TM Flashcards
How do you determine the ground state orbital angular momentum, L, of an electron config?
Disregard full subshells as no contribution to am
Add ml values for each e- (if two in same orbital then add twice) following Hunds rule
The highest L value is the ground state
Where |L|=0,1,2,3,4,5 is S,P,D,F,G,H
How can you evaluate the spin quantum number, S?
Add the unpaired spins of e-
What is the spin multiplicity of a term?
2S+1
Where S is the spin quantum number
What are the J-values of a term and ground state?
J = L+S, L+S-1,…|L-S|
When < half full orbital then Jmin is the lowest energy
When > half full orbital then Jmax is the lowest energy
How does spin multiplicity correspond to energy level?
Largest spin multiplicity is the most stable
What is the ground state when there is a half-filled orbital?
L = 0, and therefore J=S
Filled, 1/2 filled, or empty orbitals represent orbital singlets
How does the sublimation/energies change across the first TM period?
s has metallic band structure (s&d), no nodes in band
Ca → Cr there is an increase as fills the band and therefore more bonding
After this generally decreases as fills antibonding orbitals so bonding strength in solid decreases
Cr, Mn, Fe (lesser extent) low as no exchange energy in solid, spin energy gained in gas
Why is exchange energy available in gas and not in solid metallic band structure?
Valence e- in metallic bonding randomises relative spin and so increases e- e- repulsion relative to the exchange energy in free atom
Most relevant for d4, d5, d6 where most repulsion and exchange energy
What orbitals are stabilised and raised in energy in CFT theory for octa?
How does CFT fail?
Doesn’t describe true nature of chemical bonding or some effects
By how much are the t2g and eg stabilised/destabilised?
t2g stabilised by -2/5 ΔO
eg destabilised by 3/5 ΔO
What is the Barycentre?
Energy when there is a spherically uniform distribution of negative charges
In the MO picture, what orbitals are filled in the ligand field?
Bonding and non-bonding filled by ligand electrons
Valence e- from metal are in the eg* and t2g* which are mainly d orbital character
If the 3d orbital is lower E than 4s, why is 4s occupied in Sc and beyond?
3d orbital is compact, and outermost 4s lobe contains most of e- density so 4s is diffuse
e- e- repulsions are significant in the contracted 3d orbitals, so more favourable to be in slightly higher 4s
How does 4s, 3d and 4p change going from group 1 to 3?
3d lowers in energy across the groups as is more contracted so higher Zeff affects it more
3d lowers to less than 4s by Sc
What is the relation between orbtial energy and Zeff?
(revision)
Orbital energy ≈ -Zeff2/n2
What are the factors a 4s experiences across a period?
Innermost lobe experiences slow increase in nuclear charge
Outermost lobe effectively screened from increase in nuclear charge by 3d e- density
Why do neutral atoms in the 1st row of TM have 3dn-2 4s2 (or 3dn-1 4s1)?
Strong 3d electron repulsion
What occurs to 3d and 4s orbitals as ionisation occurs?
3d orbital has increased Zeff and contracts more rapidly than 4s
3d orbital contracts and penetrates core more
What are the microstates with L values?
2L+1 microstates with values from L,L-1,L-2, … -L+1,-L
Gives rise to 2J+1 microstates
How well do the 4s orbitals overlap with ligands?
Can overlap even better with ligands and make v stable bonding & v destabilised antibonding (compared to 3d)
Due to 4s being more diffused than the 3d
What symmetry do the eg and t2g orbitals overlap with?
eg - σ symmetry
t2g - π symmetry
What occurs to bonding strength as electrons are put into t2g* or eg*?
t2g* π* weakens bonding less than eg* σ*
What is the change of hydration enthalpies of M2+?
Hydration/lattice enthalpies should scale as 1/r (predict increase approx linearly)
Ca2+, Mn2+, Zn2+ are linear, others are more negative than expected
Due to LFSE from water in aq.
How does the standard reduction potential change across the 1st period of TM
General increase - metals at the end of the period are less reducing
ΔGº=-nFEº
Dips at Mn due to premature filling of antibonding orbital, exhange energy of gaseous ion and non-close packed structure
Cu high as very -ve ΔHhyd and high I2
Zn low as low ΔHhyd and ΔHatm
What are the steps in the reduction potential?
M(g) → M2+(g) + 2e-
Via - ΔHatm + ΔHox - ΔHhyd(M2+)
What is the stability of +2 ox state across 1st row TM?
Decreasing stability of +2 oxn state
Factors are: ΔHf(M2+) - 2ΔHf(X-) + ΔHL(MX2)
ΔHf(M2+) less favourable across the group as higher IE, increases faster than ΔHL (which is negative)
What is the relative stability of dihalides and monoxides?
All due to ΔHf(Xm-)
Oxides less stable than dihalides
Fluorides more stable than chrlorides
What is the bonding like in high oxn compounds?
More covalent
What is the relation between ΔHL and ionic radii?
ΔHL α 1/(r+ + r-)
What does a high oxn state suggest about the magnitude of ΔHL?
Large magnitude of ΔHL
What are the symmetry labels of the 3d, 4s and 4p orbitals in a TM?
4p - t1u
4s - a1g
3d (dz2 & dx2-y2) - eg
3d (dxy & dxz & dyz) - t2g
What 3d orbtial has a π-overlap in ligands?
t2g - 3d (dxy & dxz & dyz)
π donator - t2g interacts with px & py
π acceptor - t2g interacts with π* orbital
What is the symmetry of the ligand group orbitals and how do they interact with orbitals on a metal?
Ligands: t1g + t2g + t1u + t2u
Metal t1u involved in σ bonding, leaves t2g to interact with the ligand one
What is the MO diagram for a ML6 with σ bonding only?
What is the MO diagram for a ML6 with π donor ligands?
What is the difference in the MO diagram for a ML6 with σ bonding only and one with π donor ligands?
π donor ligands have a t2g split into bonding and anti
t2g filled with electrons from π donor
t2g* is now HOMO, which is closer to eg* so Δo decreases
What is the MO diagram for a ML6 with π acceptor ligands?
How is the MO diagram of a ML6 with σ only and π-acceptor ligands different?
vacant π-acceptor t2g orbitals overlap with those on metal
t2g from vacant higher in E than filled so t2g split more
Bonding t2g houses metal e-
What is the relative size of Δo in different ML6 ligands?
Δo (π-donor ligands) < sigma donor < π acceptor
How can you determine the bonding orbitals in different ligand field geometries?
Uses group theory character tables
On the RHS find which orbitals degen under point group
Establish which orbitals involved in different bonding
What is the d-orbital splitting pattern in Td geometry?
t2 is raised in energy by (2/5)Δt
e lowered in energy by (3/5)Δt
Why is Δo >> Δt ?
Poorer overlap of metal orbitals with ligand orbitals
What is the approx between Δt and Δo?
Δt = (4/9)Δo
When is Δo maximised?
High spin d3, d8 or low spin d6
What spin is Δt complexes?
Almost all high spin due to small |Δt|
What does Δ vary with?
Metal
Oxn state
Ligand
Coordination #
3d vs 4d vs 5d metals
What is the Δ of 4d & 5d compared to 3d?
4d and 5d larger due to better overlap with ligands
This is due to more diffuse orbitals
What is the relation between oxn state and Δ?
Higher oxn states have a larger Δ
Larger charge on metal so nd lower in E and better energy match with ligand orbitals
What is the spectrochemical series?
Series of ligands
From those which give large Δ to lower Δ
What type of Δ is there when mainly ionic M-L bonding?
Less covalence
Smaller Δ
Includes: Hal-, OH-
Where are π-donors in the spectrochemical series?
t2g* raised in energy and smaller gap between t2g* and eg*
Therefore Δ small
Where are strong σ donors in the spectrochemical series?
Just higher than middle of series
Ligand orbitals higher in E so better energy match with nd & better overlap and larger Δ
Where are π-acceptor ligands in the spectrochemical series?
High in series, large Δ
Splits t2g , now gap between t2g and eg* as t2g* now higher than eg*
What is the interaction when there are π acceptors?
Ligand to metal σ donation
Metal to ligand π back donation
How do EWG substituents effect back-donation?
EWG π-acid ligands have more π back donation
When are M2/3+ high or low spin for the 1st, 2nd and 3rd rows?
1st row M2+ - Generally hs, needs v strong field ligands (CN-, bipy) for ls
1st row M3+ - Ls when NH3 (and higher field) & hs when lower, Δo increases with charge faster than pairing energy of e- (e- e- repulsion)
Td are nearly all hs
2nd and 3rd row - LS as high Δo and less e- e- repulsion as more diffuse orbital
How and why does Δ change across a TM series?
Δ increases as more stable d orbitals have better energy match for lower E ligand orbtial
How does the cationic radii of 1st row TM complexes change?
LS - decrease to Fe2+ then increase to Zn2+
HS - same to V2+ then increase to Mn2+, then decrease to Ni2+ and follows same to Zn2+
What is the LFSE for d0, d5, d10?
When Oh not preffered as LFSE is 0
Otherwise Oh more stable as inversion of d-orbitals, can have more e- in lower E t2g
What is the general formula and structure of spinels?
A2+(B3+)2O4
ccp O
What holes are in the ccp O array in the spinel structure?
4 x O
4 x Oh holes
8 x Td holes
What is the structure of a normal and inverse spinel?
Normal: 2xB(M3+) ions in 1/2 Oh holes, 1xA(M2+) in 1/8 of Td holes
Inverse: 1xB(M3+) + 1xA(M2+) in 1/2 Oh holes, 1xB(M3+) in 1/8 of Td holes
How can you tell if a normal or inverse spinel structure observed?
One B3+ always in oct
When normal: calc LFSE for A2+ in tet and B3+ in oct
When inverse: calc LFSE for B3+ in tet and A2+ in oct
Difference in LFSE (in terms of Δo) = normal - inverse, when -ve is normal
What should be taken into account when determining the geometry of a complex?
Absolute value of Δ and ligand repulsion
For 1st TM elements and weak field ligands the LFSE is small and ligand repulsion is dominant factor
When do Td complexes occur?
Ligands that are very bulky or -ve charge
MX42- preffered, MX64- not seen
Exception: CoX42- d7 has low change in LFSE from Oh to Td
What is the structure of d8 complexes?
Anion repulsion can force Td
Less repulsion for water so Oh preffered
1st row: LFSE only influences stereochem when Δ is large, square planar (D4h) only present when Δ large as strongly antibonding σ* not occupied
What is the Jahn-Teller theorem?
Non-linear molecule with an orbitally/spatially degen ground state is unstable wrt a distortion that removes degeneracy
What degenerate states are found in the octahedron geometry?
t2g1, t2g2, t2g4, t2g5
t2g3eg1, t2g6eg1, t2g6eg3
eg more sensitive to M-L bond length change as used in σ overlap, therefore in practice:
eg1 (hs d4 & ls d7) & eg3 (d9) give rise to static distortions
What are some examples of metal ions with Jahn-Teller distortions?
Cr2+ (HS): d4 (eg1)
Cu2+ (6-coordinate solid state and complex): d9 (eg3)
What is the nature of a Jahn-Teller distortion in an octahedral configuration?
Elongation along 4-fold axis to remove eg degen
Elongated rather than compressed which also lifts degen, as 3dz2 can be mixed with 4s
sdz2 hybrid more extended in z direction - more PE gained by elongation along z than in xy plane
What stability is shown in a frost diagram?
Stability wrt zero oxidation state
Lowest lying species is most stable as most negative ΔGf
Redox states high in diagram as strongly oxidising, poor stability wrt 0 oxidation state
What do the lines on a pourbaix diagram show?
Vertical - protonation/deprotonation process, non redox process
Horizontal - redox process, not a protonation/deprotonation process
Why are higher oxn states of TM found as oxy ions in solution?
Extensive hydrolysis of highly charged ions
Stabilised in alkali
What is the effect of precipitation on redox potentials?
The cation of the least soluble salt has a lower activity in equilibrium with the solid
e.g. Fe(H2O)63+ ⇔ Fe(OH)3 , where ΔG3(Ksp)
What is Ksp ?
Solubility product
Larger the value the increased solubility
Why are there differences in redox potentials with different ligands?
Due to stronger interaction of some ligands with one of the oxidation states
What oxidation states do π-acceptor ligands stabilise?
Low oxidation state
π* acceptor orbitals on the ligand are closer in energy to the higher
energy 3d orbitals of the lower oxn state
low spin complex with acceptor - larger LFSE for lower oxn state
Lower oxn state has less solvent ordering to potential more +ve
What oxidation states do anionic ligands stabilise?
Higher oxn state
Interact and form more stable complex with metal ions of a higher charge, better energy matched with d orbitals
When hard ligands is driven by entropy as lower orders the solvent more
Δ small and LFSE not a major effect
How do cyanide ligands effect oxidation states?
Anionic, strong σ donor - stabilises higher oxn state
π acceptor - stabilises lower oxn state
Overall - anion effect overcomes the π acceptor effect
What oxidation states do strong σ donors stabilise?
High oxn states as stronger interaction as better energy match
How does the atomic/ionic radii across each TM series change?
At first decreases, as Zeff increases and fills more e- into bonding orbitals
Then radii increases from Fe group as antibonding orbitals are filled
What is responsible for the similar radii of 2nd and 3rd TM series elements?
Lanthanide contraction
Lanthanide series occurs before 3rd TM series and corresponds to filling of 4f which has no radial node and shields poorly, which results in higher Zeff for 3rd TM series
How are 4/5d orbitals comparable to 4d orbitals?
4/5d more penetrating (1/2 nodes) and more extended
More diffusion means reduced e- repulsion, spin pairing occurs more readily as exchange energies are small
More overlap with ligand orbitals as more amplitude outside core - more covalence
What are the atomisation energies for 2nd/3rd row TM series compared to 1st row?
2nd is much larger than 1st, and 3rd is sig larger again
As stronger covalent overlap leads to stronger bonds in metallic elements
How does atomisation energy change across the TM series?
In all series:
Increase to middle as bonding orbitals filled
Exchange stabilisation of free atom causes dip (Mn, Mo, Re), less in lower series are more diffuse orbitals
What are the IE of the 2nd and 3rd row of TM?
Larger than 1st group as larger Zeff
Slower rise in successive IE
Increased bonding overlap increases stability of higher oxn states
Why are 2nd and 3rd row low oxidation states less stable?
Less stable at low oxidation states
High IE and high atomisation energies
Tend to disproportionate or form M-M bonds
What are the common configurations of solid state compounds of 2nd/3rd row?
More extended 4/5d orbitals with better overlap, lower e- repulsion, and larger Δ values
All are low spin - small pairing energy and high Δ
Higher coordination numbers more common
M-M bonding more common
Why are high coordination numbers comon with 4/5d metals?
Larger size so less ligand repulsion, stronger bonds
High charges more common as high oxn states more stable (less steep increase in atomisation E)
Why can 4/5d metals have M-M bonding?
4/5d orbtials more extended so better overlap
M-M clusters common in low oxn state 4/5d metal compounds
What orbitals are involved in metal-metal bonding?
dz2 / pz hybrids - σ overlap
dxz and dyz - π overlap
dxy - δ overlap
dx2-y2 - involed in metal ligand σ bonding
Why are compounds with metal-metal bonds often coloured?
Low difference in energy between the δ and δ* orbitals, and the transition causes colour
What elements often participate in metal-metal bonding?
Tend to be d4 or d5
Group 6 (starting Cr): Mo, W
Group 7 (starting Mn): Re
Group 8 (starting Fe): Os
What is often found with metal-metal bonding compounds?
Halide or carbonyl bridges
Why is [Cr2Cl9]3- paramagnetic and [W2Cl9]3- diamagnetic?
Both are face-sharing MIIICl6 octahedra
Cr linked by briding chlorides, d3 of CrIII gives rise to unpaired t2g3
W has triple metal-metal bonds between W centres - all are paired
