We study the instantaneous virial balance of clumps and cores (CCs) in 3D simulations of driven, MHD, isothermal molecular clouds (MCs). The models represent a range of magnetic field strengths in MCs from subcritical to non-magnetic regimes. We identify CCs at different density thresholds, and for each object, we calculate all the terms that enter the Eulerian form of the virial theorem (EVT). A CC is considered gravitationally bound when the gravitational term in the EVT is larger than the amount for the system to be virialized, which is more stringent than the condition that it be large enough to make the total volume energy negative. We also calculate, quantities commonly used in the observations to indicate the state of gravitational boundedness of CCs such as the Jeans number J_c, the mass-to magnetic flux ratio mu_c, and the virial parameter alpha_vir. Our results show that: a) CCs are dynamical out-of-equilibrium structures. b) The surface energies are of the same order than their volume counterparts c) CCs are either in the process of being compressed or dispersed by the velocity field. Yet, not all CCs that have a compressive net kinetic energy are gravitationally bound. d) There is no 1-to-1 correspondence between the state of gravitational boundedness of a CC as described by the virial analysis or as implied by the classical indicators. In general, in the virial analysis, we observe that only the inner regions of the objects are gravitationally bound, whereas J_c, alpha_vir, and mu_c estimates tend to show that they are more gravitationally bound at the lowest threshold levels and more magnetically supercritical. g) We observe, in the non-magnetic simulation, the existence of a bound core with structural and dynamical properties that resemble those of the Bok globule Barnard 68 (B68).
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