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B: Liquids, Chemical and Dynamical Processes in Solution, Spectroscopy in Solution
The Interplay of Methyl-Group Distribution and Hydration Pattern of Isomeric Amphiphilic Osmolytes Vira N. Agieienko, Christoph Hölzl, Dominik Horinek, and Richard Buchner J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.8b01699 • Publication Date (Web): 04 May 2018 Downloaded from http://pubs.acs.org on May 5, 2018
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The Interplay of Methyl-Group Distribution and Hydration Pattern of Isomeric Amphiphilic Osmolytes Vira Agieienko,† Christoph Hölzl,§ Dominik Horinek,*§ Richard Buchner*§ †
A. M. Butlerov Institute of Chemistry, Kazan Federal University, 420008 Kazan, Russia
§
Institut für Physikalische und Theoretische Chemie, Universität Regensburg, D-93040 Regensburg, Germany
Supporting Information ABSTRACT: The intermolecular interactions and dynamics of aqueous 1,1-dimethyurea (1,1-DMU) solutions were studied by examining the concentration dependence of the solvent and solute relaxations detected by dielectric spectroscopy. Molecular dynamics simulations were carried out to facilitate interpretation of the dielectric data and to get a deeper insight into the behavior of the system components at microscopic level. In particular, the simulations allowed for explaining the main differences between the dielectric spectra of aqueous solutions of 1,1-DMU and of its structural isomer 1,3-DMU. Similar to the previously studied compounds urea and 1,3-DMU, 1,1-DMU forms rather stable hydrates. This is evidenced by an effective solute dipole moment that significantly exceeds the value of a neat 1,1-DMU molecule, indicating pronounced parallel alignment of the solute dipole with 2÷3 H2O moments. The MD simulations revealed that the involved water molecules form strong hydrogen bonds with the carbonyl group. However, in contrast to 1,3-DMU, it was not possible to resolve a “slow-water” mode in the dielectric spectra, suggesting rather different hydration-shell dynamics for 1,1-DMU as confirmed by the simulations. In contrast to aqueous urea and 1,3-DMU, addition of 1,1-DMU to water leads to a weak decrease of the static permittivity. This is explained by the emergence of antiparallel dipole-dipole correlations among 1,1-DMU hydrates with rising concentration.
1.INTRODUCTION Small non-ionic cosolutes like urea (U) and its derivatives stabilize or denature proteins. The relation of the detailed chemical structure of the cosolute and its stabilizing or destabilizing effect is hereby still an open question. This relation is more complicated than presumed, because intermolecular forces of osmolyte molecules are not just simply a sum of atomic contributions. Furthermore, the cosolute action on protein stability is not solely caused by its mutual interactions with polar and/or nonpolar parts of the protein surface, as the solvent water is an essential component in the system and its interactions with the protein and the cosolute 1-2 give crucial contributions. Understanding the solvation properties of cosolutes will therefore be a necessary ingredi-
ent of a model that links the chemical structure of cosolutes to their thermodynamic effect on protein stability. The data on aqueous solutions of methylated ureas (MU) found in the literature concern properties such as enthalpies 3-6 7-10 enthalpies of solution and transfer, of dilution, 9,11-17 16-17 7,11,14 density, speed of sound, heat capacity, viscosity 13 18-19 20 and surface tension, osmotic and diffusion coefficients. Applied spectroscopic techniques were infrared spectrosco21 22 22-24 py, ultrasonic and dielectric relaxation, as well as 7,25-26 NMR. Despite this impressive amount of work, an overall picture of MU hydration is still lacking and peculiarities of solute-solute interactions in such systems are far from being understood. First of all, this is due to the lack of reliable experimental data on some MU/water systems. For example, although aqueous solutions of 1,3-dimethylurea (1,3-DMU) and tetramethylurea (TMU) have been studied by a plethora of methods almost no attention has been paid to the systems containing 1,1-dimethylurea (1,1-DMU) or trimethylurea (1,1,3TMU). Moreover, the scarce experimental data available on 3-11 these systems mainly deal with thermodynamic properties that do not provide any atomistic details on MU hydration and MU-MU interactions. Recently we used dielectric relaxation spectroscopy (DRS) 27 24 to investigate the hydration pattern of U, 1,3-DMU and 28 TMU. It was shown that in the case of U and 1,3-DMU a part of the solvent water exhibits dynamics indistinguishable from the solute. Computational methods confirmed that these highly retarded H2O molecules are H-bonded to the carbonyl oxygen of the solute. Additionally, the methyl groups of 1,3-DMU and TMU moderately retard the water molecules surrounding them. While for the first compound this yielded a well-defined “slow-water” mode, separation from the solute dynamics was not possible for the second. 24 Interestingly, the simulation results for 1,3-DMU also suggested notable self-aggregation of the solute molecules with parallel alignment of 1,3-DMU dipoles. According to its chemical structure, 1,1-DMU shares structural fragments of its parent U (a hydrogenated nitrogen atom), of 1,3-DMU (two methyl groups) and of TMU (a fully methylated nitrogen). Interestingly, its behavior in water differs significantly from that of U and other methylated 1 derivatives. For example, with 3.0 mol kg‒ in molality scale, the solubility of 1,1-DMU is much lower compared to U (18.0
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mol kg‒ ), 1,3-DMU (≈38 mol kg‒ ) and TMU, which is fully miscible with water. Also, addition of 1,1-DMU to water promotes a decrease of the static relative permittivity (dielectric 23 23,27,30-33 constant), ε, of water whereas in the presence of U, 23-24 23,28 1,3-DMU and TMU ε increases in comparison to pure water. So far, no explanation for these differences has been proposed in the literature. As a continuation of our previous studies we report here results on the hydration and self-aggregation of 1,1-DMU and its influence on solvent dynamics. To this end, we combine dielectric relaxation spectroscopy (DRS) and molecular dynamics (MD) simulations to reach a better molecular-level understanding of the impact of the number of methyl substituents and their position on solute hydration and aggregation. Specifically for this task, a force field model for 1,1-DMU was developed.
2. EXPERIMENTAL SECTION 2.1. Dielectric relaxation spectroscopy. DRS probes the total polarization of a sample as a function of the electric field frequency, ν. The sample polarization is usually expressed as the complex permittivity, ε̂(ν) = ε'(ν) – iε''(ν), which contains in-phase polarization components given by the relative permittivity, ε'(ν), and out-of-phase components described by the dielectric loss, ε''(ν). In the present study, the dielectric spectra were measured over the frequency range 0.05 ≤ ν / GHz ≤ 89. Frequencies within 0.05 ≤ ν / GHz ≤ 50 were covered with a frequencydomain reflectometer based on Agilent 85070E-20 and 85070E-50 dielectric probes connected to an Agilent E8364B vector network analyzer (VNA). As primary calibration standards for the instrument air, mercury and water were used. Calibration errors arising from the relative character of the measurements were corrected with a Padé approximant using water, N,N-dimethylformamide, and propylene car34 bonate as secondary standards. All VNA measurements were done at least in duplicate with each run independently calibrated. The data for each of the two VNA probes were then averaged and ‒provided both dielectric spectra were coinciding within their noise level (0.5% of the static relative permittivity for ε'(ν)) in the 5-20 GHz region‒ concatenated at 10-18 GHz, depending on solute concentration. For 60 ≤ ν / GHz ≤ 89 data were determined with a variable path-length 35 waveguide interferometer. To avoid bias in the fitting procedure the number of VNA data points in the final spectrum (91, equally spaced on the log ν scale between 0.05 and 50 GHz) was chosen in such a way that the four waveguide points have comparable weight in the analysis. Figure S1 of the Supporting Information (SI) gives an example for this concatenation procedure. Note, that data points at ν < 100 MHz were generally discarded due to excessive noise. All DRS measurements were performed at (25.00 ± 0.05) °C. 1,1-DMU (99 %) purchased from Aldrich was recrystallized from a water-methanol mixture (1:1 v/v) and dried at 50 °C under vacuum to constant mass. All samples were prepared by weight on an analytical balance without buoyancy correction from 1,1-DMU and Millipore Milli-Q water. Solute molal–1 ities, m, ranged from 0.1 to 3.0 mol kg . Densities, d, necessary for determining the molar concentration, c [in M = mol 3 dm‒ ], of the solute were measured with an Anton Paar DMA 5000 M vibrating tube densimeter yielding d with a nominal −6 −3 uncertainty of ± 5·10 g cm at (25.000±0.005) °C. The dy-
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namic viscosities, η, of the solutions were determined using an Anton Paar AMVn rolling ball viscometer with a 1.6 mm capillary at (25.00±0.01) °C. The values obtained for d and η are summarized in Table S1 of the SI. 2.2. Computational details. The charges, bonded and initial nonbonded parameters were obtained from the general AMBER force field (GAFF) method, where the charges were 36 determined using AM1-BCC. The geometry of a single 1,1DMU molecule was calculated on the MP2//cc-pVDZ level 37 using the ORCA package. The equilibrium angles of the force field were then optimized to reproduce the angles of this geometry. The σ parameters were then scaled by a constant factor to accurately reproduce the experimental densities of the 0.5 and 3.0 molal aqueous solutions. Molecular dynamics (MD) simulations were performed by 38 means of the GROMACS package (version 4.5.6). The nonbonded van der Waals interactions were calculated using the Lennard-Jones 12−6 potential. The nonbonded interactions between distinct atom types were calculated using the Lorentz-Berthelot combination rules. For water the SPC/E model was used. All force field parameters are given in the SI. The geometry of 1,1-DMU obtained from quantum chemical calculations and the atom labeling used in further discussions are shown in Figure 1.
Figure 1. (A) Spatial configuration and (B) schematic representation of the 1,1-DMU molecule with the atom labeling used in this paper. MD simulation runs for the 1,1-DMU/water systems were performed in the isothermal−isobaric (NPT) ensemble using the usual periodic boundary conditions, with an integration time step of 1 fs. The van der Waals interactions were computed with a cut-off of 1.0 nm with a smooth decay of the forces starting at 0.9 nm. The reciprocal space was computed by the particle mesh Ewald method with a grid spacing of 39 0.12 nm. Before running the production MD trajectory, the starting structure was equilibrated as follows: first, configurations were generated by placing the appropriate number of 1,1-DMU and H2O molecules randomly inside a cubic box with sides of 4.5 nm. Next, a 2000 ps run was used to equilibratethe system. Finally, a 2 ns NPT-MD production run at 298.15 K and 1 Bar was performed; the coordinates were saved every 200 fs. The temperature was controlled by the stochas40 tic v-rescale thermostat using a time constant for heat bath coupling of 0.1 ps. The pressure coupling to the external bath 41-42 was achieved by an isotropic Parrinello-Rahman barostat with a time constant of 1.0 ps. Analysis was conducted with 43 the TRAVIS program and the GROMACS tools. The dynamics was examined using pair contact time autocorrelation functions (ACFs) defined as 2
C(t) = / ,
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where aij is a binary parameter for a pair of atoms i and j at the time origin t = 0 and at time t ≥ 0. The quantity aij(t) = 1 if a pair of atoms i and j satisfies a set of criteria for a period of time shorter than t, otherwise aij(t) = 0. As the limiting case for t infinity (∞) was applied assuming that atoms i and j stay coupled at time t regardless of the number of times this coupling turned off and reformed during the time interval [0, t]. For contact dynamics, the distance (radial cut-off) corresponding to the first minimum in the radial distribution functions (RDFs) was used as the criterion. For H-bonding, an additional hydrogen-donor-acceptor angular cut-off was introduced. In order to determine the proper region for Hbond formation the combined radial and angular distribution functions (CDFs) were analyzed. The figures demonstrating this analysis are shown in the SI. After correcting for finite size effects the corresponding lifetimes were obtained by the integration
.
(2)
The contact, τC, and H-bond, τH, time constants were found by analytical integration of the corresponding ACFs. To do this, the latter were fitted by three exponential decay functions C(t) = c1exp(‒t/τ1) + c2exp(‒t/τ2) + c3exp(‒t/τ3),
(3)
where c3 = 1 ‒ c1‒ c2.
3. RESULTS AND DISCUSSIONS 3.1 DIELECTRIC RELAXATION Relaxation model. The experimental dielectric spectra shown in Figure 2 and in Figures S1 & S2 of the SI clearly represent a single loss peak exhibiting a marked shift of its peak frequency from νpeak = 18 GHz in pure water to νpeak = 10.5 GHz at c = 2.4 M. Despite their apparent simplicity, the determination of the relaxation-time distribution function 44 with the method of Zasetzky indicated three well-resolved modes for all solution spectra (Figure S3). Indeed, evaluation of the spectra with sums of up to five Havriliak-Negami (HN) 45 equations or simplified versions thereof revealed that, except for the highest concentration, a sum of three Debye equations
ε ε∞ ,
(4)
(the D+D+D model) provided their best fit in terms of the 2 46 reduced error function, χr . In eq 4 Sj (j = 1, 2, 3) is the relaxation strength (amplitude) and τj is the relaxation time of mode j and ε∞ the extrapolated high-frequency (ν → ∞) limit of ε'(ν). An example of this decomposition is shown in Figure 2B, a comparison of tried fit models is given in Table S2 and the obtained fit parameters for the D+D+D model are summarized in Table S3 of the SI. For the sample with m = 2.9964 1 mol kg‒ the assumption of a HN equation for the lowestfrequency mode (i.e. a HN+D+D model) yielded a slightly 2 better χr value (Table S2) but the resulting parameter values did not match those for the other samples. Thus, also for this sample the result of the almost equally well fitting D+D+D description was preferred. All three resolved modes exhibit a systematic lowfrequency shift with increasing 1,1-DMU concentration (Figure 2C). The slowest relaxation, j = 1, is not present in the 47 dielectric spectrum of pure water and thus can be clearly
Figure 2. Spectra of (A) the relative permittivity, ε′, and (B) the dielectric loss, ε'', for the 2.4 M aqueous 1,1-DMU solution at 25 °C. Symbols correspond to the experimental data (for clarity only every second point shown at ν ≤ 50 GHz); lines are the result of the D+D+D fit with eq 4, with the shaded areas in (B) indicating the loss contributions of the resolved modes, j. (C) Positions of the peak frequencies, νpeak, for the resolved modes as a function of 1,1-DMU molarity, c. assigned to 1,1-DMU. As expected for a solute mode, its amplitude, S1, increases linearly with increasing c, yielding a value of ~21 at c = 2.4 M (see Figure 3A and Table S3 of the SI). Its relaxation time smoothly rises from 27 to 42 ps in agreement with increasing solution viscosity as shown in Figure 4A. It is comparable with the solute relaxation times 27 of the related compounds U (τ1 = 19…22 ps) and 1,3-DMU (τ1 24 = 37…60 ps) in the same concentration range. The present assignment is also in line with an earlier DRS study of a 1.0 M 23 solution of 1,1-DMU in water. The intermediate relaxation mode, j = 2, whose relaxation time increases from τ2 = 8.35 ps in pure water to 12.0 ps at the highest solute concentration, definitely corresponds to the cooperative reorientation of water dipoles which are –more 47 or less‒ unaffected by the presence of the solute. For brevity, this relaxation time will be termed bulk-water relaxation
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tions, P(τ ), show no indication for an additional mode with τs ≈ 15 to 20 ps (Figure S3). Water relaxation. Relaxation amplitudes, Sj, are linked to the concentration, cj, of the causing dipoles via the 51,53 equation
!" #$ %ε&
'
ε 2 '() , *++ ) , ε (" ε
(5)
where NA and kB are Avogadro’s and Boltzmann’s constants, ɛ0 is the vacuum permittivity, T is the thermodynamic temperature, ɛ is static permittivity, and Aj is the cavity-field factor reflecting a deviation of the molecular shape from spherical. The effective dipole moment, μj,eff, differs from the molecular (permanent) dipole moment in vacuum, μj, due to the polarizability of the molecule and possible orientational correlations among neighboring dipoles, see ref. 51 for details. Figure 3. Concentration dependence of the solute amplitude, S1 (A), and static relative permittivity, ε (B) in the 1,1-DMU (green) and 1,3-DMU (red) aqueous solutions. Symbols show experimental data points connected with solid lines as a guide to the eye; dashed lines are predictions from the dipole moment values of the neat compounds. time, τb, further on. Its amplitude, S2, steeply decreases to 48.9 units in the 2.4 M solution compared to 72.5 in pure water (see Figure 4B). As shown below, this decrease is not only due to the decreasing number density of the H2O molecules but it is also caused by a partial immobilization (rotational freezing) of solvent dipoles by the solute. The weak high-frequency mode, characterized by relaxation time and amplitude , is compatible with the fast 47 relaxation observed in pure water and almost certainly associated with the fast hydrogen-bond switch occurring in the jump-relaxation mechanism proposed for water by Laa48 geet al. With relaxation times increasing from 0.3 to 2.3 ps this mode is essentially outside the covered frequency range and only its low-frequency wing is detected. Accordingly, its amplitude, ≈ 2 to 4, is not very reliable but the increase in seems to be systematic (Figure 2C). A possible reason for this shift of might be an increasing contribution from the 49 ~100 GHz relaxation claimed by Vinh et al. for water or of 50 the “hypermobile water” postulated by Suzuki et al. for aqueous solutions. Unfortunately, the fit of the present spectra did not allow resolving such modes (see above). In any case, this fast switch is an integral step in the reorientation of the water dipoles and accordingly the total amplitude of bulk-like water, Sb(c) = (c) + (c) + ɛ∞(c) ‒ ɛ∞(0), will be 48 evaluated further. By using the high-frequency permittivity of pure water obtained with data in the terahertz region, ɛ∞(0) = 3.52, the lack of terahertz data for the present spectra 51-52 is at least approximately corrected. It is interesting to note that, in contrast to the aqueous so24 lutions of 1,3-DMU, no ‘slow’ (moderately bound, retarded) water relaxation, with a relaxation time of τs ≈ 15 to 20 ps and associated amplitude, Ss, could be resolved from the DR spectra of aqueous 1,1-DMU. Thus, for the present system Sb is identical to the total amplitude of DRS-detected solvent, 24 Sw, whereas for 1,3-DMU Sw = Sb + Ss. This finding is corrob44 orated by the analysis of ε̂(ν) with the Zasetsky procedure. The obtained relaxation-time probability distribution func-
Using the effective dipole moment of μeff = 3.8 D obtained with eq 5 from the data for pure water and its analytical concentration, cw°, in the solutions, we can calculate the value of Sw that would be expected if all solvent molecules were exhibiting unperturbed dynamics. Due to very similar solution densities these nominal Sw values (dashed lines in Figure 4B) are practically identical for 1,1- and 1,3-DMU and decrease linearly with c. On the other hand, experimental data for Sw (filled symbols in Figure 4B) also decrease linearly with c but exhibit larger slopes with a slight difference between 1,1-DMU and 1,3-DMU. This discrepancy between nominal and experimental Sw clearly indicates that both DMU isomers ‘freeze’ some of the H2O dipoles to such an extent that their dynamics is considerably slower than that of –more or less‒ unperturbed bulk-like water (τ2) and even slower than the moderately retarded (slow) water (τs) detect24 ed for 1,3-DMU. Evaluation of Sw, Sb and Ss with eq 5 normalized to pure water yields the total concentration of DRS-detected water, cw, as well as the concentrations of bulk-like, cb, and slow water, cs, respectively. This allows calculation of the effective hydration number Zt = (cw° ‒ cb)/c, which gives the total amount of bound water per equivalent of solute, and of Zs = cs/c and Zib = Zt ‒ Zs = (cw° ‒ cw)/c as the corresponding numbers of retarded (slow) and strongly bound (frozen, ib) sol51 vent molecules. Obviously, for 1,1-DMU Zt = Zib as no slow water (Zs = 0) was detected for this compound. Within experimental uncertainty, Zib values obtained for 1,1-DMU are independent of the solute concentration with an average of Zib = 2.6±0.4, see Figure S4. This value is somewhat larger 24 than that found for 1,3-DMU, Zib = 1.6±0.4, which is also independent of c in contrast to urea, where Zib = (1.85±0.05) – 27 (0.103±0.006)×c [= Zt]. The obtained effective hydration number of 1,1-DMU from DRS is somewhat smaller than the 17 c → 0 value of 4.24 determined from compressibility data. Almost certainly, this difference reflects that both techniques monitor different properties. Of relevance here is that the effective hydration numbers of both techniques are significantly smaller than the coordination number, CN, i.e. the number of first-shell water molecule surrounding the solute, obtained from the MD simulations. This quantity decreases from 24.5 at c → 0 to 18.5 at 2.4 M (Figure S6). This means that –similar to U and 1,3-DMU– only for a small fraction of the hydrating water molecules the reorientational dynamics is strongly impeded by 1,1-DMU. For U and 1,3-DMU it was 24,27 shown that these are the H2O molecules hydrogen
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The Journal of Physical Chemistry Solute relaxation. Figure 3A compares the experimentally observed relaxation strengths for both dimethylureas, S1 (symbols), with the amplitude values (dashed lines) predicted by means of eq 5 from the theoretical effective dipole moment (μeff = 5.8 D for 1,1-DMU and μeff = 5.5 D for 1,3DMU, obtained with GAUSSIAN) of a single solute molecule embedded in a dielectric continuum with the permittivity of 56 water. Due to similar μeff values the predicted amplitudes are very close with S1(1,1-DMU) > S1(1,3-DMU). Interestingly, the experimental amplitudes are much larger with inverted sequence, i.e. S1(1,1-DMU) < S1(1,3-DMU). As a consequence, the static relative permittivity of the solution, ε = S1 + Sw + ε∞, is not decreasing with c, as expected from the theoretical μeff values, but remains practically constant for 1,1-DMU and even increases for 1,3-DMU (Figure 3B).
Figure 4. (A) Relaxation times of bulk-like, τb, and slow water, τs, in aqueous solutions of 1,3-DMU and of τ2 for 1,1DMU(aq) as a function of solution viscosity, η. In both panels the solid lines are a guide to the eye. (B) Concentration dependence of the amplitude of DRS-detected water, Sw, in aqueous solutions of 1,1-DMU (green) and 1,3-DMU (blue). Symbols show experimental data points; dashed lines are predictions from the dipole moment values of the neat compounds. Additionally the experimental amplitude of bulklike water, Sb, in the 1,3-DMU/water systems is shown. bonded to the carbonyl group. The present simulations suggest that this is also the case for 1,1-DMU, see below. As indicated above, no slow-water relaxation could be resolved in the dielectric spectra of aqueous 1,1-DMU solutions. Such a contribution is commonly found for hydrophobic 24,28,54-55 solutes and due to the retardation of H2O molecules hydrating the hydrophobic moieties. In essence, this slowdown is an excluded-volume effect as the involved H2O mol48 ecules are screened by the solute. The lack of such a contribution for 1,1-DMU seems surprising as this molecule has the same number of methyl groups than its isomer, 1,3-DMU. A first hint why this is the case comes from a comparison of the concentration dependence of τb for 1,1-DMU(aq) with that of τb and τs for 1,3-DMU(aq), Figure 4A. According to this graph, the two water-related relaxation times resolved for 1,3DMU are well separated and the difference increases with rising c as τb exhibits only a weak increase. Also, already at low solute concentrations the slow-water amplitude, Ss = Sw – Sb (Figure 4B), is rather large. Both effects facilitate the detection of the slow-water mode in the evaluation of ε̂(ν). In contrast to that, for 1,1-DMU the bulk-water relaxation time τb = τ2 increases significantly with c, exhibiting practically the same slope as τs of 1,3-DMU. We cannot exclude that the impact of 1,1-DMU on bulk solvent dynamics, i.e. beyond the first hydration shell is larger than that of 1,3-DMU. However, more likely is a scenario where for 1,1-DMU the amplitude, Ss, or/and the relaxation-time ratio, τs/τb, is simply too small to allow resolution of the slow-water mode.
Assuming that all solute molecules contribute to S1, eq 5 thus yields the experimental effective dipole moments of μeff = (10.1±0.5) D for 1,1-DMU. The value for 1,3-DMU, μeff = 24 (11.3±0.5) D, was already published previously and a similar effect was also observed for U, albeit with concentration27 dependent μeff/D = (10.0±0.1) – (0.133±0.005)×c. For the latter two compounds it was shown that these large effective solute dipole moments mainly arise from the roughly parallel alignment of the solute dipole with the moments of the Zib strongly bound water molecules. Additionally, solute-solute correlations play a role. The MD simulations discussed below suggest, that this is also the case for 1,1-DMU. The rotational correlation times of 1,1-DMU, τrot,1, calculated from the corresponding solute relaxation times, τ1, according to ref. 57 increase linearly with increasing viscosity, η (Figure S5). This suggests rotational diffusion of individual dipoles. Application of the generalized Stokes-Debye-Einstein equa58-59 3 tion yields an effective volume of Veff = (23 ± 2) Å for the solute. With the molecular volume of a 1,1-DMU molecule, 3 60 Vm = (120 ± 12) Å , obtained with GAUSSIAN this yields a friction parameter of C = 0.13, which is only slightly larger than the expected value for rotation with slip boundary conditions, Cslip = 0.08. This suggests that solute hydration and solute-solute interactions do somewhat impede the reorientation of 1,1-DMU. However, long-lived 1,1-DMU⋅Zib H2O complexes –or even stable 1,1-DMU aggregates– which rotate as an entity are unlikely in view of the experimental C value, which is still far from the theoretical stick limit, Cstick = 1. As for 1,3-DMU and U it rather appears that the exchange of the Zib H2O molecules hydrogen bonded to the solute’s carbonyl group occurs on the timescale of solute rotation. This view is supported by the MD simulations discussed below.
3.2. MOLECULAR DYNAMICS SIMULATIONS Structure around 1,1-DMU. To start the discussion of the DRS results from the viewpoint of atomistic simulations let us first analyze the nearest environment of a 1,1-DMU molecule in aqueous solution. The proximal radial distributions functions (pRDFs), gij(r), describe the probability to find a site j in the shell layer of width Δr that tracks the surface built up by the volumes of spheres of radius rij centered on 61-63 each atom of the reference molecule i. Their integration allows obtaining the number of H2O and other 1,1-DMU molecules in direct contact with the chosen reference solute molecule. As an example, Figure 5 shows the pRDFs between the oxygen atom on water, ,, -./ 01 2, respectively the carbon atom, C, of the carbonyl groups of neighboring 1,1-
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DMU molecules, g1,1-DMU‒C(r), with all atoms of the reference, as well the corresponding coordination numbers, CNW and CNDMU. As these functions do not change significantly with concentration only pRDFs for the 1.7 M solution are present2 ed. Note that these pRDFs are not normalized to 4πr .
Figure 5. Proximal radial distribution function, ,, -./ 01 2 and corresponding coordination number, CNW, for the oxygen atom of water molecules, OW, surrounding the solute (left axis) in the 1.7 M solution. Also shown (right axis) is the pRDF of carbonyl carbon atoms, C, of 1,1DMU molecules surrounding the reference solute molecule, g1,1-DMU‒C(r), for this solution and the corresponding coordination number, CNDMU. The dotted lines indicate the connection of the minima of the pRDFs and the corresponding coordination numbers. Figure 5 shows one clear minimum for the 1,1-DMU‒OW pRDF. The right shoulder, at 2.0 Å, is related to contacts between the hydrogen atoms on 1,1-DMU, H and HC, and OW. The complete first hydration layer of the solute extends up to the well-defined minimum at 4.0 Å. The latter incorporates the interactions of the heavy atoms of the solute, namely C, O, NH, NC, and CH, with the OW atoms of water. Integration of the pRDF to this minimum yields a number of CNW = 20.0 H2O molecules surrounding each 1,1-DMU molecule in the 1.7 M solution. Due to solvation shell overlap, the coordination number significantly decreases with increasing concentration. While at c→0 24.5 H2O molecules are hydrating the solute, CNW has dropped to 18.5 at the highest concentration, c = 2.4 M (see Figure S6 of the SI). Note that according to the procedure for the calculation of this pRDF water molecules that are in contact with n 1,1-DMU molecules are counted ntimes, once for every solvation shell they are in. As a consequence, at high c the thus obtained nominal amount of hydration water overestimates the fraction of H2O molecules actually in direct contact with the solute. As far as the 1,1DMU‒C pRDF is concerned, the first and second minimum observed at respectively 4.5 Å and 5.8 Å do not represent the first and second interacting layers. Instead, both minima correspond to different orientations of neighboring 1,1-DMU molecules with respect to each other (see Figure S7 of the nd SI). Integration of this pRDF to the 2 minimum yields a coordination number of 2.2 1,1-DMU molecules for a 1.7 M solution. Due to increasing solute number density, this value increases with c, reaching 3.1 close to the solubility limit. DRS revealed that the dynamics of 2.6±0.4 H2O molecules is not distinguishable from that of 1,1-DMU. It is reasonable to assume that these solvent molecules are nearest neighbors
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to the solute and interacting with the carbonyl group. Indeed, the obtained O‒OW radial distribution functions revealed a pronounced peak at ~2.7 Å, with the associated coordination number decreasing from ~2.6 at c = 0.47 M to ~2.3 for the 2.43 M solution (Figure S8 of the SI) in good agreement with Zt. To identify their arrangement we determined spatial distribution functions (SDFs) for the OW and HW atoms of the three water molecules closest to 1,1-DMU (Figure 6A). Here, the distance C‒OW between the carbonyl C and water oxygen was used as a selection criterion. It is clearly seen that all three H2O molecules, showing up as bent toroidal clouds, are hydrogen bonded to the carbonyl oxygen of 1,1-DMU. Interestingly, the NH2 group of 1,1-DMU, which could act as an H atom acceptor, does not show interaction with the solvent at the isovalue applied for Figure 6A (sOW = 15.5). Only when sOW is decreased to 3.3, i.e. 17% of its maximum value, a roughly ellipsoidal cloud appears near the trans-H atom (hereinafter the cis- and trans-positions of the H and CH atoms are with respect to the carbonyl oxygen). These weak populations, as well as all other populations weaker than O‒OW, are better seen in the plane projection distribution (PPD) functions. These are projections of the three-dimensional distributions of the OW (Figure 6B) and HW atoms (Figure 6C) onto planes defined in a coordinate system specific to the reference molecule. In the present case the xy projection is onto the plane defined by the C, NC and NH atoms of 1,1-DMU (see Figure 1). The xz plane is perpendicular to the first and along the CO axis. The third plane, yz,
Figure 6. (A) Spatial distribution functions for the oxygen, OW, and hydrogen, HW, atoms of the three H2O molecules closest to 1,1-DMU in the 1.7 M solution. The shown isovalues, s, correspond to 80% of their maximum intensities which are s = 19.4 for the OW and s = 21.2 for the HW. Also shown are the plane projection distribution functions of the OW atoms (B) and HW atoms (C) of these closest water molecules onto the xy, xz and yz planes of the reference 1,1-DMU molecule. Here, the relative intensities increase in the sequence blue < green < red.
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The Journal of Physical Chemistry
is perpendicular to both of them and thus points along the NCNH axis. These PPDs clearly show that the probability of finding both OW and HW atoms near functional groups of 1,1DMU decreases in the sequence O > cis-H > trans-H > CH3. The hydrating water molecules are mainly located above and below the xy plane of the solute molecule and their dipole vectors are essentially parallel to the dipole moment of 1,1DMU, see the combined distance-angle distribution function (CDF) provided in Figure S9 of the SI, corroborating thus the inference from DRS. The SDFs of the C, O, cis-H and trans-H atoms of the three 1,1-DMU neighbors closest the reference solute molecule are shown in Figure 7. These functions reveal that the nearest solute molecules are preferably located above and below the CNHNC plane of the reference. Thus, stacking-type aggregates are formed. Despite the diffuse nature of the SDFs and strong overlap of C and O atom distributions a roughly antiparallel orientation of the nearest-neighbor 1,1-DMU relative to the reference can be noted. This observation is confirmed by the CDFs shown in Figure S13 of the SI. With low –but still detectable‒ probability 1,1-DMU molecules can also interact via their cis- (s = 2.1) and trans-H (s = 1.7) atoms with other carbonyl oxygens but the weight of these in-plane structures is low. This finding is in line with a recent quantum mechan64 ical investigation of U dimers in water which showed that the solvent hinders the formation of cyclic U dimers. Dynamics of 1,1-DMU hydrate complexes, solute aggregates and H-bonds. It is generally accepted that the presence of the ‘slow’ and ‘bound’ water fractions are caused by the specific interactions of H2O molecules contributing to the hydration layers of the hydrophobic respectively hydro24,27,54-55 philic moieties of the solutes. However, as already mentioned, no separate ‘slow’ water mode could be resolved from the dielectric spectra of 1,1-DMU(aq) despite the presence of two methyl groups. Instead, somewhat retarded dynamics of the dominating ‘bulk-water’ mode (τ2) was found, Figure 4A. To get some molecular-level insight into the observed dielectric relaxation, information related to this process was extracted from the MD simulations. A natural choice for a direct comparison would be the determination of the time correlation functions (tcf) and the associated rotational correlation times,τµ, of the dipole vectors of water molecules in the vicinity of a specific solute moiety and in the bulk. However, this calculation is associated with some difficulties. First, fast solvent exchange around the functional groups of 1,1-DMU [and 1,3-DMU] leads to a very poor statistics for the tcfs. Second, due to the collective wait, jump and 48 settle mechanism of water reorientation, which also applies to the H2O molecules in the hydration shell, albeit with waiting times different from the bulk, solvent exchange will also influence the experimental relaxation times. Therefore, we confine our discussions here to the analysis of the contact times, τC, of H2O molecules adjacent to hydrophilic (O, cisH, trans-H) and hydrophobic (cis-CH3, trans-CH3) groups of 1,1-DMU and to the lifetimes of solute-solvent and solutesolute aggregates. In order to estimate to which extent these interactions are due to hydrogen bonding we also analyze Hbond lifetimes, τH. The corresponding values as well as the applied radial and angular cut-offs are given in Table 1. Table 1 clearly reveals that the contact times of the H2O molecules hydrating 1,1-DMU moieties, respectively other H2O molecules in bulk, increase in the sequence cis-H
