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The nucleus 'Be is investigated by an extended molecular-orbital model and by the generator coordinate method in the simple LCAO approximation. The Hartree-Fock calculations show that a-cluster structures are stable in intrinsic states and the degree of clustering depends crucially on motions of the valence neutron. The generator coordinate calculations give good descriptions of the energy level structures of normal and non-normal parity states in terms of rotational bands. Energy spectra of 'B are given as well. A K"=1/2-band is also predicted. The ground state properties, that is, r.m.s.-radius, Q-moment and .a-moment are reproduced as quite well as electric transitions and charge form factors for the members of the ground rotational band. It is concluded that the molecular model admirably succeeds in systematic explanation of the low energy properties of 'Be. Comparisons are made with the simple shell model and the projected Hartree-Fock calculation by Bouten et al. § I. IntroductionIn the last 15 years, investigations of the cluster structures in light nuclei have been developed st'eadily from molecular viewpoints. It is found that a number of states in the light 4N-selfconjugate nuclei, which include both normal and anomalous states in the shell model versions up to rather high excitation energies, can be successfully explained as some modes of cluster motions."a> Compared with 4N-nuclei, odd-A and odd-odd nuclei have not been studied so well. 2 b> Especially as for 4N + 1-nuclei, a problem of the coupling of a valence nucleon to the motions of clusters has never been fully discussed in any nuclei_ In this and forthcoming papers, 9 Be nucleus is taken up as a typical example in order to study the probelm, because the a-cluster structure of 8 Be is well established_ The experimental data on this nucleus have been accumulated, 3 > not only about nuclear levels but also form factors for electron scattering which are able to give a definite test of model wave functions.As shown in the middle column of Fig. 4, this nucleus has a clear ground rotational band and the moment of inertia is very close to that of 8 Be nucleus (h 2 /2J' =0.49 MeV), which denotes a certain large deformation. Slight et al. 4 > used an extended Nilsson model, which includes major shell mixings up to N + 6, to analyze electromagnetic properties_ They obtained a good fit to the ground n The preliminary results were reported at