A valence-bond (VB)/coherent-states (CS) approach to the charge equilibration (CE) model for diatomic molecules is presented in this work (VB part) and its sequel (CS part). By emphasizing theoretical aspects, this approach obtains the classical-electrostatics CE model from a quantum VB model in conjunction with the CS theory. For the VB part, a VB generalized CE (VB/GCE) model, which contains the CE model as a subcase, is derived from a two-electron, three-state VB model via the sequential application of seven approximations. Unlike its CE subcase, the VB/GCE model provides a satisfactory charge-transfer description at dissociation as illustrated with HF((g)) and other molecules. Through the previous derivation, CE charges and CE Coulomb interactions are elucidated in terms of VB Mulliken charges and VB atomic interactions, respectively. Modifications in the above derivation can generate a family of related VB/GCE models that includes the aforesaid VB/GCE model. Despite their classical appearance, all of the VB/GCE and CE models involve VB wave functions corresponding to ground and first-excited states. Moreover, all of the VB/GCE and CE energy and charge optimizations are proven to be equivalent to the variational eigenvector equation procedures of the underlying VB models. The quantum-mechanics/classical-electrostatics connection implicit in this work is further elaborated by means of VB CS sets in the sequel. The VB/CS treatment of polyatomic molecules and additional tests of the present approach will be reported in later papers in this series.