Structural and electronic properties of sodium clusters under confinement

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Using real-space density functional theory, electronic structure and equilibrium geometries of sodium clusters in the size range of 2--20 atoms have been calculated as a function of confinement. We have examined the evolution of the five lowest isomers as a function of volume for six different compressions. The minimum volume considered is about $1/15$ to $1/10$ of the free-space box volume. We observe a strong tendency for isomeric transitions in many cases, with the higher isomers evolving into the ground state under confinement. In general the clusters tend to become more spherical. The changes in the total energies and the geometries are not significant until the volume gets reduced beyond the 1/3 of the original volume. In this sense, the clusters are not easy to compress. Once the critical volume is reached, the changes in the total energies and geometries are rapid. It turns out that the increase in the total energy is mainly due to the ion-ion and Hartree energies of electrons. We also address how anisotropic confinement affects the geometry of clusters. We further show that geometries obtained with anisotropic confinement are strongly supported by the simulation of clusters inside a carbon nanotube using a hybrid quantum-mechanical and molecular-mechanics approach.