  The frustrated quantum spin system on the distorted diamond chain lattice
suitable for the alumoklyuchevskite is investigated using the numerical
diagonalization of finite-size clusters and the level spectroscopy analysis. It
is found that this model exhibits three quantum phases; the ferrimagnetic
phase, the spin gap one, and the gapless Tomonaga-Luttinger liquid depending on
the exchange coupling parameters. The ground state phase diagram is presented.
