Ab initio all-electron molecular-orbital calculations are carried out to study the structures and relative stability of low-energy silicon clusters (Si(n),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 Si(n) (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.
By means of a large-scale molecular dynamics simulation, we show that the Tolman length, although positive, is much smaller in magnitude than previously reported. We found that the range of interparticle interaction can significantly affect the magnitude of the Tolman length. When the range of interaction is longer than five molecular diameters, the Tolman length is on the order of a few hundredths of the molecular diameter, rather than a few tenths known previously.
Molecular dynamics simulation has been performed to study the effect of the polarizabilities of model anions on the ionic solvation in water clusters. The primary focus is given to the surface versus interior solvation behavior of the anions. To this end, various combinations of polarizable/nonpolarizable water and anion models were considered. Using the nonpolarizable TIP4P water with polarizable Cl− and Br− models, the Cl− is fully solvated inside the (H2O)60 cluster, whereas the Br− is partially solvated at the surface of the cluster. However, when the polarizability of the Br− is turned off, the “Br−” anion is fully solvated. Using the polarizable Dang–Chang water, both Cl− and Br− reside at the surface of (H2O)60 as well as (H2O)500 clusters, consistent with the finding of Stuart and Berne [J. Phys. Chem. 100, 11934 (1996)] based on the polarizable TIP4P-FQ water with the polarizable Drude halide model. When the polarizabilities of the halide anions are turned off, the smaller size “Cl−” anion is fully solvated in the interior of the Dang–Chang water cluster, whereas the larger “Br−” anion is still partially solvated at the surface of the cluster, indicating the importance of the anion-size effect. We have also calculated the free energy change for the Cl− moving from the center of a lamella water slab to the surface. The free-energy change is on the order of 1 kcal/mol, indicating that the Cl− can easily access the surface region of the Dang–Chang water slab.
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