Thermodynamics of solvent competition in mixed carbonate lithium-ion solvation: A DFT study of Li⁺(EC)_4-n(DMC)_n...

Lithium-ion solvation in carbonate electrolytes plays a central role in determining the performance and stability of lithium-ion batteries, yet the molecular factors governing solvent competition within the Li⁺ coordination shell remain incompletely understood. In this work, density functional theory calculations combined with continuum solvation modeling were used to investigate ligand substitution in Li⁺(EC)_4-n(DMC)_n complexes, where ethylene carbonate (EC) was systematically replaced by dimethyl carbonate (DMC). The calculated stepwise free energies are _-0.58, +0.39, _-2.84, and +0.50 kcal mol^-1 for n = 1-4, respectively, producing a distinctly non-monotonic substitution profile. The overall free-energy minimum occurs at n = 3 (ΔG = _-3.03 kcal mol^-1), identifying Li⁺(EC)(DMC)₃ as the lowest-free-energy member of the modeled microsolvation series under the adopted computational conditions. Structural analysis shows that Li⁺ maintains a four-coordinate inner-shell geometry throughout the substitution series, indicating that ligand exchange occurs within a constrained coordination framework rather than through expansion of the coordination number. An expanded outer-shell analysis further shows that five of six nominally outer-shell Li⁺(EC)₃···(DMC)₂ starting topologies underwent inward migration of one DMC molecule during unconstrained optimization. Only the topology in which the two outer-shell DMC molecules were associated with the same EC ligand retained both DMC molecules outside the first coordination shell, and this structure lies 8.53 kcal mol^-1 above the lowest-energy optimized structure in that set. Across n = 0-3, the summed principal LP(O) → LP*(Li) natural bond orbital second-order perturbation energies change by +0.52, -0.47, and +0.88 kcal mol^-1 for the first three substitutions, respectively, following the same favorable, unfavorable, and strongly favorable pattern as the corresponding stepwise free energies. These NBO quantities are comparative electronic descriptors rather than additive components of ΔG; the calculated free energies also include contributions from structural relaxation, continuum solvation, thermal and entropic effects, and interligand interactions. Published ¹⁷O NMR and FTIR/NMR measurements support carbonyl-oxygen coordination and mixed EC/DMC solvation while demonstrating that bulk speciation depends on electrolyte composition, salt concentration, and ion pairing. The present calculations therefore provide a controlled salt- and additive-free thermodynamic baseline for intrinsic EC/DMC competition rather than quantitative populations for a practical electrolyte.