  While hydrogen-rich materials have been demonstrated to exhibit high T$_c$
superconductivity at high pressures, there is an ongoing search for ternary and
quaternary hydrides that achieve such high critical temperatures at much lower
pressures. First-principles searches are impeded by the computational
complexity of solving the Eliashberg equations for large, complex crystal
structures. Here, we adopt a simplified approach using electronic indicators
previously established to be correlated with superconductivity in hydrides.
This is used to study complex hydride structures, which are predicted to
exhibit promisingly high critical temperatures for superconductivity. In
particular, we propose three classes of hydrides inspired by the FCC RH$_3$
structures that exhibit strong hydrogen network connectivity, as defined
through the electron localization function. The first class [RH$_{11}$X$_3$Y]
is based on a Pm$\overline{3}$m structure showing moderately high T$_c$, where
the T$_c$ estimate from electronic properties is compared with direct
Eliashberg calculations and found to be surprisingly accurate. The second class
of structures [(RH$_{11}$)$_2$X$_6$YZ] improves on this with promisingly high
density of states with dominant hydrogen character at the Fermi energy,
typically enhancing T$_c$. The third class
[(R$^1$H$_{11}$)(R$^2$H$_{11}$)X$_6$YZ] improves the strong hydrogen network
connectivity by introducing anisotropy in the hydrogen network through a
specific doping pattern. These model structures and the design principles
provide the enough flexibility to optimize both T$_c$ and the structural
stability of complex hydrides.
