Distorted angular coordinates

Tor the purpose of this brief account we will provide only a notional definition of optical aberrations. In an optical system, the angular coordinates of incident rays are transformed according to sequential applications of Descarte s law from one optical surface to the next. Aberrations are essentially the non-linear terms of the transformation, the angular coordinates of emerging rays not being strictly proportional to those of the incident ones -thereby generating distorted and/or blurred images. 

Distortion of coordination polyhedra is commonly observed in silicates. Because distortion of the coordination field implies elimination of degeneracy, it is important to evaluate to what extent the nondegenerate condition contributes to the stability of the phase. Systematic MO calculations in this direction have been carried out by Wood and Strens (1972) on the basis of the AOM (Angular Overlap Model) integrals of Ballhausen (1954). 

Table 1.10 Angular coordinates of the ligands as point charges for the three coordination polyhedra and distorted coordination polyhedra ...

Angular coordinates (6 distorted square prism (CN = 8) with D4 symmetry ... 

A parameterization method of the Hamiltonian for two electronic states which couple via nuclear distortions (vibronic coupling), based on density functional theory (DFT) and Slaters transition state method, is presented and applied to the pseudo-Jahn-Teller coupling problem in molecules with an s2-lone pair. The diagonal and off-diagonal energies of the 2X2 Hamiltonian matrix have been calculated as a function of the symmetry breaking angular distortion modes and r (Td)] of molecules with the coordination number CN = 3... 

The four terms in X7, however, require closer attention. The second term, which in molecule-fixed cartesian coordinates may be expressed as L2X + L2y, affects all levels equally and is therefore usually omitted. The third term, which does not involve the orbital angular momentum, is known as the rotational distortion term. Its matrix elements are readily obtained ... 

---