Principles of Organic Chemistry lecture 5, page 1

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1 Principles f Organic Chemistry lecture 5, page 1 Bnding Mdels Fact: electrns hld mlecules tgether. Theries: mre than ne way t cnceptualize bnding. Let s fllw Carrll in the cnsideratin f tw theries f bnding. Befre we try t wrap ur minds arund the mlecular rbitals f methane let s play with sme ther mlecular rbitals. The authr spends sme time discussing the difference between MO thery and Valence Bnd thery. In ne case MO thery we are taking abut electrn energies and ppulatins arund mlecules. Put the nuclei and thrw the electrns at them. In the ther case VB thery, we are talking abut the energetic and ppulatin changes that ccur when atms with their cre and valence electrns arund them frm bnds with between themselves. Let s discuss electrns in terms f mlecular rbitals (MOs) and atmic rbitals (AOs). In yur chemical educatin yu have mre than likely been expsed t valence shell electrn pair repulsin (VSEPR) thery. N P Predictin f the bnd angles f ammnia and phsphine are prblematic fr VSEPR. That f ammnia is The structure is dynamic at rm temperature underging fast inversin. The bnd angle f phsphine is 93.7 (Cttn, Wilkinsn, Murill, and Bchmann in Advanced Inrganic Chemistry 6 th ed. p 388) What makes the lne pair n the phsphrus atm any bigger (mre repulsive) than thse n the nitrgen atm? It might have made just as much sense t argue that P 3 shuld flatter than N 3 because the lne pair is further away frm the nucleus and shuld thus affect the bnded atms t a lesser extent than in N 3. wever we can talk very sensibly abut the gemetry f the hydrides f N and P n the basis f hybridizatin and bnd strength. The bnds are strnger when bth species (N and P) are flat. But electrn repulsin is als greatest in the planar gemetry.* The flat structures are sp 2 hybrids. There is a p-rbital with a lne pair in it. Ammnia has a wider bnd angle and is clser in energy t its flat transitin state because its bnds are ptimized by better verlap. Overlap between principle quantum number 1 and 2 ccurs in N 3 whereas in P 3, verlap ccurs between principle quantum number 1 and 3. * Frm S.F.A. Kettle, Symmetry and Structure, Readable Grup Thery fr

2 Principles f Organic Chemistry lecture 5, page 2 Chemists p 6-7. The ptential energy barrier fr the inversin is equal t the difference in ttal energy between the ammnia mlecule in its nrmal, pyramidal, shape and the planar cnfiguratin. In rder t btain a theretical value fr this barrier, Clementi carried ut rather detailed calculatins fr each gemetry. The results were very surprising. They shwed that the N- bnding is greater in the planar mlecule there is a lss f bnding f N- bnding energy f apprximately 7.0 x 10 2 kj mle -1 (167 kcal mle -1 ) in ging frm the planar t the pyramidal gemetry; this lss is accmpanied by a slight lengthening f the N- bnd. Bnding favurs a planar ammnia mlecule. A cmparisn f the mst stable pyramidal and mst stable planar gemetries shws that the electrn-electrn and nuclear-nuclear repulsin energies favur the pyramidal mlecule ver the planar by abut 7.2 x 10 2 kj mle -1 (172 kcal mle -1 ). Repulsive frces favur a pyramidal mlecule. Nte the way that the bnding and repulsive energy changes between the tw shapes almst exactly cancel each ther. It is the slight dminance f the repulsive frces by 20 kj mle -1 (5 kcal mle -1 ) which leads t the equilibrium gemetry f the ammnia mlecule in its electrnic grund state being pyramidal. We are left with a mst disturbing situatin. There is n dubt that the strngest N- bnding in the ammnia mlecule is t be fund when it is planar yet tw f the simple mdels cnsidered earlier in this chapter explained its gemetry by the assumptin that this bnding is a maximum in the pyramidal mlecule! Similarly, the mdels based n electrn-electrn repulsin ignred bth the fact that nuclear-nuclear repulsin is f cmparable imprtance and the fact that their sum is almst exactly cancelled by changes in the bnding energy. This wuld nt matter s much if there were sme assurance that repulsive energies wuld utweigh the bnding in all mlecules (mlecular gemetries culd then reliably be explained using a repulsin-based argument). Unfrtunately, n such general assurance can be given. This can be seen if the discussin f the ammnia mlecule is extended t include sme related species. The mlecules N 3, P 3, N 2 F, P 2 F, NF 2 PF 2 NF 3, and PF 3 all have similar, pyramidal, structures and wuld be treated similarly in all simple mdels. But calculatins by Schmiedekamp and c-wrkers6 have shwn that the first fur we their pyramidal gemetry t the dminance f repulsive frces (bnding is strnger when they are planar) but the last fur are pyramidal because the bnding is greatest in this cnfiguratin and dminates the repulsive frces. The take hme message is that the sweeping generalizatins that yu learned in Chem I and Organic I d nt reflect reality that well. The universe is nt that simple. Nature challenges us when ever we examine it with intentins t explain it. With the caveat that yur last learned paradigm was flawed let s lk at MO thery as a paradigm t explain the behavir f electrns in mlecules. Let s start ff by being a bit hnest. An MO is a mathematical equatin that des its best t describe the behavir f electrns in mlecules. It is nt reality; it is a mdel f reality. If an electrn wuld behave like a particle at all velcities we culd treat cllectins f electrns, prtns and neutrns with classical Newtnian mechanics. They dn t; they behave like waves mst f the time. A few principles f MO thery, the LCAO methd.

3 Principles f Organic Chemistry lecture 5, page 3 AOs cmbine t make an MO via linear cmbinatins. The number f these rbitals is cnserved. #AOs = #MOs MOs are space arund the mlecule in which electrns have a high prbability f ccupatin. This space // is cnserved. example C C C pi MOs f Allyl anin C C O pi MOs f an enlate The diagram abve was adapted frm Ian Fleming, Frntier Orbitals and Organic Chemical Reactins J. Wiley, The all carbn structure is electrnically symmetric The O in the enlate hgs rbital space in MO1. C-C bnd rder decreases and C-O bnding increases. In the hm C-C bnd rder increases. Let s mess with hydrgen t keep things as simple as pssible. We will als ignre the cefficients (the relative sizes f the rbitals) als t keep things simple. a hydrgen s rbital. An electrn in this rbital has a certain energy and this can be represented by an rbital energy diagram. Electrns behave like waves and waves have phase. When there is nly ne rbital in the picture the phase des nt matter. Only when the rbital interacts with anther rbital can we have tw pssible cmbinatins.

4 Principles f Organic Chemistry lecture 5, page 4 The lwer cmbinatin is the bnding cmbinatin (mlecular rbital). The upper cmbinatin is the antibnding cmbinatin (mlecular rbital). The same-phase cmbinatin makes it advantageus fr electrns t ccupy it because it has less energy than the upper cmbinatin. We say that the upper rbital cntains a nde, a plane r a vlume that electrns d nt ccupy. The rbital with the nde is high-energy when ccupied by electrns. These are the nly pssible phase cmbinatins f tw rbitals. Shall we d three? + A C B D These are all pssible cmbinatins f three rbitals. Yu will ntice that B has n ndes. Thus, by analgy t what was said abve, it is lwest in energy. wever A has tw ndes. That is the phase changes tw times as we g frm ne end f the mlecule t the ther. If symmetry is beautiful rbitals C and D are ugly little things. A and B have tw axes f symmetry but C and D nly have ne. Furthermre C and D shuld be degenerate (pssessing the same energy). Let s take a clser lk at C and D. C and D are different frm A and B by anther characteristic. Where as there is n way t cnvert A t B by an peratr that changes the phase. Multiplicatin by -1 C and D can be cnverted t ne anther by multiplicatin by -1. C and D are called reducible representatins. We can get t an irreducible representatin by cmbining C and D.

5 Principles f Organic Chemistry lecture 5, page 5 C + D = The last mlecular rbital that we generated in the list is called a nn-bnding MO. A mlecular rbital energy diagram will shw yu why it is nt beneficial fr 3 t frm. anti-bnding nn-bnding bnding energy 0 Ψ 3 = c 31 φ 31 - c 32 φ 32 + c 33 φ 33 Ψ 2 = c 21 φ 21 - c 23 φ 23 Ψ 1 = c 11 φ 11 + c 12 φ 12 + c 13 φ 13 We will take a clser lk at hw t calculate these cefficients and what the nature f the φs is. Take a lk at the bnding descriptin f XeF 2 in yur reading assignment (J. Chem. Ed. 1977, 54, ) Nte hw the atmic rbitals in the diagram that transfrm t becme mlecular rbitals are remarkably similar t the 3 and the allyl example abve. All examples have bnding, nn-bnding and antibnding rbitals. A bnding Mdel f C 4. It certainly is lgical t cnsider the simplest alkane. If yu can t understand methane what can yu understand? The Organic I explanatin ges as fllws. Methane is cmpsed f atmic s and p rbitals f principle quantum number 2. There are three p rbitals and ne s rbital. t explre space equally these rbitals are mixed t prduce fur identical sp 3 rbitals. The atms are held by electrns that brrw spatial character frm all three Cartesian crdinates. z x y bnd vectrs: <1,1,1>, < 1, 1, 1>, < 1, 1, 1>, <1, 1, 1> cs(a) = u v/( u v ) cs(a) = ( 1 1+1)/[( )( )] = 1/3 a =

LCAO APPROXIMATIONS OF ORGANIC Pi MO SYSTEMS The allyl system (cation, anion or radical).

LCAO APPROXIMATIONS OF ORGANIC Pi MO SYSTEMS The allyl system (cation, anion or radical). Principles f Organic Chemistry lecture 5, page LCAO APPROIMATIONS OF ORGANIC Pi MO SYSTEMS The allyl system (catin, anin r radical).. Draw mlecule and set up determinant. 2 3 0 3 C C 2 = 0 C 2 3 0 = -