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3. 3. ) Group [À2], {À2} Td ½E 2 ¼ A þ E 2 ½T1;2 ¼ A þ E þ T2 2 fÀ8 g ¼ A1 þ E þ T2 Th ½Eg2 ¼ ½Eu2 ¼ Ag þ Eg ½Tg2 ¼ ½Tu2 ¼ Ag þ Eg þ Tg fÀ28g g ¼ fÀ28u g ¼ Ag þ Eg þ Tg Oh ½Eg2 ¼ ½Eu2 ¼ A1g þ Eg 2 2 ½T1g2 ¼ ½T1u ¼ ½T2g2 ¼ ½T2u ¼ A1g þ Eg þ T2g 2 2 fÀ8g g ¼ ½À8u ¼ A1g þ Eg þ T2g I ½T12 ¼ ½T22 ¼ A þ V ½U 2 ¼ A þ U þ V ½V 2 ¼ A þ U þ 2V fÀ28 g ¼ A þ V fÀ29 g ¼ A þ U þ V Ih 2 2 ½T1g2 ¼ ½T1u ¼ ½T2g2 ¼ ½T2u ¼ Ag þ Vg 2 2 ½Ug ¼ ½Uu ¼ Ag þ Ug þ Vg ½Vg2 ¼ ½Vu2 ¼ Ag þ Ug þ 2Vg fÀ28g g ¼ fÀ28u g ¼ Ag þ Vg fÀ29g g ¼ fÀ29u g ¼ Ag þ Ug þ Vg The kernel of À in G, denoted K(G, À), is the subgroup of G that includes all symmetry elements that are represented in À by unit matrices (see tables in the appendix).
38)). It follows from Eq. 25) that the distorting influence of the electrons on the ðÀÀÞ is produced additively by all the correnuclear framework with a force FÀ ðiiÞ sponding MO single-electron contributions fÀ . A clear physical meaning for ðiiÞ the linear diagonal orbital vibronic constant follows immediately: fÀg equals the force with which the electron of the ith MO distorts the nuclear configuration in the direction of the symmetrized displacement QÀg minus the corresponding part of the internuclear repulsion in this direction (see Eq.
Similarly, the electron on the py orbital pushes away ligands 2 and 4, distorting the complex equivalently to the previous case, but along the Oy axis; and for the electron on the pz orbital the distortion is along Oz. Note that in the absence of the ligands the electron has no specific location within the degenerate manifold, but in the presence of the ligands the distorted configuration with the electron in one of the three orbitals becomes preferable energetically. Since the three states in cubic fields remain equivalent, the system has three minima, corresponding to the three directions of distortions, 40 2 Vibronic interactions and no minimum in the high-symmetry octahedral configuration due to obvious electrostatic forces.