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Montmorillonite is a kind of clay mineral which often causes large deformation in soft-rock tunnel engineering and thus brings about safety problems in practice. To deal with these engineering safety problems, the physical and chemical properties of montmorillonite should be studied from basic viewpoints. We study the atomic and electronic structures of montmorillonite by using density-functional theory within the local-density approximation (LDA). The results of calculation show that Al-O bond lengths are longer than Si-O bond lengths. It is found that both the valence band maximum (VBM) and the conduction band minimum (CBM) of montmorillonite are at point Γ, and the calculated direct band gap of montmorillonite is 5.35 eV. We show that the chemical bonding between cations and oxygen anions in montmorillonite is mainly ionic, accompanied as well by a minor covalent component. It is pointed out that the VBM and CBM of montmorillonite consist of oxygen 2p and cation s states, respectively. Our calculated results help to understand the chemical and physical properties of montmorillonite, and are expected to be a guide for solving the problem of large deformation of soft-rock tunnels.