Ab initio electronic structure calculations of the Mg15TMH32 (TM - transition metals - 6.25聽at.%) systems for the entire 3d TM series have been performed using full-potential (linearized) augmented plane waves with addition of local orbitals (FP-LAPW聽+聽LO and APW聽+聽lo) as implemented in WIEN2k code and projected augmented waves (PAW) method using Abinit code. Details of bonding and mechanism of the TM impurities influence on destabilization of MgH2 were established by investigation of changes of electronic structure after the TM impurities insertion into MgH2 and by using the 鈥渁toms in molecules鈥?(AIM) Bader's charge density topology analysis. The obtained trends of all calculated observables show that along the 3d series TMs accomplish different kinds of bonding with nearest and next-nearest neighbor hydrogen atoms that in general weaken related Mg-H bonds and destabilize the surrounding MgH2 matrix.