Collision-Induced Effects on the Dielectric Properties of Liquid Dimethylsulfoxide

[摘要] Dimethyl sulfoxide (DMSO) is a highly polar (μ≈4.3D) aprotic solvent which has broad practical applications in chemical, biochemical, and pharmaceutical sciences.1-3 It has been widely used as crioprotectant agent of biological tissues because it prevents water from freezing within cells, and as a coadjuvant drug carrier because of its high permeability across biomembranes.3 It is also one of the most popular protein-dissolving organic solvents. The behavior of DMSO aqueous solutions has also attracted a great deal of interest because of the large deviations from ideal mixing found in several physicochemical properties.4-13 The prevailing view is that most of these effects are associated with DMSO's strong hydrophilic nature, which leads to the formation of stoichiometrically well-defined DMSO-water aggregates and pronounced structural microheterogeneities.10,14-17 Hydrophobic hydration effects may also play a role in the structural properties of these mixtures.18 The wealth of interesting experimental data on DMSO systems has prompted several theoretical and computer simulation studies seeking to better understand this liquid from a microscopic perspective.14-17,19 In the last ten years or so, a number of force fields have been taylored to reproduce the overall thermodynamical, structural and dynamical behavior of DMSO and its aqueous mixtures.15,20-23 Some of these interaction potential models have also been subject to extensive molecular dynamics (MD) simulations specially aimed at characterizing their dielectric behavior.24-25 It is found that the dielectric constant of all simulated models are in good agreement with the experimental estimates for DMSO at room temperature. The dipole-dipole spatial correlations as measured by the Kirkwood g-factors and the dipolar symmetry projetions,26 , are consistent with the physical picture portrayd by several experimental measurements which suggest that DMSO molecules form head-to-tail dipole chains such that adjacent chains have dipoles pointing in opposite directions.24 This local structure, reminiscent of the solid phase,4 is predominantly due to dipolar interactions. The keen interest in the dielectric behavior of polar liquids is largely due to the fact that these properties are essential to characterize the liquid as a reactional medium for chemical processes involving ionic or polar species.27 Dielectric properties such as dielectric constants, dielectric relaxation times, frequency dependent far infrared (FIR) absorption coefficients, and longitudinal dielectric relaxation times are key ingredients to the description of a variety of physicochemical phenomena, specially solvation dynamics and charge transfer reactions.28 Unlike the static (i.e., zero frequency) dielectric behavior of DMSO, which has been well described by MD simulations,24 the dynamical or relaxation properties still need further studies. In particular, we mention that the main relaxation time obtained from our previous MD simulations25 using the nonpolarizable P2 model (~16 ps) is roughly 30% too low compared with experimental values. Although, discrepancies like these between simulated and experimental estimates are not uncommon for dielectric properties in view of their complexity from a molecular standpoint, it is highly desirable to explore alternative routes that might lead to improvements in the modelling of such properties. The force fields for liquid DMSO available in the literature consist of nonpolarizable interaction potentials. Therefore, a feature common to previous simulations of these systems is the lack of collision-induced effects that are present in the real liquid due to the molecular polarizability. In other polar liquids such as acetonitrile, methanol, water, and carbonyl sulfide (OCS), for instance, polarizability effects have been shown to be an important component of their dynamic dielectric behavior, including the line shape of the FIR absorption spectra.29-32 The question then arises as to what extent induced dipoles contribute to the dielectric properties of DMSO. In order to address this problem, we have carried out lengthy (5 ns) MD simulations in which the effects of molecular polarizability upon the liquid dielectric properties are taken into account within the context of a first order perturbation theory, analogous to that implemented for acetonitrile,29 metanol,30 and water.31 In this approach, the MD trajectories are generated exclusively under the original nonpolarizable Hamiltonian. At each timestep, the electric field set up by the permanent interaction-site charges is used to evaluate the induced dipoles assuming a model polarizability tensor. Our primary goal is to investigate on general grounds the effects of the induced dipoles upon the simulated dielectric relaxation and the FIR spectrum of DMSO.   Computational Details Interaction potentials and simulations We have used the P2 interaction model for liquid DMSO developed by Luzar and Chandler,15 which consists of four interaction sites representing the oxygen atom (O), sulfur (S), and the methyl groups (C) treated as united atoms centered at the carbons. The molecular geometry is kept fixed with bond lengths OS=1.53Å and SC=1.80Å, and bond angles OSC=107.75° and CSC=97.4°. This model has been used in previous simulations and reproduces well several physicochemical properties of DMSO.15,24 The potential energy between molecules i and j is a sum of site-site pair interactions involving standard (6-12) Lennard-Jones plus Coulombic termsIn these equations, rαi denotes the position of the α-th site in the i-th molecule, and qα identifies the site charge in units of the electron charge, e. Additional details of the intermolecular potential parameters are given in Table 1.   The simulations were performed in the NVE ensemble with N=500 DMSO molecules placed in a periodically replicated cubic box whose dimensions are such as to reproduce the liquid density at an average temperature of 298 K.5 Lennard-Jones forces were cut-off at half the box length and Coulomb forces were treated via Ewald sums with conducting boundaries to ensure proper treatment of the dielectric properties within the formalism used here.33 The equations of motion were integrated with SHAKE34 leap-frog algorithms35 with a timestep of 6 fs. Total energy conservation is achieved within 0.2% during unperturbed 24 ps runs. Approximately 200 of such runs were used for data analysis, each separated by smaller runs (4 ps) during which the velocities were rescaled to the desired temperature of 298 K. The trajectories were discarded during velocity rescaling. Molecular polarizability model Ideally, in the simulation of dielectric properties of liquids, one would like employ model potentials that fully embody the fluctuating nature of the molecular charge distribution due to interparticle interactions. However, the intrinsic many-body nature of polarizable Hamiltonians renders such simulations quite demanding computationally, which explains the scarcety of simulation studies of dielectric properties using polarizable potentials. In contrast, nonpolarizable force fields, such as the P2 potential for DMSO, in which the magnitude of the electric multipole moments are held fixed, are widely used because of their pairwise additivity. The success of nonpolarizable models in describing dielectric properties reasonably well relies in the enhancement of the molecular dipole moment with respect to the gas phase value, which is typical of most models. For the P2 model specifically, one has μ = 4.48 D, while the gas phase value for DMSO is estimated at 3.93 D. This dipole enhancement takes into account some of the interaction induced effects present in real condensed phases. Nevertheless, potentially important dynamical effects may be entirely left out. In order to gain better understanding of the role of induced dipoles on the dielectric properties of the P2 model, we treat induction effects more explicitly by considering the contributions from induced dipoles to the collective polarization of the system but without considering the forces due to induction in the equations of motion.29-30 In this scheme, the electric field on each molecule along the MD trajectory generated by the nonpolarizable P2 potential is used to compute the induced dipole according toHere, αi is the polarizability tensor of molecule i rotated into the lab frame of reference and Ei is the electric field at the center of molecule i created by all the other molecules in the system. The molecular induced dipoles μiI, therefore, fluctuate with time. The molecular polarizability tensor expressed in the body-fixed coordinate axes has been obtained from Thole's model36 and is given by:The molecular coordinate axes are defined with the z axis along the SO bond while the xy plane bisects the CSC angle. Diagonalization of this tensor yields α1 = 8.07, α2 - 8.86, and α3 = 6.54 Å3 for the principal polarizabilities. The molecular polarizability,= 1/3Trα = 7.76 Å3, is in good agreement with the experimental values of Miller37 (7.97 Å3) and Pacak38 (8.00 Å3). Theoretical Background Within linear response theory, the frequency dependent macroscopic dielectric permittivity of an infinite system (albeit an infinitely periodic one) is given by:39where y = Nμ2/9VkBTε0 is the usual dipolar strength of the system andis the unnormalized time-correlation function (TCF) of the system's (collective) dipole densitywhich has contributions from permanent, , and induced, , molecular dipole moments. Accordingly,has contributions from permanent and induced autocorrelations as well as from cross-correlations between permanent and induced components:withIn a highly polar fluid such as DMSO, the μiI(t) dipole moments are predominantly induced by the collection of permanent molecular dipoles μi0(t). The dynamics of the total induced dipole MI(t) is then expected to be strongly influenced by its permanent counterpart M0(t). The distinct relaxation mechanisms due to interaction-induced dipoles can be conveniently investigated by projecting out of MI(t) the part that relaxes as M0. According to the projection scheme of Madden and Kivelson,39,40 the induced collective dipole is separated into "local field" and "collision-induced" contributions:whereis the static projection of the induced collective dipole over the permanent one (it is, therefore, a measure of the extent of static correlation between permanent and induced dipoles). The quantityrepresents the fluctuations of the induced moments around the permanent collective dipole renormalized by the induced effects. Notice that unlike MI(t), the vector ΔM(t) is orthogonal to M0(t) at any given time (i.e., ‹ΔM(t) . M0(t)› = 0). In terms of projected variables, the total time-correlation function, equation 9, can be separated into a purely "reorientational" (R), a "collision-induced" contribution (Δ), and their cross correlation (X):withand In these equations,is the collision-induced collective dipole autocorrelation, andis the cross-correlation between collision-induced and renormalized permanent collective dipole. Notice that = 0.   Results and Discussion Static Properties We begin discussing our data by providing some quantitative assessment on the how the computed quantities vary with the length of the simulation run. This is specially important in view of the notoriously slow convergence of static dielectric properties calculated from computer simulations.41,42 For that purpose, we display in Figure 1 the cumulative average ofas a function of the simulation time (in units of ns). The values ofand ΨII(t) converge a little faster than the purely permanent dipole contribution and, therefore, are not shown. As clearly shown, the computed static correlations are well-converged within the length of our simulations.   Results for the static dielectric constant of the simulated model and its various contributions are collected in Table 2. By considering only the permanent dipoles, the value of ε(0) - ε∞ is 41.7, in reasonable agreement with the experimental data, (ε(0) - ε∞)exp = 42.7,12 as noted earlier.24 When induced effects are taken into account, ε(0) - ε∞, which by virtue of Eqs. (6), (9)-(12) equals 9y[Ψ00(0) + Ψ0I(0) + ΨII(0)], jumps to 68.5. This value is roughly 50% too large compared to experiments and should not be unexpected since some of the induced effects were already implicitly incorporated into the intermolecular potencial model in order to reproduce thermodynamic and structural features of DMSO without explicit induction forces.15 A smaller value, ε(0) - ε∞ = 57.5, is obtained if the gas phase dipole moment is used to compute the collective dipoles. This is equivalent to scaling the quantity Ψ00(0) by [μgas/μP2]2 and Ψ0I(0) by μgas/μP2 (see Eqs. (6)-(12)).43 This value for the dielectric constant is still substantially larger than the experimental data, but again, the situation is unescapable within the present formalism since the structure of the simulated liquid itself results from a molecular model whose dipole moment corresponds to the condensed phase value. Similar observations have been made in previous studies.29-31   Further inspection of Table 2 shows that induced dipoles autocorrelation (ΨII) corresponds to less than 10% of the permanent counterpart, Ψ00, while the cross-correlations between permanent and induced dipoles, Ψ0I, is nearly 50% of Ψ00. This indicates that a large portion of the induced dipoles does follow the permanent ones. In terms of projected variables, one can see clearly through the magnitudes of ΨR and ΨΔ, that the main effect of the induced dipoles upon the static dielectric properties is to enhance the value of the purely permanent dipole autocorrelation through a local field factor L = (1 + G)2 = 1.656 (cf. equation 17). Similar observations have been made in simulation studies of induction effects in acetonitrile29 and methanol.30 The results reported above can be used to test molecular theories of dielectric properties of polarizable polar fluids. In the celebrated theory of Madden and Kivelson, 39 the local field factor is given bywhen one neglects anisotropies in the molecular polarizability tensor, which in our

[学科分类] 化学（综合）