  Many promising nanophotonics endeavours hinge upon the unique plasmonic
properties of nanometallic structures with narrow non-metallic gaps, which
support super-concentrated bonding modes that singularly redshift with
decreasing separations. In this letter, we present a descriptive physical
picture, complemented by elementary asymptotic formulae, of a nonlocal
mechanism for plasmon-redshift saturation at subnanometric gap widths. Thus, by
considering the electron-charge and field distributions in the close vicinity
of the metal-vacuum interface, we show that nonlocality is asymptotically
manifested as an effective potential discontinuity. For bonding modes in the
near-contact limit, the latter discontinuity is shown to be effectively
equivalent to a widening of the gap. As a consequence, the resonance-frequency
near-contact asymptotics are a renormalisation of the corresponding local ones.
Specifically, the renormalisation furnishes an asymptotic plasmon-frequency
lower bound that scales with the $1/4$-power of the Fermi wavelength. We
demonstrate these remarkable features in the prototypical cases of nanowire and
nanosphere dimers, showing agreement between our elementary expressions and
previously reported numerical computations.
