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.
The molecular geometries and the torsional potentials about the inter‐ring C‐C bond in α‐oligothiophenes (α‐nTh, n=2–4) have been calculated by means of conventional ab initio and density functional theory (DFT) calculations employing the hybrid B3LYP and BH&HLYP functionals. The position and the energetics of the critical points in the potential energy curve generated by rotation about the inter‐ring CC bond are shown to be dependent on the computational method. DFT calculations, in comparison with MP2 calculations, favour conjugative interactions, while steric and coulombic interactions are equally treated by both methods. On oligomerization the electron delocalisation increases slightly, the p‐charge being preferentially confined within the rings, although it is sufficient to move the molecular structure towards co‐planarization and to increase the barrier through the perpendicular conformation. The IR and Raman spectra on the relevant rotamers of α‐2Th have been computed at HF/6–31G* and B3LYP/6–31G* levels. The comparison with the experiment is excellent. It has been found that small twisting from the planar conformation has no apparent effects, while 90° twisting and isomerization to the syn‐gauche form produce significant frequency and intensity variations which could be useful probes in conformational studies. The simulated IR and Raman spectra of the α‐2Th rotamers are consistent with a smallπ‐electron delocalisation between the rings.
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