Molecular Orbitals in Inorganic Chemistry. Dr. P. Hunt Rm 167 (Chemistry)

Transcription

1 Molecular rbitals in Inorganic Chemistry Dr. P. unt Rm 167 (Chemistry)

2 Lecture 2 utline L2 build a M diagram to show you the process quick revision stage 1: basic M diagram for 2 stage 2: include M mixing real Ms (how good are qualitative diagrams) Walsh or correlation diagrams L3 come back and look closely at the details

3 Revision M are combinations of As Fig. 1 details: Maths lectures with Joao Malhado Foundation from last year atomic orbitals radial and angular components radial: as quantum shell increases inner nodes radius max density increases cartoons represent outer portion shaded part represents negative part of function angular nature represented by the lobes the rbitron link from my website removed due to copyright ψ 1s R 1s Y 1s 2Z 3 2 e ρ 2!#" # $ (1 4π )1 2!#" # $ R 1s Y 1s z θ y=ax 2 +bx+c positive θ x negative sign change with θ Fig. 2 Fig. 3

4 Setting Up determine the shape of the molecule Lecture 1 find the point group of the molecule: C2v define the axial system find all of the symmetry elements C 2v A 1 E C 2 σ v (xz) σ v '(yz) h= z y z C 2 (z) x σ v (yz) 1 2 σ v (xz) A Fig. 4 B 1 B x y your character tables

5 Fragments map onto each other under the symmetry operations atoms map onto each other atom maps onto its self 2 and atom are the fragments use place holders! z x y 2 fragment place holder whole molecule place holder fragment Fig. 5

6 Fragments map onto each other under the symmetry operations atoms map onto each other atom maps onto its self 2 and atom are the fragments use place holders! z x y 2 fragment place holder whole molecule place holder fragment reproduce the whole of the molecular structure in the M fragment orbitals 2 orbitals atom orbitals 2 orbitals (s and p) orbitals Fig. 6

7 Set Up M Diagram Important! vertical axis: Energy 1s A position As more electronegative than so valence orbitals lie below 1s reference orbital atoms are further apart than in 2 so stablilsation and destabilsation are less ie splitting energy is less more on this next lecture! y z x??? 2 p y p x p z s Fig. 6

8 Fragment rbital Symmetry ow does each orbital transform under the symmetry operations of the group? orbital is unchanged => character = 1 a sign change => character = -1 check against the character table σ v (yz) Lecture 1 No change under σ χ = 1 v σ v C 2v E C 2 σ v (xz) σ v '(yz) Short-Cut! Γ Fig. 7 totally bonding orbitals are always totally symmetric which is the first symmetry label listed for all point groups for C2v this is the a1 irreducible representation

9 Short Cuts! look in the last columns of the character table find Tx, Ty, Tz sometimes also written as just x, y, z gives you the axis symmetry label Short-Cut! C 2v A 1 E C 2 σv (xz) σ v '(yz) h=4 T z Important! A 2 B 1 B T x T y Fig. 7

10 Fragment rbitals look for similarities in the phase of orbitals and the cartesian axes Short-Cut! Γ C 2v E C 2 σ v (xz) σ v '(yz) T y b 2 x Γ Γ T x T z b 1 2 C 2v E C 2 σ v (xz) σ v '(yz) Γ Γ b 1 Fig. 7 Fig. 8 look for similarity in phase patterns!

11 Fragment rbitals look for similarities in the phase of orbitals and the cartesian axes Short-Cut! C 2v E C 2 σ v (xz) σ v '(yz) Γ p y b 2 Γ p x b 1 Γ p z Fig. 7

12 Add symmetry labels to M diagram Fig. 9

13 Form the Ms work out Ms first then the splitting Important! nly fragment orbitals (Fs) of the same symmetry can combine for water: a1 and b1 F can only combine NCE more than one F of same symmetry? then combine the lowest energy two leave the last one non-bonding (for now!) Form Ms by adding Fs together as is adding Fs with NE F phase inverted + + b 1 Fig 10

14 Stage ne M Diagram b 1 Evaluate splitting b 2 b 1 Fs far apart in energy interact only weakly in-phase interactions are bonding destabilisation is always larger more on this next lecture! TEN Ms on the diagram z x y 2 Fig 11/12

15 Stage ne 2b 1 M Diagram b 1 Evaluate splitting b 2 b 1 Fs closer in energy interact more destabilisation is always larger more on this next lecture! TEN Ms on the diagram z x y 2 Fig 11/12

16 Stage ne 2b 1 M Diagram 4 b 1 Label Ms 1b 2 b 2 b 1 number within symmetry label count the core orbitals only if molecule is small 3 1b 1 2 z x y 2 Fig 11/12

17 Stage ne antibonding M is always destabilised more than the bonding M is stabilised 2b 1 M Diagram 4 b 1 Annotate your diagrams! Important! F left nonbonding in the first stage diagram 1b 2 3 1b 1 b 2 Fs are closer in energy and so the interaction between the orbitals is larger for the b 1 M b 1 do not repeat information z 2 1 is the 1sA which is not shown because this is a valence M diagram x y Fig 11/12

18 Stage ne antibonding M is always destabilised more than the bonding M is stabilised 2b 1 M Diagram 4 b 1 add the electrons! fill sequentially F left nonbonding in the first stage diagram 1b 2 3 b 2 b 1 1b 1 Fs are closer in energy and so the interaction between the orbitals is larger for the b 1 M 2 z 1 is the 1sA which is not shown because this is a valence M diagram x y 2 valence e 6 valence e Fig 11/12

19 Stage 2: M Mixing necessary conditions NLY Ms of the same symmetry can mix to occur mixing MUST stabilise the total energy mixing tends to be large when: Ms are close in energy one M is non-bonding or unoccupied orbitals are in M-LUM region Important!

20 M Mixing mixing orbitals add Ms together as is 0 add Ms with NE M phase inverted inspect to determine which is the bonding mixed M occupied + unoccupied antibonding due to increased out-ofphase interaction ψ (3 ) ψ (4 ) ψ 1 = ψ (3 ) + ψ (4 ) antibonding M Fig 13

21 In-Class Activity mixing orbitals add Ms together as is add Ms with NE M phase inverted 0 inspect to determine which is the bonding mixed M form -ψ(3 )+ψ(4 ) Fig 14

22 In-Class Activity mixing orbitals add Ms together as is add Ms with NE M phase inverted 0 inspect to determine which is the bonding mixed M form -ψ(3 )+ψ(4 ) + bonding due to increased inphase interaction ψ (3 ) ψ (4 ) ψ 2 = ( ψ (3 )) + ψ (4 ) = ψ (4 ) ψ (3 ) "non-bonding" or slightly antibonding M Fig 14

23 4 Mixing 2b 1 strong mixing: 4a1 M unoccupied 3a1 M non-bonding in M/LUM region close in energy occupied M is stabilised b 1 1b 2 3 1b 1 b 2 b 1 significant mixing drives 3 M down in energy and chanes the shape of the M extra lines drawn to show the main mixing interaction 2 z x y 2 valence e 2 6 valence e Fig 15

24 4 Final M antibonding M is always destabilised more than the bonding M is stabilised 2b 1 Diagram of the 4 lies above the 2b 1 M because there is strong directional antibonding overlap in the 4 M and weaker less directional overlap in the 2b 1 M 2 b 1 b 2 F left nonbonding as there is no other F of this symmetry for it to interact with Fs are closer in energy and so the interaction between the orbitals is larger for the 1b 1 than the 2 M 1b 2 3 1b 1 2 b 2 b 1 significant mixing drives 3 M down in energy and chanes the shape of the M z 1 is the 1sA which is not shown because this is a valence M diagram x y 2 valence e 2 6 valence e Fig 15

25 Real Ms computed molecular orbitals 2 1b 1 we have solved the Schrödinger equation!!! 3 b 2 Fig 16

26 Experimental Evidence Photoelectron spectrum energy required to eject an electron from its orbital traditional theory: expect 2 equivalent bonds and 2 equivalent lone pairs for water = 2 lines in photo-electron spectrum removed due to copyright Fig 17 BUT have 3 lines in photo-electron spectrum which relate to delocalised 1b1, 3a1 and 1b2 Ms Fig 18

27 Delocalisation Ms are delocalised not 2 center 2 electron most of Ms extend over ALL atoms in molecule there are no bonds where have the bonds gone??? Bonds represent a build up of the TTAL electron density We keep ideas of hybridisation and 2c-2e bonds because they are USEFUL

28 Analysis 4 M diagrams are transferable 2b 1 one diagram is good for many molecules or fragments! molecules Be2 (homework), 2S fragments C2 (lecture 4), N2 we can even treat metal fragments: M2 b 1 1b 2 3 b 2 b 1 general formula A2 1b 1 A=main group element, M=metal slight modifications: different numbers of electrons slightly different position of the fragment orbitals z x y 2 valence e valence e

29 Correlation Diagram Walsh diagram: change one geometric parameter and examine changes in Ms and energies normally a bond distance or angle link the Ms for two extreme geometries removed due to copyright example: Why is 2 bent? start with high symmetry Fig 21 C 2v 105º 180º D h Prof. A.D Walsh University of Dundee from: scientists.htm end with lower symmetry -- angle

30 Walsh Diagram typically start from the highest symmetry I ve constructed the M diagram for linear 2 for you (Self-study for you to reproduce) Fig 21

31 Walsh Diagram then examine how Ms change under geometric distortion Qualitative not Quantitative! Fig 21

32 Energy of Ms then examine how Ms change under geometric distortion 2σ g + (2a1) stabilised BNDED overlap dominates directed & overlap is stronger in linear structure on bending - bonding overlap ALS... through space bonding overlap net result small stabilisation Fig 21

33 Energy of Ms then examine how Ms change under geometric distortion 1σ u + (1b1) destabilised - bonding overlap ALS... through space antibonding net result destabilisation Fig 21

34 Energy of Ms then examine how Ms change under geometric distortion 1π u (1b2) no change non-bonding orbital Fig 21

35 Energy of Ms then examine how Ms change under geometric distortion 2σ u + (2b1) stabilised socrative quiz! WZ9KBWC3 Fig 21

36 Energy of Ms then examine how Ms change under geometric distortion 2σ u + (2b1) stabilised - antibonding overlap also... through space antibonding BNDED overlap dominates net result destabilisation Fig 21

37 Energy of Ms then examine how Ms change under geometric distortion 1π u 3σ g + / or 3a1/4a1 special as planar molecule 1πu and 3σg + cannot mix (not same symmetry) when molecule distorts they become the same symmetry: mixing occurs 1πu goes to 3a1 3σg + goes to 4a1 on mixing the 1πu ( 3a1) is stabilised Important! Fig 21 18

38 Change of Axes When the symmetry point group changes the axial definition changes! y z x y z x y x z y x z z-axis reorientated orbital remains the same only labels change then follow with mixing 4 2σ g + 3 1π u mixing Fig 22

39 Walsh Diagram rbital changes As move with the atoms form or shape of As remains constant!! except for Ms which undergo mixing Molecular stability examine how occupied Ms change under geometric distortion look for occupied Ms which show a large change in energy these orbitals drive the change in shape self-study questions Fig 22

40 Symmetry Breaking But how does the drop in symmetry start? nuclear vibrations provide infinitesimal distortion required for M mixing vibronic coupling = coupling of electronic and nuclear motions breakdown of the Born-ppenheimer approximation! collapse of a VERY fundamental approximation more common than you think! of which Jahn-Teller theorem is a special case

41 Symmetry Breaking symmetry & symmetry breaking underlies many theories in physics and chemistry Noether s Theorem Shows that a conservation law can be derived from any continuous symmetry. invariance with respect to translation gives the law of conservation of linear momentum invariance with respect to time translation gives the law of conservation of energy general relativity magnetism standard model of particle physics superconductivity Serious Stuff! existence of iggs particle eisenberg Uncertainty Principle field theory removed due to copyright Emmy Noether source: Image:Noether.jpg accessed 17/08/07

42 M checklist steps we have used today to form a M diagram VERY Important! Steps to construct a M diagram determine the molecular shape and identify the point group define the axial system and all of the symmetry operations identify the chemical fragments, put them on the bottom of the diagram determine the energy levels and symmetry labels of the fragment orbitals (use 1s as a reference) combine fragment orbitals of the same symmetry, determine the Ms and then estimate the splitting energy; draw in the M energy levels and Ms (in pencil!) determine the number of electrons in each fragment and hence the central M region, add them to the diagram identify if any M mixing occurs, determine the mixed orbitals and redraw the M diagram with shifted energy levels and the mixed Ms annotate your diagram use the M diagram to understand the structure, bonding and chemistry of the molecule

43 Key Points be able to form M diagrams for molecules with the general formula A2 and A3 (tutorial) where A= main group element or a metal be able to explain and illustrate M mixing be able to critically evaluate VSEPR theory, localised 2c-2e bonding and the delocalised M picture of bonding be able to describe how a PES is formed and be able to relate a spectrum to the Ms, and M diagram of a molecule be able to form correlation diagrams and explain why a particular geometry is more stable than another with reference to the stability of the Ms be able to discuss symmetry breaking and vibronic coupling be able to describe the process of forming a M diagram (the M checklist)

44 Finally See my web-site notes AND slides link to panopto when it becomes available optional background support for beginners optional material to take you a little further links to interesting people and web-sites links to relevant research papers on Ms model answers!!