Aqueous hydroxyl group as the vibrational probe to access the hydrophobicity of amide derivatives

Journal Pre-proof Aqueous hydroxyl group as the vibrational probe to access the hydrophobicity of amide derivatives

Sohag Biswas, Bhabani S. Mallik PII:

S0167-7322(19)34650-1

DOI:

https://doi.org/10.1016/j.molliq.2019.112395

Reference:

MOLLIQ 112395

To appear in:

Journal of Molecular Liquids

Received date:

19 August 2019

Revised date:

28 November 2019

Accepted date:

24 December 2019

Please cite this article as: S. Biswas and B.S. Mallik, Aqueous hydroxyl group as the vibrational probe to access the hydrophobicity of amide derivatives, Journal of Molecular Liquids(2018), https://doi.org/10.1016/j.molliq.2019.112395

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© 2018 Published by Elsevier.

Journal Pre-proof

Aqueous Hydroxyl Group as the Vibrational Probe to Access the Hydrophobicity of Amide Derivatives Sohag Biswas and Bhabani S. Mallik* Department of Chemistry, Indian Institute of Technology Hyderabad, Kandi-502285, Sangareddy, Telangana, India

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Abstract: First principles molecular dynamics (FPMD) simulations of relatively dilute aqueous solutions of N-methylformamide (NMF), N, N-dimethylacetamide (DMA), N-methylacetamide (NMA) were carried out to elucidate the effects of variation of hydrophobicity of amide molecules on structure, dynamics and spectral properties of solvating water molecules. A quantitative analysis of dangling OH groups of water molecules, one of the consequences of hydrophobicity, around the amide molecules was performed to explore the structure of surrounding water molecules. We observe that DMA has the most hydrophobic character among the three amide molecules; the lifetime of dangling OH mode of water molecules and the number of such modes are found to be more inside the solvation shell of DMA as compared to NMA and NMF molecules. Overall this lifetime is more inside the solvation shell of amides compared to the bulk water molecules for all aqueous solutions of amides. Rotational dynamics calculation suggests significant retardation of OH bonds of water near the amide oxygen atom (O) due to the Ow-Hw…O strong hydrogen bonds. A moderate slowdown of reorientational dynamics is also observed for OH modes that are close to the hydrophobic surface of DMA in its aqueous solution. Vibrational density of states (VDOS) and frequency distribution calculations point out the higher average stretching frequency (~3600-3850 cm-1) of free OH groups. Hydrogen bond lifetime calculations conceive that DMA, having three methyl groups, makes stronger hydrogen bonds through the C=O moiety. Vibrational spectral diffusion of bulk water and solvation shell water molecules were also calculated in combination with wavelet transform and frequency-frequency autocorrelation functions. The C=O group affected OH stretching frequency bands for aqueous solutions of NMF, and NMA molecules are more pronounced than that of DMA. However, N-H affected OH frequency bands are less pronounced for NMA and DMA due to the presence of more number of hydrophobic methyl groups. Going from NMF to DMA, the OH frequency bands inside the amide solvation shells shift towards the higher value due to the enhancement of hydrophobicity. The vibrational spectral diffusion of OH modes around C=O and N-H (N for DMA) groups, as well as for bulk water molecules, are also investigated. Three time scales were found for these calculations for all the cases. The fast time scales in the range ~50-100 fs are due to the amide-water intact hydrogen bonding, and two slower time scales in the range ~0.6-3.90 ps and ~10 - 20 ps were found. The time scales in the range of ~0.6 to 3.90 ps can be attributed to carbonyl-water and NH-water hydrogen bonding, and the very long time scales are due to the escape dynamics water molecules from the solvation shell of C=O and N-H (N for DMA) groups. Keywords: N-methylformamide; N, N-dimethylacetamide; N-methylacetamide; First principles molecular dynamics; Hydrophobicity; Ultrafast spectroscopy

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Introduction The peptide unit, the primary structural part of the proteins, is responsible for the biological and chemical activities of the living cells in aqueous environments. The interactions between amides and water molecules provide a simplified model of the peptide bond via C-N linkage between C=O and N-H units. Hydrophobic groups of the amide molecules play a major role in these interactions. Moreover, the stability of the structure can be affected by the interactions between hydrophobic side chains within alpha-helix.[1,2] The hydrophobicity of the peptide C=O…H-N group also determines the structure of

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aqueous proteins and biological membranes.[3] The hydrophobic amino acids with high helical

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propensity can form polypeptides bearing an alpha-helical conformation.[4–6] Here, we report the effects of the methyl groups that differ in the number and positions on the interaction of water molecules with

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three simple amide molecules: NMF, DMA, and NMA. Due to the variation of a number of the hydrophobic groups, these amide molecules show different extent of hydrophobicity in the presence of

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water molecules. Both NMF and NMA molecules have one hydrogen donor site and one acceptor site, but on the other hand, DMA has only one hydrogen bond acceptor site. Therefore, liquid NMF and NMA

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exhibit intermolecular hydrogen bonding.; they are known as the protic solvents. DMA is known as an aprotic solvent as it has no hydrogen donor site. However, in aqueous solutions, all three amide molecules

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can form intermolecular hydrogen bonding with the surrounding water molecules; amide molecules mainly form C=O…Hw and N-H…Ow hydrogen bonds. Therefore, amide-water hydrogen bonding and

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fundamental vibration associated with it were often used in both experimental and computational studies to explore the secondary structure of proteins.[7–14]

Recently, NMA[15] has been chosen for

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mimicking the intrinsically disordered proteins (IDPs)[16–18], which are mainly characterized by a simple sequence of peptide unit, the strength of hydrogen bonding interaction and less hindered side chain. The amide molecules are not only used as a model of the peptide bond but also used as a solvent in chemical synthesis and artificial fiber production industries.[19,20] Anomalies have been observed in physical and chemical properties like density, viscosity, molar volume, surface tension, and 1H NMR chemical shift in 33% mole fractions of amides[21–23] in aqueous solutions; the intermolecular amidewater hydrogen bonding is one of the reasons for these anomalies. NMF was used in sonodynamic therapy for producing CH2R-type radicals to treat the tumor cell.[24,25] The structure of the molecule was studied in both liquid and gas phases by various experimental techniques such as NMR,[26] X-ray diffraction study,[27–31] IR spectroscopy,[32] electron diffraction,[33] Neutron diffraction,[34] synchrotron radiation[35] and by computer simulations.[36–43] One of the X-ray scattering studies of liquid NMF suggested an intermolecular hydrogen bonding between two trans isomers via C=O and N-H

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Journal Pre-proof moieties.[28] Moreover, the gas-phase structure of NMF molecule has also been studied theoretically.[44–47] A good amount of effort has been devoted by both theoretically[48–51] and experimentally[52,53] to study the NMF-water interactions in the aqueous phase. Nasr et al.[52] reported the NMF-water hydrogen-bonding interactions with the help of X-ray scattering and DFT calculations in aqueous solution. They reported that NMF molecule was associated with water through C=O…Hw and NH…Ow hydrogen bonds and this molecule participated in three hydrogen bonding interactions: two via C=O moiety, and the other one through N-H moiety. The theoretical studies by Corderio et al.[41] and Mu et al.[48] also suggested a similar kind of hydrogen bonding interactions between NMF and water. Wang et al.[51] performed computational calculations to explore the strong NMF-water along with the

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weak O=C-H…Ow hydrogen bonding interactions in the gas phase. Soper et al.[34] also observed weak

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C-H…O hydrogen bonds in liquid NMF with the help of neutron scattering technique, and this type of weak interaction provided stability to the chain type structure of NMF. Zaichikov et al.[50] reported

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several water molecules attracted by NMF at water-rich regions. On the other hand, NMA has been studied extensively by using vibrational spectroscopy to capture the amide I, amide II and amide III

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bands.[54–60] The theoretical calculations including classical molecular dynamics and ab initio molecular dynamics suggested the existence of three hydrogen bonds between NMA and H2O

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molecules.[38,61–65] Yang et al. applied QM/MM molecular dynamics simulations to calculate the IR spectrum of NMA and deuterated NMA in aqueous media.[66] Markus et al.[67] calculated two-

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dimensional IR spectrum of NMA in water. Another line of effort has been attempted to get insight into the frequency shift of the amide I band in NMA-water cluster with the help of ab initio molecular

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dynamics simulations.[68,69] The obtained full width at half maximum (FWHM) of the frequency distribution was found to be closer to the experimental values of amide I band.[57,59] A classical

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molecular dynamics simulation was performed by Iuchi et al.[70] by using polarizable five-site water model to compute the IR and Raman spectra of liquid water along with amide bands ranging from I-VII modes. In DMA molecule, all the hydrogen atoms in formamide skeleton are replaced by methyl groups, and hence DMA has only one oxygen atom, which acts as a hydrogen bond acceptor. The lone pair of the nitrogen atom in DMA is completely shielded by two methyl groups. Therefore, it is expected that in aqueous solution its behavior will be more like N, N-dimethylformamide. The DMA/LiCl in water is being used as a common cellulose solvent in which Li+ cation is solvated by DMA molecules.[71,72] In most of the cases, all the chemical, and biochemical phenomena related to the amide-water system are governed by the solute-solvent hydrogen bonding interactions. Both the molecular dynamics and the IR spectroscopy experiment pointed out that the response frequencies of amide I and amide II vibration were susceptible to the local hydrogen bonding environment.[57,68,73–76] A combined experimental and theoretical study suggested that in aqueous solution, the hydrophobicity of substituted amide molecule

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Journal Pre-proof depends upon the number of methyl groups present in it.[77] The dynamics of water molecules next to the hydrophobic surface has been drawn much attention due to the elusive nature in dynamical behavior.[78– 83] Not only this, the hydrophobic hydration plays a vital role in many fundamental biochemical phenomena such as protein folding, micelles formation, surfactant aggregation, and gas clathrates.[84–89] A time-resolved experiment by Rezus et al. concluded that 2 to 4 water molecules were immobilized by methyl groups in aqueous amphiphile solutions.[90] Their dynamical results directly supported the iceberg structure[91–94] of water molecules but faced a serious disagreement with the NMR[95–99] and classical MD simulations.[100,101] Later Laage et al.[78] reported that the retardation dynamics were due to the lack of hydrogen bond exchange partners near the methyl groups. Since the moderate

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amphiphiles like TMAO,[78,102] neopentanol,[83] tertiary-butyl-alcohol[103] molecules expose a

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hydrophobic surface in aqueous solutions; however, the observing a hydrophobic surface in substituted amide molecules in aqueous solution is not much clear yet. A recent FTIR and theoretical study of

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different amides in HDO revealed that amide derivatives might show the hydrophobic character in aqueous solution.[77]

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In the present work, we carried out first principles molecular dynamics simulations along with wavelet transformation to calculate various structural, dynamical and spectral properties to understand the

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nature of hydrophobicity induced by these three amides in the presence of solvation shell water molecules. The impact of methyl groups was also studied on both the hydrophobic and hydrophilic

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interactions along with the spectral diffusion of solvation shell and bulk water molecules.

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Computational Methods

The first principles molecular dynamics (FPMD) simulations were carried out with CP2K[104,105]

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program package using the Quickstep (QS)[106–108] module, where the electronic structure was calculated by utilizing the BLYP[109–111] exchange-correlation function coupled with Grimme’s D3[112,113] dispersion correction. A triple zeta valence potential (TZV2P)[114] basis set with p and dtype polarization functions together with Godecker-Teter-Hutter (GTH) pseudopotentials was applied. A time step of 0.5 fs was used for each system, and the value of density cut-off was taken as 600 Ry for Gaussian plane wave. The temperature was kept at 300 K, and periodic boundary conditions were applied in all XYZ directions. Each solution contains a single amide molecule and 100 H2O molecules. In this study, we considered trans isomer of NMF[115,116] and NMA[117] molecules because of the greater stability over cis isomer. The initial configurations for FPMD simulations were generated from force fields based on classical molecular dynamics simulations by using AMBER[118] simulation package. For the force field-based molecular dynamics, we used SPC/E[119] and GAFF[120,121] force fields for water and amide molecules, respectively. Before taking the starting geometry for first principles, each system

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Journal Pre-proof was sufficiently equilibrated during force field-based MD. The equilibrated density for the simulation box was determined from the FPMD simulations of 15 ps within the NpT ensemble. The size of simulation boxes for NMF-H2O, NMA-H2O, and DMA-H2O were 14.56, 14.60, and 14.63 Å, respectively, which lead to the density of each system approximately 1.0 gm cm-3. After that, each system was simulated at NVT ensemble for 50 ps followed by another 50 ps simulation at NVE ensemble for calculating the desirable properties. We performed the FPMD simulations in the isobaric-isothermal ensemble where massive Nose-Hoover thermostats[122] were used to control the temperature. The pressure was controlled by the barostat suggested by Mundy and co-workers.[123]

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We calculated the instantaneous stretching of OH bonds of water molecules using the wavelet

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method[124] by following mother wavelet:

(1)

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In this equation, the parameter, a, is related to a frequency that determines the window scale. The other

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parameter, b, depicts the shifting of the window used for the calculations of the frequency. Using the time-dependent trajectories obtained from FPMD simulations, we define a time-dependent function for

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the OH bond as f(t) that is a complex function: the real part is represented by OH distance, and the corresponding momentum depicts the imaginary part. The following Morlet-Grossmann function as the

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respectively.

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mother wavelet[125] is used for the analysis, where the values of parameters  and  are 1 and 2,

(2)

The details of the wavelet transform for frequency calculations are elaborated in these references.[126– 131]

Results and Discussion Hydrophilic Interactions: It is well known that C=O and N-H groups of amide molecules can form hydrogen bonds with water molecules, and these groups are responsible for hydrophilic interactions. We present various structural properties in Figure 1: O(amide)–Ow as well as O(amide)–Hw radial distribution

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Journal Pre-proof functions(RDFs), combined distribution functions (CDFs) including distance vs. angle as shown in inset models and spatial distributions which are described in detail in the figure caption. The values of number integral(NI) corresponding to RDFs are shown in Figure SI 1. Here, we use subscript ‘w’ for atoms of water molecules. The first peak positions of oxygen-oxygen RDFs are found to be same for all cases; O(NMA)–Ow interaction is stronger than the O(DMA)–Ow and O(NMF)–Ow RDFs due to its higher peak height and deeper first minima. The peak height for O(DMA)–Ow and O(NMF)–Ow RDFs are found to be almost the same, but the minima positions are shifted slightly towards the higher distance compared to the O(NMA)–Ow pair. The corresponding oxygen coordination numbers of C=O are found to be 2.8 and 3.16 Å for NMF and DMA, respectively. The first peak positions for O–Hw mediated hydrogen bonding for all

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amides are located around 1.8 Å, and the corresponding minima positions are found to be at 2.5 Å except

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for DMA (2.65 Å). The oxygen atom of each carbonyl group participates in approximately 2.5 hydrogen bonds with neighboring water molecules. In Figure SI 2, we present the H–Ow RDF due to hydrogen

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bonding interaction between the N-H group and the oxygen atom of water along with corresponding NI. In DMA, no hydrogen atom is attached to the nitrogen atom to participate in hydrogen bonding. The

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hydrogen bond number of N-H hydrogens are found to be less than one for NMA and NMF molecules.

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Hydrophobic Interactions: The hydrophobic hydration plays a significant role in many biochemical processes in aqueous solutions. In this context, we calculated RDFs between N-terminal methyl groups

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and water molecules and are shown in Figure SI 3. The peak positions of C–Ow RDFs for all amides are found to be at 3.7 Å. The first solvation shell structure for NMA and NMF around methyl carbon atom

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extends up to 5.03 Å. However, for C(DMA)-Ow, this RDF shows a minimum at 4.50 Å with a higher depth compared to C(NMA)–Ow and C(NMF)–Ow RDF pairs. This makes a difference in number of water

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molecules present inside the C–Ow solvation shells. Approximately, 11 water molecules are found inside C(DMA)–Ow solvation shell, while this number is higher(~15) for C(NMA)–Ow and C(NMF)–Ow. Blanco et al.[132] suggested the presence of a weak C-H…Ow hydrogen bonding interaction in the formamidewater complex. Later, Caminati et al.[133] also reported similar interactions in the NMF-water complex in the gas phase. In order to quantify this fact in an aqueous solution of NMF, we calculated the RDF between hydrogen attached to carbonyl carbon and Ow, and the result is shown in the bottom panel of Figure SI 3 as HC(NMF)-Ow RDF pair. No pronounced peak is found for conventional hydrogen bonding between carbonyl hydrogen and water oxygen atoms. However, we find a tiny hump at 2.00 Å (inset bottom panel), which may be due to the weak interaction between these two atoms.

Amide-Water Molecular Interactions: The amide-water structural correlation was studied by calculating the center of mass (COM) RDF between amide and water molecules, and results are shown in

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Journal Pre-proof Figure SI 4. For NMF-water, the peak is found at 4.0, followed by a minimum at 5.5 Å. The NMA-water COM RDF shows first maximum and minimum positions at 3.74 and 4.37 Å, respectively. The second minimum position is found to be at 5.15 Å. DMA-water shows a small peak at 4.27 followed by a minimum at 4.4 Å. The second broad peak is observed at 5.10 Å followed by a minimum at 5.90 Å. Two well-defined solvation shells are observed for NMA-water system due to its unique chemical structure. Havenith and coworkers[134–136] reported an extended hydration layer well beyond 5 Å for the biomolecular solutes in aqueous solutions with the help of Terahertz spectroscopy. The same cutoff distance was used to define the hydration layer of TMAO for studying the structural, dynamical and spectral properties.[102,137] A much higher cutoff value of 6.5 Å was used for neopentane[138] and

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neopentanol[83] solutions for hydrophobic hydration phenomena. Here, we are very much interested in

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hydrophobic hydration layers formed by these three amides, which have a difference in the number and position of methyl groups. In order to account for all the water molecules near the hydrophilic and

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hydrophobic groups, we used a larger cutoff value of 5.90 Å despite being smaller first solvation shell of NMA and DMA. It is found that a small hydrophobic molecule (methane) can easily fit into the water

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clathrate and to induce the hydrophobicity, a hydrophobic molecule requires a minimum 5.20 Å diameter (a good example is a neopentane molecule).[139] Therefore, choosing the solute-solvent intermolecular

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distance is very crucial to study the hydrophobicity.

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Combine and Spatial Distribution Functions (SDFs): For better understanding the hydrogen bonding and solvation layers of water molecule around the C=O

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groups of amides, we calculated two combine distribution functions (CDFs) and SDF of water within 5.90 Å from the center of mass amide molecules. These properties are shown in Figure 1. The CDF represents

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the combination of RDF and angular distribution function (ADF). Here, we consider two types of CDFs: O–Ow distance vs. O…Hw–Ow angle (panels A, B, and C) and O…Hw distance vs. O…Hw–Ow hydrogen bond angle (panels D, E, and F). The corresponding vectors and orientation of molecules are shown in the inset model for each amide molecule. We choose O–Ow as RDF (X-axis) and the angle between Ow–Hw and O–Hw vectors (Y-axis) for CDFs presented in panels A, B, and C. The most probable angle distributions due to amide-water hydrogen bonding via C=O group are in the range between 160 to 180 degree, and the preferred O–Ow distances that correspond to the first peak positions of O–Ow RDFs are found to be around 2.8 Å. The angle distribution of NMA-water is narrower compared to the NMF-water and DMA-water systems. Similarly, we also present the CDFs corresponding to O…Hw hydrogen bond distance, and the angle between Ow–Hw and O–Hw vectors in panels D, E and F. According to chosen orientation, the most probable angle and hydrogen bond distribution is found around 22 degrees and 1.9 Å, respectively. This indicates that the NMA-water hydrogen bonding interaction is more prominent as

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Journal Pre-proof compared to DMA-water and NMF-water. SDF represents the three-dimensional density around the particular group or atom of interest. Both the SDFs and CDFs were calculated by using TRAVIS[140] software package. From the SDFs, it is found that hydrogen cloud around the amide molecules remains mostly in the second solvation shell of the center of mass amide-water RDFs, and the hydrogen cloud around oxygen atom of NMA is denser compared to the NMF and DMA. It is also found that the peak height of O(NMA)–Hw RDF is more with a deeper minimum as compared to O(DMA)–Hw and O(NMF)– Hw pairs. The second and subsequent solvation shells are different for three amides. The secod solvation shell of NMF is prominent with appearance of second minimum in O–Ow RDF. NMA shows almost similar type of solvation structure as that of NMF; but, DMA shows little different.

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Thus, from the analysis of RDFs, SDFs, and CDFs, it is evident that NMA acts as a better

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hydrogen bond acceptor and donator. This fact is further explained by a gas phase optimization followed by electrostatic potential (ESP) and natural bond order (NBO) analysis. The ESP and NBO calculations

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were performed with Gaussian09 module[141] within BLYP/6-311+g(2d,p) level of electronic structure theory. The results for the ESP analysis and charges from the NBO calculations are shown in Figure SI 5,

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which represents the ESP mapping and charge density of amide oxygen and hydrogen atoms, respectively. From the NBO analysis, we find that the oxygen atom of NMA accumulates near more

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negative charge compared to the NMF oxygen atom, and hence it acts as a better proton acceptor. Although the negative charge on oxygen DMA molecule is more as compared to NMA, the first peak

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height for O(NMA)-Hw RDF is found to be more, which is due to the steric crowding in DMA molecules

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due to the presence of three methyl groups.

Dynamics of Dangling OH groups: The SDF figures reveal that the presence of the hydroxyl group

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around the methyl groups, which is not participating in any hydrogen bonding interaction. This group is instead known as dangling or free OH groups. In order to study the dynamics of these free OH groups of water molecules, an analysis is performed to calculate the lifetime of dangling OH bonds. More precisely, a time correlation function is constructed for dangling OH bonds of water, and it is written as

( )

The time average 〈

〈 ( ) ( )〉 〈 ( )〉

(3)

〉 is taken over all considered OH groups present either in the hydration shell or in

the bulk water. The radius of the hydration shell is determined from the center of mass RDF between amide and water molecules. Here, d(t) is unity when a particular OH bond is in non-hydrogen bonded or free or dangling state at time t according to the adopted definition and zero otherwise. D(t) = 1, when a particular OH group remains continuously in the same state, otherwise zero. Therefore, SDH(t) represents

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Journal Pre-proof the conditional probability that OH groups remain continuously free that were initially identified as dangling at a time t, and the time constant associated with it is known as the lifetime of dangling OH groups before obtaining a hydrogen-bonded partner. The results of dangling OH correlation for solvation shell and bulk water molecules are represented in Figure 2 for all the systems. The lifetime of dangling OH groups within a 5.90 Å radius from the center of mass of DMA is found to be slightly higher compared to the outside water molecules. The same lifetime values for solvation shell and bulk OH modes are found to be 0.36 and 0.30 picoseconds (ps) for this system. Inside the first solvation shell of NMA, the dangling OH groups seem to be slightly longer-lived compared to the bulk water, and these values are 0.26 (solvation shell) and 0.23 (bulk) ps. For NMF water system, these two time scales occur

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in 0.28 (solvation shell) and 0.14 (bulk) ps time scales. Overall, in the DMA-water system, the lifetime of

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dangling OH groups is more due to the presence of three methyl groups, which make it more structure breaker or hydrophobic compared to NMA and NMF. The hydrophobic surface area for NMA and NMF

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is smaller than DMA due to less number of methyl groups. Thus lifetimes of the dangling OH bonds

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obtained for these two systems are shorter.

Hydrogen Bond Dynamics: In this section, now we look at the dynamics of hydrogen bonds in terms of

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water-water and amide-water hydrogen bond correlation functions. We used a well-known population correlation function[142–149] for the purpose. In this approach, we defined two variables H(t) and h(t),

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which are used to define the hydrogen bond correlation function. The variable h(t) is unity when a particular water-water or amide-water pair is hydrogen-bonded at time t, otherwise zero. The other variable H(t) = 1 if the water-water or amide-water pair remains continuously hydrogen-bonded from

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time t = 0 to t and it is zero, otherwise. With the help of this assumption, we calculated continuous

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hydrogen bond correlation function for intermolecular Ow…Hw, O…Hw and H…Ow pairs and this correlation function can be presented mathematically as

( )

In the above equation 〈

〈 ( ) ( )〉 〈 ( ) 〉

(4)

〉 indicates the average overall amide-water or water-water pairs in the three

amide-water systems. Therefore, SHB(t) represents the probability of hydrogen bond that was initially hydrogen-bonded remains in the same state up to time t. The integration of the correlation function gives the hydrogen bond lifetime. The hydrogen bond autocorrelation functions are shown in Figure 3. In the present case, we used the distance criterion for calculating the hydrogen bond autocorrelation function. Ow-Hw hydrogen bond autocorrelation function decays faster for the DMA-water system compared to the NMA-water and NMF-water systems. The hydrogen bond lifetime of Ow-Hw pair is found to be 0.90 ps in

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Journal Pre-proof an aqueous solution of DMA, and for NMA-water and NMF-water systems, these values are 1.30 and 1.34 ps, respectively. The faster relaxation of the correlation function of Ow-Hw hydrogen-bonding partner in DMA-water system is due to the presence of three methyl groups, which accelerate the dynamics of the water molecule. Therefore, water molecules undergo faster breaking and making of hydrogen bonds within themselves in DMA-water system. The slower hydrogen bond dynamics are observed in DMAwater for O…Hw hydrogen bonding partner, and the lifetime value is found to be 4.45 ps, which is almost two-fold higher than that of the NMA-water and NMF-water systems. The lifetimes of carbonyl oxygenwater hydrogen bonds for NMA-water and NMF-water systems are found to be very similar, and these values are 2.90 and 2.93 ps, respectively. The H…Ow hydrogen-bonding partner in NMF-water solution

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possesses a slightly higher hydrogen bond lifetime value compared to the NMA-water solution. The hydrogen bond lifetimes for this kind of pair H-Ow in NMA-water and NMF-water are found to be 0.70

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and 0.88 ps, respectively. Our reported values of hydrogen bond lifetime of O…Hw and H…Ow partners

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in NMA-water with BLYP-D3 functional are found to be similar compared to the earlier reported

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value.[65]

Vibrational Density of States: To study the frequency shift of OH vibrational frequency of water

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molecules inside and outside the amide solvation shell, we calculated the vibrational density of states (VDOS) of OH groups. The VDOS is the Fourier transform of the velocity-velocity autocorrelation

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function and can be expressed as

time 〈

〈

( )

( )〉

(5)

( ) represents the velocity of the hydrogen atom of OH bond at time t. The cutoff

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In this equation,

∫

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( )

was set to 1 picosecond in the present simulation studies for different amide-water systems.

〉 indicates the average overall OH groups present inside and outside the solvation shells of amides.

The calculated VDOS for OH groups inside and outside the solvation shell of amides are shown in Figure 4. The VDOS of the solvation shell OH groups exhibit peak centered around ~3400 cm-1; This peak is due to OH groups that are hydrogen-bonded to C=O group of amides. These peak centers are red-shifted compared to the peak center of bulk OH groups. The peaks centered at ~3470 cm-1 for NMF-water and NMA-water are due to the hydrogen bonding interaction between N-H moiety and water molecules. The blue shifting of these peak centers demonstrates that N-H…Ow hydrogen bonding interaction is weak. From the SDF figures, it is found that atomic density related to non-bonding hydrogen atoms are present around the methyl groups, which are primarily known as dangling or free and non-hydrogen bonded OH groups. The peak centered in the range ~3600-3700 cm-1 is due to these OH groups. The red shifting of

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Journal Pre-proof the strong hydrogen-bonded and the blue shifting of free OH stretching frequency are in line with the experimental results. For the NMA-water system, the strongly hydrogen-bonded, weakly hydrogenbonded, and non-hydrogen bonded OH frequency region is observed, which is due to the presence of methyl groups. The width of VDOS in solvation shell is broad though amide molecules make a stronger hydrogen bond with water, the presence of methyl groups makes structural inhomogeneity, which is also found in the center of mass radial distribution functions.

Vibrational Spectral Diffusion of Solvation Shell and Bulk OH modes of Water molecules:

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The time-indendent VDOS was calculated from velocity-velocity auto correlation function. We calculated

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the instantaneous time-dependent hydroxyl stretching frequencies from wavelet analysis of FPMD trajectories in the domain of only stretching frequency of hydroxyl groups of water molecules. We

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captured the vibrational spectral diffusion of water molecules inside and outside the solvation shells of C=O and N-H groups by calculating frequency-frequency time correlation function using the

( ) ( )〉 ( )

(6)

( ) is the fluctuation of frequency from its average frequency value at time t. From the RDFs, it

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Here,

〈

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( )

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instantaneous hydroxyl stretching frequencies , which can be defined as

is found that inside amide solvation shell, water molecules make a hydrogen bond with C=O and N-H

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moieties; therefore, vibrational spectral diffusion of water molecules inside the solvation shell reflects the hydrogen bond and escape dynamics of water molecules. The C=O solvation shell is defined by the O-Ow

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RDFs for amide-water systems, and hence the C=O solvation shell contains those OH modes, which are essentially present inside the cut of distances of O-Ow minima. The N-H solvation shells for NMA and NMF molecules are defined by the corresponding N-Ow RDFs. Since DMA molecule lacks the amide hydrogen, we defined nitrogen solvation shell by calculating N-Ow RDF. The N-Ow cut off distances for NMF, NMA, and DMA are taken as 5.90 Å. The frequency-frequency time correlation functions for the various solvation shells are shown in Figure 5. In order to extract the data from the normalized decays, we fitted the normalized decay with a tri-exponential function with dumped cosine term as follows

( )

(

)

(7)

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Journal Pre-proof The fitted parameters and various time constants are listed in Table 1. In the case of C=O solvation shell of all amides, we observed a fast decay with weak damping oscillation at a short time followed by two longer time scales, which lasted up to few picoseconds. The short time component is due to the hindered translational and rotational of carbonyl-water intact hydrogen bond, and two long time scales are due to the carbonyl-water hydrogen bond and escape dynamics of water molecules from C=O solvation shell. We also observe three time scales for water molecules of N-H solvation shells for NMF-water and NMAwater. The very short time scale here also is due to the intact N-H…Ow hydrogen bond and the short time scale, 0.60 (for NMF), and 0.61 (for NMA) can be compared with N-H…Ow hydrogen bond lifetime. The longer time scales are due to the escape dynamics of water molecules from the N-H hydration shell. For

of

DMA-water system, the correlation function of water molecules inside the nitrogen solvation shell decays

ro

faster compared to the N-H solvation of NMA and NMF; because water molecules are not hydrogenbonded to the N of DMA as it lacks the N-H hydrogen or weakly hydrogen-bonded with very less

-p

probability. High damping oscillation constant compared to the N-H solvation shell of water molecules of NMA and NMF, and shorter second-time scale ( ) value, 0.34 ps, indicates the presence of free OH

re

groups. Here, the longer time scale is due to the escape dynamics of water molecules from the nitrogen solvation shell. We have also calculated spectral diffusion data for bulk OH bonds, and the results are

lP

included in the same Table 1, and the correlation functions are shown in Figure SI 6. For bulk OH modes, we observe only two time scales due to water-water under damped intact hydrogen bonds and water-water

na

hydrogen bonding. The time scale for escape dynamics of the water molecule is absent when all the water molecules are considered for vibrational spectral diffusion calculation. In order to quantify the fact that

Jo

solvation shell.

ur

the longer time scales in each respective region, residence dynamics calculations were performed for each

Residence Dynamics of Water Molecules: In order to quantify the fact of longer time scale observed in frequency-frequency time correlation function of water molecules in C=O and N-H solvation shells (N for DMA) of amide molecules, we calculated residence dynamics correlation function of water molecules inside C=O and N-H (N for DMA) solvation shells separately. Here, we define the probability of water molecules that were in the hydration shell of the respective group of amide molecules at time t=0, remains continuously in the same hydration shell up to time t. Here, we have considered the first minima of O-Ow and N-Ow RDFs as the distance criteria to represent the hydration shell. The results concerning the decay of the residence dynamics are shown in Figures SI 7 (O-Ow) and SI 8 (N-Ow). The obtained time constant is the residence time of a water molecule from the corresponding solvation shell. The residence time for water molecules for DMA-water around C=O group is found to be more compared to the other two amide-water systems. The time constants for escape dynamics of water molecules from C=O solvation

12

Journal Pre-proof shell for DMA-water, NMA-water, and NMF-water systems are found to be 22.1, 15.6 and 14.5 ps, respectively, and these time scales can be compared with longer time scales obtained from spectral diffusion of water molecules inside C=O solvation shell. As it can be seen from the Figure SI 7, the residence correlation function of DMA inside N-Ow decays faster compared to NMA and NMF; it indicates that water molecules escape from the N-Ow solvation shell very fast due to the hydrophobicity of methyl groups. The time constant is also found to be short for DMA, and the residence time constants for water molecules inside N-Ow solvation shell are found to be 15.23, 17.30, and 5.32 ps for NMF, NMA, and DMA, respectively. These time constants can also be compared with spectral diffusion data of

of

longer time scales in N-H hydration shell.

ro

Distribution of Stretching Frequencies of OH Bonds of Water: For presenting the frequency distribution of OH bonds of water molecules, we categorized OH modes in two subgroups as bulk OH

-p

and solvation shell OH modes. The frequency distribution of solvation shell and bulk OH groups are shown in Figure 6 for NMF-water (a), NMA-water (b), and DMA-water (c) systems. The different cases

re

are observed for solvation shell OH vibrational frequency distribution for NMF-water and NMA-water systems. An asymmetric nature is observed in solvation shell OH frequency distribution for NMF-water

lP

and NMA-water, which are due to the multiple hydrogen bonding and hydrophobic interactions imposed by amide molecules. This asymmetric nature is less pronounced in DMA-water system; it is because the

na

lack of N-H group in DMA does not involve hydrogen bonding with surrounding water molecules. The peak center of OH frequency distribution inside DMA solvation shell is located at ~3525 cm-1 (Figure 6c).

ur

The solvation shell OH vibrational frequencies of DMA in the range of 3525-3800 cm-1 are mostly affected by three methyl groups of DMA. The asymmetry nature is more pronounced in solvation shell

Jo

OH frequency distribution of NMF (Figure 6a); particularly in the frequency region around 3450-3525 cm-1. For NMA-water system, this asymmetry nature solvation shell frequency distribution is found to be less compared to the NMF. The high asymmetry nature in NMF-water system indicates that N-H moiety of NMF molecule interacts relatively strongly with the neighboring water molecules, which cause asymmetry in solvation shell frequency distribution compared to the NMA. We show that N-H…Ow hydrogen bond of NMF-water possesses higher stability than the NMA-water system. This indicates that the probability of finding the number of free OH groups around the NMA molecule is more. The solvation shell OH frequency distribution of NMA is shown in Figure 6b. It is seen that C=O affected OH bands are well observed, but N-H affected OH bands are not well pronounced like NMF. The presence of more number of methyl groups hinders the strong N-H…Ow hydrogen bonding interaction, and on further progressing from NMA to DMA, the peak maximum of solvation shell OH frequency distribution shifts towards the higher frequency region. This is because from NMF to DMA, upon increasing the number of

13

Journal Pre-proof methyl groups, the average OH frequency also shifts towards the higher value. This is the indication of presence of more number of free OH groups in the solvation shell of amides going from NMF to DMA. Along with the solvation shell OH frequency distribution, we show the frequency distribution of bulk OH modes of water for each system. The pattern of the frequency distribution of bulk OH of water frequency is similar to the pure water frequency distribution pattern; it signifies that NMF molecule is easily acquired by the water cavity. On the other hand, for NMA-water and DMA-water systems, the shape of the OH frequency distribution peaks is broader compared to the NMF-water system. These results indicate that overall OH frequency distribution is affected by the NMA and DMA molecules and this is due to the bulkiness nature of NMA and DMA molecules. The average stretching frequencies of OH

of

modes of bulk water molecules are found to be 3442, 3434, and 3421 cm-1, respectively, for DMA-H2O,

ro

NMA-H2O, and NMF-H2O systems. In order to get quantitative information, we calculated the percentage of free OH modes inside the solvation shell of each amide molecule as compared to the total number of

-p

OH bonds. The free or dangling OH groups are defined by the free OH bond criterion which is discussed in the previous section. We find 66.5 % free OH groups inside the solvation shell of NMF, and these

re

values for NMA and DMA are 71% and 81%, respectively. Thus it can be said that the presence of more number of methyl groups in DMA causes the maximum percentage of free OH groups, which ultimately

lP

cause the blue shifting of OH modes in the solvation shell than NMF and NMA. As a result, it behaves more hydrophobic among these three amides. The NMA molecule falls under the borderline due to its

na

unique chemical structure, and NMF is the least hydrophobic. The higher frequency bands in the solvation shell of amide molecules are due to the weak N-H…Ow hydrogen bonding and strong

ur

hydrophobic interactions by methyl groups. The lower OH frequency bands are due to the very strong C=O…Hw hydrogen bonding interaction. The redshifting of hydrogen-bonded OH and the blue shifting of

Jo

weakly hydrogen-bonded OH or free OH frequency are in line with a general agreement with the experimental finding of aqueous solutions with low amide contents.[77,150]

Rotational Dynamics: Since we have an interest in elucidating the hydrophilicity and hydrophobicity of different amide molecules in this present study, we categorized all the OH groups in three groups geometrically, namely S1, S2, and S3. The ensemble S1 contains those OH groups of water molecules, which are hydrogen-bonded to the carbonyl group of amides. Hydrogen-bonded OH groups are separated based upon the position of minima of O-Hw RDFs. Ensemble S2 contains those OH groups that are close to the hydrophobic methyl groups, and these OH groups fall into the N-Ow solvation shell. We did not categorize separately those OH groups, which are hydrogen-bonded to the N-H groups of amides. Since N-H hydrogen of NMA and NMF makes a single hydrogen bond with water molecule on average and this N-H…Ow hydrogen bond is weak compared to the O…Hw and Ow…Hw hydrogen bonds. Ensemble S3

14

Journal Pre-proof contains the rest of the OH bonds of water molecules, which are outside the first solvation shell of amides; these OH groups are expected not to be influenced by the amide molecules. For illustration purposes, the OH modes belonging to S1, S2 and S3 ensembles around the one of the amide molecule, DMA, are shown in Figure 7. The rotational dynamics of water molecules are studied by calculating the second-order Legendre polynomial of OH vectors of water molecules and can be defined by

( )

(|

( ) ( )||

( ) )+ ( )|

(8)

indicates the OH vector of water molecules at time t, and ( )

Legendre polynomial in the form of

represents the second-order

of

where

*

( ⁄ )(

);

is the function of OH. Thus C2(t)

ro

represents the second-order rotational dynamics of OH modes, which can be correlated directly to the time-resolved IR experiments.[151] The calculated rotational dynamics of S1, S2 and S3 ensembles of

-p

OH modes are shown in Figure 8. The various time constant for rotational dynamics are shown in Table

re

2. Here, we used the bi-exponential function for fitting the rotational correlational functions and the longer time scales are reported here for rotational time constants. Our calculations suggest a significantly

lP

slower rotational dynamics of S1 OH groups compared to the S2 and S3 ensembles. This slowing down of OH rotational dynamics is due to the formation of strong O…Hw-Ow hydrogen bonds. However, the slowing down of rotational dynamics for DMA is more compared to the NMA and NMF molecules. The

na

hydrogen bond autocorrelation function of O…Hw pair also indicates higher hydrogen bond lifetime. Therefore, it can be concluded that incorporation of three methyl groups makes the DMA molecule strong

ur

structure maker through the C=O moiety, and this result directly reflects on the rotational dynamics of S1 OH groups. Moreover, the slowness phenomenon is in good agreement with the previously calculated

Jo

results of ab initio and forced field-based simulations of aqueous TMAO solutions.[102] For DMA-water system, The S2 OH groups show slower rotational dynamics compared to the bulk OH (S3) groups. This result implies that the moderate slowing down of rotational dynamics of water molecules near the hydrophobic surface. However, for NMA-water and NMF-water systems, the slowing down of OH groups near hydrophobic groups could not found, as it can be seen that rotational dynamics of S2 OH groups decay faster compared to the bulk OH groups, which is due to the presence of less number of methyl groups in these two amides. Therefore, DMA molecule behaves as a hydrophobic one due to more number of methyl groups as compared to other amides. Forced field[78,137] and ab initio[102] based molecular dynamics simulations of an aqueous TMAO solution also suggested slower orientational dynamics of OH groups near the hydrophobic surface. Laage et al.[78] illustrated that the moderate slowdown of the rotational dynamics of OH groups is mainly due to slower hydrogen bond exchange. Our

15

Journal Pre-proof calculated result of dangling OH lifetime also suggests a comparatively longer lifetime of dangling OH inside solvation shell of DMA than the bulk. Overall, a faster rotational dynamics are observed in S2 and S3 OH groups in DMA-water, and for NMF-water systems, water molecules are not perturbed by the methyl groups.

Conclusions In this paper, we present first principles molecular dynamics simulation studies including dangling OH as well as hydrogen bond dynamics, vibrational spectral diffusion, structural correlations of solute-solvent, and rotational dynamics in aqueous solutions of DMA, NMA, and NMF molecules. BLYP functional, in

of

combination with Grimme’s D3 dispersion corrections, was used for trajectory generation, and time series

ro

wavelet transformation was used for calculation of stretching frequencies of OH bonds. Our calculations suggest that the carbonyl oxygen of DMA molecule makes a stronger hydrogen bond with water

-p

molecules as compared to the carbonyl oxygen of NMA and NMF molecules. The overall carbonyl oxygen of amides molecule forms a stronger hydrogen bond than the N-H group with surrounding water

re

molecules. The various amide-water hydrophilic and hydrophobic interactions are explained with the help

lP

of RDFs, SDFs, CDFs, dangling OH correlation, hydrogen bond dynamics, and rotational dynamics. Our FPMD simulations predict a very slow rotational dynamics of S1 OH modes, which are hydrogen-bonded to the oxygen of amide molecules. The S2 OH groups in DMA-water solution show moderate retardation

na

of rotational dynamics compared to the bulk OH (S3) modes. This retardation is not observed for the other two aqueous amide molecules. The hydrophobic effect enhances the probability of finding dangling

ur

hydroxyl groups around a solute of consideration. As compared to lifetime of hydrogen bonded OH mode, the lifetime of dangling modes is more facilitated by hydrophobic group. The information we

Jo

obtain from the frequency distribution as well as frequency-frequency correlation data and the dynamics of the non-hydrogen bonded groups provides the extend of the effects of hydrophobicity on the nearby water molecules. The lifetime of dangling OH bonds in the first solvation shell of DMA is found to be more compared to NMA and NMF due to more hydrophobic. We also find a maximum number of dangling OH modes inside the solvation shell of DMA, and minimum number of dangling OH inside solvation shell of NMF. The C=O group affected OH stretching frequency bands for NMF-water and NMA-water are more pronounced than DMA-water, while N-H affected OH frequency bands are less pronounced for NMA and DMA molecules due to the presence of more number of hydrophobic methyl groups. Inside the amide solvation shell going from NMF to DMA, the OH frequency bands shift towards the higher value due to higher hydrophobicity. The bulk OH frequency distribution of NMF-water system is found to be similar to pure water, which indicates that the presence of single methyl group in NMF is unable to affect the overall frequency distribution pattern of water molecules. These facts indicate the

16

Journal Pre-proof stronger association of water through carbonyl moiety and weaker water association through N-H moiety. The similar conclusions are drawn from the hydrogen bond population correlation functions as the carbonyl-water hydrogen bond lifetime is found to be more compared to the water-water hydrogen bond lifetime. However, the N-H…H2O hydrogen bond lifetime is found to be less than that of the water-water hydrogen bond. The vibrational spectral diffusion of OH modes around C=O, N-H (N for DMA), and bulk was investigated through frequency-frequency correlation functions. Three time scales are found for these calculations of all the cases. The fast time scale in the range ~50-100 fs are due to the amide-water intact hydrogen bonding, and two slower time scales in the range ~0.6-3.90 ps and ~10 - 20 ps were found. The time scales in the range of ~0.6 to 3.90 ps can be attributed to carbonyl-water and N-H…Ow

of

hydrogen bonding. Moreover, the largest time scale is due to the escape dynamics of water molecules

ro

from the solvation shell of C=O and N-H (N for DMA) groups. These facts of getting very high time scales later are quantified by calculating the residence dynamics of water molecules inside the C=O and

-p

N-H (N for DMA) solvation shell. However, these longer time scales in the range ~10 to 20 ps are absent in vibrational spectral diffusion of bulk water molecules for all aqueous amide solutions. Our calculations

re

suggested that these three amide molecules show hydrophobicity; however, DMA is more hydrophobic due to its three methyl groups. NMA molecule falls in a borderline in the hydrophobicity scale due to its

lP

unique chemical structure.

Corresponding author

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Author information

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*Email: [email protected] , Phone no. +91 40 2301 7051

Acknowledgments

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Notes: The authors declare no competing financial interest.

The authors acknowledge the financial support from the Department of Science Technology (DST), Government of India (EMR/2016/004965).

17

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Table 1. Results of vibrational spectral diffusion obtained from frequency-frequency correlation functions of water molecules in the solvation shell of C=O, N-H (nitrogen for DMA) solvation shells, and bulk. Relaxation times are expressed in ps unit, and the damped oscillation frequencies are expressed in cm-1 unit

NMA-water

0.66 0.59 0.23 0.57 0.50 0.27 0.70 0.45 0.24

0.20 0.33 0.49 0.18 0.35 0.52 0.16 0.50 0.48

44.02 56.52 161.96 43.96 81.64 146.57 44.21 101.23 152.54

0.09 0.07 0.10 0.07 0.08 0.08 0.11 0.07 0.10

2.56 0.61 0.11 2.98 0.65 0.10 3.65 0.34 0.11

10.05 15.01 1.01 13.00 10.55 1.27 19.00 5.02 0.60

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DMA-water

Shell C=O N-H Bulk C=O N-H Bulk C=O N Bulk

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Quantity ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )

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S1 6.03 3.80 16.27

S2 3.48 2.35 1.52

S3 4.60 2.79 1.15

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Systems NMF-water NMA-water DMA-water

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Table 2. Time constants (in ps) for rotational dynamics of S1, S2 and S3 OH groups of water for all aqueous amide solutions

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Figure 1. Radial distribution functions (RDFs) of oxygen of amide with water oxygens (panels A, B, and C) and oxygen of amides with water hydrogens (panels D, E, and F). The panels A, B, and C also represent CDFs of NMF, DMA, and NMA, respectively, along with models showing distance and angle. The panels G, H, and I depict the spatial distribution functions of water around NMF, DMA, and NMA molecules, respectively. Red color represents the oxygen clouds, and yellow color represents the hydrogen cloud. The SDFs were calculated from 5.9 Å from the center of masses of amide molecules.

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Figure 2. The continuous autocorrelation functions for dangling OH modes of water molecules. Panel (a) depicts the dangling autocorrelation function for all OH modes present in the first solvation shell. Panel (b) presents the dangling autocorrelation function for the bulk OH modes of water molecules.

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Figure 3. The continuous hydrogen bond autocorrelation functions for Ow…Hw, O…Hw, and H…Ow hydrogen bonding partner for three aqueous solutions of amides.

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Figure 4. Vibrational density of states (VDOS) of OH modes of aqueous solutions of three amides. The black color represents the bulk OH modes, and the red color represents the first solvation shell of OH modes of water molecules. The panel (a) represents the NMF-water system, the panel (b) represents the NMA-water system, and the panel (c) represents DMA-water system, respectively. The first solvation shell is defined by the center of mass RDF between amide and water molecules.

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Figure 5. The time-dependent frequency-frequency correlation functions (FFCF) are shown in blue color for water molecules for the NMF-water (A and B), NMA-water (C and D), and DMA-water (E and F) systems. The panels A, C, and E represent the FFCF for C=O hydration shells, and the lower panels (B and D) represent the N-H hydration shells. The panel, F, represents the nitrogen solvation shell. The C=O and N-H or N hydration shells are defined by the corresponding O-Ow and N-Ow RDFs. The solid grey curves in all the figures represent the fitted data by equation 7.

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Figure 6. Stretching frequency distribution of various OH modes of water molecules. Panels (a), (b), and (c) represent NMF, NMA, and DMA systems, respectively. Red and green colors represent the solvation shell and bulk OH groups, respectively.

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Figure 7. Snapshot from the simulation of the DMA-water system represents the categorization of OH groups of water molecules. S1 represents the OH groups, which are hydrogen-bonded to the C=O group. S2 represents those OH groups, which are close to the methyl groups, and S3 represents the rest of the OH modes of water molecules.

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Figure 8. Rotational anisotropy decays of the S1 (red), S2 (green), and S3 (blue) OH groups of water molecules of all amide-water solutions. The panels a, b, and c represent the NMF-water, NMA-water, and DMA-water, respectively.

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Journal Pre-proof Author Contribution Sohag Biswas: Investigation, Formal analysis, Visualization, Validation, Writing - Original Draft

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Bhabani S. Mallik: Conceptualization, Methodology, Writing - Review & Editing, Supervision, Project administration, Funding acquisition

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Graphical Abstract

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Spectral signature of water molecules in the vicinity of three amide derivatives The dynamics of dangling OH bonds facilitate the hydrophobicity of amides The presence of hydrophobic methyl groups affect the spectral behavior N, N-dimethylacetamide is the most hydrophobic among three amides

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