  A precise understanding of solvation is essential for rational search and
design of electrolytes that can meet performance demands in Li-ion and beyond
Li-ion batteries. In the context of Li-O$_2$ batteries, ion pairing is decisive
in determining battery capacity via the solution mediated discharge mechanism
without compromising heavily on electrolyte stability. We argue that models
based on coordination numbers of the counterion in the first solvation shell
are inadequate at describing the extent of ion pairing, especially at higher
salt concentrations, and are often not consistent with experimental
observations. In this study, we use classical molecular dynamics simulations
for several salt anions (NO$_3^-$, BF$_4^-$, CF$_3$SO$_3^-$,
(CF$_3$SO$_2$)$_2$N$^-$) and nonaqueous solvent (DMSO, DME, ACN, THF, DMA)
combinations to improve the understanding of ion paring with the help of a new
metric of ion-pairing. We proposed a metric that defines the degree of
clustering of a cation by its counterions and solvent molecules on a continuous
scale, the limits if which are based on a simple and intuitive condition of
charge neutrality. Using these metrics, we identify the extent of ion pairing
in good agreement with experimental solvation phase diagrams and further
discuss its usefulness in understanding commonly employed measures of salt and
solvent donicity such as the Gutmann donor number.
