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 use of the bond valence sum in Fe−O
complexes is discussed using data from the Cambridge Structural
Database. The oxidation state of Fe in complexes containing Fe
bonded only to O can be calculated by ∑
i
exp[(R
0 −
r
i
)/b], where
r
i
is the observed
Fe−O
i
bond length, R
0
is a constant = 1.745 Å, and b is taken to be 0.37.
The R
0 value can be viewed as a bond length
of unit valence. Deviations from an integer value indicate a
problem with the crystal structure or electron delocalization in
multinuclear complexes. The oxidation-state-independent
R
0 value of 1.745 Å was calculated using 297
FeO
n
complexes with n = 3−8.
An R
0 value of 1.714 Å for Fe(II) was
determined using 74 complexes, and a value of 1.750 Å was determined
for Fe(III) using 223
complexes.
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