  Lanthanum hydride is the superconductor with the highest known critical
temperature. It is believed that the superconductivity is of standard BCS-type,
with electrons forming Cooper pairs and opening the superconducting band gap.
Here we show that the BCS electron pairing is in competition with an
alternative pairing: covalent bonding. We show that the covalent pairing is
favored at lower pressures, the superconducting cubic phase becomes unstable as
pressure is reduced. Previous calculations based on static relaxation neglect
three factors, all of which are important in stabilizing the cubic phase.
Finite temperature plays a role, and two quantum effects are also important -
the nuclear wavefunction contributes to destablizing the H$_2$ molecules, and
the zero-point pressure means that calculated pressures are significantly
overestimated by standard methods. We demonstrate these phenomena using
Born-Oppenheimer and path-integral molecular dynamics: these give the same
qualitative picture, with nuclear quantum effects (NQE) increasing the
transition pressure significantly. This competition between molecularization
and superconducting gap formation is the fundamental reason why hydride
superconductors have so far been found only at high pressure.
