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Topics • • • • • • • • Introduction Molecular Structure and Bonding Molecular Symmetry Molecular Orbital Theory Coordination Complexes Electronic Spectra of Complexes Reactions of Metal Complexes Organometallic Chemistry Molecular Structure and Bonding • Lewis Structures • Valence Bond Theory • MO Theory 1 Lewis Structures • “first step” bonding model • Simple rules, no calculations but easy to use – 1. Two electrons pair to form each bond – 2. Eight electrons are present to form a filled valence shell (the octet rule). • Process – 1. Add up all of the available valence electrons – 2. Use two to form each bond between atoms – 3. Distribute the electrons in pairs so that each atom has an octet of valence electrons from a combination of lone pairs and bonds. Lewis Structures: Addendum • Resonance – it might require the construction of resonance structures to adequately describe the electron distribution • Formal charge – required to determine which possible structures are the lowest energy – The lowest formal charge resonance structure is the most energetically favorable. • Hypervalence 2 Valence Bond Theory • expresses Lewis concepts in quantum mechanical ways • VB for H2: • for two hydrogen atoms: ψ = ψ A(1)ψ B ( 2) • bringing them together improves the energetics and we have a first approximation: ψ = ψ A(1)ψ B ( 2) + ψ A( 2)ψ B (1) VB: Improving H2 • including other possible arrangements paints an increasingly realistic picture • it is possible that the two electrons could be found at or near one nucleus: ψ = ψ A(1)ψ B ( 2 ) + ψ A( 2)ψ B (1) + λ (ψ A(1)ψ A( 2 ) + ψ B (1)ψ B ( 2) ) covalent ionic 3 VB Theory Describing H2 • Improving our VB model of H2 using various assumptions brings us closer to the experimental results Bond Length (pm) Experimental Bond Energy (kJ mol-1) 458 Initial 24 90 Mixing 303 86.9 Shielding 365 74.3 Ionic Contrib. 388 74.9 VB Theory Model 74.1 VB: Hybridization • integral to forming bonds in VB theory • formally based on the concept of promotion, mixing of similar wavefunctions to form degenerate wavefunctions • process involves mixing pure atomic orbitals to form new “hybrid” orbitals • Stated another way, we use linear combinations of atomic orbital wavefunctions to meet the demands of geometry and valence. • requires that you get out as many orbitals as you put in 4 VB: sp3 Hybridization • most well known example constructed from one s and three p orbitals: 1 1 1 1 ψ sp 3a = ψ s + ψ px + ψ py + ψ pz 2 2 2 2 1 1 1 1 ψ sp 3b = ψ s − ψ px − ψ py + ψ pz 2 2 2 2 1 1 1 1 ψ sp 3c = ψ s + ψ px − ψ py − ψ pz 2 2 2 2 1 1 1 1 ψ sp 3d = ψ s − ψ px + ψ py − ψ pz 2 2 2 2 Other Popular Hybridizations Hybrid Geometry Bond Angles sp Linear 180 sp2 Trigonal 120 sp3 Tetrahedral 109.5 dsp3 TBP or Square pyramidal 90, 120 d2sp3 Octahedral 90 5 Molecular Orbital Theory • similar tools, fundamentally different approach – two nuclei are positioned at an equilibrium distance and electrons are added to the system – rather than assuming that two atoms come together • we are still unable to solve the Schrodinger equation, so we use an approximation to provide the correct MOs: – Linear Combination of Atomic Orbitals (LCAO) LCAO • Same idea as hybridization: get the same number of MO’s out as atomic orbitals you put in. ψ b = ψ A +ψ B ψ a = ψ A −ψ B bonding antibonding • Bonding: interference increasing the electron density between nuclei • Antibonding: interference decreasing the electron density between nuclei 6 MO Theory for H2+ • Given the H2+ system (I.e. two hydrogen nuclei, one electron) • Formation of the MO’s of the system gives us two orbitals: ψ b = ψ A +ψ B ψ a = ψ A −ψ B • Add in one electron: you get an electron configuration of : ψb(1) • This is the same as saying: ψA(1)+ ψB(1) MO Theory for H2 • Now take two hydrogen nuclei but add two electrons instead of just one ψ b = ψ A +ψ B ψ a = ψ A −ψ B • So when we put the electrons into the system, the wavefunction for the entire system becomes: ψ = ψ b (1)ψ b (2) = [ψ A (1) + ψ B (1)][ψ A (2) + ψ B (2)] ψ = ψ A (1)ψ A (2) + ψ B (1)ψ B (2) + ψ A (1)ψ B (2) + ψ A (2)ψ B (1) 7 Electron Distribution: the Overlap Integral • the electron distribution is given by ψ2 • So for ψb and ψa : ψ b2 = ψ A2 + 2ψ Aψ B + ψ B2 ψ a2 = ψ A2 − 2ψ Aψ B + ψ B2 • When integrated over space the cross term becomes the overlap integral (S) and is very important for bonding theory • Effectively measures the extent to which the wavefunctions alter the electron density between the nuclei Symmetry and Overlap • So in general: – S>0 gives bonding – S<0 gives antibonding – S=0 gives nonbonding orbitals • Consistent with previous VB and “handwaving” arguments that strength of bonding derives from degree of overlap 8 Energetics and Overlap • molecular orbital energy level diagram (MOELD) _ ψ a = ψ A −ψ B Energy 1sA + 1sB ψ b = ψ A +ψ B + ψA ψB Populating the MOELD: H2 • MO Energy Level Diagrams are not very interesting ..... without electrons in them • let’s use our MOELD for H2: ψa Energy 1sA 1sB ↑↓ ψb ψA ψB • Each H brings one electron • Each orbital can hold two electrons • Electrons will populate the lowest available energy level 9 Bond Order Bond _ Order = 1 ( n − n* ) 2 • where – n is the number of electrons in bonding orbitals – n* is the number of electrons in antibonding orbitals • So for H2 Bond order = ½ ( 2 – 0 ) = 1 Populating the MOELD: He2 • Let’s try He2 with our MOELD ↑↓ ψa Energy 1sA 1sB ↑↓ • Bond Order is 0 ψb ψA • Each He brings two electrons • Each orbital can hold two electrons ψB 10 Symmetry Labels: Names of MO’s • σ, π, δ are symmetry labels, used to identify the MO’s that we construct • similar to s, p, d etc. • σ - sigma symmetry indicates that the MO is symmetrical with respect to rotation around the internuclear axis, i.e. has no nodal planes. • π - pi symmetry indicates that the MO has a nodal plane at the internuclear axis. • δ - delta indicates that there are two internuclear nodal planes. Symmetry Labels: Additional Information • *, g, u are used to provide as super and sub scripts to provide further information • * indicates the presence of a nodal plane perpendicular to the internuclear axis – designates the orbital as antibonding • g (gerade, german for even) indicates the parity of a MO, i.e. does it change sign when it is inverted through its center? g = no • u (ungerade, german for odd) indicates that the MO does change sign upon inversion 11 σ Molecular Orbital Construction • s+s and s-s • pz+pz and pz-pz π Molecular Orbital Construction 12 MO’s for Homonuclear Diatomics • preceding pictures of MO’s formed from atomic orbitals can be summarized as: Sigma Orbitals Pi Orbitals σ1s = 1sA + 1sB π2py = 2pyA + 2pyB σ*1s = 1sA - 1sB π2px = 2pxA + 2pxB σ2s = 2sA + 2sB π*2py = 2pyA - 2pyB σ*2s = 2sA - 2sB π*2px = 2pxA - 2pxB } } σ2p = 2pA + 2pB σ*2p = 2pzA - 2pzB MO Energy Level Diagrams II • π orbitals are formed – degenerate set • Hund’s rule: “electrons occupy orbitals to maximize the spin multiplicity where possible” • σ 1s combination typically isolated from other orbitals – inner shell/core electrons similar to atomic orbitals 13 Electronic Configuration in MO’s H2 1σg2 Li2 1σg2 1σu*2 2σg2 F2 1σg2 1σu*2 2σg2 2σu*2 3σg2 1πu4 1πg*4 or KK 2σg2 2σu*2 3σg2 1πu4 1πg*4 Mixing: A Complication • assumption: only atomic orbitals of identical energy contribute to molecular orbitals • actually: any orbital with the same symmetry may contribute to the composition of an MO, energy differences only reduce the degree of contribution. • case in point: – 2s, 2p orbitals are very similar in energy – σ orbitals formed from combinations of 2s and 2p orbitals undergo mixing 14 Mixed MOELD No Mixing Mixing 1σg 2σg Properties of C2 ↑ ↑ ↑↓ ↑↓ ↑ ↓↑ ↓ ↑↓ ↑↓ ↑↓ Paramagnetic Diamagnetic 15 Heteronuclear Species • energy level comparisons are relatively simple for homonuclear species • MO’s built for heteronuclear species depend on the relative energy levels of the contributing atomic orbitals CO: A Heteronuclear Species • the molecular orbitals of CO 16 Nonbonding Orbitals • Effectively, orbitals present in a molecule from one of the substituents that do no overlap with orbitals of other substituents • As they do not combine with other components they are not raised or lowered in energy • They are not used in the bonding but still are present in the molecule – Present in the electron energy levels – Can be very important source or sink of electron density, particularly in transition metal complexes Polyatomics • Typically a ligand field is constructed corresponding to group orbitals around a central atom • These are derived from symmetry operations which arise from the overall shape and symmetry of the molecule or complex 17 Generalizations on Polyatomics ψ = ∑ ciφi i • Linear combination of all the atomic orbitals of the same symmetry – Some ci will be very small depending on energy levels • Forming MO’s – Antibonding character and Orbital energy increase with number of orbital nodes. – Minimal interactions exist between non-nearest neighbour atoms – Atomic Orbitals with lower energy produce lower energy Molecular Orbitals, i.e E(s+s ) < E(p+p) More Symmetry Labels • With mixing and non-linear molecules, labels become very difficult to assign • Symmetry is used to assign the labels to particular orbitals – – – – A non-degenerate B non-degenerate E double degenerate T triply degenerate • These typically replace the σ and π labels used for linear systems 18 Comparison of VB and MO Theory • VB – rapid, graphical way of determining possible bonding – predicts structure and overall geometry well • MO – lots of energy information – great for spectroscopy and predicting electronic behaviour – requires symmetry resources to determine structure and bonding 19