Coordination Chemistry: CFT, LFT, Spectra, Magnetism: Unit Review

Introduction

This unit has moved from geometric orbital splitting to many-electron terms, measured spectra and magnetic dynamics. These topics are connected by one underlying electronic structure. Crystal field theory predicts a useful first orbital pattern; ligand field theory explains σ and π bonding; term diagrams organise interacting electrons; spectroscopy measures energy gaps and transition probability; magnetism probes ground-state angular momentum and coupling. A complete solution chooses the simplest model that explains the evidence and knows when to extend it.

Core explanation

Start with the coordination environment. Octahedral ligands approach along axes and make e g-like d orbitals strongly σ-antibonding relative to t₂g-like orbitals. Tetrahedral coordination reverses the e/t₂ ordering and lacks inversion symmetry. Square-planar splitting is highly uneven and often stabilises paired d⁸ arrangements. Lower-symmetry distortions, especially Jahn–Teller effects for certain degeneracies, further separate orbital levels. These patterns set the first electron occupancy and spin-state hypotheses.

The MO view adds ligand orbital character. σ donation builds metal–ligand bonding and antibonding combinations; π donation can raise metal t₂g-derived energies, while π acceptance can stabilise them through back-bonding. The angular overlap model decomposes these interactions into directional σ and π parameters. Δₒ is the resulting one-electron orbital separation, not a universal measure of bond strength or covalency by itself. Racah B and C separately describe interelectronic repulsion and many-electron term separations; a lower B than for the matching free ion is the nephelauxetic effect.

Free-ion dⁿ configurations have LS terms such as ^3F, ^5D or ^6S. Hund's rules select the free-ion ground term by maximising S and then L. Octahedral symmetry splits S→A₁g, P→T₁g, D→E g+T₂g, F→A₂g+T₁g+T₂g and G→A₁g+E g+T₁g+T₂g, with spin multiplicity preserved in the first approximation. Orgel diagrams give qualitative weak-field, spin-allowed correlations. Tanabe–Sugano diagrams plot E/B versus Δₒ/B and can include spin-forbidden and high-/low-spin states. Their ground-state baseline is reset to zero at each field strength.

Selection rules explain intensity. Electric-dipole transitions ordinarily conserve S; in a centrosymmetric complex they must change inversion parity. Octahedral d–d transitions are g→g and therefore weak through vibronic borrowing, while spin-forbidden bands can be weaker still. Tetrahedral complexes lack the strict parity prohibition. LMCT and MLCT redistribute electron density between ligand and metal and often absorb much more intensely. A d⁰ metal can have vivid charge-transfer colour despite no conventional d–d excitation.

For quantitative band analysis, convert wavelength to wavenumber and assign bands before fitting. Ratios of two observed d–d energies can locate Δₒ/B on the correct diagram. An absolute energy then yields B, and Δₒ=xB. A third band checks the assignment. Band maxima are broad and can overlap, so do not overstate precision. An intense CT peak belongs to a different electronic configuration and should not be forced into a dⁿ term fit.

Magnetism tests the same model from another direction. Count unpaired electrons to get μ so≈√[n(n+2)] μ B, after correcting susceptibility for diamagnetism and stating units and temperature. A orbital-singlet ground state often quenches first-order orbital moment; a T ground term can give larger and temperature-dependent moments. Spin–orbit coupling produces smaller corrections even for A/E states. Lanthanide 4f ions often need a J-based, anisotropic treatment rather than a 3d-style spin-only formula. Bridged metal centres can exchange-couple into low or high total-spin states, and anisotropy plus slow relaxation can create single-molecule-magnet behaviour.

The key strategic move is cross-validation. An octahedral d⁶ complex claimed to be low spin should be nearly diamagnetic; a high-spin d⁵ Mn²⁺ d–d spectrum should be very weak; an octahedral d³ sample should have a quartet A₂g-ground diagram and roughly three unpaired spins. If one observation contradicts the model, revisit oxidation state, geometry, spin, speciation, CT overlap or assumptions before polishing calculations.

Step-by-step reasoning

For any unfamiliar complex: calculate oxidation state and d count; identify coordination number and symmetry; build the σ/π orbital picture; fill d levels and consider pairing; derive a plausible ground term; predict allowed and forbidden optical transitions; classify measured bands by position and ε; fit Δ and B only from credible d–d bands; calculate and correct magnetic moment; then verify that structure, spectra and χ(T) all support one chemical species.

Visual explanation

Draw a central metal–ligand structure branching to three panels. The MO panel shows t₂g/e g and ligand σ/π effects. The spectrum panel shows a term diagram with weak d–d, faint spin-forbidden and tall CT arrows. The magnetism panel shows local spin arrows, an A/T ground-state label and χT(T). Connect the panels with arrows labelled “same d count,” “same geometry” and “same spin state.”

Real-world analogy

A building's plan, its sound response and how it sways in wind are different tests of the same structure. A plan predicts some behaviour, but measurements may expose hidden features. Bonding diagrams, optical spectra and magnetic response likewise test one electronic structure from different directions.

Real-world example

For [Ni(CN)₄]²⁻, Ni²⁺ is d⁸ and the strong-field four-coordinate complex is commonly square planar and diamagnetic. Applying an octahedral d⁸ Tanabe–Sugano diagram because the d count is eight would be wrong. Geometry and magnetic evidence select the model before optical bands are interpreted; strong absorption may contain charge-transfer character.

Why?

Why are both CFT and LFT retained? CFT gives a compact, useful orbital-splitting and spin-count picture. LFT explains how ligand σ and π orbitals, covalency and symmetry actually produce or modify those levels. They answer related questions at different levels of approximation.

Common misconception

“One formula predicts all coordination properties.” Δ controls a simplified orbital gap, B controls term repulsion, spin–orbit and exchange influence magnetism, and transition moments determine intensity. Each observable depends on a different combination, so one number cannot replace a coherent electronic model.

Worked example

An octahedral Cr³⁺ ion is d³ with t₂g³, n=3 and ^4A₂g(F) ground. It predicts μ so=√15≈3.87 μ B and three main quartet targets, ^4T₂g(F), ^4T₁g(F) and ^4T₁g(P). Their d–d bands are g→g and weak. Two assigned band energies can fit Δₒ/B and B; a third verifies the fit. If a very intense UV band appears, evaluate CT rather than automatically treating it as the P-derived target. This short chain links electron count, terms, selection rules, parameters and moment.

Quick check

1. Which parameter measures effective interelectronic repulsion, B or Δₒ? Answer: B is a Racah repulsion parameter; Δₒ is the octahedral t₂g–e g splitting scale. Both can influence many-electron transition energies.

Exam focus

Label assumptions and units at every stage. Keep free-ion ^(2S+1)L terms distinct from complex ^(2S+1)Γ states and lowercase orbitals. State the diagram's d count and spin region, write the exchange Hamiltonian before interpreting J, and explain contradictions between spectra and magnetism rather than discarding inconvenient data.

Advanced insight

The apparent separation between “spectroscopic” and “magnetic” parameters is partly pedagogical: both arise from one electronic Hamiltonian containing orbital energies, electron repulsion, spin–orbit coupling, ligand covalency and exchange. Jointly fitting optical energies, g tensors and χ(T) can constrain this Hamiltonian more tightly than any one experiment, while also exposing when an idealised point-group model fails.

Summary

Coordination chemistry links geometry and σ/π bonding to orbital levels, many-electron terms, absorption and magnetic response. CFT supplies the first pattern; LFT and term diagrams refine it; spectra and magnetism test it. A successful assignment is chemically consistent across all measurements.

Practice questions

1. Why is an intense band in a d⁰ oxo ion excluded from a d–d Tanabe–Sugano fit? Answer: No metal d electron is available for a conventional d–d excitation, and intense ligand-to-metal charge transfer is plausible; the dⁿ term diagram models a different type of transition. 2. A high-spin octahedral d⁷ complex has a moment above its three-unpaired-electron μ so. Name a plausible reason. Answer: Its orbitally degenerate T ground term can retain orbital angular momentum, and spin–orbit coupling can raise the measured effective moment above √15≈3.87 μ B. 3. Why can a bridged Cu²⁺ dimer show little low-temperature magnetism despite two local unpaired electrons? Answer: Antiferromagnetic exchange can couple the two S=1/2 local spins into a total singlet ground state; the triplet is thermally depopulated on cooling. 4. Why can a d⁰ ion still be strongly coloured? Answer: Ligand-to-metal charge transfer or ligand-centred absorption can be intense even though a conventional metal d–d excitation requires occupied d orbitals.