DFT-based pseudo-Jahn-Teller coupling studies on the steric and energetic lone pair effect of four- and...

The energetical and stereochemical effect of the s(2) lone pair in the title molecules and complexes is investigated using a pseudo-Jahn-Teller coupling model with parameters adjusted to energies and wave functions from DFT calculations. Vibronic coupling parameters were calculated and compared with those of the coordination number (CN) 3. Inspecting the correlation between the chemical hardness and the vibronic coupling energy (hardness rule), it is found that the tendency to distort decreases with increasing CN. While all considered molecules AX(3) (A(III) = P to Bi; X(-) = F to I) undergo lone pair deformations (D(3h)---> C(3v)), only part of the AX(4)(-) and BX(4) species (B(IV) = S to Po) do so (T(d)---> C(2v)-and even less the ones with CN = 5 (D(3h)---> C(2v) (congruent with C(4v)), AX(5)(2-), BX(5)(-), and CF(5) (C(V); Cl to I). The distorted polyhedra of minimum energy possess usually the butterfly C(2v) shape (CN = 4, tau(2)(zeta) displacement path) and a C(2v) = C(4v)geometry (CN = 5, epsilon' (epsilon) distortion path). A further symmetry lowering to C(s) occurs, if the central ion becomes too small with respect to the ligands (ionic size influence, PCl(Br)(4)(-), PCl(5)(2-)), with the tendency to reduce the CN toward 3 + 1 and 4 + 1, respectively. For CN = 4 the various stationary points of, for example, compressed and elongated C(3v), C(4v), etc. in the multidimensional ground-state potential surface have been characterized. Though of higher energy than the absolute C(2v) minimum, they are shown to govern the dynamics and reactivity of the CN = 4 species to a large extent. To simulate the chemical environment (positively charged counterions, polar solvents), the DFT calculations were performed using the polarizable continuum model COSMO (conductor-like screening model). Though the electronic energy gain upon distortion is not significantly affected by the solvent, the total stabilization energy is distinctly enhanced, frequently leading to lone pair deformations of otherwise electronically stable species. All results obtained by the combined vibronic/DFT approach are well in accord with available experimental data.