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Adiabatic and Nonadiabatic Charge Transport in Li–S Batteries

Summary

Hybrid-functional and constrained DFT calculations are used to clarify electronic and ionic transport in α-sulfur and Li\(_2\)S, the insulating redox end members in Li–S cells. The study contrasts adiabatic vs nonadiabatic charge transfer: Li\(_2\)S is treated as adiabatic (standard DFT adequate for hops), whereas S\(_8\) ring–ring transitions require nonadiabatic treatment—conventional DFT can overestimate charge-transfer rates by orders of magnitude. Polaronic carriers (holes dominant in Li\(_2\)S; delocalized holes and localized electron polarons in α-S) have very low equilibrium concentrations but sufficient mobility to matter for practical sulfur loadings.

Broader motivation is that Li–S cathodes are limited by shuttle chemistry and poor electronic conduction in S\(_8\) and Li\(_2\)S; clarifying whether charge transport is Marcus-like and adiabatic in both phases versus nonadiabatic in S\(_8\) sets expectations for rate-limiting steps in thick-electrode models.

Methods

  • Electronic structure: Primarily VASP with hybrid functionals (e.g. HSE) for bulk and defects; PAW pseudopotentials; plane-wave cutoffs ~450–500 eV; spin-polarized calculations; Γ-centered k-point meshes with density reduced for large α-S supercells (see article tables).
  • Supercells: α-S conventional cell (128 atoms) and Li\(_2\)S 96-atom supercell from 2×2×2 replication; lattice dimensions for α-S from prior vdW-DF relaxation where noted; forces converged to 0.04 eV/Å (α-S) and 0.01 eV/Å (Li\(_2\)S).
  • Defect space: Many vacancy, interstitial, and polaron configurations (charged/neutral); formation energies; Frenkel and Schottky defects for Li\(_2\)S.
  • Nonadiabatic / localization: Constrained DFT (cDFT) implemented in GPAW using PBE and grid spacing ~0.16 Å to build localized diabatic states and coupling; analysis of Marcus-type rates comparing adiabatic vs cDFT-based approaches for sulfur.
  • Properties computed (reported observables): formation energy trends, barrier estimates along reaction coordinates, electronic structure / band alignment where tabulated, and charge-transfer / Marcus rate metrics from cDFT vs standard DFT (verify every number in the Chem. Mater. PDF).

Findings

  • Li\(_2\)S: Charge transport is adiabatic; hole polarons on S are key; carriers have extremely low equilibrium concentrations but mobilities still relevant for high energy-density targets.
  • α-S: Ring-to-ring transitions are nonadiabatic; standard DFT overestimates transfer rates by up to ~100× relative to the constrained/nonadiabatic analysis; delocalized holes and localized electron polarons dominate mobility discussions.
  • Connecting to cells: low equilibrium carrier concentrations contribute to sluggish transport in both end members; increasing hole concentrations is discussed as a strategy to improve performance.
  • Comparisons / limitations / PDF: The authors compare adiabatic DFT rate estimates to cDFT-based nonadiabatic rates for α-S (orders-of-magnitude gap) and tie Li\(_2\)S transport to hole polaron mechanisms. Hybrid functionals and finite supercell charged-defect corrections introduce uncertainty; device-relevant amorphous sulfur morphologies exceed the idealized bulk models. Verify all barriers and concentrations against the PDF (pdf_path).

Limitations

Functional choices (HSE cost vs PBE/cDFT); finite supercells and charged defect corrections; α-S amorphous/molecular real cathodes differ from idealized bulk models.

Relevance to group

DFT transport benchmark for S/Li\(_2\)S—complements ReaxFF electrolyte and interface kinetics elsewhere in the corpus.

Citations and evidence anchors

  • DOI: 10.1021/acs.chemmater.7b04618.