Chap.4 Molecular Orbital Theory

Transcription

1 Chap.4 Moleular Orbital Theory The M.O. of a moleule is treated as the linear ombination of atomi orbitals LCAO-MO i n n i i The energy of the M.O. system is obtained by solving equation. amiltonian igen operator value The energy of a moleule arises from eletron motions, internal vibrations, rotations, translation. The eletron motion an be treated separately from nulear motion. amiltonian operator gives the energy of eletrons, for e -, nulei n i e h i m i i i i ze R i ze R e r d τ Ε d τ distane between eletron and nulei d τ dτ distane between eletron

2 Ab initio Moleular Orbital Theory Solve the Shrodinger equation with approximations, but no empirial parameters. Born-Oppenheimer Approximation: separtion of nulei and eletrons, keeping nulei fixed. The orbital approximation: the total wavefuntion is onsidered as a produt of one eletron wavefuntions-orbital. Ψ.m Pauli Priniple: the total wavefuntion of an atome or moleule Must be antisymmetri with respet to an exhange of the oordinates of any two eletrons. Semi-empirial Method NDO, MNDO, AM, PM Density Funtional Theory Calulating the eletron density ρ aross the entire moleule, whih orrelate with the total energy of the moleule T V J C T : eletron kineti energy term V : potential energy term J : Coulumb self-interation term C : exhange orrelation term

3 ükel Moleular Orbital Theory. only π-eletrons are treated σ-π separation. the basis set onsists of N p orbitals, one on eah of the N arbon atoms of the π system e.g For ethene π Ε define d d τ τ d τ d τ dτ S dτ S S by variation priniple S to solve, S S dτ S S dτ Coulomb integral energy of an eletron in its own orbital Resonane integral interation energy Normalization integral Overlap integral for adjaent atoms S S assume S ii, S ij for i j ii, ij β if i and j are σ-bonded energy of an eletron in i orbital. same for all i interation energy of an e - in basis orbital i and orbital j.

4 β β, ± bonding anti bonding non bonding β β β ± if -/β x,, π β π β with for p-orbitals of allyl system β β C C C C zero e - -density Node moleular plane antibonding bonding β β C C C C C C C _

5 For four p-orbitals of butadiene and 4 ± ±

6 Benzene OMO 6 5 4

7 Generalization:.The number of nodes inreases from to n-.the bonding and antibonding orbitals are symmetrially plaed above and below or non-bonding level.coeffiients are symmetrial with respet to atomi orbital s s

8 Correlation of Physial Properties with Results of MO Calulations nergy for ethylene, e - in, π β for allyl system deloalized system Compare to loalized referene system deloalization energy.88β in VB, the extra stability is alled resonane energy For benzene 68β, resonane energy 6kal β8kal

9 π-bond order butadiene e e in in P P P ij oup'd n i j n:no. of eletron in a partiular orbital i, j : the oeffiient of i, j bonded together for the M.O For exited state of butadiene e in e e P P in in total bond order C C C C total bond order σ bond order π-bond order C C C C C C C C

10 eletron density k k L k L ρ op'd i n i for allyl to normalize, if one eletron oupies the orbital, i is the fration of eletron density on ith arbon, or i for e - /orbital harge density on ith atom i i q ρ for ation, e - -density on for radial, on for anion, on harge density

11 Correlation of Bond Order and Bond length C-C.54Å CC.4Å C C.4Å benzene bond order.6.4å expt l bond length.9å CC-CO after n π exitation e from Oxygen s non-bonding e - bond length hange upon n π transition al d obs d Δr.4Å.6Å Δr -.Å -.4Å

12 Free Valene F 4. maximum possible bond order for sp -C P ij o. obtained from trimethylene methane radial C C C C bond order unused bonding power Free valene values free valene orrelate the reativity of radial rxns suh as C, CCl toward onjugate moleules.

13 ükel 4n Rule: Planar yli system with 4n π-eletron aromati extra stability relative to ayli analogs Planar yli system with 4n π-eletron antiaromati less stable than ayli analogues Cirle Method for arriving the energy levels for monoyli π-system β

14 Alternate ydroarbon no. of starred positions no. of unstarred positions even Non-alternate ydroarbon Coulson-Rushbrooke Theorem even odd no. of starred positions no. of unstarred positions odd. In an alternate hydroarbons, the MO energy levels are symmetrially paired above the level. kβ -kβ. In an alternate hydroarbon, the LCAO-oeffiient of any pair of omplementing orbitals are idential exept for a hange of sign in the oeffiients of atomi orbitals entered on the unstarred atoms.. In a neutral alternate hydroarbon or hydroarbon-radial eletron density on various C-atom are, in the ground state, all unity. self-onsistent Corollary:For odd alternate hydroarbon, there is at least one non-bonding MO, at.or odd number or NBMO

15 more about NBMO: 4. The NBMO will have non-zero oeffiients only at the starred position. 5. The sum of the oeffiients of the atomi orbitals of the starred atoms diretly linked to a given non-starred atom is zero , let ± NBMO NBMO determine the unpaired eletron density or the harge density in anion or ation benzyl ation eletron density radial anion For non-alternate hydroarbon, the eletron density in eah ontributing arbon is not unity, not equivalent. δ - δ

16 Benzene and Aromatiity aromati Benzene and derivatives exhibit speial properties -thermal stability -substitution reation with eletrophili reagents -resistane to oxidation -different physial properties as analogous aliphati ompounds resonane energy:.4å Δ -8.6kal/mole.8Å.9Å a riteria of aromatiity Δ -55.4kal/mole kal Δ -49.8kal/mole kal β owever, the double in bond in. is different from the double

17 A true referene should be a ylohexatriene with same bond lengths but no deloalization. no deloalization hypothetial moleule kal -kal -6kal by al. -6kal. So R.. inrease with no. of rings. bent poly ring more stable in a linear R.. by MO by xpt l β 6kal.68β 6kal 5.β 8.5kal 5.45β 9.kal

18 Aromatiity in Small Rings β C C neutral antibonding [C Cl ] would be stable with β resonane energy. [C - ] would be unstable AlCl AlCl 4 - NaN liq. N not observed C 4 4 β C 4 4 if planar and square a triplet ground state unstable β -β l β s β l -β s degeneray removed redued anti-aromati -ity retangle long short O O hν C O O hν in matrix of Ar at 8 o K C 5 5 [C 5 5- ] would be more stable β resonane energy.4β B B C 5 5 neutral pka 6

19 C β C neutral anti bonding [C ] would be more stable resonane energy.99β C 8 8 The planar struture involves severe angle strain 5 that the moleule bukles non-aromati C 8 8 planar Azulene dianion losed shell diation aromati δ - δ dipole.55d exist Cylotriapentafulvalene δ δ - dipole 6.D for hexaphenyl substituted derivative! N both 6-e - N

20 Larger Annulenes [] Annulene planar, severe angle strain 44 Severe non-bonded strain non-planar, more stable kal/mole more stable than all is-planar The observed isomers are non-aromati, due to non-planarity, not due to breakdown of ükel s Rule. CO show diamagneti ring urrent no signifiant bond alternation observed xperimental videne for aromatiity: Bond length:aromati systems show C-C bond length.8~.44 and uniform around the ring. non-aromati systems show sp -sp single bond and sp -sp double bond length. NMR hemial shift:shielding effet for nulei above/below the ring Upfield by 6~ ppm deshielding effet for nulei attah to the ring Down field by ~4 ppm due to diamagneti anisotropy

21 []-Annulene show paramagneti urrent at - [4]-Annulene δ.6 show diamagneti urrent bond length.5~.4å, no alternation distortion from planarity due to non-bonded strain of internal. R t, R R show bond length.9~.4å [8]-Annulene lose to planar, bond length.8~.4å, not alternating no angle strain. Aromati δ. δ 8.8 δ -6~-9 ~δ 9.5 The resonane energy dereases with ring size. more effetive than the flexible [8]-annulene

22 Other definitions of Aromatiity Resonane nergy f f ref f :heat of formation of an organi pd f ref:heat of formation alulated for loalized referene alulated from bond energies of C -, C C, C O, C - O. f ref Dewar Resonane nergy DR DR > aromati DR < antiaromati DR non-aromati Absolute hardness resonane energy per π-eletron η LUMO OMO relate to e - -affinity relate to ionization potential the wider the gap, the lower the hemial reativity, the higher the aromatiity for benzenoids for non-alternate hydroarbons aromati for ükel hardness < -.β antiaromati for ükel hardness > -.5β for heteroyles

23 Perturbation MO Theory Orbital mixing rules The interation of two orbitals atomi or moleular an be seen as a perturbation on the original orbital. new orbitals and energies are resulted..symmetry: only orbitals of like symmetry an interat.. Overlap: orbitrals must overlap in order to interat, the greater the overlap, the stronger the interation.. Relative energy: the loser the energy, the stronger the interation. -if the two interating orbitals are of the same energy, degenerate---first order perturbation iis ij S Δ Δ ii S - ij S The antibonding orbital is destabilized more than the bonding orbital is stabilized. -if the two interating orbitals are of different energy non-degenerate ---seond order perturbation Δ j λ i j ' j j j ' ij i ' ij ' i jdτ i Δ i λ j ' i i i ' ij j

24 .The lower orbital, mixing with the upper orbital, gives a bonding orbital, between the interating region. The upper orbital, mixing with the lower orbital, gives an antibonding orbital, between the interating region..the perturbation auses the lower energy orbital to be even lower in energy and vie versa. The energy hanges are larger for larger overlap, and smaller if the initial differene is larger..the orbital initially of lower energy is altered by adding in mixing a portion of the higher one in a bonding way. The orbital initially of higher energy is altered by adding in mixing a portion of lower one in an anti-bonding way. The mixing is larger the larger the overlap, and smaller the larger the initial energy differene. no net stabilization or even destabilization net stabilization useful interation usually involves one filled orbital and one empty orbital, suh as a OMO of one system and the LUMO of the other system.

25 Norbornadiene m m the mixing of π after interation perturbation AA SS SA π AS the mixing of π π SA SS AS AA Consequenes:. the ionization potential of norbornadiene should be smaller than the model ompound norbornene.. π, π transition SA AS should be red-shifted, but it is also a forbidden transition.. The π, π exitation promote an e - from an orbital whih is -6 and -5 anti-bonding to one whih is bonding in the same region. photohemial losure to is promoted. 4. removing one e - from SA or adding one e - to AS promote the bond formation between C -C 6 and C -C 5.

26 xtended ükel Theory Take into aount of all atomi orbitals s, p e.g. the basis set for ethene 4 6 C C 5 Y Z s C p p, s xc zc C, p, p, s xc zc, s, p 4 yc, s, p 5 yc, s, 6, 6. s. s. s C C. p. p. s xc xc 4.6 p. 6 p. s 5 yc yc. s. p. p 6 zc zc. s. s C C. 6 s. p. p xc xc. 6 s. p. p 4 yc yc. 6 s. 55 p. 55 p 5 zc zc. 6 s s.49 s.5 s C C. 4 p.4 p 5. s 4 xc xc. p. p.5 s yc yc 5. p. p 5. s zc zc 6 All MO s must be symmetri or anti-symmetri to the symmetry element of the moleule.

27 Qualitative Moleular Orbital Theory

28 Group orbitals from qualitative moleular orbital theoryqmot planar methyl pyramidal methyl Walsh diagram

29 Building larger moleule from group orbitals The group orbital for methylene

30 Formation of ethylene by mixing of two C group orbitals

31 The effet of heteroatoms Similar moleules have similar MO diagrams, with altered orbital energies.