We propose a generalization of the formula that gives an integrable quantum 1D spin Hamiltonian with nearest-neighbour interactions as a logarithmic derivative of a vertex model transfer matrix in order to include in this scheme more realistic integrable models. We compute exactly this generalized formula using the R matrix of the XXX model, obtaining the Majumdar-Ghosh Hamiltonian plus a charge-like interaction term. We diagonalize this Hamiltonian using the quantum inverse scattering method and present the Bethe ansatz equations of the model.