Solvation Structure and Dynamics of Lithium Polysulfides

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1 Supplemental Information Solvation Structure and Dynamics of Lithium Polysulfides Nav Nidhi Rajput 1,5 *, Vijayakumar Murugesan 2,5, Yongwoo Shin 1, Kee Sung Han 2,5, Kah Chun Lau 3,4, Junzheng Chen 2, Jun Liu 2,5, Larry A. Curtiss 3,5, Karl T. Mueller 2,5, Kristin A. Persson 1,5 * 1 Lawrence Berkeley National Laboratory, Berkeley, CA 9472, USA 2 Pacific Northwest National Laboratory, Richland, WA 99352, USA 3 Materials Science Division, Argonne National Laboratory, Argonne, IL Department of Physics and Astronomy, California State University, Northridge, CA 9133, USA. 5 Joint Center for Energy Storage Research (JCESR) Classical Molecular Dynamics Simulation Classical molecular dynamics (MD) was performed using GROMACS MD simulation package version The molecules are initially packed randomly in a cubic box of size 6*6*6 Å 3 periodic in XYZ direction using PACKMOL. 2 The initial configuration is minimized in two steps first using steepest descent employing a convergence criterion of 1 kcal/mol*å. and then conjugated-gradient energy minimization scheme employing a convergence criterion of 1 kcal/mol*å. The systems were equilibrated in the isothermal-isobaric ensemble (constant NPT) using the Berendsen barostat to maintain the pressure of 1 bar with a time constant of 2 ps for 2 ns. 3-5 All systems were then melted at 4 K for 2 ns and subsequently annealed from 4 to 298 K in three steps for 3 ns. Finally, the production runs of 2 ns were then obtained in the canonical ensemble (NVT) using an improved velocity-rescaling algorithm proposed by Parrinello et. al. with a time constant of.1 ps at 298 K. The simulation time was long enough to sample adequately the Fickian (diffusive) regime (Figure S11) of all systems and the results were averaged over at least two independent realizations of the same system. We obtained 12ns long trajectories for Li 2 S 4 +LiTFSI and Li 2 S 8 + LiTFSI in DOL:DME solution. Figure S11 shows the comparison of diffusion coefficient obtained from 12 ns long trajectory with the diffusion coefficients obtained from NMR experiments. There is a slight increase in the diffusion coefficient as compared to the ones obtained from 2 ns long trajectory (Figure 3 in manuscript), however it is still much slower than the experimentally measured ones. As reported in the manuscript this is well known limitations of the non-polarizable force field used in this work. Nernst-Einstein relation was used to measure the diffusion coefficient from the mean squared displacement of atoms. The resulting coefficient is fitted from a leastsquares minimization for a straight line for a time period in the diffusion regime and then averaged over two independent realizations of the same system. Single particle dynamics obtained from mean square displacement (MSD) can be divided into three regimes (1) ballistic at early times when the ions have not interacted much with their neighbors (MSD α t 2 ) (2) subdiffusive at intermediate times where ions rattle inside a cage formed by their neighbors (MSD α t 1/2 ), and when the ions escape from these cages, they reach the diffusive or Fickian regime at larger times (MSD α t). In this work we only captured the behavior at diffusive regime. 6 Figure S11(a) shows the log-log plot of MSD obtained from 2 ns long trajectory. It can be seen that the MSD is proportional to t with slope = 1, suggesting that the diffusion coefficients reported in Figure 3 in the manuscript is obtained from the diffusive regime. The bonded and non-bonded parameters for DOL, DME are taken from General Amber Force Field (GAFF), for TFSI - anions from Kelkar et. al. and lithium from Sano et. al. 7 The partial atomic charges for all molecules were derived by first optimizing the geometry using Becky s three-parameter exchange function combined with Lee-Yang-Parr correlation functional (B3LYP) at aug-cc-pvdz theory level using the 1

2 Gaussian 9 8 package and then fitting the electrostatic potential surface using RESP method. Longrange electrostatic interactions were handled by the particle-mesh Ewald (PME) method with a grid spacing of.1 nm. The cutoff distance of 1.2 nm was used for electrostatic and Lennard Jones interactions. Other simulation details are very close to our previous publication. 9 The non-bonded parameters for polysulfides are taken from GAFF, whereas the bonded parameters for polysulfide were developed using DFT calculations (see Table 1). The proper dihedral potential of tetrasulfide has been fitted with the Ryckaert-Bellemans function. = Each Ryckaert-Bellemans parameters are fitted with the corresponding equilibrium torsion angles on the adiabatic potential energy surfaces (PES) using the nonlinear least-squares Marquardt-Levenberg algorithm, here the PES are calculated by the second-order truncated Møller Plesset correlation energy correction method (MP2) with the G(d,p) basis set. Figure S1(a) shows the fitting of the dihedral parameters for tetra-sulfide. The structures obtained from MD simulations are in good agreement with previous DFT results 1 as well as our AIMD results (Fig S1(b)). The difference in the peak height from AIMD and MD simulations is due to different length of trajectories. A well defined peak at ~ 7 Å (Fig S5 (a)) suggest the formation of cluster size of ~ 14 Å radius with long-raged structure in Li 2 S 4, which is agreement the hydrodynamics radius measured for Li-PS with pulse field gradient NMR (Fig 2(b)) results and further validates our force field parameters. The bonded parameters for tetra-sulfide are provided in Table 1. Bonded parameters for other polysulfides are same as tetra-sulfide. Ab Initio Molecular Dynamics Ab Initio Molecular Dynamics (AIMD) was performed using CPMD simulation package 11. For the solvated Li 2 S 4 in bulk electrolytes simulations, a simulation cell 18*18*18 Å 3 consisting of 51 atoms was used, which the system is consists of four Li 2 S 4 species solvated by 18 DOL:DME (1:1) solvent molecules. All the AIMD calculations were carried out using the CPMD program package using periodic boundary conditions, planewave basis sets as the expansion of electronic wavefunctions, and atomic pseudopotentials. In particular, one-electron orbitals were expanded in a planewave basis with a kinetic energy cutoff of 45 Ry restricted to the Gamma point of the Brillouin zone. Medium soft normconserving Trouiller-Martins pseudo-potentials were selected for all the elements in the generalized gradient approximation. All AIMD simulations utilized the PBE functional 12 within the spin-polarized Kohn-Sham formalism with the Grimme dispersion correction for van der Waals interactions. 13 Throughout the simulation, a molecular dynamics time step of 4 atomic units was used and the electrolyte density was fixed and the system was thermally equilibrated at T = 3 K using the Nose-Hoover thermostat via canonical ensemble (NVT). To obtain for radial distribution function as shown (Fig. S1(b), the AIMD trajectories (~ 5 fs) were obtained after ~ 1 ps of thermal equilibration. Pulsed Field Gradient (PFG) NMR Diffusion coefficients of Li + cations, anions and solvent molecules for a range of samples were measured using 7 Li, 19 F and 1 H pulsed-field gradient (PFG) NMR, respectively, on a 6 MHz NMR spectrometer (Agilent, USA) with a 5 mm z-gradient NMR probe, which has a maximum gradient strength of ~31 T/m. Diffusion coefficients were determined from the 7 Li, 19 F and 1 H echo profiles using the Stejskal-Tanner equation, 14 2

3 = where S(g) and S() are echo intensities at a gradient strength of g and, respectively, D is the diffusion coefficient, γ is the gyromagnetic ratio of 7 Li, 19 F or 1 H, g is the gradient strength, δ is the gradient pulse length, and is the diffusion time. The echo profiles were obtained using a stimulated echo sequence with a bipolar gradient (Dbppste, a vendor supplied pulse sequence in Vnmrj) as a function of gradient strength (g) with an appropriate values of gradient length (δ) and diffusion time ( ). The gradient strength was varied in 16 equal steps until the echo signal decays sufficiently at a maximum gradient strength. The effective hydrodynamic radius for Li + cations and DME solvent molecules: r Li * and r DME * were determined from the measured diffusion coefficients of D Li, D DME and D DOL based on the Stokes- Einstein relation of diffusion, = where, k B is the Boltzmann constant, T is the absolute temperature, η is the viscosity and r s is the hydrodynamic radius of the diffusing molecules. The details for the determinations of the effective hydrodynamic radius (r*) for Li + cations and DME molecules can be found in our previous publication. 15 The Li 2 S x solutions were prepared by dissolving stoichiometric amount of elemental sulfur and lithium sulfide (Li 2 S) in mixed DOL/DME (1:1 by volume) based electrolyte at 6 o C overnight in a glove box. FigureS1: (a) Fitting of dihedral parameters for tetra-sulfide (S 4 2- ) (b) comparison of radial distribution function of Li + -DME and Li + -DOL from MD and AIMD simulations 3

4 g(r) (a.u) 6 3 (a) S2 S 2 S3 S 3 S4 S 4 S5 S 5 S6 S 6 S7 S 7 S8 S 8 g(r) (a.u) 8 4 (b) S 2 S2 S3 S 3 S4 S 4 S5 S 5 S6 S 6 S7 S 7 S8 S 8 g(r) (a.u) (c) S 2 S2 S3 S 3 S4 S 4 S5 S 5 S6 S 6 S7 S 7 S8 S 8 g(r) (a.u) S2 S (d) 2 S3 S 3 S4 S 4 S5 S 5 S6 S 6 2 S7 S 7 S8 S Figure S2. Radial distribution function of (a) Li + -S(terminal), (b) Li + -S(inner), (c) Li + -DME and (d) Li + - DOL in Li 2 S x (x=2 to 8) in DOL:DME Figure S3. Representative simulation snapshot of (a) Li 2 S 2 /DOL:DME, (b) (Li 2 S 2 +LiTFSI)/DOL:DME at 298 K. Li + depicted in pink in space-filling format, S 2 2- in yellow in space-filling format, TFSI - in blue licorice format, DME and DOL in grey in line format. 4

g(r) (a.u) 8 6 4 2 Li2S2_DOL:DME 2 S 2 /DOL:DME Li2S2+LiTFSI_DOL:DME 2 S 2 + (LiTFSI)/DOL:DME 1 2 3 4 5 6 Figure S4.

5 g(r) (a.u) Li2S2_DOL:DME 2 S 2 /DOL:DME Li2S2+LiTFSI_DOL:DME 2 S 2 + (LiTFSI)/DOL:DME Figure S4. Radial distribution function of (a) Li + -Li + and (b)li + -S 2 2-, (c) coordination number of Li + - Li +, Li + -S 2 2-, Li + -DME and Li + -DOL in Li 2 S 2 /DOL:DME and (Li 2 S 2 +LiTFSI)/DOL:DME Coordina on Number Li2S2_DOL:DME 2 S 2 /DOL:DME Li2S2+LiTFSI_DOL:DME 2 S 2 + (LiTFSI)/DOL:DME Li-Li Li-S Li-DME Li-DOL (a) (b) (c) Figure S5. (a) Radial distribution function of Li + -Li + in Li 2 S x (x= 2 to 8) in DOL:DME (b) Radial distribution function of Li + -Li + and (c) Li + -TFSI - in Li 2 S x (x= 2 to 8) + Li(TFSI) in DOL:DME Figure S6. Radial distribution function of Li + -Li +, Li + -DME, Li + -DOL, Li + -S x 2- in (a).25 M Li 2 S 4 (b) M Li 2 S 6 and (c).25 M Li 2 S 8 in DOL:DME(1:1) at 298 K. 5

6 Figure S7. The effective hydrodynamic radius of Li + cations and DME molecules determined by pulse field gradient NMR using diffusion coefficients (a) (b) Figure S8 Representative simulation snapshot of (a).25 M Li 2 S 4 (b).25 M Li 2 S 4 +LiTFSI/DOL:DME. Li + depicted in pink in space-filling format, S 2 2- in yellow and TFSI - in blue licorice format. Solvent is removed for the sake of clarity 6

Self-diffusion coefficients of Li +, TFSI - and S x 2- in Li 2 S x (x = 2 to 8) + Li(TFSI) in DOL:DME measured from MD simulations (a) (b) 1

7 Extended Li-S x ordering indicating the cluster formation Figure S9 (a) Radial distribution function of Li + -S x 2- in Li 2 S x + LiTFSI (x= 2 to 8)/DOL:DME solution D* 1-11 (m 2 /s) Li TFSI Sx.4 S S S S S S S Figure S1. Self-diffusion coefficients of Li +, TFSI - and S x 2- in Li 2 S x (x = 2 to 8) + Li(TFSI) in DOL:DME measured from MD simulations (a) (b) 1 Li Log 1 (Δr 2 (t)) 1.1 TFSI S2 Slope = Log 1 (t) Figure S11. (a) Self-diffusion coefficients of Li +, TFSI -, DOL, DME and PSs in.25m Li 2 S x (x =4, 8) 7

8 + 1M Li(TFSI) in DOL:DME computed from 12 ns long trajectory MD simulations and PFG-NMR (b) Log-log scale plot of mean square displacement of Li +, TFSI - and S 2 2- in Li 2 S 2 + LiTFSI in DOL:DME solution show the slope of 1 at longer time scales indicating diffusive regime within 2ns. Table 1. Non-bonded parameter for tetra-sulfur (S 4 2- ). Bond b(nm) K b (KJ mol -1 nm -2 ) s-s s-s Angle θ K θ (kj mol -1 rad -2 ) s-s-s Dihedral C1 C2 C3 C4 C5 s-s-s-s References 1. M. J. Abraham, D. v. d. S., E. Lindahl, B. Hess and the GROMACS development team, GROMACS User Manual version , GROMACS User Manual version Martínez, L.; Andrade, R.; Birgin, E. G.; Martínez, J. M., Packmol: A package for building initial configurations for molecular dynamics simulations. Journal of computational chemistry 29, 3, Berendsen, H. J.; Postma, J. P. M.; van Gunsteren, W. F.; DiNola, A.; Haak, J., Molecular dynamics with coupling to an external bath. J. Chem. Phys. 1984, 81 (8), Bussi, G.; Donadio, D.; Parrinello, M., Canonical sampling through velocity rescaling. The Journal of Chemical Physics 27, 126, Bussi, G.; Zykova-Timan, T.; Parrinello, M., Isothermal-isobaric molecular dynamics using stochastic velocity rescaling. The Journal of Chemical Physics 29, 13, Del Pópolo, M. G.; Voth, G. A., On the structure and dynamics of ionic liquids. J. Phys. Chem. B 24, 18 (5), Takeuchi, M.; Kameda, Y.; Umebayashi, Y.; Ogawa, S.; Sonoda, T.; Ishiguro, S.-i.; Fujita, M.; Sano, M., Ion ion interactions of LiPF6 and LiBF4 in propylene carbonate solutions. J. Mol. Liq. 29, 148, Frisch, M.; Trucks, G.; Schlegel, H.; Scuseria, G.; Robb, M.; Cheeseman, J.; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, G., gaussian 9, Gaussian. Inc., Wallingford, CT 29, Rajput, N. N.; Qu, X.; Sa, N.; Burrell, A. K.; Persson, K. A., The Coupling between Stability and Ion Pair Formation in Magnesium Electrolytes from First-Principles Quantum Mechanics and Classical Molecular Dynamics. J. Am. Chem. Soc Vijayakumar, M.; Govind, N.; Walter, E.; Burton, S. D.; Shukla, A.; Devaraj, A.; Xiao, J.; Liu, J.; Wang, C.; Karim, A., Molecular structure and stability of dissolved lithium polysulfide species. Phys. Chem. Chem. Phys. 214, 16, CPMD, C., opyright IBM Corp Copyright MPI für Festkörperforschung Stuttgart 1997, Perdew, J.; Burke, K.; Ernzerhof, M., Phys Rev Lett 77: Errata:(1997) Phys Rev Lett 1996, 78, Grimme, S.; Ehrlich, S.; Goerigk, L., Effect of the damping function in dispersion corrected density functional theory. J. Comput. Chem. 211, 32,

9 14. Stejskal, E. O.; Tanner, J. E., Spin diffusion measurements: spin echoes in the presence of a time dependent field gradient. J. Chem. Phys. 1965, 42 (1), Chen, J.; Han, K. S.; Henderson, W. A.; Lau, K. C.; Vijayakumar, M.; Dzwiniel, T.; Pan, H.; Curtiss, L. A.; Xiao, J.; Mueller, K. T.; Shao, Y.; Liu, J., Restricting the Solubility of Polysulfides in Li S Batteries Via Electrolyte Salt Selection. Adv. Energy Mater. 216, 6 (11),

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