Supporting information for: Atomistic Modeling of the Charge Process in. Lithium/Air Batteries

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1 Supporting information for: Atomistic Modeling of the Charge Process in Lithium/Air Batteries Tatjana Dabrowski, and Lucio Colombi Ciacchi,, Hybrid Materials Interfaces Group, Faculty of Production Engineering, Bremen Center for Computational Materials Science (BCCMS) and Center for Environmental Research and Sustainable Technology (UFT), University of Bremen, Am Fallturm, 8359 Bremen, Germany, Fraunhofer Institute for Manufacturing Technology and Advanced Materials IFAM, 69 Oldenburg, Germany, and MAPEX Center for Materials and Processes, University of Bremen, 8359 Bremen, Germany Phone: +49 () Fax: +49 () To whom correspondence should be addressed University of Bremen Fraunhofer IFAM University of Bremen S

2 Cluster structures Li O (i) (ii) (iii) singlet (spin restricted).58å Å Å singlet (spin unrestricted).58å Å Å triplet (spin restricted).38å; Å; Å; Figure S: Li O clusters. S

3 Li 4 O 4 (i) (ii) (iii) singlet (spin restricted) Å Å Å Å - singlet (spin unrestricted) Å Å Å triplet (spin restricted).44å; Å;..39Å; Å; Å; Å;.7 triplet (spin unrestricted).39å; Å;.3 Figure S: Li 4 O 4 clusters. S3

4 Li 6 O 6 (i) (ii) (iii) singlet (spin restricted) Å Å Å singlet (spin unrestricted) Å Å triplet (spin restricted).45å; Å; Å; -.5.4Å; Å;..45Å; Å; Å;.8. ; -.8 triplet (spin unrestricted) Figure S3: Li 6 O 6 clusters. S Å; Å; Å;

5 Li 8 O 8 (i) (ii) (iii) singlet (spin restricted) Å Å Å Å.44Å Å.45Å singlet (spin unrestricted).54å Å.53Å Å triplet (spin restricted).4å; Å; Å; Å; Å; Å; Å; Å; Å; triplet (spin unrestricted).43å; Å; Å; Å; Å; Å; Figure S4: Li 8 O 8 clusters. S5

6 Li 8 O 8 (i) (ii) (iii) quintet (spin restricted).43å; Å; Å;.4..38Å; Å; Å; Å; septet (spin restricted).36å; Å; Å; Å; Figure S5: Li 8 O 8 clusters in a quintet and a septet state. Li 8 O 4 (i) (ii) (iii) singlet (spin unrestricted) Figure S6: Li 8 O 4 clusters. S6

7 Cluster energies Table S: Cluster energies per Li O unit with respect to the lowest energy for the particular Li n O n cluster (marked in red and green for singlet and triplet states, respectively). The (i) restricted Li 8 O 8 cluster (gray) is not considered in the evaluation of the energy minimum of the peroxide-type clusters, since its structure does not form a closed Li 8 O 8 cluster, and is assumed as an artifact of the initial conditions. Gibbs free energy of formation / ev singlet triplet Li O (i) restricted.4 (i) restricted.95 (ii) restricted. (ii) restricted.947 (iii) restricted.8 (iii) restricted.95 (i) unrestricted. (ii) unrestricted.53 (iii) unrestricted. Li 4 O 4 (i) restricted. (i) restricted.83 (ii) restricted.698 (ii) restricted.693 (iii) restricted. (iii) restricted.637 (i) unrestricted.35 (iii) unrestricted.84 (ii) unrestricted.885 Li 6 O 6 (i) restricted.57 (i) restricted.77 (ii) restricted.645 (ii) restricted.55 (iii) restricted.47 (iii) restricted.56 (i) unrestricted.64 (iii) unrestricted. (ii) unrestricted.75 Li 8 O 8 (i) restricted.35 (i) restricted.4 (ii) restricted.85 (ii) restricted.43 (iii) restricted.878 (iii) restricted.3557 (ii) unrestricted.349 (i) unrestricted. (iii) unrestricted.4 quintet septet (i) restricted.563 (i) restricted.37 (ii) restricted.93 (ii) restricted.934 (iii) restricted.37 (iii) restricted.934 S7

8 Gf / ev T / K Table S: Cluster energies of the Li 8 O 4 clusters per Li atom with respect to the lowest energy for the Li 8 O 8 clusters at 98 K. Gibbs free energy of formation / ev Li 8 O 4 (i) unrestricted.566 (ii) unrestricted.34 (iii) unrestricted.36 Figure S7: Gibbs free energy of formation per Li atom as a function of temperature for Li 8 O 4 (red) and Li 8 O 8 (green) clusters, and best-fit lines of the linear regression in orange (correlation coefficient is r =.9984). Bader charge differences Table S3: Bader charge difference between the initial clusters before removal of electrons and the clusters after removal of electrons and an electron minimization (min.) and between the initial clusters before removal of electrons and the final clusters after removal of electrons and an simulation () in vacuum and in DMSO. q e / e q e / e min. min. in vacuum Li 8 O O O O O O5 O O7 O sum(oxygens) in DMSO DMSO Li 8 O O O O O O5 O O7 O sum(oxygens) S8

9 e - e - Figure S8: Visualization of the charge differences upon removal of electrons from negative values (red) to positive values (blue) in DMSO. S9

10 Densities of states O7 O8 O O O - Li e- e- O-O O- Li O7 O O Li Li O4 O4 O-O Li O-O O-O.5 O3 O5 O6 Figure S9: DOS for Li+ and O O pairs in vacuo before removal of electrons in red, after removal of electrons and an electron minimization in purple and after an simulation in green. The initial and final clusters with corresponding atom numbers are shown below the DOS. For comparison, the DOS of the spinpaired O ion of a Li O molecule, the O ion of a LiO molecule and the O molecule are shown in gray. S

11 O-O Li e O-O O- Li O-O Li O3 O-O O-O Li O3 Li O4 O4 Figure S: DOS for Li+ and O O pairs in DMSO, before removal of one electron in red, after removal of one electron and an electron minimization in purple and after an simulation in green. The initial and the final cluster with corresponding atom number are shown below the DOS. For comparison, the DOS of the spinpaired O ion of a Li O molecule, the O ion of a LiO molecule and the O molecule are shown in gray. S

12 O-O Li e O-O O- Li O-O O- Li O-O Li O3 O-O O-O O3 Li O4 Li O4 Figure S: DOS for Li+ and O O pairs in DMSO, before removal of electrons in red, after removal of electrons and an electron minimization in purple and after an simulation in green. The initial and both final clusters with corresponding atom number are shown below the DOS. For comparison, the DOS of the spinpaired O ion of a Li O molecule, the O ion of a LiO molecule and the O molecule are shown in gray. S