Coordination Chemistry Mastery: CFT and Isomerism

In an octahedral field, the ##e_g## orbitals point directly at the ligands along the axes, causing higher repulsion and energy compared to the ##t_{2g}## orbitals which point between the axes.

A high-spin ##d^4## octahedral complex has the configuration ##t_{2g}^3 e_g^1##. CFSE = ##[3 \times (-0.4) + 1 \times (0.6)] \Delta_o = -0.6 \Delta_o##.

Linkage isomerism occurs when an ambidentate ligand (like ##NO_2^-##) can coordinate to the metal center through two different atoms (N or O).

For octahedral complexes of the type ##[Ma_3b_3]##, the two geometrical isomers are facial (where three identical ligands occupy one face of the octahedron) and meridional (where three identical ligands occupy a meridian).

Tetrahedral splitting is significantly smaller than octahedral splitting, approximately ##4/9 \Delta_o##, because there are fewer ligands and they do not point directly at any d-orbitals.

##CN^-## is a strong-field ligand located at the high end of the spectrochemical series, causing large d-orbital splitting compared to halides or water.

##[Co(en)_3]^{3+}## is a chiral molecule with a non-superimposable mirror image, making it optically active. It does not show cis/trans isomerism because all positions are equivalent.

A low-spin ##d^6## complex has the configuration ##t_{2g}^6 e_g^0##. CFSE = ##[6 \times (-0.4) + 0 \times (0.6)] \Delta_o + 3P = -2.4 \Delta_o + 3P##, where P is the pairing energy.

Ionization isomers result in different ions in solution; here, the first releases ##SO_4^{2-}## and the second releases ##Br^-## when dissolved in water.

In tetrahedral geometry, the ##e## set (##d_{x^2-y^2}## and ##d_{z^2}##) is lower in energy because these orbitals point further away from the approaching ligands than the ##t_2## set.

##Fe^{2+}## is ##d^6##. In the presence of strong-field ##CN^-##, electrons pair up in the ##t_{2g}## level (##t_{2g}^6##), leaving zero unpaired electrons and a magnetic moment of 0.

Coordination isomerism occurs in compounds containing both complex cations and complex anions, where ligands can be exchanged between the two metal centers.

High-spin ##d^5## has the configuration ##t_{2g}^3 e_g^2##. CFSE = ##[3 \times (-0.4) + 2 \times (0.6)] \Delta_o = (-1.2 + 1.2) \Delta_o = 0##.

For the ##MA_4B_2## type octahedral complex, there are two geometrical isomers: cis (Cl ligands adjacent) and trans (Cl ligands opposite).

A low-spin configuration occurs when the energy required to promote an electron to the higher orbital (##\Delta##) is greater than the energy required to pair it in the lower orbital (P).

Solvate isomerism involves the exchange of a solvent molecule (like water) between the coordination sphere and the outer sphere (crystal lattice).

In a tetrahedron, all four positions are equivalent and equidistant from each other (bond angles of ##109.5^\circ##), so there is no "trans" position available.

For ##d^1##, ##d^2##, and ##d^3## configurations, there is only one way to fill the orbitals (filling the lower ##t_{2g}## set first) regardless of ligand strength.

The ##e_g## set consists of the ##d_{x^2-y^2}## and ##d_{z^2}## orbitals, which lie directly along the x, y, and z axes.

The facial (fac) isomer has three identical ligands occupying the corners of one of the eight triangular faces of the octahedron.

The cis isomer of ##[M(AA)_2X_2]## lacks a plane of symmetry and is chiral, while the trans isomer has a plane of symmetry and is achiral.

The spin-only formula is ##\mu_s = \sqrt{n(n+2)}## Bohr Magnetons (BM).

In high-spin ##d^7##, electrons fill ##t_{2g}## and ##e_g## singly first, then pair up in ##t_{2g}##: three in ##t_{2g}##, then two in ##e_g##, then two more pair in ##t_{2g}##, resulting in ##t_{2g}^5 e_g^2##.

##SCN^-## (thiocyanate) is an ambidentate ligand that can bond via Nitrogen (isothiocyanate) or Sulfur (thiocyanate).

Because ##\Delta_t## is only about half the size of ##\Delta_o##, it is rarely large enough to overcome the pairing energy, making tetrahedral complexes almost always high-spin.