electron config and CFSE

what does paramagnetic mean?

there are unpaired electrons

what does diamagnetic mean?

there are no unpaired electrons

what are the 5 d orbitals?

d_yz, d_xy, d_xz, d_z², d_x²-y²

what is the shape of d_yz?

what is the shape of d_xy?

what is the shape of d_xz?

what is the shape of d_z²?

what is the shape of d_x²-y²?

in an octahedral complex, which orbitals are higher energy?

d_z² and d_x²-y²

the d_z² lobes are pointing directly at negative point charges on z axis = electrostatic repulsion between electron and ligands (point charges)

d_x²-y² lobes point at negative point charges on x and y axes

why are d_yz, d_xy, d_xz lower in energy for octahedral complexes?

lobes point between negative point charges on axes

no electrostatic repulsion between electron and point charges

what are the two orbital energy levels for octahedral complexes?

3 lower = t_2g

2 higher = e_g

what is ∆oct?

what is the ratio of heights?

energy difference between t_2g and e_g

e_g is 3/5∆oct and t_2g is -2/5∆oct

draw an energy level diagram for octahedral complexes

diagram of tetrahedral in cube (with cartesian axes)

axes aligned through centre of faces of cube

which are the lower orbitals for tetrahedral complexes?

d_z² and d_x²-y²

lobes point between point charges (no repulsion between electron and point charge)

which are the higher orbitals for tetrahedral complexes?

d_yz, d_xy, d_xz

lobes point near to point charges. energy destabilised due to repulsion between electron and point charge

what are the two orbital energy levels for tetrahedral?

lower = e

higher = t₂

what is ∆tet?

what is the ratio of heights?

energy difference between e and t₂ sets of orbitals

e is -3/5∆oct and t₂ is 2/5∆oct

what is the crystal field splitting diagram for tetrahedral complexes?

is ∆tet or ∆oct bigger? what is the relationship?

∆tet is much smaller

∆tet = 4/9∆oct for same metal and ligands

what is the crystal field splitting diagram for square planar?

why is d_x²-y² highest in energy?

on same axes as negative point charges

most destabilised

why is d_xy the second highest energy?

in same plane as negative charges as negative charges

also destabilised but by a lot less

why is d_z² lower in energy?

has some orbital lobes in the same plane as negative charges

overall stabilised as most of orbital is away from negative charges

why are d_xz and d_yz lowest in energy?

furthest away from negative charges

stabilised and degenerate

does high or low spin maximise unpaired electrons?

high spin maximises unpaired electrons

low spin minimises unpaired electrons

how does low spin happen?

all degenerate sets of orbitals are filled before higher energy orbitals

how does high spin happen?

all d orbitals are given an electron before spin pairing

what is P?

spin pairing energy

energy cost of having two negatively charged electrons in one orbital

how to determine if a complex is low or high spin?

depends on ∆ and P (spin pairing energy)

high spin - ∆ < P

low spin ∆ > P

are tetrahedral complexes typically high or low spin?

high spin as ∆tet is small

energy cost of filling higher energy orbitals is smaller than spin pair repulsion

are square planar complexes typically high or low spin?

low spin as ∆ between d_xy and d_x²-y² is large

what is crystal field stabilisation energy?

energy gained from electrons filling d orbitals in crystal field

• in comparison with no crystal field

how is CFSE calculated?

what is CFSE expression when there are paired electrons?

add P for the number of pairs compared to no crystal field

for which configurations is CFSE zero?

high spin d⁵

d¹⁰

what is the maximum stabilisation?

low spin d⁶

what is the general expected trend for ionic radii across the periodic table?

ionic radii to decrease

increasing effective nuclear charge, poor shielding by d orbitals

how does CFSE affect ionic radii?

is high or low spin smaller?

when there are crystal field effects the observed radii are smaller than expected

low spin ions are smaller than high spin (for same metal)

if all d orbitals contain equal number of electrons, what is distribution around metal?

spherical

if only some d orbitals filled, what is distribution around metal?

non spherical

what makes M-L bond shorter?

t_2g orbitals don’t point towards M-L bond but between

less repulsion between electrons in t_2g and ligand

what makes M-L bond longer?

e_g orbitals point towards M-L bonds - more repulsion between electrons in e_g orbitals and ligand

how does radii change across periodic table from t_2g⁰e_g⁰ → t_2g⁶e_g⁰

radii decreases with an increase in effective nuclear charge and t_2g occupancy

how does radii change across periodic table from t_2g⁶e_g¹ → t_2g⁶e_g⁴

increasing e_g occupancy increases overall repulsion hence radii increases

overall, how does occupancy of t_2g and e_g change ionic radii?

t_2g decreases ionic radii

e_g increases ionic radii

does low spin favour a small or large crystal field splitting parameter?

large Δ

Δ > P

does high spin favour a small or large crystal field splitting parameter?

small Δ

Δ < P

what 4 things does the size of Δ determine?

structure

magnetic properties

colour

reaction kinetics

what 5 things determine the size of Δ?

oxidation state of metal

transition series of metal

identity of metal across row

geometry of complex

identity of ligands

how does oxidation state of metal affect Δ?

greater the charge on M, the greater Δ

larger charge = ligands attracted closer to metal = stronger interaction with metal

is M(II) or M(III) complexes more likely to be high/low spin?

M(III) more likely to be low spin

Δ is larger

how does transition series of metal affect Δ (down group)?

how does P change?

Δ increases down the group

larger d orbitals have lower spin pairing energies (P)

are complexes of 2nd and 3rd more likely to be high/low spin?

2nd and 3rd row are more likely to be low spin than 1st row

Δ increases down group

how does identity of metal across row affect Δ?

across first row, for same ligand and ox state, varies irregularly across 1st row

how does geometry of complex affect Δ?

what is ratio of tetrahedral and octahedral?

square planar has large Δ

tetrahedral has small Δ

Δtet = 4/9 Δoct

how does identity of ligands affect Δ?

different ligands have different crystal field strengths

depends on position in spectrochemical series

what is the spectrochemical series?

halides are weak = low Δ

how does crystal field theory not explain spectrochemical series?

how do C≡O and halides show this?

assumes ligands are negative point charges and uses ideas of repulsion to explain d orbital splitting

halides are negatively charged and spherical so would expect to be strong

C≡O is neutral but is strong field

what are the two conditions that tetrahedral complexes tend to occur in?

small Δ

d⁷ electron counts

why does tetrahedral favour d⁷?

gives all filled or half filled sub shells (only small difference in CFSE for two geometries)

which electron configuration does square planar favour? (for small or large Δ?)

d⁸ when Δ is large

fully filled sub shells

large negative CFSE

why does larger Δ affect CFSE for square planar?

pushes lower down orbitals more so more energy gained

why do d¹⁰ show less of a tendency to favour particular geometries?

do not have CFSE so show less tendency to favour particular geometries

what is Jahn-Teller theorem?

any degenerate quantum mechanical state will distort in such a way to remove that degeneracy

for Cu²⁺ in octahedral geometry, what is electron configuration? what are the two ways to arrange this config?

how does Jahn-Teller correct this?

why is this energetically favourable?

d⁹

t_2g⁶e_2g³

orbitals split to break degeneracy

two electrons go lower and only one goes higher

considering the directions each orbital faces, how will the overall shape of the complex stabilise orbitals to lower energy?

elongating octahedral complex along z axis

this is for when d_z² is lower

considering the direction each orbital faces, how will the overall shape of the orbital stabilise orbitals to higher energy?

compression of octahedral complex along z axis

this is for when d_z² is higher

what is a tetragonal distortion?

elongation of axial bonds (z direction)

for what configurations is Jahn-Teller distortions of octahedral most pronounced for?

odd number of e_g electrons

how does tetragonal geometry affect t_2g orbitals?

not affected as much as don’t point directly to ligands

how does Jahn-Teller work when t_2g is unevenly filled?

distortions occur so one of the d orbitals becomes lower energy

the distortions are relatively small as orbitals don’t point directly at ligands

how do individual atoms behave in paramagnetism?

behave independently unless inside external magnetic field

what is the equation for spin-only magnetic moment µ_so?

n is number of unpaired electrons

units are BM

how is µ_eff related to µ_so?

approximately equal

how is µ_eff determined?

experimentally by measuring magnetic susceptibility of complex

measuring weight changes inside magnetic field caused by alignments of moments with the field

what colour is present if no visible light is absorbed?

white light is reflected = no colour

what causes colour in transition metal complexes?

electronic transitions of electrons in split d orbitals

what is the frequency for red and violet light?

14,300 red

23,800 violet

what is a d-d transition?

from t_2g to e_g

what do you need for a d-d transition?

d electrons

split d orbitals with unfilled higher energy d orbital in ground state

what are charge transfer transition?

electronic transitions from ligand to metal and vice versa