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A new Combination of Atomic Boxes (CAB) molecular orbital model is introduced, having the following characteristics:1)Atomic model potentials are one-dimensional potential boxes of finite depth UA and of length LA, the box-parameters being chosen to give valence electron ionization energies.2)Explicit molecular model potentials are constructed by combining all the model potentials of the atoms in the molecule.3)A minimum computational effort leads to rigorous solutions of the resulting Schroedinger equation.