Intrinsic energy of two-dimensional square lattice single-ion anisotropic Heisenberg ferromagnets,antiferromagnets,and ferromagnetic single-walled nanotubes are calculated with many-body Green's function method in quantum statistical theory.Calculated results of ferromagnets and antiferromagnets are compared.Between zero temperature and phase transition point,including zero temperature,anti-ferromagnetic energy is always lower than that of ferromagnetic energy.Calculation method of intrinsic energy in this paper is applicable not only to ferromagnetic system,but also suitable for antiferromagnetic system and ferrimagnetic system,as well as ferromagnetic single-walled nanotubes.Intrinsic energies are greatly lower than classical energies, which shows that transverse correlation effect is important.

Configurations and electronic properties of Cu_n-lNi and pure Cu_n(n=3-14) clusters are calculated in the framework of all-electron density-function theory. It demonstrates that structure of Cu_n(n=3-14) clusters does not grow in a compact pattern but tends to a platelet-like configuration. Cu_nNi(n=2-13) clusters grow in an icosahedral pattern and doping of one Ni atom increases stability of pure Cu_n clusters. Ni atom prefers maximum numbers of neighboring Cu atoms and gradually falls into interior of the Cu framework as number of Cu atom increases. It shows that even-atom clusters have relatively higher stability. Especially, Cu₃Ni, Cu₇Ni and Cu₉Ni are more stable. In Ni-doped copper clusters, impurity atom exhibits positive charge and donates electron to copper atoms. The presence of a doping atom like Ni atom affects chemical activity of copper clusters including corrosion-resistant properties.