Structures and stabilities of small silicon clusters: Ab initio molecular-orbital calculations of Si7–Si11

Abstract

Ab initio all-electron molecular-orbital calculations have been carried out to study the structure and relative stability of small silicon clusters (Sin, n=7–11). A number of low-energy geometric isomers are optimized at the second-order Møller–Plesset (MP2) MP2/6-31G(d) level. Harmonic vibrational analysis has been performed to assure that the optimized geometries are stable. The total energies of stable isomers are computed at the coupled-cluster single and double substitutions (including triple excitations) [CCSD(T)] CCSD(T)/6-31G(d) level. The calculated binding energies per atom at both the MP2/6-31G(d) and CCSD(T)/6-31G(d) levels agree with the experiments. For Si7, Si8, and Si10, the lowest-energy structures are the same as those predicted previously from the all-electron optimization at the Hartree–Fock (HF) HF/6-31G(d) level [Raghavachari and Rohlfing, J. Chem. Phys. 89, 2219 (1988)]. For Si9, the lowest-energy isomer is same as that predicted based on density-functional plane-wave pseudopotential method [Vasiliev, Ogut, and Chelikowsky, Phys. Rev. Lett. 78, 4805 (1997)]. Particular attention has been given to Si11 because several low-energy geometric isomers were found nearly isoenergetic. On the basis of MP2/6-311G(2d)//CCSD(T)/6-311G(2d) calculation, we identified that the C2v isomer, a tricapped trigonal prism with two additional caps on side trigonal faces, is most likely the global-minimum structure. However, another competitive geometric isomer for the global minimum is also found on basis of the MP2/6-311G(2d)//CCSD(T)/6-311G(2d) calculation. Additionally, calculations of the binding energy and the cluster polarizability offer more insights into relatively strong stability of two magic-number clusters Si6 and Si10.