At present, element 112 (E112, eka-mercury) can be unambiguously identified only by its chemical properties due to the contradictory nuclear-physical experimental data. Chemical experiments on E112 are currently under way at FLNR (Dubna, Russia); similar work is in progress at GSI (Darmstadt, Germany) and PSI (Villigen, Switzerland). It also involves an attempt to confirm the synthesis of E114 and E116 (being their decay product, E112 should be detectable in these experiments). Superheavy element properties are very difficult to study experimentally, because only single atoms are available. In this connection, theoretical predictions of their properties based on accurate ab initio calculations are highly desirable. Because of the strong relativistic contraction and stabilization of the 7s orbital, E112 in its closed shell ground state configuration 7s2 6d10 was expected to behave like a rare gas than like Hg. As a first step in the extensive study of E112 chemistry, bonding in simple diatomic molecules is modeled. Our first results of relativistic correlation calculation of spectroscopic properties for the ground states of the E112H, E112H+, E1122 and E112Au molecules are reported and compared with those of the corresponding compounds of its lighter homologue Hg. The methods of generalized relativistic effective core potential, fully relativistic Fock-space coupled clusters with single and double cluster amplitudes (RCCSD), scalar relativistic UCCSD(T) and spin-orbit direct configuration interaction are used to ensure high accuracy. The primary importance of the proper account for the spin-orbit interactions in E112 compound calculations have been demonstrated. The most dramatic impact of spin-orbit effects was observed for E112H. The calculated equilibrium distance, Re=1.662 A, in E112H is notably smaller than Re=1.738 A in HgH, whereas the E112H dissociation energy is at least as large as in HgH. These data are quite different from the values previously obtained within the scalar-relativistic Douglas-Kroll approximation for E112H [Nakajima and Hirao, Chem. Phys. Lett. 329, 511 (2000)], Re=1.829 A and very small De (0.06 eV). Although the contribution of the spin-orbit interaction for the E112Au and E1122 molecules is smaller than for E112H, it still significantly affects the calculated spectroscopic parameters and, therefore, it should not be neglected in reliable calculations. Our results indicate that the ground-state monovalent E112 compounds resemble the Hg ones whereas no similarity between the behaviour of E112 and inert gases was found. The present work is supported by the RFBR (grants No. 06-03-33060 and 06-03-32346).