  The properties of the electronic ground state of the polar and paramagnetic
europium-$S$-state-atom molecules have been investigated. Ab initio techniques
have been applied to compute the potential energy curves for the
europium-alkali-metal-atom, Eu$X$ ($X$=Li, Na, K, Rb, Cs),
europium-alkaline-earth-metal-atom, Eu$Y$ ($Y$=Be, Mg, Ca, Sr, Ba), and
europium-ytterbium, EuYb, molecules in the Born-Oppenheimer approximation for
the high-spin electronic ground state. The spin restricted open-shell coupled
cluster method restricted to single, double, and noniterative triple
excitations, RCCSD(T), was employed and the scalar relativistic effects within
the small-core energy-consistent pseudopotentials were included. The permanent
electric dipole moments and static electric dipole polarizabilities were
computed. The leading long-range coefficients describing the dispersion
interaction between atoms at large internuclear distances $C_6$ are also
reported. The EuK, EuRb, and EuCs molecules are examples of species possessing
both large electric and magnetic dipole moments making them potentially
interesting candidates for ultracold many-body quantum simulations when
confined in an optical lattice in combined electric and magnetic fields.
