Coordination of dissolved transition metals in pristine battery electrolyte solutions determined by NMR and EPR spectroscopy

The solvation of dissolved transition metal ions in lithium-ion battery electrolytes is not well-characterised experimentally, although it is important for battery degradation mechanisms governed by metal dissolution, deposition, and reactivity in solution. This work identifies the coordinating species in the Mn2+ and Ni2+ solvation spheres in LiPF6/LiTFSI–carbonate electrolyte solutions by examining the electron–nuclear spin interactions, which are probed by pulsed EPR and paramagnetic NMR spectroscopy. These techniques investigate solvation in frozen electrolytes and in the liquid state at ambient temperature, respectively, also probing the bound states and dynamics of the complexes involving the ions. Mn2+ and Ni2+ are shown to primarily coordinate to ethylene carbonate (EC) in the first coordination sphere, while PF6− is found primarily in the second coordination sphere, although a degree of contact ion pairing does appear to occur, particularly in electrolytes with low EC concentrations. NMR results suggest that Mn2+ coordinates more strongly to PF6− than to TFSI−, while the opposite is true for Ni2+. This work provides a framework to experimentally determine the coordination spheres of paramagnetic metals in battery electrolyte solutions.


DFT
Prior to tackling the DFT calculations of the EPR shifts, a series of complexes, [Mn(EC) x ] 2+ (x=1,...,8), were constructed to see effect of increasing solvation on the energetics of the ECsolvation of Mn 2+ .Initial structures were the idealised forms, e.g.tetrahedral for x = 4 and trigonal bipyramidal for x = 5.In each case, the structures had their geometry optimised with the B3LYP functional (D3BJ dispersion correction) with the def2-TZVP basis set.Orca version 5.0.3 was used throughout this section along with the default RIJCOSX settings.Furthermore, the tight SCF convergence criteria was used along with the enhanced defgrid3 grid settings.
After optimisation, frequency calculations were performed to confirm convergence and get thermochemistry results.In some cases, very tight geometry and SCF convergence criteria were required to ensure proper geometry convergence.The results are shown in Table S1.
Table S1.Results of DFT calculations exploring the level of EC-solvation of Mn 2+ .The ∆E complex was calculated by E complex -x*E EC -E Mn with stepwise comparison shown with ∂∆E complex .The Gibbs free energy, ∆G complex , was calculated similarly.

Complex
∆E complex / kJ•mol -1 As the number of EC molecules increase the electronic and Gibbs free solvation energy of the systems increase, albeit with diminishing returns.Thus, as seen in Table S1, there is a local free energy minimum at x = 6.This was used then as a starting point for an in-depth analysis of EPR data along with additional DFT calculations (described in the main matter). 1 Electronic Supplementary Material (ESI) for Physical Chemistry Chemical Physics.This journal is © the Owner Societies 2024 The optimised [Mn(EC) 8 ] 2+ structure had one EC not participating in the solvation of the Mn 2+ .
Instead, this extra EC was interacting with other EC molecules, i.e. solvent-solvent interaction, causing a lowering of energy.As the study is on the solvent-metal interaction and as the [Mn(EC) 7 ] 2+ system was already shown to have a positive ∆G, further attempts to force a structure without solvent-solvent interactions were abandoned.peak positions and intensity ratios are strong indicators for significant rhombicity of the zerofield splitting interaction of the Mn 2+ complex.

Variable Temperature NMR
The T 1 minimum, in principle, provides a mechanism for estimating the type and magnitude of the interaction that drives relaxation.To explore this, we modelled the 1 H EC and 19 F PF 6 -data using Equation 7 from the main text, assuming a single Arrhenius-type behaviour for the correlation time, , where E a is the activation energy of the process driving relaxation, is a hypothetical correlation time at infinite temperature, and R is the universal  0 gas constant.Since E a , , and the distance r are linearly independent, they can be extracted  0 from a fit of the VT data (Figure S7).For 19 F PF 6 -paramagnetic relaxation, values of E a = 15.2 kJ/mol, = 8.5x10 -13 s, and r = 18.1 Å are obtained.This calculation implicitly assumes that  0 all PF 6 -ions are simultaneously affected by the same dipolar interaction quantified by a single Mn-F distance, r.This assumption was made so as to allow an estimate for the size of the interaction that causes the observed R 1p maximum (which is a T 1 minimum).This assumption is clearly not valid, however, given the 1000:1 ratio of PF 6 -:Mn 2+ ions, but f M and r cannot be fitted at the same time.An alternative approximation is to use the Mn-F distance at the closest point of approach, r = 6.9 Å, as determined from Davies ENDOR of frozen solutions (Figure S6); this leads to a much shorter T 1 minimum.However, we now must account for the fact that not all PF 6 -can be simultaneously nearby Mn 2+ and we may attempt to estimate the fraction of coordinated Mn 2+ coordinated to PF 6 -(i.e., f M ).Using the value of r obtained above (18.1 Å) as an effective distance r eff yields an estimate of f M of r 6 /r eff 6 ≈ 1/325, which is of the same order of magnitude as [Mn 2+ ]:[PF 6 -].Or if we assume that two PF 6 -ions are nearby Mn 2+ for charge balance (in either inner or outer sphere complexes) and f M = 1/500, then a new value of r of 6.43 Å is obtained.The 19 F R 1p data are therefore consistent with PF 6 -ions occupying outer sphere sites.Alternatively, we may treat the data with the assumption that an inner sphere complex is present: if on average only 10% of Mn 2+ ions form an inner sphere complex with PF 6 -, then r = 3.9 Å, which is also not unrealistic.This calculation provides a rough estimate for the concentration of such inner sphere species (which we note were not observed in the ENDOR experiments at 20 K).Since the different relaxation processes may show considerable variations in their activation energies, they will likely depend on sample composition, temperature, or magnetic field.Given the large numbers of approximations and assumptions made to generate these two estimates, either is consistent with EPR and DFT data; an inner sphere complex with low probability could by itself explain the observed 19 F R 1p results.We suggest that further EPR experiments with different metal-ion and salt concentrations are needed to eliminate the need for some of the approximations.The same approach can be followed to analyse the 1 H EC VT R 1 data (Figure S7b).Values of E a = 14.9 kJ/mol, = 5.2x10 -13 s, and r = 17.9 Å are obtained.In this electrolyte solution, EC  0 is present at 4.5 M. The DFT simulation of [Mn(EC) 6 ] 2+ suggests an inner sphere EC coordination with 1 H pointing away from the Mn 2+ ion.Using the average Mn-H distance of r = 5.85 Å, then f M ≈ 1/820 is obtained, which is consistent with a theoretical value of f M = 1/750 for Mn 2+ sixfold coordinated by EC.This estimate for r is likely an upper limit, since in a liquid electrolyte such a complex is flexible, and the distance of closest approach is likely shorter.On the other hand, this flexibility may also hint at a reason for the shorter correlation time found for EC compared to PF 6 -: PF 6 -is a rigid molecule that rotates or moves as a whole, implying a somewhat longer correlation time.However, a very similar activation energy for the relaxationdetermining step is found for both ligands, which indicates that a similar overall process may be responsible.Figure S11 shows the R 2 /R 1 ratios for the solutions whose R 1p values are shown in Figure 6.

Ambient
R 2 /R 1 ratios are small for the diamagnetic solution (Figure S11a) and all the Ni 2+ -containing solutions (Figure S11b).In the Mn 2+ -containing solution (Figure S11c), the EC R 2 /R 1 ratios are again smallest (1.80 average), followed by the TFSI -R 2 /R 1 ratios (3.50 average), while the PF 6 - R 2 /R 1 ratios are the largest by far (9.04 average).The R 2 /R 1 ratios of these solutions are not inconsistent with the idea that Mn 2+ prefers coordination to PF 6 -and Ni 2+ prefers coordination to TFSI -.In Mn 2+ -containing solutions (Figure S11c), reducing the fraction of TFSI -in solution does not appear to lead to an increase in the 19 F PF 6 -R 2 /R 1 ratio (unlike the increase that was observed in Figure 5b when the EC fraction was reduced).Although the 19 F TFSI -R 2 /R 1 ratios are smaller than the 19 F PF 6 -R 2 /R 1 ratios, this does not necessarily suggest that the PF 6 - residence time is longer than the TFSI -residence time, because different hyperfine constants apply, with small 19 F hyperfine coupling constants being predicted for TFSI -and thus smaller R 2 /R 1 ratios.

Figure S1 .
Figure S1.Comparison of experimental pulsed EPR spectra recorded using field-swept Hahnechoes at X-band.Paramagnetic Mn 2+ is studied in premixed electrolytes based on LiPF 6 or LiTFSI salts.Spectra are normalised to show the resemblance of the outer transitions, characterised by the shoulders of the central transitions.Not exactly overlapping peak positions visible in (b) result from slightly different applied X-band microwave frequencies.

Figure S2 .Figure S3 .
Figure S2.Simulations of EPR spectra with variable zero-field splitting parameters using the EasySpin software.Simulations are performed using identical parameters as for Figure 1 in the main text, varying as indicated and = 0.1 (blue), 0.2 (green), and 0.33 (red).Experimental  / data of 8 mM Mn 2+ in 1 M LiPF 6 in 3:7 EC:EMC is shown in black for comparison.The and  strain parameters are assumed to be proportional to the splitting parameters and are set equal  to and , respectively.These strain values are used to mimic the absence/blurring of   additional shoulders at around 300 and 400 mT in the experimental spectrum.The experimental field-swept Hahn-echo spectrum of Mn 2+ in LiPF 6 electrolyte is overlayed for comparison (black) and scaled to match the outer transitions.The full spectra shown in (a) reveal that increasing values of lead to increasingly broadened central transitions and increasing  intensity and breadth of the outer transitions.The low-field outer transitions magnified in (b) compare the curvature of experiment and simulation.Compared with the least-squares fit referenced in the main text with , the best match lies slightly above 500 MHz, || ≈ 415  somewhat depending on the chosen .Imperfect fitting of the experimental data can result / from a superposition of several similar ligand spheres/conformers of Mn 2+ complexes or fielddependent dispersion.2

Figure S4 .
Figure S4.Two-pulse (2p) and three-pulse (3p) electron spin echo envelope modulation (ESEEM) spectra at X-band frequencies of a solution containing 8 mM Mn 2+ and 1 M LiPF 6 in 3:7 EC:EMC.Nuclear Larmor frequencies with nucleus at the measurement field of    325 mT are shown as dashed lines.Hyperfine interactions involving 7 Li and 31 P nuclear spins (in the weak coupling regime) are highlighted in yellow and are absent for this sample.Resonances from 14 N are typically also observed in that range, depending on hyperfine and quadrupolar couplings.Asterisks denote artefact peaks from baseline distortions.

Figure S5 .
Figure S5.Comparison of experimental (black) and calculated (blue) ENDOR spectra at Qband frequencies, indicating the absence of fluorine in the first coordination sphere, i.e., directly bound to Mn.Experiments were performed on the sample containing 8 mM Mn 2+ and 1 M LiPF 6 in 3:7 EC:EMC.Several acquisition parameters were used to circumvent influences from spectral blind spots (Mims) and hyperfine contrast selectivity (Davies).The peak around of the experimental data is truncated for clarity.The traces simulated with coupling  1 constants from DFT calculations in the Davies ENDOR patterns only include the 19 F couplings.

Figure S6 .
Figure S6.Structure proposition of the ethylene carbonate-separated ion pair of Mn 2+ with two PF 6 − anions.[Mn(EC) 6 ] 2+ atomic positions are taken from geometry-optimised DFT calculations.A separately geometry-optimised PF 6 − anion was added to match the Mn−F distance of 6.9 Å, extracted from the 19 F Davies ENDOR measurement.The circle with radius 6.9 Å indicates spherical symmetry of the Davies ENDOR-extracted Mn−F connection vector.

Figure S7 .
Figure S7.(a) 19 F and (b) 1 H NMR longitudinal paramagnetic relaxation enhancement of a solution of 1 M LiPF 6 in 3:7 EC:EMC + 1 mM Mn(TFSI) 2 .Diamagnetic data and transverse relaxation rates are also shown in Figure 3. Measurements were performed at a field strength of 11.7 T. Data are fitted using Equation 7 from the main text, assuming a single Arrheniustype behaviour for the correlation time.

Table S2 .
DFT-calculated 1 H hyperfine coupling constants of [Mn(EC) 6 ] 2+ .The given order corresponds to the 1 H nuclear positions as provided in the xyz-file.

Table S3 .
DFT-calculated 19F hyperfine coupling constants of [Mn(EC) 5 PF 6 ] + .The given order corresponds to the 19 F nuclear positions as provided in the xyz-file.