Influence of the Hydrophobic Domain on the Self-Assembly and Hydrogen Bonding of Hydroxy-Amphiphiles

Figure S1. XRD patterns obtained for ODA films. Figure S2. Displacements of the vibrations due to the νOH normal mode in methanol models. Figure S3. Schematic representation of in-phase and out-of-phase coupling due to the νOH mode. Figure S4. Calculated IR spectra in the νOH region for different methanol models (MA)n. Figure S5. Calculated integral intensity of the νOH band. Figure S6. Magnitude of the calculated static dipole moment. Figure S7. Displacements of the vibrations due to the νOH normal mode in ethanol models. Figure S8. Representation of 9 PBC cells for the MD simulations of ODA systems. Figure S9. RMSD plots of the MD simulations of (ODA)98 and (DOG)10. Figure S10. Summarized and digitized literature data for ν(OH) vs r(O...O). Figure S11. Starting structures for the MD simulations of the hydration of the (ODA)98 bilayer. Figure S12. Schematic representation of averaging steps for generation of the computed (DOG)10 spectra. Figure S13. Comparison of the hydration of (ODA)98 and (DOG)60.

Table S2.Main geometrical parameters for optimized methanol models and vibrational assignments in the νOH region.Table S3.Atomic charges for a trans (t) ODA conformer.Table S4.Atomic charges for a gauche (g) ODA conformer.Table S5.Atomic charges for a DOG molecule.

References
Electronic Supplementary Material (ESI) for Physical Chemistry Chemical Physics.This journal is © the Owner Societies 2019 Periodic boundary conditions (PBC) were used for all the simulations.The size of the single PBC cell was set by tleap module of Amber 9 using Van-der-Waals box dimensions.The starting structure consisting of 98 ODA molecules was first subjected to 2500 steps of initial minimization to relax possible bad geometrical contacts (1000 steps with steepest descent and the rest with conjugate gradient algorithms) with a 12 Å cut-off of Lennard-Jones interactions.The initial minimization was followed by the heating of the system from 0 to 295 K in the NVT ensemble for 20 ps and by subsequent equilibration at 295 K in the NPT ensemble for 100 ps.Finally, the 20 ns production run was performed at 295 K in the NPT ensemble.Both equilibration and production steps were done with 10 Å cut-off using Langevin dynamics with the collision frequency γ=1 and employing SHAKE algorithm on the hydrogen atoms with a tolerance of 10 -5 Å and 2 fs time step.The particle mesh Ewald method (PME) was used for handling long-range electrostatic interactions.The resulting PBC box sizes were 48.6 × 32.7 × 29.8; 48.8 × 31.7 × 30.5 and 47.5 × 32.4 × 29.1 Å 3 for trans-gauche (tg) and trans-trans (tt) models of γ-form, and for βform, respectively.
For the simulation of bilayer hydration, the system (ODA)98 was surrounded by a shell containing either one (representing 10 % hydration level) or 10 (representing full hydration) water molecules per amphiphile, using tleap module of Amber 9 (Figure S11).The TIP3P force field 10 was used for water.
Initially, three stages of restrained minimization were done to relax possible bad geometrical contacts between water and ODA molecules.Each stage consisted of 500 steps of minimization with steepest descent algorithm followed by 500 steps of minimization with conjugate gradient algorithm and the ODA atoms fixed with force constants of 80, 40, and 2 kcal/(mol Å 2 ) at each stage, respectively.Then unrestrained minimization was performed with 1000 steps of steepest descent and 1500 steps of conjugate gradient algorithms.Hereafter, the system was heated from 0 to 295 K in the NVT ensemble within 20 ps, keeping the ODA atoms fixed with a force constant of 10 kcal/(mol Å 2 ).The heating was followed by 100 ps of NPT equilibration at 295 K without any restraints.Finally, the 20 ns production run was performed at 295 K in the NPT ensemble.All other parameters of the simulation were the same as described above for the non-hydrated systems.For the systems with one water molecule per amphiphile, the resulting PBC box sizes were 46.7 × 35.4 × 29.3, 48.0 × 32.7 × 30.9 and 53.2 × 32.0 × 28.1 Å 3 for trans-gauche (tg) and trans-trans (tt) models of γ-form, and for β-form, respectively.The box size for tg model with 10 water molecules per amphiphile was 45.2 × 51.3 × 32.9 Å 3 .

QM calculations.
All QM calculations were performed with GAUSSIAN 09 software package. 9The initial structures for MA, (MA)2, (MA)3, (MA)10, EA, (EA)2, (EA)3 and (EA)10 were optimized in vacuum by an energy minimization with B3LYP functional 11 and the Pople-type 6-31++G** basis set.We consider the vacuum approximation appropriate as the experimental IR data are obtained in dry films.For the optimized structures, harmonic vibrational frequencies and IR intensities were calculated.The anharmonic effects were neglected.Although anharmonic corrections can significantly shift νCH and νOH bands, 12 we supposed that the anharmonic effects are still smaller than the harmonic coupling as long as the bands are well separated.Indeed, as it will be shown below, the harmonic approximation provided the most important spectral features observed experimentally.Frequency scaling was not performed.
For the (MA)10 and (EA)10, a plane symmetry (Cs) was used as previously applied to ethanol systems. 13All the other structures were fully optimized without any symmetry restrictions.The larger BA and DA systems were optimized at a semi-empirical PM3 level including the computations of IR frequencies and intensities.In order to obtain the IR spectra of larger hydrogen-bonded systems, which are not applicable to direct QM calculations, the force field and intensity tensors [14][15][16] of (MA)40, (EA)40 and (MA)200 were constructed from the (MA)10 or (EA)10 fragments, respectively, by applying the Cartesian coordinate transfer (CCT) technique 17,18 .To generate the spectra with finite bandwidth, the computed line spectra were extracted from the GAUSSIAN 09 output and convoluted with Lorentzian curves with bandwidth of 10 cm -1 using a set of home-built programs.

Dioleoylglycerol computations
A multi-scale MD/DFT approach 19,20 accounting for the conformational and dynamic effects was applied to the DOG system.MD simulations.An initial geometry for the DOG molecule (Figure 1) was created using MCM program 2 .
Ten DOG molecules ((DOG)10) were put randomly inside a cube with 35 Å side dimension (avoiding intermolecular clashing) by means of Packmol program 21 and subjected to 10 ns of Generalized Born (GB) MD run.The GB approach is appropriate for water-depleted DOG with implicit solvent simulating the bulk DOG molecules around the ten explicit ones.Both GB and PBC simulations with different initial arrangement of individual molecules (random, bilayer, micellar) were shown to converge to very similar assembly structures. 22The ensemble size of (DOG)10 is considered as realistic resulting from our preceding simulations with (DOG)6 and (DOG)60 systems. 22All MD simulations were done with Amber 9 package 4 using GAFF forcefield.Atomic charges for the DOG molecule were assigned semi-empirically with the help of antechamber module from Amber 9 package, which, in this case, makes use of divcon program and AM1-BCC (Bond Charge Correction) method for charge calculation (Table S5). 4 Because DOG is very flexible and can exist in multiple configurations, it is more suitable to use the BCC method, computing the average charge without accounting for a particular conformation.The RESP charge fitting would require in this case QM calculations for a very large number of possible DOG configurations.All simulations were done with dielectric constant ε=2.0 (value for carbohydrates approximately representing the bulk DOG molecules), with GB model II 23 employing the Analytical Linearized Poisson-Boltzmann (ALPB) model. 24This model provides higher accuracy for the treatment of the electrostatic interactions in the case of finite solvent dielectric constants compared to standard GB.Effective electrostatic size (radius) of the molecule was estimated by the elsize utility from the Amber 9 package to be 6.94 Å.The constructed ensemble of 10 DOG molecules was first subjected to 2500 steps of initial minimization to relax possible bad geometrical contacts (1000 steps with steepest descent and the rest with conjugate gradient algorithms) with no cut-off.The initial minimization was followed by 20 ps of equilibration with the system heated from 0 to 300 K.The 10 ns production run was performed at 300 K.Both equilibration and production steps were done with a 50 Å cut-off of Lennard-Jones interactions, using Langevin dynamics with the collision frequency γ=1 and employing SHAKE algorithm on H atoms with a tolerance of 10 -5 Å and 2 fs time step.The results of the MD simulations, including the analysis of H-bonds, were treated with the ptraj utility from the Amber 9 package.Further analysis of the ptraj output was done by a home-built program "Ptraj HBOND" 25 .
The resulting geometries of six random MD snapshots and the lowest potential energy structure were used for further QM calculations.All DOG molecules in the ensemble were classified in two types, which comprise either hydrogen-bonded (inter-or intramolecularly) or free species.A total of 14 free and 8 H-bonded molecules with different H-bond patterns were used for QM calculations.The H-bonded molecules were further classified according to the bonding pattern.
QM calculations.For all the molecules, the hydrocarbon tails, less essential in this case, were truncated so that only the capping methyl groups were left.Such a reduction of the molecular size allowed us to perform high-level DFT computations necessary for the correct representation of vibrational frequencies.
The molecular fragments were subjected to full DFT optimization and frequency calculations with GAUSSIAN 09 in vacuum at the B3LYP/6-31++G** level.Two H-bonded molecules were considered and computed as one system.Altogether, 22 DFT calculations were done.Since the resulting MD structures were close to the local minima, the geometry of the fragments did not change significantly during the QM optimization procedure.
Infrared spectra were generated for all the fragments from the GAUSSIAN 09 frequency calculation output using Lorentzian bands with a width of 10 cm -1 utilizing a set of home-built programs.
Frequency scaling was not performed.The spectra were averaged in three steps as illustrated in Figure S12.First, the spectra of the systems with the same H-bond pattern as well as the spectra of free molecules were time-averaged with equal weight to represent the dynamics of the system.In the second step, the time-averaged spectra for the H-bonded species were weighted according to their relevant occurrence obtained in the course of the MD run (see Table 4, 3 rd column).And finally, the weighted spectrum of the H-bonded molecules and the averaged spectrum of the free species were again weighted according to their occurrence obtained in the MD run (see Table 4, 2 nd column).The final result was then compared with the experimental DOG spectrum.

Detailed analysis of the calculated IR spectra of ethanol models
The two H-bonded ethanol molecules of (EA)2 (note that the H donor molecule is in trans conformation while the acceptor is in gauche conformation) have two separate bands at 3819 and 3669 cm -1 arising from free (coming from the gauche conformer) and H-bonded (from the trans conformer) OH groups, respectively (Figures 4 and S7).The free OH group vibrates at higher frequency compared to the H-bonded one and has a much lower intensity as it was shown before. 26The presence of the two H-bonds in (EA)3 leads to coupling of the νOH vibrations of the H-bonded groups.This results in appearance of two coupled modes at 3592 and 3550 cm -1 , corresponding to out-of-phase and in-phase coupled vibrations, respectively.The dipole moments of these modes are nearly perpendicular to each other (Figure S7).The highest-frequency mode at 3832 cm -1 arises from the free OH group of one of the trans conformers.
The coupling of the νOH modes of different molecules in (EA)10 gives rise to several out-ofphase and in-phase vibrations (Figure 4 and Table 2).As for methanol, the splitting into multiple bands can be referred to end effects.Vibrational displacements for the most intense bands at 3585 and 3508 cm -1 are illustrated in Figure S7.
The IR spectrum of (EA)10 with tg conformation of the monomers is largely similar to its counterpart with tt conformers (Figure 4).The multiple-split bands converge in the spectrum of (EA)40 into two main νOH peaks at 3586 and 3498 cm -1 , corresponding to out-of-phase and in-phase coupled vibrations, respectively (Figures 4 and S7).There is a considerable difference between these latter two wavenumbers compared to the corresponding values for (MA)40 by about 85 cm -1 on average.As in the methanol models, the integral intensity of the H-bonded νOH bands and the magnitude of the static dipole moment linearly increase with the number of H-bonded monomeric units in the system (Figures S5 and   S6), suggesting the absence of cooperative effects in the formation of the H-bond network.
The dipole moments of the coupled out-of-phase and in-phase modes are nearly perpendicular to each other for all the studied ethanol systems (Figure S7), as for methanol.The computed geometrical parameters (bond lengths and angles) for (EA)10 (Table 2) generally agree well with crystal-XRD data. 3e exception is the O-C-C angle in the gauche conformers (113.32°), which is larger than that obtained by XRD (109.18°),whereas that angle is in perfect agreement with experimental data for the trans conformer (109.2°).However, the gauche conformer has an intrinsically larger value of the O-C-C angle close to 113°, as can be seen for gauche EA monomer and the gauche conformers in (EA)2 and (EA)3 (Table 2) and also from literature data 13 .Water Liquid 3390 ± 10 own data a Compounds are the primary (n-)alcohols in each case, if not specified otherwise.
b These wavenumbers were estimated (rounded to the next decade) from the catalogue spectra (Aldrich 31 and AIST 32 ) since the explicit values were not provided there.
c Rapidly resolidified after melting.For an illustration of the longer string of H-bonded molecules see Figure S2.

Figure S4
. IR spectra in the νOH region calculated with the CCT method for different methanol models (MA)n; spectral intensity is expressed as molar extinction coefficient (ε).    .Summarized and digitized literature data for ν(OH) vs r(O⋅⋅⋅O). 33,34 he dotted straight lines show the range of (O⋅⋅⋅O) distances obtained from the MD data for (ODA)98 trans-gauche model of γform and corresponding range of ν(OH) vibration wavenumbers.

Figure S2 .
Figure S2.Displacements of the vibrations due to the νOH normal mode in methanol models.

Figure S3 .
Figure S3.Schematic representation of in-phase and out-of-phase coupling due to the νOH mode.

Figure S4 .
Figure S4.Calculated IR spectra in the νOH region for different methanol models (MA)n.

Figure S5 .
Figure S5.Calculated integral intensity of the νOH band.

Figure S6 .
Figure S6.Magnitude of the calculated static dipole moment.

Figure S7 .
Figure S7.Displacements of the vibrations due to the νOH normal mode in ethanol models.

Figure S8 .
Figure S8.Representation of 9 PBC cells for the MD simulations of ODA systems.

Figure S11 .
Figure S11.Starting structures for the MD simulations of the hydration of the (ODA)98 bilayer.

Figure S12 .
Figure S12.Schematic representation of averaging steps for generation of the computed (DOG)10 spectra.

Figure S1 .
Figure S1.XRD patterns obtained for films of ODA at 0 % RH in the small-angle (SAXS, a) and wideangle (WAXS, b) scattering regions.

Figure S2 .
Figure S2.Displacements of selected vibrations due to the νOH normal mode (thick magenta arrows) in systems composed of two, three, ten and 40 methanol molecules; the red lines show the directions of resulting O-H transition dipole moments.

Figure S3 .
Figure S3.Schematic generalized representation of vibrations for the in-phase (left) and out-of-phase (right) coupling due to the νOH mode as occurring in a string of O-H…O hydrogen bonds; large solid and small grey balls represent oxygen and hydrogen atoms, respectively.In the case of in-phase coupling, O-H bonds of all molecules in the string elongate or shorten simultaneously (all hydrogen atoms in all O-H…O bonds in the string move synchronously in the same direction).In the case of out-of-phase coupling, the O-H bond in one molecule elongates while the O-H bond in the neighboring molecule shortens (hydrogen atoms in neighboring O-H…O bonds move asynchronously, in opposite directions).For an illustration of the longer string of H-bonded molecules see FigureS2.

Figure S5 .Figure S6 .Figure S7 .Figure S8 .
Figure S5.Calculated integral intensity of the νOH band arising from the H-bonded OH groups plotted against the number of the monomeric units (n) in methanol ((MA)n), ethanol ((EA)n) and butanol ((BA)n) systems; the calculations were done at B3LYP/6-31++G** level for (MA)n and (EA)n and at semiempirical PM3 level for (BA)n.The CCT method was used for the systems with 40 and 200 monomeric units.The inset shows expanded scale for X-axis between n=0 and n=40.
Figure S10.Summarized and digitized literature data for ν(OH) vs r(O⋅⋅⋅O).33,34The dotted straight lines show the range of (O⋅⋅⋅O) distances obtained from the MD data for (ODA)98 trans-gauche model of γform and corresponding range of ν(OH) vibration wavenumbers.

Figure S11 .
Figure S11.Starting structures for the MD simulations of the hydration of (ODA) 98 bilayer in the transgauche model of γ-form with 1 water molecule (left) and 10 water molecules per amphiphile (fully hydrated system; right).

Figure S12 .Figure S13 .
Figure S12.Schematic representation of the averaging steps to generate simulated (DOG)10 spectra.The originally computed spectra were averaged in three steps: (i) for each of the 5 H-bond patterns and for the free molecules, the spectra obtained from different randomly chosen snapshots were averaged with equal weight for the last 3 ns of the simulation (8-10ns) to represent the dynamics of the system; (ii) the resulting spectra for all the H-bonded species were weighted according to their relevant percentage populated during the MD run, which provided a spectrum arising from all the H-bonded molecules; (iii) the resulting spectrum of the Hbonded species from the step (ii) along with the resulting spectrum of the free species from the step (i) were again weighted according to the percentage of H-bonded and free molecules.For simplicity, the H-bonded species occurring < 2% in step (ii) are not shown but used in the calculations.The final result was compared with the experimental DOG spectrum (see text).

Table S1 .
Peak wavenumbers for νOH bands arising from several compounds; values for the films measured in our laboratory were obtained at relative humidity of 0 %.

Table S2 .
Main geometrical parameters for optimized (B3LYP/6-31++G**) methanol models and vibrational assignments in the νOH region; the individual molecules in (MA)2 and (MA)3, structures are labeled with subscript indices as shown in Figure3in the main text.
a "(av)" stands for average.b This structure could not be optimized due to large system size.

Table S3 .
Atomic charges for a trans ODA conformer determined with the RESP potential fit method 8 .

Table S4 .
Atomic charges for a gauche ODA conformer determined with the RESP potential fit method 8 .

Table S5 .
4tomic charges for a DOG molecule determined with divcon program using AM1-BCC semiempirical method4.