The properties of the alkali metal clusters have been investigated by using ab initio electronic structure calculations, with special reference to their structural evolution and the size dependence of several reactivity descriptors, such as ionization potential, electron affinity, polarizability, chemical potential, hardness, softness, etc. Also shown is a good inverse correlation between the dipole polarizability and the ionization potential of the neutral clusters. Similarly, the softness parameter has also been shown to correlate strongly with the dipole polarizability of the clusters. The present work thus will have some important implications in the calculation of polarizability of metal clusters in terms of the corresponding ionization potentials directly.