figure 8a, the SHB(t) and CHB(t) curves of hydration H2O−SAM HBs (including both H2O−NH3+ and H2O−COO− HBs) in the C12 systems decay much slower than those of bulk H2O−H2O HBs. Similar phenomena can be also observed for the C6 systems in Figure S9 of the Supporting Information. Then, we can see from Table 3 that the τHB S values of H2O−SAM HBs are in the range between 0.84 and 0.93 ps in both the C12 and the C6 systems, which are approximately 3 times greater than those τHB S of hydration H2O−H2O HBs in region 1 (see Table 1). Meanwhile, the corresponding τHB C values are from 19.3 to 24.1 ps, which are more than 4 times greater than those τHB C of H2O−H2O HBs in region 1. Such strong H2O−NH3+ and H2O−COO− HBs can obviously restrict the translational and rotational motions of hydration water molecules in region 1, as shown in Figures 3 and 4. However, it should be noted that, like the structure and dynamics of hydration water, the ligand composition also has a little influence on the hydration H2O−H2O HBs and H2O− HB SAM HBs so that their τHB S and τC values are comparable with each other in different compositions as shown in Tables 1 and 3. To further analyze the H2O−SAM HBs, the SHB(t) and CHB(t) curves of H2O−NH3+ and H2O−COO− HBs in three compositions of the C12 systems are illustrated in Figure 8b−d, and τHB and the corresponding τHB S C values are also listed in Table 3. By comparison, we can find from Table 3 that the strength of H2O−NH3+ HBs is always comparable with that of H2O−COO− HBs in different ligand compositions and lengths. Hence, the variation of ligand composition has a little influence on the solvation structures and the translational and rotational motions of hydration water molecules around the mixed MPAN, as shown in Figures 1, 3, and 4. 3.3. Far-IR Spectra of Hydration Water Molecules. Experimentally, the IR spectroscopy is one of the most powerful techniques to characterize the relevant HBs of hydration water molecules at different interfaces,21,27,51 which can be also obtained from MD simulations by the Fourier transformation of the velocity autocorrelation function (VACF) of hydration water molecules. The presence of mixed MPAN affects not only the translational and rotational motions of hydration water molecules but also the HB dynamics and vibrational spectra.48,55−57 In this section, we turn our attention to the vibrational spectra in far-IR region of hydration water molecules around the mixed MPANs. First, the normalized VACF can be defined as56−58,79

should be emphasized that the presence of HBs are defined in terms of the following distance and angular criteria76−78 R XY < RcXY

and

θ XYH < θcXYH

(8)

where X is the atom of HB acceptor and Y is the non-hydrogen atom of HB donor. RXY is the distance of X and Y atoms, while XY θXYH is the X···Y−H angle. Accordingly, RXY c and θc are the upper limit distance and angle of HB formation, respectively. In + − this work, the RXY c values of H2O−NH3 , H2O−COO , and H2O−H2O HBs are 3.5, 3.5, and 3.5 Å, which are obtained from the first minimum of the corresponding radial distribution functions,43 and the θXY c value is always fixed at 30° for all HB types.42 Besides the H2O−H2O HBs of bulk water, the calculated SHB(t) and CHB(t) curves for the H2O−H2O HBs of hydration water molecules in regions 1 and 2 of the C12 systems are shown in Figure 7a,b. Unexpectedly, we can see from the insets of this figure that the SHB(t) curves of hydration water molecules in both regions 1 and 2 are consistent with that of bulk water. And, the calculated τSHB of hydration water molecules values are almost identical to the τHB S = 0.29 ps of bulk water, as shown in Table 1. Nevertheless, Figure 7a,b

Figure 7. Intermittent TCF CHB(t) for the H2O−H2O HBs around the mixed MPAN: (a) region 1 and (b) region 2 of the C12 system and (c) region 1 of the C6 system. The inset shows the corresponding continuous TCF SHB(t). For comparison, the functions CHB(t) and SHB(t) for the bulk water are also shown.

Cv(t ) = 1775

⟨vi⃗(0)vi⃗(t )⟩ ⟨vi⃗(0)vi⃗(0)⟩

(9) DOI: 10.1021/jp506875m J. Phys. Chem. C 2015, 119, 1768−1781

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Figure 8. (a) Intermittent TCF CHB(t) for hydration H2O−SAM HBs (including both H2O−NH3+ and H2O−COO− HBs) of the C12 systems. For comparison, the results for the bulk water are also shown. Meanwhile, the intermittent TCF CHB(t) for individual H2O−NH3+ and H2O−COO− HBs in three compositions: (b) x = 0.25, (c) x = 0.50, and (d) x = 0.75. The insets show the corresponding continuous TCF SHB(t).

Table 3. Structural Relaxation Time τHB C and Average − + Lifetime τHB S of H2O−SAM, H2O−NH3 , and H2O−COO HBs at the Interface of Mixed MPANs for the C12 and C6 Systems types

compositions

τHB C (ps) (C12)

x x x x x x x x x x x x

τHB S (ps) (C12)

τHB C (ps) (C6)

τHB S (ps) (C6)

= = = = = = = = = = = =

0.25 0.50 0.75 0.25 0.50 0.75 0.25 0.50 0.75 0.25 0.50 0.75

H2O− SAM

H2O− NH3+

H2O− COO−

24.0 21.8 24.1 0.88 0.93 0.88 19.3 20.8 20.3 0.92 0.86 0.84

21.3 18.8 19.7 0.89 0.91 0.88 17.4 16.7 15.5 0.93 0.85 0.90

20.0 23.1 22.1 0.91 1.00 0.99 20.2 20.5 20.0 0.87 0.85 0.78

almost exhibit identical behavior among themselves, which is a direct consequence of that the strength of H2O−NH3+ HBs is comparable with that of the H2O−COO− HBs. Nevertheless, their minima of COv (t) curves are obviously deeper than that for bulk water, suggesting enhanced rigidity of the hydration water layer in region 1 of the C12 systems. For the C6 systems, all SAM compositions display the same behavior as those of the C12 systems, as shown in Figure S10 of the Supporting Information. Similar patterns of the COv (t) curves can be also observed for the water molecules around the protein and the DNA molecules due to the strong interaction between protein (or DNA) and water moelcules.56,57 On the other hand, we can see from Figure 9b that the COv (t) curves in region 2 of the C12 systems are closer to that of bulk water only with subtle differences. This is because the hydration water molecules in region 2 are far away from the terminal groups of SAM so that their behavior is closer to that of bulk water compared to the hydration water molecules in region 1. Such behavior of hydration water molecules can be further supported by the analysis of CHv (t) curves (see Figure 9c,d). The corresponding far-IR spectra in the 0−1000 cm−1 range calculated by the Fourier cosine transformation of VACF are shown in Figures 10 and 11. As shown in Figure 10a,b, the farIR spectra SO(ω) of the C12 systems are obtained from the VACF of O atoms (hydration water molecules in regions 1 and 2). As shown in Figure 10a, we can observe a considerable blueshift in the frequency of O···O···O bending mode (i.e., transverse oscillations arising from triplets of hydrogen-bonded water molecules) of hydration water molecules in region 1 by about 25−30 cm−1 compared to around 50 cm−1 of bulk value,56,57 which confirms a significant increase in the rigidity of hydration water molecules in region 1. Meanwhile, the intensity of SO(ω) at ω = 0 can provide a measure of the diffusion coefficient of water molecules. Then, we can see from Figure 10a that the zero-frequency intensities for hydration water

where vi⃗ (t) is the velocity of atom of type i (H atom or O atom of water molecule in defined regions) at the time of t. The angular brackets denote that averaging is carried out over all atoms of the particular type at different reference initial times. Then, the far-IR vibrational density of states (VDOS) S(ω) can be calculated routinely by the Fourier cosine transformation of VACF38,56,58 S(ω) =

∫0

∝

Cv(t ) cos ωt dt

(10)

COv (t)

The calculated VACF of the oxygen and hydrogen CHv (t) atoms of the hydration water molecules in the C12 systems are shown in Figure 9. For different ligand compositions of the C12 systems, we can see from Figure 9a that the COv (t) curves of hydration water molecules in region 1 1776


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Figure 9. Velocity autocorrelation function for the oxygen atom of water molecules (COv (t)) in (a) region 1 and (b) region 2 of the C12 systems as well as the corresponding hydrogen atom (CHv (t)) in (c) region 1 and (d) region 2 of the C12 systems. For comparison, the results for the bulk water are also shown.

Figure 10. Far-IR spectra in the 0−1000 cm−1 range for the oxygen atom of water molecules (SO(ω)) in (a) region 1 and (b) region 2 of the C12 systems as well as the corresponding hydrogen atom (SH(ω)) in (c) region 1 and (d) region 2 of the C12 systems. For comparison, the results for the bulk water are also shown.

molecules in region 1 of the C12 systems are lower than that of bulk water, suggesting the restricted translational motions of hydration water molecules. By comparison with Figure 11a, furthermore, we can find that the zero-frequency intensities in region 1 of the C6 systems are considerable lower than those of the C12 systems, suggesting that decreasing the ligand length can further restrict the translational motions of water molecules

in region 1, as discussed in Figure 3. Similar phenomena have been observed for the hydration water molecules at the interface of reverse micelles, 55 protein,56,57 and DNA molecules.80 The other O···O stretching mode arises from the longitudinal oscillations between pairs of HB water molecules, which is observed unclearly and seems to be unaffected by the mixed MPANs. In other words, the transverse 1777


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hydration water molecules around the mixed MPANs by using classical MD simulations. Various mixed MPANs [Au140(SH(CH2)n(NH3+)x(COO−)1−x)62] (n = 12 and 6, x = 0.25, 0.50, and 0.75) with Na+ (or Cl−) counterions are considered here. Our simulations show that both the translational and the rotational motions of hydration water molecules around the mixed MPANs are suppressed considerably with respect to the bulk water, especially in the proximity of charged terminal NH3+ and COO− groups of ligands. Meanwhile, the structural relaxation times of hydration H2O−H2O HBs are much longer than the bulk value. By comparison, we further find the structural relaxation times of H2O−SAM HBs (including the H2O−NH3+ and the H2O−COO− HBs) are about 4 times greater than those of hydration H2O−H2O HBs. Such strong H2O−SAM HBs significantly restrict the dynamics and HBs of hydration water molecules around the mixed MPANs. Accordingly, the frequency of O···O···O bending mode in the far-IR spectra of O atoms SO(ω) has a blue-shift of 25−30 cm−1 for hydration water molecules in the proximity of terminal NH3+ and COO− groups with respect to that of bulk water, which agree with the slowdown of translational mobility of these hydration water molecules. In addition, their far-IR spectra of H atoms SH(ω) illustrate that a more blue-shift of 100−150 cm−1 can be observed for the HB librational motions between hydration water molecules, which is well consistent with the restricted rotational motions and the enhanced H2O− H2O HBs of water molecules in the proximity of terminal NH3+ and COO− groups. More importantly, our simulations reveal that the ligand length can control the morphology in water of mixed SAMs on the Au core due to the hydrophobic interaction between alkane chains and water molecules, where the spherical and uniform distribution is found for the SAMs with short ligands (i.e., the C6 systems) while two large ligand bundles can be found for long ligands (i.e., the C12 systems). Meanwhile, decreasing ligand length can result in an increase of charge density at the interface so that stronger electrostatic interactions can significantly restrict the translational motions of hydration water molecules. Furthermore, our comparison results confirm that the rotational relaxation of hydration water molecules should be dominated by the local and directional HBs at the interfaces, rather than the previous explanation of the ratio between hydrophobic/hydrophilic exposed regions.75 Through a detailed analysis of both continuous and intermittent dynamics of H2O−NH3+ and H2O−COO− HBs at different ligand compositions and length, we find that the ligand composition of terminal NH3+ and COO− groups has a little influence on the structure, dynamics, HBs, and vibrational spectra of hydration water molecules around the mixed MPANs mainly due to the comparable strength between H2O−NH3+ and H2O−COO− HBs. In this work, detailed structures, dynamics, HBs, and far-IR spectra of hydration water molecules studied at a molecular level can be of great benefit for experimental scientists to understand the unique behavior of hydration water molecules around various mixed MPANs as well as biomolecules.

Figure 11. Far-IR spectra in the 0−1000 cm−1 range for (a) the oxygen atom and (b) the hydrogen atom (SH(ω)) of water molecules (SO(ω)) in region 1 of the C6 systems. For comparison, the results for the bulk water are also shown.

and longitudinal degrees of freedom of hydration water molecules around the mixed MPAN are not affected in a uniform manner. On the other hand, the far-IR spectra SH(ω) from the VACF of H atoms (hydration water molecules) are shown in Figure 10c,d. For the bulk water, the HB librational motions between water molecules can be characterized from the peak around 500 cm−1 of SH(ω).56,81,82 As shown in Figure 10c, a more considerable blue-shift (about 100−150 cm−1) can be observed for the hydration water molecules in region 1 of the C12 systems with respect to the bulk value. Such large blue-shift means clearly the enhanced H2O−H2O HBs in the proximity of terminal NH3+ and COO− groups, which agrees well with the longer structural relaxation time discussed in Figure 7. However, whether for the C12 or C6 systems, the far-IR spectra of SO(ω) and SH(ω) show the same vibrational modes for different ligand compositions due to the comparable strength of H2O−NH3+ and H2O−COO− HBs. Similarly, recent experimental observations showed that the citratecapped Au nanoparticles with the SAM consisting of the SH(CH2)10(NH3+)x(SO3−)1−x ligands exhibit identical UV−vis spectra in different mixing ratios.34 By comparing Figure 10 with Figure 11, similar blue-shifts with comparable magnitude can be also found for the far-IR spectra SO(ω) and SH(ω) of the C6 systems, indicating that the ligand length also has a little influence on the far-IR spectra of hydration water molecules around the mixed MPANs.

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ASSOCIATED CONTENT

* Supporting Information S

(1) Lennard−Jones parameters and partial atomic charges used in this work; (2) the distribution of NH3+ and COO− terminal groups on the surface of Au core; (3) normal angle distribution of the ligands of mixed C12 and C6MPANs in vacuum; (4)

4. CONCLUSIONS In this work, we have systematically investigated the structure and dynamics properties, HB dynamics and far-IR spectra of 1778


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illustration of regions 1 and 2 defined here; (5) comparison details of MSD curves in region 2 with different definitions; (6) rotational TCFs (l = 1) of hydration water molecules in regions 1 and 2 of the C12 systems; (7) rotational TCFs (l = 1 and 2) of hydration water molecules of the C6 systems; (8) comparison in the TCFs for H2O−NH3+ and H2O−COO− HBs of the C6 systems; (9) velocity autocorrelation functions of hydration water molecules in the C6 systems. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Authors

*E-mail [email protected] (Z.Y.). *E-mail [email protected] (X.S.C.). Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS This work was supported by the Natural Science Foundation of China (Nos. 21306070 and 21463011), National High Technology Research and Development Program of China (No. 2012AA03A609), Key Technology R&D Program of Jiangxi Province (No. 20114ACB01200), and Science and Technology Project of Universities in Jiangxi Province (No. KJLD12005). We are very grateful to Professor Shuhua Li (Nanjing University) for providing the supercomputers at Institute of Theoretical and Computational Chemistry, Nanjing University, China.

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