The dependency of the magnetic susceptibility on temperature has elucidated that the mineral atacamite Cu2Cl(OH)(3) has the antiferromagnetic property. In order to explain this behavior and the spin arrangement derived from experimental studies, the ab initio UHF MO and UNO CASCI calculations were carried out for the tetranuclear cluster of copper(II), Cu4Cl(OH)(3), which is the constitution in the atacamite crystal structure. The results of the CASCI calculations appreciate the relative stabilities among various spin arrangements for the tetranuclear cluster, being consistent with the experiments.