Transition Metal Complexes - PV

Multi-electron system energy levels

*L* - Vectorial sum of l of each electron (L=0,1,2,3... (known as S, P, D, F...). *Ml* = ∑ml. 2L+1 values of Ml Ml = L, (L-1)...-(L-1), -L *S*- total spin quantum number S = 1/2, 3/2, 5/2 or S = 0,1,2 *Ms* = ∑ms 2S+1 values of Ms Ms = S, (S-1)...-(S-1), -S

Racah Parameter, B

- A measure of electron-electron repulsion - B for a free ion is greater than B for the same ion in a complex - In a complex, electrons can access more volume than in a free ion. Electron-Electron repulsion is reduced if they occupy more volume. - The decrease in B between free ion and complex can be used to access the degree of covalency - this is called the nephelauxetic effect. (means cloud expanding)

Tanabe-Sugano Diagrams

- Axes are E/B and ∆oct/B (where B is Racah parameter). - Ground state is defined as E=0 (runs along x axis). - Accommodates high and low spin configurations. For d4 configuration: - High and low spin possible - Orgel diagram only shows high-spin - Tanabe-Sugano shows both possibilities. At low values of ∆oct/B (WF) HS complex At high values of ∆oct/B (SF) LS complex The ground state switches from 5E1g to 3T1g at the dashed line. States with different spin to that of their ground state are often shown as dashed lines (spin selection rule).

Guoy Balance

- Diamagnetic compound is repelled by magnetic field. - Paramagnetic compound is attracted by magnetic field. - Magnetic field is initially switched off. - Change in weight on switching the field is recorded (=xm) Related methods include an Evans Balance and SQUID ( Superconducting Quantum Interference Device)

Total spin quantum number

- For one electron, spin takes values ±1/2. - For compounds, we calculate a total spin quantum number (S), which is related to the number of unpaired electrons (n). 3 unpaired electrons S = 1/2+1/2+1/2 = 3/2 therefore S=n/2

Charge transfer bands

- Intensely coloured - colour cannot arise from d-d. - Colour related to electron transfer between ligand and metal orbitals. - Allowed by selection rules, therefore intense. LMCT: electron transferred from ligand to metal. L easily oxidised bound to easily reduced M (high oxidation state). MLCT: electron transferred from M to L. L easily reduced bound to metal readily oxidised (low oxidation state). π acceptor ligands: empty π* at relatively low energy.

Orbital Contribution

- Moments arising from both the spin and the orbital angular momenta can contribute to the observed magnetic moment. - For most complexes of the 1st transition series. orbital contribution is small. Fields from other atoms/ions quench the orbital contribution. - For 3d transition metals, some orbital contribution will be expected when the term symbol of the ground state is T. - For heavier transition metals and for rare-earth elements, the orbital contribution is larger and must be taken into account.

Factors which effect size of ∆oct/tet

- Nature of the ligand (spectrochemical series) - Oxidation state of the metal - greater charge = greater ∆ - The position of the metal in the d-block - ∆ increases on descending the periodic table. • Oxidation state explanation - increase in charge at the metal causes ligand to be more strongly attracted. This increases repulsion between d orbitals and ligands, hence increasing ∆oct.

Jahn - Teller Distortion in diagrams

- Orgel and Tanabe-Sugano diagrams assume Oh symmetry in excited states as well as in ground state. - If excited state is JT distorted, 2 excited states with slightly different energy are seen.

Jahn-Teller effect

- Strong for the eg set as the orbitals point directly towards the ligands. This affects octahedral complexes d4 high spin and d9. - Weaker for the t2g set, as orbitals don't point directly towards ligands. This affects octahedral complexes with d1, d2, d4 LS, d5 LS, d6 HS, and d7 HS. - Also occur for excited states (electron spectroscopy). When an electron is promoted to a higher energy orbital, the new electron configuration can be distorted.

Barycentre

Average energy of orbitals The eg orbitals increase their energy by +3/5∆Oct from barycentre the t2g orbitals decrease their energy by 2/5∆Oct from barycentre

D-block series

∆Oct increases when descending from 1st to 2nd to 3rd row of the periodic table. d orbitals increase in size - 3d<4d<5d. Larger d-orbitals interact more strongly with ligands and therefore ∆oct increases. Low spin configurations favoured for 2nd and 3rd row transition metals.

Spin selection rule

∆S = 0 No change in the number of unpaired electrons. eg. 3F - 3p allowed but 3F - 1D forbidden.

Square pyramidal complexes

CFS similar to that if an elongated octahedron. Important in biological systems, where the vacant site is reversibly occupied (seen with Fe(acac)2Cl).

Site preferences in spinels, AB2O4

Cubic close-packed array of oxide ions. A cations occupy 1/8 tetrahedral holes. B cations occupy 1/2 larger octahedral holes Normal structure [A]tet[B2]oct O4 Inverse structure [B]tet[AB]oct O4 When A and/or B in the first row of transition metals, CFSE can determine site preference.

Term Symbols

Denotes a group of micro states with the same energy. 2S+1 - degeneracy (or multiplicity) of the spin (number of allowed values of Ms for a given S). 2S+1 = 1 Singlet, =2 Doublet, =3 Triplet etc. L=0 S term, L=1 P term etc. Only electrons in incomplete shells contribute to the term symbol. Degeneracy of term symbol: (2S+1)x(2L+1)

Notation of e, g, and t

E - doubly degenerate T - triply degenerate G- gerade (Ignore caps, should all be lower case)

Multi-electron systems

For octahedral complexes with partially filled d levels, we would expect a single transition. However, spectra of d2, d3, d7 and d8 octahedral complexes consist of 3 absorption bands. In multi-electron systems, we need to consider interactions between electrons (coupling). eg. Free ion with d2 configuration. 45 possible ways (µ states) of arranging the 2 electrons in the 5 orbitals. Stating the electron configuration is not enough. We need to take into account the interaction between electrons. If >1 electron, spin and orbital angular momenta can interact: - Spin-spin coupling - Orbit-Orbit coupling

CFSE - octahedral vs. Tetrahedral

For tetrahedral complexes, max stability at d2 and d7. For octahedral complexes, max stability at d3 and d8. No stabilisation for d0, d5 and d10. Octahedral CFSE larger - other factors can stabilise tetrahedral geometry (eg. Sterics) CFSE affects trends in ionic radii, lattice energies, hydration energies etc.

Jahn-Teller Distortion

If there are 2 electrons in dz2 and 1 in dx2-y2 then repulsion between dz2 and ligand is larger than that between dx2-y2 and ligand. Therefore, bonds along z become longer. Octahedron is elongated (point groups changes from Oh to D4h). Similarly, if there is 1 electron in dz2 and none in dx2-y2, repulsion between dz2 and ligand is larger and octahedron is elongated.

Electronic spectra: weak field

In a weak octahedral field, the spin multiplicity doesn't change (high-spin). In an octahedral field, D2 splits into 2T2g and 2Eg terms.

dz2 and dx2-y2 lobes

Lobes along axes

dyz, dxy, dxz lobes

Lobes between axes

Square planar complexes: d8

ML4 complexes with a d8 configuration (group 10) are often square planar. For Pd2+ and Pt2+ (4d8 and 5d8), the difference in energy between dry and dx2-y2 is very large, and square planar coordination is always preferred. Ni2+ (3d8) form square planar complexes with strong field ligands, and tetrahedral complexes with weak-field ligands.

Spin-only formula

Magnetic moment (µ) per atom depends on number of unpaired electrons (n). The units of magnetic moment are Bohr Magnetons (BM or µB). Total spin quantum number S=n/2 µ (spin only) = 2√s(s+1) =√n(n+2)

Diamagnetic Materials

Magnetic susceptibility v.weak ≈ -10^-5 Atoms with close shells of electrons - no net moment per atom. No temperature dependence.

Spin crossover complexes

Spin state transitions (or spin crossover) from a high spin state with the maximum number of electrons to a low spin state with a minimum number of unpaired electrons can occur for transition metal compounds with d4-d7 configurations. For spin crossover to occur, the energy of both states should be similar. Under those conditions, a transition can be induced by varying the temperature, applying a pressure or even under irritation. Eg. Fe2+ d6 HS s=2 - Paramagnetic - Pale colour LS s=0 - Diamagnetic - Dark colour

Magnetisation, M

The field of a material in an applied field, B.

Magnetisation and Magnetic Susceptibility

The number of lines of force per unit volume is different inside the material, as a consequence of the interaction of the applied magnetic field with the electrons in the material.

Jahn-Teller Theorem

A non-linear molecular in a degenerate electronic state (unevenly occupied orbitals) is unstable and will undergo distortion to achieve a lower energy.

High and Low spin

Electrons will fill orbitals in a way that minimises the total energy - fills t2g first. 2 electrons in the same orbital repel each other more than 2 electrons in 2 different orbitals (pairing energy, P). Therefore will fill orbitals with 1 unpaired electron first before filling a half-empty orbital. D4 - where does the 4th electron go? weak field - small ∆oct, high spin (goes into eg) Strong field - large ∆oct, low spin (goes into t2g and pairs) Octahedral complexes between d4 - d7 can be high or low spin. Only 1 configuration for the remaining d1, 2, 3, 8and 9.

Crystal field theory

Electrostatic model (positive attracts negative and vice versa) Metal ion = positive point charge Ligand = negative point charges Electrons in the d-orbitals of the metal increase in energy due to the repulsion by the negatively charged ligands The increase in energy of the d-orbitals depends on the distance between d-orbitals and ligands. In the presence of ligands, the 5 d-orbitals are no longer degenerate. Orbital splitting occurs.

Microstates

How many different ways of arranging electrons in the orbitals of the outer sub shell

Selection rules and Band Intensities

Laporte Selection Rule: A transition involving a redistribution of electrons within the same orbital shell is forbidden. - says d-d transitions are forbidden. A Laporte forbidden transition may still occur if there is 'vibronic coupling' (mixing of p and d orbitals), but the corresponding UV-Vis peak will be weak.

Octahedral complexes

Ligands act as negative point charges that repel electrons in d-orbitals Lobes along axes = larger repulsion and therefore higher energy orbitals involved (dz2 and dx2-y2)

Distorted Octahedra

Octahedral complexes with d4 and d9 configurations are often distorted.

∆oct

Octahedral crystal field splitting energy Energy difference between t2g and eg levels.

Co-operative magnetic phenomena

Paramagnetic - All atoms randomly oriented magnetically. Ferromagnetic - All atoms parallel in alignment. Antiferromagnetic - Antiparallel alignment. Zero magnetic moment overall. Ferrimagnetic - Antiparallel alignment, unequal moments. The ordered states can be destroyed by raising the temperature.

Magnetic field

Produces lines of force which penetrate the medium to which the field is applied. A magnetic field (B) is produced whenever there is electrical charge in motion. Atoms contain electrons in motion - magnetic fields will be produced. Magnetic moment per atom depends on number of unpaired electrons.

Tetrahedral Crystal Field

Tetrahedral complex inside a cube, with ligands occupying alternate corners. In a tetrahedral crystal field, no d-orbital points directly at the ligands. 3d orbitals split into 2 levels t2 and e (t2 higher in energy than e). Orbitals that are closer to the ligands are higher in energy. As d-orbitals don't point directly towards the ligands (4 instead of 6), ∆tet is smaller than ∆oct ( ∆tet = 4/9∆oct). Tetrahedral complexes are high spin because ∆tet is small.

Tetrahedral vs. Octahedral - Magnetism

Tetrahedral d8 - Paramagnetic Octahedral d8 - Diamagnetic

Crystal field stabilisation energy (CFSE)

The difference in entry between the d electrons in an octahedral/tetrahedral crystal field and the d electrons in a spherical crystal field. There are 2 contributions: - Octahedral/tetrahedral crystal field splitting energy, ∆oct/tet - Pairing energy, P: Energy needed to convert to parallel e- in 2 degenerate orbitals in 2 spin-paired e- in the same orbital.

Spherical crystal field

Uniform sphere of negative charge surrounding the metal ion increases the energy of the d orbitals

Magnetic Susceptibility

x = M/B B generated outside the material M (magnetisation) is generated by spin and orbital angular momentum of electrons within the solid.

Paramagnetic Materials

x is positive. Unpaired electrons - net magnetic moment per atom. x decreases with increasing temperature, x=c/T (c is the curie constant)