Inorganic Chemistry. Cheesman
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1 Inorganic Chemistry Cheesman
2 Contents Mononuclear Electronic Mononuclear Magnetic Crystal Field Theory Dinuclear Polynuclar Extended Structures Mononuclear Electronic
3 Mononuclear Complexes Electronic Free Transition Metal Ion (no ligands, spherical symmetry) s, p, d, f wave functions result from Schrödinger's equation for Hydrogen atom He onwards is complicated due to electron-electron repulsion Use hydrogen orbitals as a basis set The electronic configuration (d 3 ) How many electrons are in the d-shell that can be arranged in multiple ways in the d-orbitals Orbital Angular Momentum Angular momentum properties for single orbital wave functions s p d f l m l 0 +1, 0, -1 +2, +1, 0, -1, -2 Etc Mononuclear Electronic
4 Total orbital angular momentum (L) Total spin angular momentum (S) Derived from arrangement of the spins of the individual electrons Due to the valence electrons Filled subshells don t contribute as they have total angular momenta of L=0 and S=0 Term Symbols Energy levels are labelled using term symbols showing values of L and S Needed to explain spectroscopic and magnetic properties (2S+1) L Example L = 3 and S = 3/2 4 F Mononuclear Electronic
5 Identifying the Term Symbols Single Electron Takes Spin and Orbital Angular Momentum of single electron s 1 2 S, d 1 2 D Multiple Electrons Identify all possible arrangements, microstates, of electrons using pauli exclusion principle Adding the m l and m s of each state to give total M L and M s Groups of degenerate microstates represent the components of that term Identify the highest value of M L This must have M S = 0 and will group with other M L values M s = 0 to give term 1 L (grey) The next highest M L will have more than one microstate with different spins. These will give 3 (L-1) states etc.. Mononuclear Electronic
6 Identifying the Ground Term Hund s Rule The most stable term is predicted by S has the highest value allowed by Pauli, Then, L has the highest possible value Quick Method Draw 5 d orbitals, labelled with m l values and feed in electrons +2 onwards Add up m l values to give (+)2 = L=2 = D Add up spins of 4 electrons: 4 x (+)1/2 = S=2 = 2S+1 = 5 Ground term is 5 D Mononuclear Electronic
7 What are the ground terms for V 3+ Cr 3+ Cr 2+ Ni 2+ 3 F 4 F 5 D 3 F
8 How many states are within each of these terms 1 G 3 F 1 D 3 P 1 S Work out degeneracy of L (2L+1) Work out degeneracy of S (2S + 1) Multiply together to get total number of states
9 Contents Mononuclear Electronic Mononuclear Magnetic Crystal Field Theory Dinuclear Polynuclear Extended Structures Mononuclear Magnetic
10 Magnetic Properties Electron Spin Angular Momentum s s = s(s + 1)h Magnetic Moment Combination of s and the charge (-e) gives the electron a magnetic moment μ = g eμ B s h The Zeeman Interaction Magnetic moment of electron has different energies when aligned with or against a magnetic field E = g e μ B B Magnitude of Zeeman Splitting For 1 Tesla magnetic field E = 1.8 x J = 1 cm 1 (microwave) Mononuclear Magnetic
11 Magnetic Properties Electron Temperature Dependence Sample containing molecules with one unpaired electron in magnetic field Thermal equilibrium between +1/2 and -1/2 states Magnetic moment is cancelled out Only slight excess in ground state leads to magnetisation M Net bulk magnetisation is derived from measurements of magnetic susceptibility X Use a faraday balance Mononuclear Magnetic
12 Magnetic Properties Electron Curie Temperature M or X are linearly proportional to temperature at high temperature Curie region at low 1/T Many PARAMAGNETS obey the Curie Law χ = C T Often get better fit using Curie-Weiss χ = C θ is the Weiss constant T+θ Mononuclear Magnetic
13 Measuring Magnetic Properties Measuring Magnetic Properties Boltzmann population differences increase in higher magnetic fields This leads to a lower total energy A paramagnet is pulled into regions of higher magnetic field intensity Traditional Methods Faraday balance Gouy balance Modern Method SuperConducting Quantum Interface Device (SQUID) Mononuclear Magnetic
14 Extracting μ from χ A raw measurement of paramagnetism via χ will display a strong temperature dependence We are interested in μ the magnetic moment of the individual paramagnetic transition ion This will tell us how many unpaired electrons are present μ is obtained from χ by removing the effect of temperature At high temperatures the magnetic susceptibility χ is proportional to 1/T in the curie region Magnetic moment can be obtained from the equation μ 2 = 3k μ 0 Nμ B 2 χt = x 10 5 (χt) The magnetic moment is usually called the effective magnetic moment μ eff Mononuclear Magnetic
15 Magnetic Moment μ arises from both S & L Magnetism does not just contain spin of single electron (S=1/2) but also L. L results from the freedom of electron to move between orbitals and rotate around the nucleus For free ions, the quantum numbers L and S are known from the term symbol Van Vleck s equation: Mononuclear Magnetic
16 Symmetry-Quenched Magnetic Moments Sometimes the magnetic moments observed are lower than those of the free ion This is because we assume that L = 0 and the Van Vleck s formula reduces to the spin only formula Example K 3 Mn(CN) 6 μ = 4.81 μ B μ = 2 (S(S + 1) Mononuclear Magnetic
17 Example K 3 FeF 6 μ=5.90 μ B Example K 3 MnOx 3 Spin-only Mononuclear Magnetic
18 Contents Mononuclear Electronic Mononuclear Magnetic Crystal Field Theory Dinuclear Polynuclear Extended Structures Crystal Field Theory
19 Crystal Field Theory Each ligand is a point electronic charge bound to the metal cation Effect on energy with relative d orbital ML 6 1. Surround metal with spherical shell of negative charge (barycentre) 2. Localise charge to six point charges 3. The d z2 and d x2-y2 will raise in energy as they are repelled more along the axis 4. The d xy, d yz, d zx orbitals drop in energy as they are inbetween the axis Crystal Field Theory
20 LFSE For octahedral LFSE = [(0.4 x t 2g electrons) (0.6 x e g electrons) ] o + P P = extra pairing energy compared to if it was not in a ligand field (5 degenerate orbitals) For tetrahedral tet = 4 o 9 LFSE = [(0.6 x t 2g electrons) (0.4 x e g electrons) ] tet + P Crystal Field Theory
21 High Spin Weak Field Small Low Spin Strong Field Large Spectrochemical Series o σ/π donor High Spin Halogens Sulphur I - < Br - < S 2- < SCN - < Cl - < NO 3 - < F - σ donor High Spin Oxygen < HO - < C 2 O 4 2- < H 2 O - σ donor π acceptor Low Spin Nitrogen Carbonyls Carbonyls Amines Phosphines < NCS < CH 3 CN < NH 3 < en < bipy < phen < NO 2 - < PPh 3 < CN - < CO Increases with oxidation state Higher charge smaller ion shorter M-L Increases going down a group Expanded 4d and 5d = better M-L bonding Crystal Field Theory
22 Molecular Orbital Theory Molecular Orbital Theory Orbital Overlap A bond can only be formed when two atomic orbitals of two atoms overlap Orbitals must be of similar energy To simplify the theory in our context, the 4s and 4p orbitals on the metal atom are ignored. Recall the different types of donor/acceptor behaviour
23 Sigma Donor Ligands point along axis Example, Cl -
24 Sigma Donor For the Cl - ion: Electrons are in a p-orbital Can be donated to form a sigma bond by overlapping with e g orbitals Metal based e g raised in energy No net overlap with t 2g Hence energy of t 2g unchanged
25 Sigma Donor Molecular Orbital Diagram
26 Effect of Sigma Donation What happens as strength of sigma donation increases? Energy of interaction increases Splitting between the bonding and anti-bonding orbitals gets larger e g moves higher in energy Ligand field splitting (Δo) increases
27 Pi donor Certain p-orbitals can interact with t 2g to give pi bonds Overlap is possible Example Cl - No net overlap with e g sets
28 Pi donor Molecular Orbital Diagram
29 Effect of Pi Donation What happens when Pi Donor interactions increases? Energy of inter-actions increases Splitting between bonding and anti-bonding orbitals increases t 2g moves higher in energy Ligand field splitting (Δo) decreases
30 Complete Molecular Orbital Diagram Combination of sigma and pi donor interactions
31 Pi acceptor Metal orbitals involved are the same as pi donor Symmetry of atomic orbital overlap determines sigma or pi interaction Only interacts with t 2g
32 Pi acceptor Requirements Ligand must have an empty or partially filled orbital of pi symmetry Accepting electron density Typically anti-bonding orbitals Results in Back Donation Examples, CO and CN -
33 Pi acceptor Molecular Orbital Diagram Pi acceptors increases Δo
34 Electronic Spectra Place terms on a diagram to work out transitions As octahedral ligand field is imposed, terms split and move further apart as ligand strength increases Distances between lines is proportional to energy not intensity Orgel Diagram Lowest line is ground state Same spin multiplicity as ground state are allowed Tanabe-Sugano Diagram Related to a Racah parameter Ground state runs along the x-axis Crystal Field Theory
35 Selection Rules More allowed transitions have greater intensities not energies! L = ±1 S = 0 For d-d transitions all should be weak due to L rule but d orbitals not purely d for non hydrogen atom due to mixing of orbitals with p. Laporte rule (g g and u u forbidden) But u g Allowed Therefore t 2g e g Forbidden (octahedral) t 2 e allowed (tetrahedral) Numbers Transition Type Typical epsilon (M -1 cm -1 ) Pi Pi* 10, ,000 CT 10, ,000 Spin allowed, Laporte Allowed 500 Spin allowed, Laporte Forbidden 10 Spin Forbidden, Laporte Forbidden 0.1 Crystal Field Theory
36 Contents Mononuclear Electronic Mononuclear Magnetic Crystal Field Theory Dinuclear Dinuclear Polynuclear Extended Structures
37 Cages and Clusters Cages ( M L M) Super exchange via ligands and magnetism Copper acetate nonohydrate Cluster (M M ) Multiple bonds and δ molecular orbitals Chromium acetate nonohydrate Cages Copper acetate nonohydrate Cu-Cu 2.64 A (longer than 2.56 A in metallic copper) Dinuclear
38 Cages Copper acetate nonohydrate Unpaired electron in singly degenerate orbital Magnetic susceptibility X drops at low temperatures Becomes diamagnetic < 77 K Room temperature EPR signal Dinuclear EPR disappears < 77 K
39 Coupling of spins Coupling of spins S 1 + S 2 to give maximum spin S 1 S 2 to give minimum spin Every other spin state = subtracting 1 from maximum until you reach minimum J is positive for ferromagnetic coupling J is negative for antiferromagnetic coupling Copper acetate Dinuclear For copper acetate S 1 = ½ S 2 = ½ S = 1 or 0 Drop temperature, bottom level is filled more than top Hence Cu acetate is antiferromagnetic due to RT EPR spectrum
40 Cages Magnetic Exchange Nature of M M interaction is through the ligand Ligand mediated coupling is super exchange Spin polarisation across the three atoms favours pairing of spins, leads to antiferromagnetic coupling (with exceptions) Ferromagnetic coupling requires orthogonality in coupling pathway. High symmetry required and is rare Dinuclear
41 Clusters Chromium acetate nonohydrate Evidence for M M Cr Cr = 2.36 A (shorter than that found in metal 2.58 A) Evidence for M - M Eclipsed structures and possible formation of quadruple bonds Short bond lengths (bond length increases with higher bond order) Short bond lengths have higher vibrational frequencies Dinuclear
42 Overlap of d orbitals in M 2 fragment Dinuclear
43 Overlap of d orbitals in M 2 fragment d/d* orbitals can only exist when the molecule has elipsed alignment. The formation of the d/d* orbitals rests the complex better than it being staggered due to steric strain Dinuclear Staggered Eclipsed Staggered 3.5 also Eclipsed
44 Evidence of d-bond Dinuclear
45 Valence Delocalised When you reduce this Cu A species by one electron, the electron. It is shared Cu II Cu II Cu 1.5 Cu 1.5 The MO is delocalised across both copper ions. Transitions can occur from this MO to higher antibonding Mos and this transition can be intense (Cu A is blue/purple) Valence Trapped Prussian Blue KFe III [Fe II (CN) 6 ] Inter Valence Charge Transfer Band Distinct ligand environments lock oxidation states in place Reduction of Fe III to Fe II is colourless pi system of cyanide cruicial for charge transfer process Similar IVCT bands from low level iron in brown glass and brown sandstone Dinuclear
46 Valence Trapped (More Examples) Corrundum (Crystalline Al 2 O 3 ) Little titanium = colourless Little iron = very pale yellow Both Ti and Fe = Intense blue sapphire IVCT band of Fe 2+ Ti 4+ transition Oxidation states briefly altered while the molecule is in the excited state Intermediate Behaviour Creutz-Taube ion Any degree of valence trapping e.g. Ru 2.4+ Ru 2.6+ leads to slightly different bond lengths Franck-Condon: electron jump instantanoues Then ligand environment relaxes Transition is IVCT like but bond lengths are optimised shortly after oxidation Dinuclear
47 Strength of Electronic Interactions Dinuclear
48 Contents Mononuclear Electronic Mononuclear Magnetic Crystal Field Theory Dinuclear Polynuclear Polynuclear Extended Structures
49 Trinuclear Same properties as dimers Cages M L - M Copper acetate behaviour [Cr 3 O(O 2 CC 6 H 5 ) 6 (py) 3 ]ClO 4 Even though each interaction is antiferromagnetic due to superexchange, the moments on each three centres can not be cancelled Spin states couple in the same way Couple S 1 with S 2 Couple each state with S 3 SPIN FRUSTRATION Clusters M M Chromium acetate behaviour Cs 3 [Re 3 Cl 12 ] Has Re-Re double bonds Lower Halides Early block transition metals in low oxidation states No M-M bonds ever seen for > (VI) due to d-orbital contraction High order M-M bonds encountered Steric effects compete with electronic <18 electron complexes often seen Polynuclear
50 18 electron counting 3- Re (group 7) Re 7 3 x terminal Cl - share of 2 x bridging Cl - 2 x double bonds net charge Total Polynuclear
51 18 electron counting on dimers [Re 2 Cl 8 ] 2- [Mo 2 Cl 8 ] 4- [W 2 Cl 9 ] 3- Re 7 Mo (group 6) 6 W (group 6) 6 4 x terminal Cl x terminal Cl x terminal Cl - 3 quadruple bond net charge Total quadruple bond net charge Total x bridging Cl triple bond Charge Total 4 ½ 3 1 ½ 18 Polynuclear 18 electron rule not as uniformly obeyed for d block as you go down group d d bonds are general feature of early d-block elements in low oxidation states These tend to follow 18 electron rule, especially carbonyls
52 Carbonyl Clusters Polynuclear
53 Carbon Monoxide Polynuclear Neutral ligand with small dipole Weak 2 electron sigma donor An extremely good pi acceptor
54 Nitric Oxide NO Normally NO written as NO + as a 3 electron donor Anti bonding pi electron transferred to metal giving a NO + (nitrosonium ion) ligand This is a two electron sigma donor analogous to CO It is approximately linear ( O ) The odd electron is removed from anti bonding orbital, the stretching frequency is usually similar or greater than NO itself Due to charge NO + is much better pi acceptor ligand showing better levels of back bonding Pi acceptor ligand strengths CN - < NN < CO < NO + (isoelectronic) Some complexes better describe it as NO or even NO (nitroxyl) This is bent ( O ) Do not need linear for pi overlap No analogous behaviour to CO Polynuclear
55 Nitric Oxide NO Polynuclear
56 Large Clusters Wades Rules As cluster size increase, 18 electron rule fails Polynuclear
57 Large Clusters Wades Rules As cluster size increase, 18 electron rule fails Rh 6 (CO) 16 Os 6 (CO) 18 6 x Rh 16 x CO TOTAL ELECTRONS Use 6 orbitals per metal for M-CO bonds Electrons left for bonding framework x Os 16 x CO TOTAL ELECTRONS Use 6 orbitals per metal for M-CO bonds Electrons left for bonding framework Polynuclear Electron Pairs (n+1) with n = 6 Octahedron But octahedral edges aren t bonds Did not actually have 3 CO per metal Electron Pairs Capped Trigonal Bipyramid These rules compare it to the points of an octahedron (n+1) with n = 5
58 Contents Mononuclear Electronic Mononuclear Magnetic Crystal Field Theory Dinuclear Polynuclear Extended Structures Extended Structures
59 Paramagnets Drop in temperature increases magnetisation due to population of states etc etc etc Curie temperature and that shit (go back to slide 12) NO INTERACTION ON SPIN BETWEEN DIFFERENT MOLECULES Ferromagnets Interaction tending to align the spins As T drops, X increases more rapidly than expected due to the spin-spin interaction The curie temperature thermal randomisation is overcome and all the spins align, sample has net magnetisation Antiferromagnets Interaction tending to align neighbouring spins antiparralel As T drops, X decreases more rapidly than expected. Neel temperature thermal randomisation overcome by coupling and the spins lock down onto the two interpenetrating sublattices with antiparralel allignments Usually result of superexchange Extended Structures
60 Ferrimagnets Fe 3 O 4 Magnetite Subclass of antiferromagnets Moments do not cancel due to differences in spin Large moment can persist below critical temperature (Curie temperature) Original ferrimagnet, can be permanently magnetised Magnetised by earths magnetic field Inverse spinel structure Adopted by AB 2 O 4 materials based on face-centred cubic structure of oxide ions Extended Structures
61 Domains Ferromagnetic materials, block material, large magnetic moment Magnetostatic Energy Flux lines have a magnetostatic energy. This can be reduced if the material is divided into domains Alligning ferromagnetically exchangecoupled spins in an antiparralel fashion is not the most stable arrangement. But the dominant term is the magnetostatic energy and creates the formation of domains. Domain Boundaries Domain boundaries vary in size normally a few hundred atoms. The manner in which spin orientation changes also varies Magnetocrystalline Energy Dipoles in domains will tend to align one of the easy directions wrt the lattice Extended Structures
62 Hysteresis Applying a magnetic field in a closed domain structure, returning the field to non zero, and then increasing the field in the opposite direction. Extended Structures
63 Magnetic Field Scan Paramagnet Forward and reverse scan on paramagnetic molecules, trace is reversible. The remnant magnetisation is zero Hysteresis Loop Ferromagnets Below the curie temperature, the magnetic field scan of a ferrimagnet results in a lag of magnetisation (hysteresis) First ramp is paramagnetic behaviour Saturation Magnetisation : Maximum magnetisation Remanence Magnetisation : Amount of magnetisation left when B = 0 Coercive field : value of B in opposite direction to demagnetise the sample Extended Structures
64 Single Molecular Magnets & Single Chain Magnets For a paramagnet the spins are independent of one another and no molecule is locked into one of the + ½ or - ½ states (dynamic equilibrium) For ferromagnets and ferrimagnets below their critical temperature, the domains can be locked into one orientation, and thermal energy is insufficient to randomise them. The critical property is inertia, an energy barrier, the reorientation of a large magnetisation at a particular temperature. Ferromagnetic Strategy Ferromagnetic coupling can only occur if coupling is absolutely orthogonal The oxalate ion can do this complex as ligand strategy to create polynuclear structures This results in a large ground state spin which can interact within the extended solid Extended Structures
65 Single Chain Magnet Example of Ferrimagnetic strategy to produce large spins Accepting the inevitability of antiferromagnetic ligand mediated coupling but using alternating spins of very different magnitudes so as to maximise uncancelled net spin Results in a large ladder of spin states Interactions between chains add another level of complexity, can be altered by adding substituents to the bridging ligands Extended Structures
66 Single Molecule Magnet Mn 12 can be the smallest molecular magnet Single chain magnets units with large spins, tetranuclear molecules and extended chains. Exhibit molecular magnet behaviour, such as hysteresis, but often have very low critical temperature. Challenge is to raise this temperature This compound has the specific structure to show non-paramagnetic behaviour A molecule containing lots of Fe ions wont show hysteresis MCD 4.2 K 1.7 K Extended Structures
67 Electrical Conductivity Conductivity σ = n e μ (number of current carrying species x electron charge x mobility Ionic conduction can occur with ions, but we are only concerned with electrons and holes Band Theory Imagine an alkali metal (group 1 conductors) In an extended array of solid each s AO contributes to a MO. The number of AO you overlap must be the number of MO you get out. Hence a band rather than discrete energy levels Same applies to p and d orbitals Extra MO only fills the current set, it does not raise and lower the maximum and minimum levels For alkali metal, there are N electrons and N orbitals Each orbital takes 2 electrons Therefore only lowest N/2 orbitals are filled. Highest filled orbital is the Fermi Level Extended Structures
68 Band Theory Extended Structures
69 Band Theory Extended Structures
70 Band Theory Extended Structures
71 One-dimensional solid Extended Structures
72 First row transition metals with rock salt structure Shows conductivity Does not show conductivity Extended Structures
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