We recently devised a simple scheme for analyzing on quantitative grounds the Dewar-Chatt-Duncanson donation and back-donation in symmetric coordination complexes. Our approach is based on a symmetry decomposition of the so called Charge-Displacement (CD) function quantifying the charge flow, upon formation of a metal (M)-substrate (S) bond, along the M-S interaction axis and provides clear-cut measures of donation and back-donation charges in correlation with experimental observables [G. Bistoni et al., Angew. Chem., Int. Ed. 52, 11599 (2013)]. The symmetry constraints exclude of course from the analysis most systems of interest in coordination chemistry. In this paper, we show how to entirely overcome this limitation by taking advantage of the properties of the natural orbitals for chemical valence [M. Mitoraj and A. Michalak, J. Mol. Model. 13, 347 (2007)]. A general scheme for disentangling donation and back-donation in the CD function of both symmetric and non-symmetric systems is presented and illustrated through applications to M-ethyne (M = Au, Ni and W) coordination bonds, including an explicative study on substrate activation in a model reaction mechanism.