Towards a Molecular Understanding of Energetics in Li-S Batteries using Non-Aqueous Electrolytes: A High-level Quantum Chemical Study

Transcription

1 Supporting Information Towards a Molecular Understanding of Energetics in Li-S Batteries using Non-Aqueous Electrolytes: A High-level Quantum Chemical Study Rajeev S. Assary a,b*, Larry A. Curtiss a,b,*, and Jeffrey S. Moore b,c a) Materials Science Division Argonne National Laboratories Argonne, IL, USA, b) Joint Center of Electrical Storage Argonne National Laboratories Argonne, IL, USA, c) Department of Chemistry University of Illinois at Urbana-Champaign 505 S. Mathews Avenue Urbana, IL, USA, *: corresponding authors R.S.A., assary@anl.gov, Tel: , Fax: L.A.C., curtiss@anl.gov, Tel: , Fax:

2 Table S1A. Comparison of computed (G4MP2, and B3LYP) electron affinity of S, S2, and S8 with the experiment. Computed first and second reduction potentials of S2 molecule is compared in various solvent dielectrics Electron Affinity (EA) species B3LYP/6-31+G(d) a G4MP2 Expt S(triplet) S 2 (triplet) S Reduction potential b (first and second reduction potentials in V, Li/Li+) Water DMSO Acetonitrile Acetone THF ε=78.4 ε=46.8 ε=36.7 ε=20.5 ε= (2.24) 2.77 (2.20) 2.76 (2.17) 2.71 (2.07) 2.50 (1.67) a: B3LYP provides reasonable accuracies for the EA computation of S and S 2 systems compare to other hybrid DFT methods. See Schaefer et al, Chemical Reviews, 2002, 102, for the experimental data. b :Details of the reduction potential evaluation is shown in the manuscript. Table S2B. Comparison of computed energetics (atomic units) and reduction potentials (V wr.t. Li/Li + ) gas phase optimization + solution phase single point Solution phase System a Ee (B3LYP/6-31+G* b E solv (SMD) (B3LYP/6-31+G*) G(gas phase) (G4MP2), au G(soln) = ((Esolv-Ee)+ G(gas, c Reduction potential (V) d G(soln) G4MP2 reduction potential (V) G4MP2)) S S2(1-) S2(2-) a: computed energy at the B3LYP/6-31+G(d)//6-31+G(d) b: single point solvation energy evaluation using SMD model at the B3LYP/6-31+G(d) level of theory. d: Reduction potentials are computed using the Nernst equation c: G4MP2 keyword is used along with scrf(smd,solvent=acetone) keyword in Gaussian 09 software 2

3 Table S3. Computed activation barriers (ev), rate constants (s - ), and half-life (hours) for the C-O bond cleavage reactions of TEGDME and PC. Eyring equation is used to compute the rate constant of various reactions. Note that, instead of activation free energy (ΔG ), we have used solution enthalpy (ΔH, this include solvation free energy) in the Eyring equation to approximate the rate constant to avoid overestimation of rates due to significant entropy change during the reaction. a ΔH (soln) Rate constant, k(s -1 ) ( K), b Half-life T 1/2, hours T 1/2 = ln(2)/k(t) hours -1 a ΔG (soln) Rate constant, k(s -1 ) ( K), b Half-life T 1/2, b hours T 1/2 = ln(2)/k(t) hours -1 TEGDME S 3 (-1, rad) x x x x S 3 (2-) x x x x S 4 (2-) x x x x S 2 (1-, rad) x x x x S(1-, rad) x x x x S 2 (2-) x x x x Li 2 S x x x x Li 2 S x x x 10 6 Li 2 S x x x Li 2 S x x x x PC S 3 (-1, rad) x x x x S 3 (2-) x x x x 10 6 S 4 (2-) x x x 10 8 S 2 (1-, rad) x x x x S(1-, rad) x x x x S 2 (2-) x x Li 2 S x x x Li 2 S Li 2 S Li 2 S a : ΔH (soln) = ΔEe(MP2)+ ΔHcorr(B3LYP)+ ΔG(solvation) b Approximation based on first order reaction kinetics 3

4 Figure S 1 Optimized structures of S 8, S 7, S 6, S 5, S 4, S 3, and S 2 at the B3LYP/6-31G(2df,p) level of theory Figure S 2 Optimized structures of Li 2 S 8, Li 2 S 7, Li 2 S 6, Li 2 S 5, Li 2 S 4, Li 2 S 3, and Li 2 S 2 at the B3LYP/6-31G(2df,p) level of theory 4

5 (a) (b) 5

6 (c) Figure S 3 (a to c) : The B3LYP optimizes structures of various polysulfide Sn (n = 2 to 8) mono/di anions 6

7 Table S 3. Computed free energy changes (ev) of selected reactions in gas phase and in the solution phase at the B3LYP and G4MP2 level of theory. Solvation energies are computed using the B3LYP/6-31+G* level of theory reaction G( 298 K) gas phase, ev G( 298 K) gas phase, ev G( 298 K) + c G solv, ev B3LYP/6-31+G* G4MP2 G4MP2 + SMD solvation energy S Li 8 Li 2 S S8 + 2Li Li 2 S Li 2 S 8 + 2Li 2 Li 2 S Li2S8 + 2Li Li 2 S 3 + Li 2 S Li 2 S 8 + 2Li Li 2 S 6 + Li 2 S Li 2 S 8 + 2Li Li 2 S 7 + Li 2 S Li 2 S 4 + 2Li 2 Li 2 S Li 2 S 3 + 2Li Li 2 S + Li 2 S Li 2 S 2 +2 Li 2Li 2 S Table S 4. Computed free energies (ev) of selected reactions of Li2S8 mono anion at the G4 MP2 level of theory in gas phase and in the solution Solvation energies are computed using the B3LYP/6-31+G* level of theory reaction ΔG( 298 K) ΔG( 298 K) + c ΔG solv gas phase solution likelihood of reaction 8 Li 2 S 6 + S No 8 Li 2 S 5 + S likely 8 Li 2 S 4 + S No 8 Li 2 S 3 + S No 8 Li 2 S 2 + S No Li 2 S 1-8 Li 2 S S No Li 2 S 1-8 Li 2 S S No Li 2 S 1-8 Li 2 S S No Li 2 S 1-8 Li 2 S S No Li 2 S 1-8 Li 2 S S No 8 Li 2 S 6 + S No 8 Li 2 S 5 + S No 8 Li 2 S 4 + S No 8 Li 2 S 3 + S No 8 Li 2 S 2 + S No Li 2 S S No Li 2 S S No Li 2 S S No Li 2 S S No Li 2 S S No Li 2 S 2-8 Li 2 S S No Li 2 S Li + 2 Li 2 S Yes Li 2 S Li + Li 2 S 3 + Li 2 S Yes Li 2 S Li + Li 2 S 2+ Li 2 S Yes Li 2 S Li + 2 Li 2 S + Li 2 S likely 7

8 Figure S 4. The C-O bond cleavage of Propylene carbonate by S 2 2- and S 3 2- in solution Figure S 5. The C-O bond cleavage of dioxalone by S 2 2- anion in the solution 8

9 Figure S 6. Optimized structure of tetraglyme anion upon the deprotonation of site B (See Scheme S2 of the main text) at the B3LYP/6-31G(2df,p) level of theory. 9