Structures and stability of medium silicon clusters. II. Ab initio molecular orbital calculations of $Si12–Si20$

Ab initio all-electron molecular-orbital calculations are carried out to study the structures and relative stability of low-energy silicon clusters $(Sin,n=12–20).$ Selected geometric isomers include those predicted by Ho et al. [Nature (London) 392, 582 (1998)] based on an unbiased search with tight-binding/genetic algorithm, as well as those found by Rata et al. [Phys. Rev. Lett. 85, 546 (2000)] based on density-functional tight-binding/single-parent evolution algorithm. These geometric isomers are optimized at the Møller–Plesset (MP2) $MP2/6-31G(d)$ level. The single-point energy at the coupled-cluster single and double substitutions (including triple excitations) [CCSD(T)] $CCSD(T)/6-31G(d)$ level for several low-lying isomers are further computed. Harmonic vibrational frequency analysis at the $MP2/6-31G(d)$ level of theory is also undertaken to assure that the optimized geometries are stable. For $Si12–Si17$ and $Si19$ the isomer with the lowest-energy at the $CCSD(T)/6-31G(d)$ level is the same as that predicted by Ho et al., whereas for $Si18$ and $Si20,$ the same as predicted by Rata et al. However, for $Si14$ and $Si15,$ the vibrational frequency analysis indicates that the isomer with the lowest $CCSD(T)/6-31G(d)$ single-point energy gives rise to imaginary frequencies. Small structural perturbation onto the $Si14$ and $Si15$ isomers can remove the imaginary frequencies and results in new isomers with slightly lower $MP2/6-31G(d)$ energy; however the new isomers have a higher single-point energy at the $CCSD(T)/6-31G(d)$ level. For most $Sin (n=12–18,20)$ the low-lying isomers are prolate in shape, whereas for $Si19$ a spherical-like isomer is slightly lower in energy at the $CCSD(T)/6-31G(d)$ level than low-lying prolate isomers.