Full ab initio optimizations were performed on the molecular structures of 24 fluorinated and chlorinated dibenzodioxines (PFDD/PCDD ) and dibenzofurans (PFDF/PCDF). Reasonable agreement was found by comparing the geometries of four calculated structures with known X-ray data from the literature. For the fluorine substituent, calculated electron densities (Mulliken total charges and π-electron charges) clearly demonstrate the opposite influence of the inductive (I) and mesomeric (M) effect. The changes in π-densities at carbons in ortho-, meta- and para-position are constant for each fluorine substituent (independent of degree, pattern, and position of substitution). It is thus possible to calculate the π-densities of the substituted dioxines by increments starting from dibenzodioxine. π-Charges from quantum mechanical calculations and the increment system show good agreement even for OctaFDD (O8FDD ), where eight substituent effects are acting additively. Compared with fluorine, the chlorine substituent exercises a smaller -I-effect and a clearly weaker +M-effect. The HOMO coefficients of the unsubstituted dibenzodioxine and dibenzofuran, extracted from ab initio calculations, yield a good explanation for the observed regioselective metabolic attack at the 2,3,7,8-positions. The squares of the HOMO-coefficients of the 2,3,7,8-positions in dibenzodioxine (DD ) are about ten times greater than those of the 1,4,6,9-positions. These HOMO coefficients are practically unaffected by halide substitution. But halogen substitution reduces strongly the electron density at the halogen-bound carbon, which, however, is a necessary prerequisite for the electrophilic oxygen transfer during metabolism. One would therefore expect halogen substitution of dibenzodioxine and dibenzofuran (DF) at the 2,3,7,8-position to hinder metabolism, as is indeed found. This provides a plausible explanation for the highly selective tissue retention of 2,3,7,8-substituted PCDDs and PCDFs. Our ab initio calculations of five tetra CDDs (T4CDDs) confirm the postulate of Kobayashi et al. [1 ] who, using semiempirical calculations, found a correlation between the toxicity of a dioxine congener and its absolute molecular hardness. The 2,3,7,8-T4CDD also exhibits the smallest absolute hardness (derived from the HOMO-LUMO energy gap) in our calculations.
Algebraic Approach to Exact Solution of the (2 + 1)-Dimensional Dirac Oscillator in the Noncommutative Phase Space
