  The ^1{\Sigma}^+ electronic ground states of MgLi^+ and CaLi^+ molecular ions
are investigated for their spectroscopic constants and properties such as the
dipole- and quadrupole moments, and static dipole polarizabilities. The
quadrupole moments and the static dipole polarizabilities for these ions have
been calculated and reported here, for the first time. The maximum possible
error bars, arising due to the finite basis set and the exclusion of higher
correlation effects beyond partial triples, are quoted for reliability.
Further, the adiabatic effects such as diagonal Born-Oppenheimer corrections
are also calculated for these molecules. The vibrational energies, the
wavefunctions, and the relevant vibrational parameters are obtained by solving
the vibrational Schr\"odinger equation using the potential energy curve and the
permanent dipole moment curve of the molecular electronic ground state.
Thereafter, spontaneous and black-body radiation induced transition rates are
calculated to obtain the lifetimes of the vibrational states. The lifetime of
rovibronic ground state for MgLi^+ , at room temperature, is found to be 2.81 s
and for CaLi^+ it is 3.19 s. It has been observed that the lifetime of the
highly excited vibrational state is several times larger than (comparable to)
that of the vibrational ground state of MgLi^+ (CaLi^+ ). In addition, a few
low-lying electronic excited states of {\Sigma} and {\Pi} symmetries have been
investigated for their electronic and vibrational properties, using EOM-CCSD
method together with the QZ basis sets.
