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There has been a long standing interest in developing optically pumped alkali atom lasers. Diode laser pumped alkali lasers (DPAL) hold considerable promise for efficient, scalable lasers in the visible range for Rb [1] and Cs [2] atoms. Theoretical basis and performance modeling for the DPAL systems apparently requires the extensive knowledge of thermophysical properties for the alkali-rare gas systems. We present the results of high-level electronic structure calculations of the potential energy curves (PECs) for the ground state of van der Waals molecules MeRg (Me=Rb,Cs) as well as their well-bound MeRg$^+$ cations. The energies were calculated in a wide range of internuclear distance using the coupled-cluster method with single, double and approximate triple excitations CCSD(T), with the $def2$-A(T/Q)ZV-PP basis sets for both atoms augmented by the bound functions centered on a middle of internuclear distance. The extrapolation to complete basis set was performed and the full counterpoise correction technique was employed to remove basis set superposition error. The derived \emph{ab initio} point-wise potentials have been approximated by the closed form based on Chebyshev polynomial expansion, and then, the resulting analytical PECs were used to estimate thermodynamic functions and transport properties of the Me-Rg pairs in the framework of classical, quasi-classical and quantum statistical approaches. The present results are obtained in a wide temperature range and compared systematically with available experimental data and preceding calculations. The full form of the interacting-particle partition function (including quasi-bound and continuum part of the spectra) is found to be essential to complete and correct calculation of the bulk properties of the systems studied.