We present a first principles static and dynamical study of the transition metal hydride series MH₄L₃ (M = Fe, Ru and Os; L = NH₃, PH₃ and PF₃), with a view to arriving at an understanding of how the variation in the electronic properties of the metal sites and ligands can influence the dynamics of the resulting complexes. A broad range of behaviour was observed, encompassing stable classical minima (M = Os, L = NH₃ and M = Ru, L = PH₃) to stable η²-H₂ non-classical minima (M = Fe, L = PF₃ and M = Ru, L = PH₃ or PF₃), with the other structures exhibiting dynamical behaviour that spontaneously converted between the classical and non-classical states during the molecular dynamics simulations. The importance of a small L_axial–M–L_axial angle in stabilising the non-classical state is highlighted, as is a short η²-H₂⋯H_cis distance in non-classical complexes that spontaneously convert to the classical form. We also investigated the changes in the electronic structure of the complex FeH₄(PH₃)₃ during a η²-H₂ bond breaking/bond making reaction and observed direct evidence of the ‘cis effect’, whereby a neighbouring hydride ligand acts to stabilise the intermediate classical state.