  The ab initio calculations suggest that the superconducting state in CaH6
under the pressure at 150 GPa has the highest critical temperature among the
examined hydrogen-rich compounds. For this reason, the relevant thermodynamic
parameters of the superconducting state in CaH6 have been determined; a wide
range of the Coulomb pseudopotential has been assumed:
$\mu^{\star}\in\left<0.1,0.3\right>$. It has been found that: (i) The critical
temperature (Tc) changes in the range from 243 K to 180 K. (ii) The values of
the ratio of the energy gap to the critical temperature ($R_{\Delta}\equiv
2\Delta\left(0\right)/k_{B}T_{C}$) can be found in the range from 5.42 to 5.02.
(iii) The ratio of the specific heat jump ($\Delta C\left(T_{C}\right)$) to the
value of the specific heat in the normal state ($C^{N}\left(T_{C}\right)$),
which has been represented by the symbol Rc, takes the values from 3.30 to
3.18. (iv) The ratio $R_{H}\equiv
T_{C}C^{N}\left(T_{C}\right)/H^{2}_{C}\left(0\right)$, where
$H_{C}\left(0\right)$ denotes the critical thermodynamic field, changes from
0.122 to 0.125.
  The study has brought out the expressions that correctly predict the values
of the thermodynamic parameters for the superconducting state in CaH6 and for
the compounds: SiH4(H2)2, Si2H6, B2H6, SiH4, GeH4, and PtH. Next, in the whole
family of the hydrogen-rich compounds, the possible ranges of the values have
been determined for Tc, $R_{\Delta}$, Rc, and $R_{H}$. It has been found that
the maximum value of the critical temperature can be equal to 764 K, which very
well correlates with Tc for metallic hydrogen (p=2 TPa). Other parameters
($R_{\Delta}$, Rc, and $R_{H}$) should not deviate from the predictions of the
BCS theory more than the analogous parameters for CaH6.
