Topics. Molecular Structure and Bonding. Lewis Structures Valence Bond Theory MO Theory

Transcription

1 Topics Introduction Molecular Structure and onding Molecular Symmetry Molecular Orbital Theory Coordination Complexes Electronic Spectra of Complexes Reactions of Metal Complexes Organometallic Chemistry Molecular Structure and onding Lewis Structures Valence ond Theory MO Theory 1

2 Lewis Structures first step bonding model Simple rules, no calculations but easy to use 1. Two electrons pair to form each bond. Eight electrons are present to form a filled valence shell (the octet rule). Process 1. dd up all of the available valence electrons. 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: ddendum 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

3 Valence ond Theory expresses Lewis concepts in quantum mechanical ways V for H : for two hydrogen atoms: = ( 1) () bringing them together improves the energetics and we have a first approximation: = + ( 1) () () (1) V: Improving H including other possible arrangements paints an increasingly realistic picture it is possible that the two electrons could be found at or near one nucleus: = + ( 1) () + () (1) + λ( (1) () (1) () ) covalent ionic 3

4 V Theory Describing H Improving our V model of H using various assumptions brings us closer to the experimental results V Theory Model Experimental Initial Mixing Shielding Ionic Contrib. ond Energy (kj mol -1 ) ond Length (pm) V: Hybridization integral to forming bonds in V 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

5 V: sp 3 Hybridization most well known example constructed from one s and three p orbitals: sp3a sp3b sp3c sp3d 1 1 = s = s 1 1 = s = s px px px px py py py py 1 + pz 1 + pz 1 pz 1 pz Other Popular Hybridizations Hybrid Geometry ond ngles sp Linear 180 sp Trigonal 10 sp 3 Tetrahedral dsp 3 TP or Square pyramidal 90, 10 d sp 3 Octahedral 90 5

6 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 tomic Orbitals (LCO) LCO Same idea as hybridization: get the same number of MO s out as atomic orbitals you put in. = + bonding b a = antibonding onding: interference increasing the electron density between nuclei ntibonding: interference decreasing the electron density between nuclei 6

7 MO Theory for H + Given the H + system (I.e. two hydrogen nuclei, one electron) Formation of the MO s of the system gives us two orbitals: = + b a = dd in one electron: you get an electron configuration of : b (1) This is the same as saying: (1)+ (1) MO Theory for H Now take two hydrogen nuclei but add two electrons instead of just one = + b a So when we put the electrons into the system, the wavefunction for the entire system becomes: = = (1) () = [ (1) + (1)][ () + ()] = (1) () + (1) () + (1) () + () (1) b b 7

8 Electron Distribution: the Overlap Integral the electron distribution is given by So for b and a : b a = + + = + 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 V and handwaving arguments that strength of bonding derives from degree of overlap 8

9 Energetics and Overlap molecular orbital energy level diagram (MOELD) = a _ + Energy 1s 1s = + b + Populating the MOELD: H MO Energy Level Diagrams are not very interesting... without electrons in them let s use our MOELD for H : a Each H brings one electron Each orbital 1s 1s can hold two electrons Electrons will populate the b lowest available energy level Energy 9

10 ond Order ond _ Order = ( n where n is the number of electrons in bonding orbitals n * is the number of electrons in antibonding orbitals 1 * n ) So for H ond order = ½ ( 0 ) = 1 Populating the MOELD: He Let s try He with our MOELD Energy 1s a 1s Each He brings two electrons Each orbital can hold two electrons b ond Order is 0 10

11 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: dditional 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

12 σ Molecular Orbital Construction s+s and s-s p z +p z and p z -p z π Molecular Orbital Construction 1

13 MO s for Homonuclear Diatomics preceding pictures of MO s formed from atomic orbitals can be summarized as: Sigma Orbitals Pi Orbitals σ 1s = 1s + 1s π py = p y + p y } σ * 1s = 1s -1s π px = p x + p x σ s = s + s π * py = p y -p y σ * s = s -s π* px = p x -p x σ p = p + p } σ * p = p z -p z 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

14 Electronic Configuration in MO s H 1σ g Li 1σ g 1σ u * σ g F 1σ g 1σ u * σ g σ u * 3σ g 1π u 4 1π g *4 or KK σ g σ * u 3σ g 1π 4 u 1π *4 g Mixing: 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: s, p orbitals are very similar in energy σ orbitals formed from combinations of s and p orbitals undergo mixing 14

15 Mixed MOELD No Mixing Mixing 1σ g σ g Properties of C Paramagnetic Diamagnetic 15

16 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: Heteronuclear Species the molecular orbitals of CO 16

17 Nonbonding Orbitals Effectively, orbitals present in a molecule from one of the substituents that do no overlap with orbitals of other substituents s 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

18 Generalizations on Polyatomics = c φ i Linear combination of all the atomic orbitals of the same symmetry Some c i will be very small depending on energy levels Forming MO s ntibonding character and Orbital energy increase with number of orbital nodes. Minimal interactions exist between non-nearest neighbour atoms tomic Orbitals with lower energy produce lower energy Molecular Orbitals, i.e E(s+s ) < E(p+p) i i 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 non-degenerate non-degenerate E double degenerate T triply degenerate These typically replace the σ and π labels used for linear systems 18

19 Comparison of V and MO Theory V 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