Transition Metals Flashcards
transition metals
incomplete d subshell in neutral atom or its ions (exclude Zn, Cd, Hg)
at least one stable oxidation state has partially occupied d atomic orbitals
shapes of d atomic orbitals
counting the number of d electrons in transition metal compund
n = group number - oxidation state
CrCl2, Cr2+
GN - oxidation state = 6 - 2 = d4
in neutral and isolated atoms, 4s occupies before 3d (3d above 4s)
V(0): [Ar] 4s2 3d3
in all compounds, all valence electrons in 3d AOs (4s above 3d)
(VO)SO4: V4+ [Ar] 3d1
how does M-L interaction affect energy of d atomic orbitals
metal and ligands held together by: Lewis acid-base interaction
isolated metal atom/ion: 5 d AOs are degenerate
complexes: 5 d AOs have different orientations relative to the positions of the ligands
M-L interaction resolves the degeneracy of the d levels
theories to explain splitting of d energy levels due to interaction with ligands
crystal field theory
+ first attempt to understand electronic structure of TM complexes
+ successfully predicts splitting of d orbitals and the electronic transitions
- assumes ligands as - point charges and electrostatic (ionic) interactions. this is a gross approximation which neglects bonding interactions between metal and ligands
ligand field theory
- extention of molecular orbital theory to d orbitals
- splitting is a measure of bonding strength between M and ligands
CFT - octahedral complex: how does the Oh field of the ligands interact with the lobes of the d atomic orbitals
dz^2 and dx^2-y^2 are of symmetry type eg in Oh character table
- electrons are concentrated close to the ligands along the axis
- repelled more strongly by the negative charge on the ligands
- higher in energy
dxy, dyz and dzx are of symmetry type t2g in Oh character table
- electrons are concentrated in regions that lie between the ligands
- repelled less by the negative charge on the ligands
- lower in energy
ML6: energy of the d orbitals - the crystal field stabilisation energy (CFSE)
CFT - tetrahedral complex: how does the Td field of the ligands interact with the lobes of the d atomic orbitals
dz^2 and dx^2-y^2 are of symmetry type e in Td character table
- lower in energy
- consider spatial arrangement of orbitals: e orbitals point between positions of the ligands and their partial negative charges
dxy, dyz and dzx are of symmetry type t2 in Td character table
- higher in energy
- t2 orbitals point more directly towards the ligands
ML4: energy of the d orbitals - the crystal field stabilisation energy (CFSE)
ligand-field splitting parameter in a tetrahedral complex is less than in an octahedral complex
- tetrahedral complex has fewer ligands, none of which is orientated directly at the d orbitals
octahedral vs tetrahdedral
Δt is smaller than Δo
- for the same metal ion and ligands, Δo and Δt are related by:
Δt = 4/9 Δo
geometry:
octahedral: big difference in electrostatic overlap between eg and t2g (6 ligands)
tetrahedral: smaller difference in electrostatic overlap between e and t2 (4 ligands)
CFT for other geometries start from Oh and ML6 (elongation/contraction)
elongation and contraction cause distortion in z (Oh → D4h)
- elongation: stabilise d with z component
- contraction: destabilise d with z component
destabilising along z increases overall orbital separation
CFT: d level splitting for common geometries
CFT for other geometries start from Oh and ML6 (removing a ligand)
extent of splitting Δ
depends on identity of metal (type and oxidation state) and identity of ligand (spectrochemical species)
cannot be explained by crystal field theory, CFT
- ligands represented as negative point charges which repels electrons in metal d AOs
- explains level of splitting, not the order of splitting
use ligand field theory, LFT
Transition metal MO diagrams
A = metal
B = ligand (more electronegative ∴ lower in energy)
antibonding MO has greater contribution of A (closer in energy)
bonding MO has greater contribution of B (closer in energy)
ΔE is an indicator of the strength of A-B bond
ΔE is inversely proportional to δE
when δE is large for original AOs on A and B, A and B are very different in electronegativity ∴ A-B is a very polarised bond (weak bond) - strongest A-B bonds form when A and B are close in energy (small δE)
fragment theory: formation of ethane from two methyl radicals
MO of CH3 radical similar to NH3 molecule
CH3 radical = NH3 - 1e-
fragment theory: formation of ethene from two methylene (carbene) radicals
MO of CH2 diradical similar to OH2 molecule
LFT - octahdedral complex - σ bonding
each ligand (L) has a single valence orbital directed towards metal (M)
- each of these orbitals has local σ symmetry with respect to the M-L axis
examples: NH3, F- ion
the orbitals of the central metal atom divide by symmetry into 4 sets (read off character table)
a1g
t1u
eg
t2g
6 symmetry-adapted linear combinations (SALC) of the six ligand σ orbitals
a1g
t1u
eg
irreducible representations of the Oh point group spanned by the σ orbitals of the 6 ligands:
- 1 MO on ligand (6 MOs in total): Γ 1A1g + 1Eg + 1T1u
there is no combination of ligand σ orbitals that has the symmetry of the metal t2g orbital (this does not participate in σ bonding)
The MO diagram for ML6 for sigma only ligands
- antibonding orbital polarised towards metal
- t2g from metal is non-bonding
- bonding orbital polarised towards ligand
frontier orbitals of complex: non-bonding t2g orbitals and antibonding eg orbitals
effect of donor atom on Δo - electronegativity
as electronegativity of donor atom increases:
- δE increases (M and L are further apart in E)
- more polarised and less covalent bond (less stabilising interaction)
- Δo decreases
effect of donor atom on Δo - size of AO/MOs (overlap)
as size of donor atom AOs increase:
- AOs more diffuse
- higher overlap with metal d orbitals (more stabilising interaction)
- Δo decreases
LFT - octahdedral complex - π bonding
π-donor ligands decrease Δo
π-acceptor ligands increase Δo
ligands in complex have orbitals with local π symmetry with respect to the M-L axis
12 symmetry-adapted linear combinations (SALC) of the six ligand π orbitals (2 MO on each ligand):
Γ 1T1g + 1T2g + 1T1u + 1T2u
includes SALC of t2g symmetry - has net overlap with metal t2g orbitals
- no longer purely non-bonding on metal
π-donor ligand - decrease Δo (SMALL FIELD)
ligand has filled orbitals of π symmetry around the M-L axis (before any bonding is considered)
examples:
Cl- Br- OH- O2- H2O
(π-base)
full π orbitals of π-donor ligands lower in energy than metal d orbitals
π-acceptor ligand - increase Δo (LARGE FIELD)
ligand has empty π orbitals available for occupation (vacant antibonding orbitals)
examples:
CO N2
(π acid)
vacant π* orbitals of π-acceptor ligands higher in energy than metal d orbitals
identifying the type of ligand
π - donor ligands
~ more than one donor pair on the same atom
~ have 2 active MOs, both occupied
~ VSEPR shows two double dots (lone pairs)
~ late in periodic table (group 6,7)
π - acceptor ligands
~ have an empty π* MO on the donor atom
~ look at MO to identify
examples:
CO (cabonyl complexes)
PR3 (phosphine)
C=C organic ligands
σ-only ligands
~ only have one active MO, the donor pair
~ no available π/π* MO
examples: (group 5)
NH3, NR3,
PH3, PR3,
AsH3
CO ~ π - acceptor (MO diagram)
- O more electronegative than C
- lower in energy - symmetry of AOs (relative to bond direction, z)
rotate around z axis:
- no change in sign = σ
- change in sign = π
2s - σ symmetry
2px - π symmetry
2py - π symmetry
2pz - σ symmetry
- sp hybrids (spz)
(s + pz)
(s - pz) - frontier MOs
HOMO = σ3 (lone pair on C) - acts as a Lewis σ base (an electron-pair donor)
LUMO = 2π (π*) - acts as a Lewis π acid (an electron pair acceptor) ~ accepts electron density from filled metal d orbitals
both frontier MOs are on C - CO always binds from C side (not electronegative O)
bonding in CO metal complex
π backbonding
σ bond from ligand to metal (1)
π bond from metal to ligand (2)
CO is not nucleophilic - ∴ σ bonding is weak
but d-metal carbonyl compounds are very stable ∴ π backbonding is very strong
bonding is synergic (mutually enhancing): π backbonding from metal to CO increases electron density on CO, this increases ability of CO to form σ bond to metal
using IR to assess affect of π backbonding
in isolated CO molecule, ν = 2143 cm-1 (stretching frequency)
CO stretching frequency is very intense in IR (large change in dipole) - easy to monitor
σ donation has little effect on stretching frequency
π backdonation
- electron density goes into π* of CO
- weakens C-O bond (greater C-O bond length)
- stretching frequency decreases
quantifying π backbonding
depends on:
- orbital overlap
- energy match between M d and CO π* orbitals (ΔE)
- electron density on M
influenced by:
- type and charge of M
- other ligands (competition for the same M-d electrons)
M-C≡O with no backbonding
M=C=O with complete backbonding
effect of M on π backbonding
- influence of coordination and charge
decrease in oxidation state: more electron density available for π backbonding
- greater weakening of C≡O bond
d10 metal has more electrons for π backbonding than d6
- greater weakening of C≡O bond
Td: only 3 other CO ligands comepeting for π backbonding electrons
- lower weakening of C≡O bond
CO as a bridging ligand
CO can bridge 2/3 metal atoms
CO stretching frequencies generally follow the order: MCO > M2CO > M3CO
- increasing occupation of π* orbital as the CO molecule bonds to more metal atoms
- more electron density from metals enters the CO π* orbitals
M3(μ3-CO): the symbol μ3 indicates that CO bridges 3 metals
the 18 electron rule
C-based π acceptors stable as 18 electron complexes
Cr(0): d6 (each CO brings 1 electron pair (2 electrons)
6 CO needed (6 x 2 = 12) for there to be 18 electrons
Cr(CO)6
Fe(0): d8 - 5 CO needed (5 x 2 = 10) for there to be 10 electrons
Fe(CO)5
Ni(0): d10 - 4 CO needed (4 x 2 = 8) for there to be 18 electrons
Ni(CO)4
Fe(2-) d10 - 4 CO needed (4 x 2 = 8) for there to be 18 electrons
[Fe(CO)4]2-
the 18 electron rule: for M with odd number of electrons
Mn(CO)5
Mn(0): d7 + (2 x 5) = 17 electrons ~ does not meet 18 electron rule
Mn(CO)5 ~ gain electron → [Mn(CO)5]- (18e- stable)
Mn(CO)5 ~ lose electron → [Mn(CO)6]+ (18e- stable)
Mn(CO)5 ~ react with methyl radical → Mn(CO)5(CH3) (18e- stable)
Mn(CO)5 ~ share with another complex → Mn2(CO)10 (18e- with Mn-Mn single bond. dimer of Mn(CO)5 ~ reactive)
CO and N2
- the two molecules are isoelectronic
- both are π acceptor ligands
air is 70% N2 but CO is toxic
- frontier MOs in CO are both polarised towards C
- no polarisation of HOMO/LUMO in N2: worse overlap with M-d atomic orbitals, lower bond strength
- donor pair in CO is a C-based level
- N-based in N2, lower in energy ∴ higher gap from M-d, lower bond stength
- N-N bond is more covalent than C-O
- larger split of π/π* levels
- π* at higher E in N2 than CO, N2 is a worse π acceptor
chemistry of N2 complexes
bridging and side-on interactions possible for N2, not for CO
molecules isoelectronic to CO
10e- (valence e-)
N2 dinitrogen
CN- cyano
R-NC isonitrile
same number of total electrons/same electronic structure as CO
11e- (valence e-)
NO nitrosyl
phosphine complexes
lone pair on P (HOMO: basic and nucleophilic) - σ donor
empty π* orbital on P (LUMO) - π acceptor
PH3 is σ donor only
- only active orbital is 2a1
PR3 is σ donor only (high LUMO)
PF3 is π acceptor (more electronegative heteroatom to P lowers LUMO)
bonding of phosphines to metal
electron-rich phosphines (PMe3): good σ donor but poor π acceptor
- increase e- density on M
- increase in backdonation to CO
electron-poor phosphines (PF3): poor σ donor but good π acceptor
- decrease e- density on M
- decrease in backdonation to M
lewis basicity can indicate donor/acceptor ability
σ only
PCy3 > PEt3 > PMe3 > PPh3 >
π acceptor
P(OMe)3 > P(OPh)3 > PCl3 > PF3
PF3 π acceptor of similar strength to CO
c-based ligands
alkenes bond side-on to a M, with both C atoms of double bond equidistant from M.
groups on alkene are perpendicular to plane of M and the two C atoms
alkenes have no lone pair
Dewar-Chatt-Duncanson model
the electron density of the C=C π bond (HOMO) donated to an empty orbital on M - forms σ bond
- removes e- density from π bond
- weakens the C=C bond
filled metal d orbital donates electron density to empty π* orbital of alkene (LUMO) - forms π bond
- backdonate e- into π*
- weakens C=C bond
structure tends to that of a C-C singly bonded structure
activation of C-C bond towards addition reaction
Dewar-Chatt-Duncanson model - coordination of ethylene (ethene) shown as possible resonance
when π backbonding from metal atom increases, strength of C=C bond decreases as the electron density is ocated in the C=C antibonding orbital
hapticity, η
number of C atoms bonded to the same metal
polyenes
behave as polydentate ligands, in which each C=C double bond behaves like an η2 ethylene
dihydrogen complexes
side-on interaction to M
explaining the spectrochemical series
Δo depends on the type of ligand
π donors «_space;σ only «_space;π acceptors
Δo depends on electronegativity (C > N > O > F) and period (N < P < As) of donor atom
Δo depends on period of metal (3d «_space;4d ~ 5d) and its oxidation state (Δo increases with metal oxidation state - M will be a stronger acid)
high spin/low spin complex
high spin: electrons prefer to singly occupy each orbital before pairing (weak field) - π donors - species has a high number of parallel electron spins
low spin: electrons pair in the same d orbital (strong field) π acceptors - species has a small number of parallel electron spins
ligand field stabilisation energy
which fraction of the splitting Δ is the electronic configuration in the complex more stable than in a spherical field
- depends on high/low spin arrangement
Fe3+ (d5)
[Fe(H2O)6]3+
high spin configuration
LFSE: (3 x 0.4)Δo - (2 x 0.6)Δo
LFSE = 0 ~ no stabilisation
[Fe(CN)6]3-
low spin configuration
LFSE: (5 x 0.4)Δo
LFSE = 2Δo ~ large stabilisation
ligand-field stabilisation energies for octahedral complexes
stable complexes with large LFSE
d5 high spin (max spin multiplicity)
- half filled set of MOs
d6 low spin (large LFSE)
- completely filled subset
square planar complex - d8 (stable complex with large LFSE)
tetrahedral arrangement is less sterically hindered
square planar arrangement gives d-orbital splitting with high dx^2-y^2
- this arrangement is energetically favourable when there are 8 d-electrons and strong enough crystal field (Δ) to favour low spin
- this tendency is enhanced with large 4d and 5d metal ion - larger ligand field splitting and lower pairing energy than 3d metal ions
- 3d metal has smaller, less diffuse orbitals ∴ poorer overlap with ligand
- forms low-spin square-planar metal complexes
in this case, electronic stabilisation energy can more than compensate for unfavourable steric interactions
ligand high on spectrochemical series also results in large LFSE - square-planar complex
The Jahn-Teller distortion
when a non-linear molecule is in a degenerate electronic state, it distorts in such a way as to remove the degeneracy
degenerate state
a set of MOs at the same energy, but occupied by a different number of electrons (unevenly filled)
associated with d-elements as it is common to have degenerate orbitals due to symmetry
tetragonal distortion (elongation)
if the ground electronic configuration of a nonlinear complex is orbitally degenerate, and asymmetrically filled, the complex distorts to remove the degeneracy and achieve lower energy
6-coordination d9 complex of Cu(II) departs considerably from octahedral geometry, showing pronounced tetragonal distortions
- high spin d4 complex of Cr(II) or Mn(III) and low spin d7 complex of Ni(III) show similar distortion
tetragonal distortion of regular octahedron: extention along z-axis and compression on the x-and y-axis
- lowers energy of orbitals with z-component
- raises energy of orbitals without z-component
may be electronically advantageous: if 1 or 3 electrons occupy eg (such as in high spin d4, low spin d7 and d9) - degenerate level is unevenly filled
- in d9 complex, 2 electrons go into dz^2 with lower energy and 1 in dx^2-y^2 with higher energy
Jahn-Teller distortion: consider a d4 low spin Oh complex
The Jahn-Teller distortion: rationalise the change in stepwise formation constants, kn for Cu(II) amine complexes
large drop in log(kn) for n=5
Cu(II) d9 is Jahn-Teller distorted: has a full t2g set and degenerate eg set
- complex elongates to break the degeneracy and become more stable
- 4 short (stronger) and 2 long (weaker) M-L bonds
amine bonds more strongly to metal centre than water (larger Δo)
- 4 strong bonds form with amine
- 5th amine ligand has long, weak bond
replacement of the ligands with long bonds causes smaller energy change, smaller kn (drop in rate of reaction)
reactions of transition metal complexes: ligand replacement reactions
potential energy surface: plot of energy as a function of atomic coordinates
- multi-dimensional surface: N-atoms = 3N-6 degrees of freedom (xi, yi, zi)
choose one geometric parameter that varies along the reaction - plot energy as a function of reaction coordinate
- minima: equilibrium points (reactants/products)
multiple transition states and intermediates before forming product
elementary reaction step: transition state to intermediate
three mechanisms depending on shape of potential energy surface
1. associative (A)
2. dissociative (D)
3. interchange (I)
two competing reactions: thermodynamic and kinetic control
associative mechanism
- bimolecular
2 steps → 1 intermediate in potential energy surface
two transition states and an intermediate in between
- first step is slow (largest Ea): forms an intermediate with all ligands together with metal (increases coordination number of metal)
- second step is fast: leaving group removed, return to original coordination number
this mechanism is given:
- by low coordination number transition metal complexes (e.g. square planar rather than octahedral)
- low number of valence electrons (e.g. not more than d8 - to be able to accomodate the two extra electrons from Y ligand in intermediate)
dissociative mechanism
- monomolecular
2 steps → 1 intermediate in potential energy surface
two transition states and an intermediate in between
- first step: leaving group removed before incoming ligand can combine with intermediate (decreases coordination number of metal
- second step: ligand combines with intermediate
this mechanism is given by:
- high coordination number transition metal complex
- bulky ligands
interchange mechanism
- bimolecular
1 step → 0 intermediate in potential energy surface
one transition state
this mechanism is given by:
- complexes which dont fit the other two classes
differentiating between ligand replacement reactions
differentiate by measuring rates at varying concentrations of reagents
associative and interchange are both bimolecular
- but associative has an intermediate that can be isolated
- intermediate cannot be observed for interchange
trans-directing effect
the extent to which ligand X weakens the bond trans to itself in the ground state of the complex
- correlates with the σ donor/π acceptor ability of X
- ligands trans to each other use the same orbitals on metal for bonding (compete for the same orbitals)
if one ligand is a stronger σ donor, the ligand trans to it cannot donate e- to M as well, thus has a weaker interaction with M
- bond in the trans position is weakened and is easier to replace ~ this is a kinetic effect
ligands compete for the same orbitals of the metal
ligand X trans to the leaving group in square planar complexes influence rate of substitution
trans-directing series
when a ligand binds very strongly with d-AO, it polarises the d-AO and weakens the bond in the trans position ~ making it easier to replace
magnetism: macroscopic observation
Ørsted’s Law
1. an electric current (I) generates a magnetic field (B)
2. an electric current of intensity, I in a loop with area, A generates a magnetic field: μ = IA
electrons in AOs/MOs are a microscopic version of this current:
I ∝ e/m_e
Bohr magnetron
magnetic moment of atoms/molecules
total angular momentum, J
orbital angular momentum, L
spin angular momentum, S
J = L + S
in most molecules, electrons are localised in bonds ∴ L is negligible
- in this case, we can use a spin-only formula where the magnetic moment only depends on S
spin-only magnetic moment
S can be predicted from LFT
S = 1/2(number of unpaired electrons in complex)
magnetisation M
magnetic moment per unit of mass or volume
in most materials, M = 0 unless in an applied magnetic field, H
in an applied field: M = χH
χ - magnetic susceptibility (proportionality constant)
there are two different responses to the applied field, H
χ < 0
- M points in opposite direction to H
- diamagnetic material
χ > 0
- M points in same direction as H
- paramagnetic material
diamagnetism
χ < 0
when placed in a magnetic field, atoms acquire an induced magnetic dipole moment that is in a direction opposite to the applied field
- atom has no permanent magnetic moment ~ the resultant orbital and spin angular momentum = 0
- all paired electrons
Lenz law: the applied field induces an electric current, whose associated field is opposite to the applied one
paramagnetism
χ > 0
atom has a permanent magnetic dipole moment due to both electronic orbital and spin angular momentum (has unpaired electrons)
in applied magnetic field, spins align parallel to the field
Curie’s Law
when particles are ‘independent’ (non-interacting) e.g. in dilute solution, magnetic susceptibility described by Curie’s Law
χ = C/T
C - Curie constant
linearised plot of Curie’s Law:
- plot 1/χ as a function of T
- the slope of the curve is 1/C
- curve passes through origin
magnetisation increased with applied field
M = χ H = (C/T)H
- the greater the field, the greater the tendency for moments to align with the field
- the susceptibility, χ = M/H is the same, irrespective of the field
- magnetisation disappears when the field is removed
origin of Curie’s Law
in zero applied field, moments are in random direction and fluctuating
- cancel each other out to give average zero magnetisation
when a magnetic field is applied
- moments align with the field
- net magnetic moment decreases with T
extention to Curie Law: Curie-Weiss law
if magnetic moments on neighbouring sites interact with one another, the temperature dependence of χ requires an extention to Curie’s Law:
χ = C/(T-θ)
θ - Weiss constant
1/χ = (T-θ)/C = T/C - θ/C
plot 1/χ as a function of T
- slope of the curve is still 1/C
- curve does not pass through orgin
ferromagnetic (FM) solids θ > 0
θ > 0 indicates solids where spins align in parallel fashion
below a critical T (Curie temperature, Tc), all the spins align
spin alignment is in the same direction as applied field and reinforces the field
magnetisation increases beyond the value expected from Curie’s Law
antiferromagnetic (AFM) solids θ < 0
θ < 0 indicates solids where spins align in an antiparallel fashion
below a critical T (Néel temerature, Tn), neighbour spins align in opposite directions
spin alignment in opposite direction reduces the applied field
magnetisation decreases below the value expected from Curie’s Law
ferrimagnetic solids θ > 0
θ > 0 can also be obtained when there are different spins coupled in AFM way
spins align in opposite directions but do not cancel out, hence behave as ferromagnetic solids
- have two different ions with different magnetic moments
- spins do not cancel out entirely, we have a net magnetic moment
magnetism in solids with spin-polarised ions
the interaction between magnetic moments on neighbouring sites is called magnetic superexchange
SUPEREXCHANGE: if magnetic ions have common ligands
DIRECT EXCHANGE: otherwise
e.g. in magnetic perovskite
