In radionuclide compounds undergoing electron capture (EC) decay, the electron density at the nucleus (ρ(0)) and half-life of the nucleus are inversely proportional. Thus, the decay can be accelerated by changing the chemical or physical conditions. A previous study reported a 1.1-1.5% reduction in the half-life of 7Be encapsulated in C60 compared with 7Be metal. However, 7Be was inserted into the fullerene using the rebound energy of the nuclear reaction, which may not be a practical method. This paper elucidates the mechanism of ρ(0) change in various Be compounds from density functional calculations and attempts to propose better systems that show faster EC decay (larger ρ(0)) and/or that are easier to generate than Be in C60. In typical Be compounds, ρ(0) decreases because Be donates electrons to other atoms through chemical bonds and, thus, is not effective. Among the various Be-encapsulated fullerenes (C20-C180), the largest increase in ρ(0) was obtained for C50 fullerene, but the magnitude was almost similar to that of C60. As new systems, we propose Be-encapsulated rare gas solids, which would be generated only by applying high pressure. An increase in ρ(0) from Be metal in the range 2-10%, which depends on the lattice constant, is obtained.