An expansion of energy characteristics of wide thin slab of thickness L in power of 1/L is constructed using the free-electron approximation and the model of a potential well of finite depth. Accuracy of results in each order of the expansion is analyzed. Size dependences of the work function and electronic elastic force for Au and Na slabs are calculated. It is concluded that the work function of low-dimensional metal structure is always smaller that of semi-infinite metal sample. A mechanism for the Coulomb instability of charged metal clusters, different from Rayleighs one, is discussed. The two-component model of a metallic cluster yields the different critical sizes depending on a kind of charging particles (electrons or ions). For the cuboid clusters, the electronic spectrum quantization is taken into account. The calculated critical sizes of Ag_{N}^{2-} and Au_{N}^{3-} clusters are in a good agreement with experimental data. A qualitative explanation is suggested for the Coulomb explosion of positively charged Na_{N}^{n+} clusters at 3<n<5.
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