Displacement response coordinates

Another example is provided by the minimum energy coordinates (MECs) of the compliant approach in CSA (Nalewajski, 1995 Nalewajski and Korchowiec, 1997 Nalewajski and Michalak, 1995,1996,1998 Nalewajski etal., 1996), in the spirit of the related treatment of nuclear vibrations (Decius, 1963 Jones and Ryan, 1970 Swanson, 1976 Swanson and Satija, 1977). They all allow one to diagnose the molecular electronic and geometrical responses to hypothetical electronic or nuclear displacements (perturbations). The thermodynamical Legendre-transformed approach (Nalewajski, 1995, 1999, 2000, 2002b, 2006a,b Nalewajski and Korchowiec, 1997 Nalewajski and Sikora, 2000 Nalewajski et al., 1996, 2008) provides a versatile theoretical framework for describing diverse equilibrium states of molecules in different chemical environments. 

Therefore, they reflect the minimum energy responses of the system geometrical coordinates per unit displacement in the system number of electrons. The GFF vector of Equation 30.23... 

In the open molecule coupled to an external electron reservoir, which fixes the system chemical potential, they combine the minimum-energy responses in the system number of electrons and the remaining nuclear coordinates to a unit displacement of Qs. The associated MECs,... 

In the preceding sections the optical response of matter has been described by a scalar dielectric function e, which relates the electric field E to the displacement D. More generally, D and E are connected by the tensor constitutive relation (5.46), which we write compactly as D = e0e E. The dielectric tensor is often symmetric, so that a coordinate system can be found in which it is diagonal ... 

Infrared spectral studies have shown that cis- and tram-olefins are not isomerized by coordination to, or displacement from, platinum salts 127). ras-4-Methylpent-2-ene forms a more stable complex than do trans-4-methylpent-2-ene or cis-pent-2-ene it is suggested 132) that the electron-donating nature of the methyl group is responsible for the latter result by strengthening the v-component of the metal-olefin bond. 

In some cases, the CFSE attained by a transition metal ion in a regular octahedral site may be enhanced if the coordination polyhedron is distorted. This effect is potentially very important in most silicate minerals since their crystal structures typically contain six-coordinated sites that are distorted from octahedral symmetry. Such distortions are partly responsible for the ranges of metal-oxygen distances alluded to earlier, eq. (6.6). Note, however, that the displacement of a cation from the centre of a regular octahedron, such as the comparatively undistorted orthopyroxene Ml coordination polyhedron (fig. 5.16), also causes inequalities of metal-oxygen distances. 

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