Magnetic And Spectral Properties Of Transition-Metal Compounds

Front 1

energy of triplet vs singlet states?

Back 1

ET< ES

∆E(S-T) is smaller for nπ∗ than ππ∗ configuration

Front 2

Selection rules?

Back 2

Spin selection rule:
∆S = 0,

Laporte selection rule:

a change in parity is required, since a photon has angular momentum

Front 3

equation for absorbance?

Back 3

A = log10[I₀/I]

Front 4

Discuss electronic spertra?

Back 4

electronic spetra are generally broad(due to vibrations and rotations)

-absorptions characterised by Amax and λmax

-Molar extinction coefficient εmax = Amax /c×l - how intense an absorption is

Front 5

absorption vs adsorption?

Back 5

adsorb - hold on surface

absorb - takes in

Front 6

Energy, frequency and wavelength?

Back 6

c = νλ

E = hv = hc/λ = hcv̄

Front 7

Quantify breadth of the bands in spectra?

Back 7

FWHM - full-width at half maximum

axis scale must be directly proportional to energy (not log or anything)

Front 8

symmetry of octahedral orbitals?

Back 8

t2g = dxy, dxz, dyz

eg = dx2-y2, dz2

a1g = s

t1u = px, py, pz

Front 9

Symmetry of ligand σ-bonding only orbitals?

Back 9

eg

t1u

a1g

Front 10

Crystal field theory / ligand field theory prediction of d-d transitions? what do they work for?

Back 10

one band in electronic spectra of Oh d-block complexes except d⁵ high-spin = no bands

works for d¹, d⁴, d⁶,d⁹ (high spin)

Front 11

Russel-Saunders coupling scheme?

Back 11

Spin-Spin; coupling of spin angular momenta of the two e⁻

Orbit-orbit: coupling of orbital angular momentum

spin-orbit: spin and orbital angular momenta coupling (of the same electrons)

Front 12

Russell-Saunders assumptions?

Back 12

Spin-spin> orbit-orbit> spin-orbit couplings

Front 13

For electronic spectra of 1st row TM what are we concerned with?

Back 13

spin-spin and orbit orbit coupling

Front 14

microstates?

Back 14

interactions between electrons in the same [partially filled] sub-shell produce atomic states called microstates

we don't need to worry about lower-energy fully filled sub-shells

Front 15

resultant spin angular momentum quantum number?

Back 15

(Spin-spin coupling)

S = (s₁ + s₂), (s₁ + s₂ -1) .....(s₁-s₂)

2e⁻; S = 1 or 0

3e⁻; S = 3/2 or 1/2

4e⁻; S = 2,1 or 0

(MS is the sub-quantum number = S, S-1,S-2...-S

MS = ∑ms

Front 16

Total orbital angular momentum quantum number?

Back 16

(Orbit-orbit coupling)

L = (l₁ + l₂), (l₁ + l₂-1), ....(l₁ - l₂),

for 2 p-electrons L = 2,1,0

for 2 d-electrons L = 4,3,2,1,0

(ML = sub quantum number = +L ...0....-L, ML = ∑ml

Front 17

What is a Term?

Back 17

spectroscopically distinguishable energy level, all microstates with the same energy give a TERM

Front 18

Determining ground state?

Back 18

Hunds's rules:

Ground state has the largest spin multiplicity

If two terms have the same spin multiplicity, the term with the larger value of L is the lowest in energy

Front 19

Term symbol?

Back 19

^2S+1 L
spin multiplicity = 2S + 1

L = S(0), P(1),D(2),F =

Term symbol is the shorthand describing energy, angular momentum and spin multiplicity of an atom in any state

Front 20

The Ground State?

Back 20

The Ground State is determined using Hund's Rules:

1. The Ground State has the highest spin multiplicity (2S+1)

2. If two terms have the same spin multiplicity, the term with the larger value of L is the lowest in energy

Front 21

Weak field approach?

Back 21

Assumes that the effect of the crystal field splitting is substantially less than that of interelectronic repulsion.

-We start from the free ion terms and then consider the influence of the ligand field on the terms

-orbitals split by ∆

Front 22

Orbital degeneracy of free-ion spectroscopic term?

Back 22

2L+1,

additionally, sum of the degeneracies of the group theoretical terms derived from a spectroscopic term must also be 2L + 1

e.g. ->Eg + T2g is 2+3= 5

Front 23

Discuss Strong Field approach?

Back 23

Allows us to gain information on the relative order of energy levels.

-crystal field splitting is assumed to be much larger than the interelectronic repulsion

Front 24

Strong-field approach method?

Back 24

1) The appropriate crystal field splitting diagram is used and the possible electron configurations determined

2) The terms to which each of these configurations give rise are obtained using direct products

3) The spin multiplicities of each term are deduced

Front 25

Notes for Orgel diagrams?

Back 25

1) High-spin cases only

2) Spin-allowed transitions only

3) used for qualitative purposes

4)labels on Orgel diagrams do not include the spin multiplicities or the g subscripts for octahedral cases. Multipliciets must be added when discussing specific transitions. Subscript g should be added when discussing octahedral complexes with centrosymmetry

Front 26

Orgel diagram for d¹, d⁴, d⁶, d⁹

Back 26

Front 27

How do we simply multielectron splittings?

Back 27

we limit the discussion to spin-triplets

Front 28

Spin triplets for d² + splittings of these?

Back 28

³F ->³A2g, ³T2g, ³T1g

³P ->³T1g

Front 29

strong field approach to d²?

Back 29

(t2g)² <(t2g)(eg) < (eg)²

consider interelectronic repulsion

=> (t2g)² = A1g, Eg, T1g, T2 => ³T1g or ³T2g

=> (t2g)(eg) = T1g, T2g => ³T1g and ³T2g

=> (eg)² = A1g, A2g, Eg => ³A2g

Front 30

correlating strong field and weak field

Back 30

only one ³T2g in weak field

=> (t2g)² => ³T1g

=> ³T1g is lowest in weakfield too

∴³T1g < ³T2g < ³A2g <³T1g(P )in weak field

³T1g(F) <³T2g < ³T1g (P) < ³A2g in strong field

Front 31

Discuss the two different energy triply-degenerate states for (t2g)(eg)?

Back 31

Front 32

How are energies relates to ∆₀?

Back 32

-for terms that occur once, energies = sum of one-electron energies for occupied d orbitals

³A2g = 2x0.6∆₀, ³T2g = (-0.4 + 0.6)∆₀ = 0.2∆₀ (relative to energy of ³F free ion term)

-³P is not split by ligand field ∴ ³T1g(P) has same energy as ³P free-ion term

-mean energy of ³T1g(F), ³T2g, ³A2g = 0

∴³T1g(F) = (3(0.2)+1.2)/3∆₀ = -0.6∆₀

Front 33

Discuss energy difference between ³P and ³F?

Back 33

energy difference due to differing mutual interelectronic repulsion within each term

-energy separation is 15B where B is a parameter of interelectronic repulsion (Racah parameter)

Front 34

Orgel diagram for d², d³, d⁷,d⁸

Back 34

Front 35

Estimating ∆o from spectra using Orgel diagrams?

Back 35

1) for d¹, single band observed, frequency = ∆o

2)for d³ and d⁸, ground state is A2g and the frequency of the first band = ∆o

3) for d² and d⁷, ground state is T1g(F) which is repelled by the excited state T1g(P), so energy gap is not ∆o, must use Racah parameter B

Front 36

Approximating ∆o for d²/d⁷?

Back 36

∆₀≈v₁[T1g(F) -> T2g]/0.8

∆₀≈v₃[T1g(F) -> A2g]/1.8

∆₀≈v₃[T1g(F)->A2g]-v₁[T1g(F)->T2g]

Front 37

transitions in d⁵ high spin?

Back 37

all transitions are spin-forbidden

Front 38

Tanabe-Sugano Diagram notes?

Back 38

-They are plots of E/B against ∆₀/B

-The ground term is made the horizontal base line

-include low-spin configurations

Front 39

Discuss plots of E/B against ∆₀/B?

Back 39

gets around the fact that B is a function of both the ligand and the metal: a d² diagram can be used for any d² ion with any ligand

Front 40

Discuss the ground term being the horizontal base line?

Back 40

absorption transition energies may be estimated simply by vertical measurements from the base line. In this way, experimental spectra may be compared with theory by fitting the observed bands to the Tanabe-Sugano diagram with an appropriate value of ∆₀/B

Front 41

Discuss including low-spin configurations?

Back 41

The Switch from h.s. to l.s. appears as an abrupt discontinuity in the gradients of the lines

Front 42

Nephelauxetic effect?

Back 42

Pairing energies greater in gas-phase ions than in complexes

=> reduced electron-electron repulsion

=> effective size of metal d orbitals is greater for complex

in complex electrons are spread over Metal and its ligands

Front 43

Nephelaxetic Prameter?

Back 43

β = B(complex) / B(free ion)

β≤1

β depends on identity of metal ion and nature/identity of ligand

small β = large d-electron delocalisation

large β = small d-electron delocalisation

Front 44

calculating β?

Back 44

Front 45

Nephelauxetic series?

Back 45

Front 46

Discuss breadth of bands in spectra?

Back 46

bands will be broad when gradients of ground and excited states on Orgel/Tanabe-Sugano diagram are very different from one another

Bands likely to be sharp when states have parallel lines on Orgel/Tanabe-Sugano diagram

Front 47

Mechanisms for transitions?

Back 47

transitions may occur through electric dipole or magnetic dipole mechanisms

-Components of electric dipole moment operator transform like translations (like I.R.)

-electric mechanism favoured for transition metals

-

Transition will be intense if accompanied by a large change in dipole moment

Front 48

What mechanism do transition metals complexses favour for transitions?

Back 48

TM complexses favour electric dipole over magnetic dipole transition

Front 49

How do the components of electric dipole transform?

Back 49

Translations just like the selection rules for I.R. spec but in a different region of the spectrum

Front 50

When is an electric dipole transition intense?

Back 50

if it is accompanied by a large change in the dipole moment, i.e. there is considerable charge redistribution during the transition

Front 51

Transitions between states of the same parity?

Back 51

forbidden (laporte selection rule)

Front 52

When will electric dipole transition be weak?

Back 52

(sometimes not observed) if there is a small or zero change in the dipole moment

Front 53

For the transition moment to be non-zero (for a transition to appear in the spectrum) what must happen? +discuss parity part?

Back 53

<Ψa|M|Ψb> must be totally symmetric so that the integral is non-zero (A1g for Oh)

M transforms as a translation => has an odd parity (u)=> direct product of ΨaxΨb

must be u as well so that uxu = g

=> to get u one must be u and the other g

Front 54

How to get <Ψa|M|Ψb> to be totally symmetric? example tetrahedral d²

Back 54

M = T₂

=>ΨaxΨb = T₂

A₂xT₂ = T₁ ∴ A₂ -> T₂ is forbidden

A₂xT₁ = T₂ ∴ A₂ -> T₁(P) and T₁(F) are allowed

Front 55

Getting <Ψa|M|Ψb> totally symmteric for octahedral?

Back 55

all orbitals are (g) therefore all forbidden unless we allow vibrations

Front 56

What normal model of vibrations are there for octahedral? and which ones must be used?

Back 56

A1g+Eg+T2g+2T1u+T2u

need u transitions to make product with orbitals u

must contain = T1u or/and T2u

e.g. A2g-> T2g for d³ och, A2gxT2g = T1g

M = T1u, T1gxT1u =A1u+Eu+T1u+T2u

so transition is vibronically allowed

Front 57

how can spin-forbidden transitions be enhanced?

Back 57

intensity stealing if they are close in energy to spin-allowed transitions

e.g. [Ni(H₂O)₆]²⁺ shows an extra band due to spin-allowed transition ³A2g -> ¹Eg since it is close in energy to ³A2g -> ³T1g(F), but no band for [Ni(NH₃)₆]²⁺ since the energies of these two transitions are more different in that case

Front 58

Charge-transfer transitions?

Back 58

CT bands arise from movement of electrons between orbitals that have predominant ligand character and orbitals of predominant metal character

-usually have high intensity as the selection rules seen earlier for d-d do not apply to them

Front 59

Key points for LMCT?

Back 59

-corresponds to metal reduction

-Facilitated by easily reduced metals and readily oxidised ligands (e.g. I⁻)

Front 60

Key points for MLCT?

Back 60

-requires metal to be readily oxidisable

-Facilitated by ligands, with low-lying acceptor orbitals (e.g. pyridine, pyridine, phenathroline, pheylpyridine)

readily oxidised cations - (Ti³⁺, V²⁺, Fe²⁺, Cu⁺)

Front 61

Time-resolved infrared spect?(TRIR)

Back 61

IR absorption spectroscopy of a molecule while in its electronically excited state

-technique provides direct evidience of MLCT and ever allows quantification of the degree of charge-transfer

Front 62

Note in particular for MLCT?

Back 62

Front 63

Electroluminescence?

Back 63

charge recombination generates a 3:1 ratio of triplet to singlet excited states but rate constant of triplet emission is low for organic molecules- too slow for significant emission

Front 64

Principle classes of bulk magnetism?

Back 64

1)diamagnetism

2)Paramagnetism

3)Ferromagnetism

4)Ferrimagnetism

Front 65

Diamagnetism?

Back 65

Exhibited by substances with paired electrons

-application of external magnetic field => distortion of electronic orbitals current => generates a magnetic field directed against the applied field M=> sample repelled by magnetic field

Front 66

causes of diamagnetism?

Back 66

Front 67

Paramagnetism?

Back 67

-exhibited by substances with unpaired electrons

-caused by circulation of unpaired electrons

-generates a magnetic field directed with the applied field (attracted by magnetic field)

10³-10⁴ times greater than diamagnetism

Front 68

Notes on paramagnetism

Back 68

Paramagnetism derives from spin and orbit angular momena, If all electrons are in pairs, angular momenta cancel out fully, and so paramagnetism is only observed for compounds with unpaired electrons

-substances with unpaired electrons are not always paramagnetic if they are very large molecules where the total diamagnetic effect of all atoms may be larger than the paramagnetism associated with one atom possessing unpaired electrons

Front 69

measurement of paramagnetism?

Back 69

paramagnetism expressed as magnetic moment µ and is measured by the interaction of a magnetic filed of known strength with a known mass of complex

Front 70

origins of paramagnetism?

Back 70

spin angular moment and orbital angular momentum

-most 1st row complexes, orbital contribution is suppressed by the ligands

=>µ is given by spin only formula =√4S(S+1)

Front 71

Exceptions to orbital contributino quenching?

Back 71

exceptions (t2g)ⁿ for Oh or (t₂)ⁿ for Td has n = 1,2,4 or 5

90⁰ rotation interconverts orbitals without needing to change electron sign

Front 72

Magnetic susceptibility (χ)

Back 72

observed force on 1 mol of substance as it is pulled into a magnetic field.

it is the simplest determination of magnetic moment

value that is measured is the substance's paramagnetic and diamagnetic contributions combined

Front 73

equation with χ?

Back 73

Front 74

Curie's Law?

Back 74

Front 75

What does Curie law imply?

Back 75

-each 'atomic magnetic moment' will act independently at all temperatures down to 0K

-interactions with other magnetic moments won't occur

-Plotting 1/χ against T gives a straight line passing through the origin at 0K

Front 76

Curie-Weiss law?

Back 76

Front 77

Problem with Curie-Weiss etc?

Back 77

only considered systems in which the metal centres (and hence their electrons) do not interact with one another

-only true for substances where the paramagnetic centres are well separated from each other by diamagnetic species (termed magnetically dilute)

Front 78

When do paramagnetic species interact?

Back 78

-when they are close together (e.g. bulk metals)

-when they are surrounded by ligands that transmit magnetic interactions (oxide >> fluoride>> chlorides)

Front 79

What occurs when magnetic centres interact?

Back 79

=> ferromagnetism

=> antiferromagnetism

Front 80

Ferromagnetic materials?

Back 80

Possess large domains of magnetic dipoles aligned in the same direction. this leads to greatly enhanced paramagnetism.

Front 81

Temperature at which bulk magnetism switches from paramagnetic to ferromagnetic?

Back 81

Curie Temperatur(Tc)

Front 82

Sub-classes of ferromagnets?

Back 82

Hard: magnetism retained in absence of applied field (property known as hystereses) e.g. bulk Fe, Fe alloys => used for data storage

Soft: magnetisation disappears on removal of field => used in transformer coils

Front 83

How is ferromagnetism lost?

Back 83

Heating substance above Tc -thermal motion causes domains to randomize

mechanically destroying alignments ofdomains (hitting the substance with a hammer)

Front 84

Antiferromagnetism?

Back 84

materials in which neighbouring magnetic dipoles are aligned in opposite directions

-occurs- below Neel temperature (Tn)

commonly found for transitino metal halides and oxides

Front 85

Antiferromagnetism: what occurs above Neel temperature?

Back 85

normal paramagnetism displayed

Front 86

Ferrimagnetism?

Back 86

characterised by hysteresis and reminent magnetism occurs below the ferrimagnetic Neel temperature (TfN) (above normal paramagnetism)

Front 87

What substances display ferrimagnetism?

Back 87

oxides containing Fe(III), called ferrites.

=> magnetite, Fe₃O₄

Front 88

Superparamagnetism?

Back 88

Occurs for colloidal dispersions of ferrites (e.g. Fe₃O₄) with particle size of ca. 10 nmh (corresponding to a single domain

-sometimes called ferrofluids

they are easily saturated magnetically by external fields of modest strength

-at low/modest fields the ensemble exhibts paramagnetism, having large magnetic moments µ

Front 89

Characteristics of χm

for forms of bulk magnetism?

Back 89

Front 90

Methods of determining magnetic susceptibility?

Back 90

Evans method (NMR)

goup method

Faraday balance

Johnson-Matthey-Evans (JME) balance

Vibrating sample magnetometer (physicists)

SQUID

Front 91

Spin crossover?

Back 91

d⁴-d⁷ systems, occurs when ligand field splitting energy is close to spin pairing energy

Front 92

what can initiate spin crossover?

Back 92

Thermolysis

pressure change

photolytically

Front 93

What physical changes does spin crossover lead to?

Back 93

colour change

bond lengths change