Ab Initio Study of the Structure and Polarizability of Sulfur Clusters, S_n (n = 2−12)

Abstract

The structure and the dipole polarizabilities of S n clusters (n ) 2-12) have been calculated using density functional theory within the B3LYP approximation and conventional ab initio Hartree-Fock (HF) and coupledcluster with single and double and perturbative triple excitations (CCSD(T)) methods. The results show that the binding energy per atom increases with the size of the cluster and reaches the asymptotic limit for a relatively small n value. There is an excellent agreement between B3LYP and CCSD(T) data in predicting the energy of the disproportionation reaction 2S n f S n-1 + S n+1 , which indicates that S 2 , S 6 , and S 8 are especially stable, in agreement with the experiment. 〈R〉 increases with n and linearly correlates with the molecular volume. 〈R〉/n increases with n and reaches the asymptotic limit per n f ∞ from below, contrary to what happens in small semiconductor and metallic clusters. A well-defined correlation between 〈R〉 and hardness is not found, while the 〈R n 〉 -n〈R 1 〉 difference value linearly correlates with the atomization energy. In the sulfur clusters, the minimum polarizability principle does not hold, the lone-pair electron polarizability being more diffuse, hence more polarizable, in the cluster than in the free atom. Pure vibrational effects on 〈R〉 are negligible.

Structural, energetic and response electric properties of cyclic selenium clusters: an ab initio and density functional theory study

“…This suggests that the even-numbered selenium clusters are relatively more stable than the neighbouring oddnumbered ones. Specifically, among the cyclic clusters, Se 6 and Se 8 display the highest positive D 2 E values, in agreement with the data previously reported by Li et al [44] for the Se n (n = 2-7) clusters and with the S n (n = 2-12) clusters [81]. Note that, the electron correlation effects on the D 2 E values are noteworthy for the smallest clusters, whereas they are minimal for the largest ones (Se n , n C 6).…”

“…? is estimated to be 0.44 eV smaller (-16 %) than that for the sulphur clusters, previously determined at the same level of calculation [81].…”

“…On passing from Se 2 to Se 4 the hri value increases from 2.197 to 2.430 Å , then it reduces, converging to the asymptotic limit and showing a slight even-old alternation (even-numbered clusters having smaller hri values). For both Se 11 and Se 12 the B3LYP/ccpVDZ calculations predict an hri value of 2.377 Å , which is 0.266 Å longer than the value for the S 12 clusters obtained at the same level of calculation [81]. Finally, we note that the relativistic effects on the geometries of the Se 2 -Se 6 clusters here estimated at the B3LYP/cc-pVDZ-DK level are almost negligible.…”

Conduction and Electrostriction of Polymers Induced by High Electric Fields

“…It is found that the binding energy per sulfur atom increases with the size of the cluster and reaches the asymptotic limit at about S 6 with S 2 , S 6 and S 8 particularly stable. Of interest in the context of field effects is the finding that the polarisability increases with the cluster size correlating linearly with the molecular volume [26]. The propensity of sulfur to catenation leads to over 20 crystalline allotropes all of which are composed of homocyclic rings with as much as 20 atoms.…”

Chemistry of Tetrasulfur Including Mysterious Rectangular S4 Metal Complexes

“…Moreover, Millefiori et al have considered D 2d , D 2h , C 2v , and C 2h symmetry of the neutral S 4 by using DFT within the B3LYP approximation. 22 Their results suggest that C 2v , D 2d , and C 2h are minima at B3LYP/cc-pVDZ potential energy surface but that the rectangular D 2h is a transition state and the planar C 2v form to be the ground state. The D 2h is higher in energy by 2.11 kcal mol…”