Molecular Orbitals in Inorganic Chemistry

Transcription

1 Outline Molecular Orbitals in Inorganic hemistr Dr. P. unt Rm 167 (hemistr) choosing fragments orbital smmetr (again!) bonding and antibonding character of orbitals comple MOs -> decompose into LAOs a comple MO diagram: omple Fragments Eample: MO diagrams combine two fragments Smmetr Fragments Molecular Fragments 2O formaldehde molecular fragments 2 and O smmetr fragments 2 and O use molecular fragments as there is a single atom preferred Smmetr fragments atoms that transform onto each other under operations of the point group equivalent atoms in terms of NMR O O O 2 Molecular fragments small molecules for which the MOs are well known like A2 or liner A or A3 Fig. 1 2 fragment like 2O will have the same MOs s map onto each other under 2 3 4

2 Eample: In-lass Activit 3 boron trihdride molecular fragments 2 and smmetr fragments 3 and use the smmetr fragments as there is a single atom preferred 24 ethane determine the smmetr fragments determine the molecular fragments which is the better one to use and wh? Fig. 2 2 and fragments will have the same MOs as diatomics s map onto each other under 2 Fig In-lass Activit In-lass Activit 24 ethane molecular fragments? 24 ethane molecular fragments? smmetr fragments? s map onto each other under 2 molecular 2 molecular smmetr 2 fragment like 2O will have the same MOs 2 fragment like 2O will have the same MOs s map onto each other under 2 7 8

3 In-lass Activit Orbital Smmetr 24 ethane molecular fragments? smmetr fragments? use the molecular fragments because it is easier to work out the interactions of degenerate fragments molecular preferred 2 2 Short-cuts look at the phase pattern! orbitals with the same phase pattern as an ais have the same smmetr label as the ais Fig. 4 D 2h same smmetr as the -ais 2 fragment like 2O will have the same MOs 9 10 Orbital Smmetr Short-cuts Orbital Smmetr if there are no short-cuts possible => use a representation table look at the phase pattern! orbitals with the same phase pattern as a dao have the same smmetr as the corresponding cartesian function Fig. 5 2 p π orbitals d orbital g Fig. 6 Γ D 2h E 2 () 2 () 2 () i σ() σ() σ () look at the last column on our character tables: it gives the smmetr label (IR) of the binar cartesian functions same smmetr as the d AO 11 12

4 In-lass Activit In-lass Activit test ourself! socrative qui Fig. 7 socrative qui! WZ9KW determine the smmetr of these MOs same smmetr as the d AO d p d 2 same smmetr as the d 2 AO determine the smmetr of these MOs these are MOs from 24 which belongs to the D2h point group assume the centre of the ais sstem lies on the centre of inversion for the molecule same smmetr as the p AO u onding vs Anti-bonding onding vs Anti-bonding onding bonding => in-phase overlap anti-bonding => out-of-phase overlap onding bonding => in-phase overlap anti-bonding => out-of-phase overlap out-of-phase Nodes occur where phase changes raises the energ of an orbital, more nodes indicates increasing anti-bonding character nodes at atoms are less important E E E E in-phase Fig. 2 Fig. 8 nodes where phase changes in the internuclear region 15 16

5 omple MO More omple MOs has both bonding and anti-bonding components onding character is a sliding scale σ (s) interactions are much stronger than π (p) tpe interactions the closer the orbitals the stronger the interaction (bonded vs non-bonded) Fig. 8 orbitals are close => strong (antibonding) interaction orbitals are far apart => weak (bonding) interaction this MO has onl saos so interactions are stronger than π or p interactions Important! test ourself! Fig. 9 identif the bonding/antibonding interactions in these MOs and annotate the diagrams what is the relative energ ordering of these MOs? INTS 1 2 In-lass Activit look at ALL of the interactions what is the tpe of interaction (s or p)? what is the distance between the interacting orbitals? for similar MOs how man nodes are there? In-lass Activit In-lass Activit nodal plane in the internuclear region: strong antibonding atoms directl bonded, π-tpe: strong antibondng other orbitals from Fig 7 details on m web-site node on an atom: lesser node not ver antibonding atoms medium distance apart: medium antibondng atoms directl bonded p-s overlap: strong bondng atoms far apart: weak antibonding overall: weak antibonding 19 20

6 In-lass Activit what is the relative energ ordering of these MOs? Fig. 9 1=weakl antibonding 2=strongl bonding (pi in the central region) 3=strongl bonding (σ in the central region) most bonding 3>2>1 least bonding LAO for comple MOs in research we often work in reverse optimise a molecule confirm the minima (frequenc analsis) compute the MOs ou will have seen the MO window for gaussview Important! poor attempts in last ears eam this file is available on m web-site Fig LAO for comple MOs which MOs are important?? not the deep core orbitals: AO-like jump in energ not the high energ unoccupied MOs: too diffuse LUMO+4 and above LAO for comple MOs decompose the real MOs into LAO components eamine MO look for AO contributions ver small contributions are ignored relate to known fragment orbitals relative sie is important es to valence MOs! es to lower energ unoccupied MOs this file is available on m web-site Fig. 10 Fig

7 LAO for comple MOs decompose the real MOs into LAO components eamine MO look for AO contributions ver small contributions are ignored relate to known fragment orbitals relative sie is important larger contribution combined MOs from E 2 fragments LAO for comple MOs decompose the real MOs into LAO components eamine MO look for AO contributions ver small contributions are ignored relate to known fragment orbitals relative sie is important "built" from E 2 FOs MO15 Fig LAO for comple MOs LAO for comple MOs decompose the real MOs into LAO components eamine MO look for AO contributions ver small contributions are ignored relate to known fragment orbitals relative sie is important larger contribution combined MOs from EX 2 and E 2 fragments MO18 "built" from EX 2 FOs "built" from E 2 FOs orientation!! draw what ou see, FO does not lie along the bonds 27 Fig

8 In-lass Activit draw the LAO for MO14, M24 and MO25 In-lass Activit draw the LAO for MO14, M24 and MO25 small and ignored pao is polarised MO 14 MO 24 OMO MO 25 LUMO MO14 combined MOs from E 2 fragments MO24 MO omple MO Diagrams Diborane comple molecules are built up b combining a series of fragments 1. know the 2 fragment 2. combine two 2 fragments => intermediate MO diagram 3 fragments!! form intermediate MO diagram 3. add 2 across centre =>final MO diagram Fig. 13 We could epect the bonding in 26 to be similar to that of ethane VSEPR theor does not work! make an ad-hoc correction 3 center two electron bent bonds Molecular Orbital Theor MOs are easil developed no special corrections required stabilit and bonding of diborane eplained missing bonds 3-center-2e bond Fig

9 Revision: MO checklist Setting Up Steps to construct a MO diagram 1. determine the molecular shape and identif the point group of the molecule 2. define the aial sstem and find all of the smmetr operations on the molecule 3. identif the chemical fragments, and put them along the bottom of the diagram 4. determine the energ levels and smmetr labels of the fragment orbitals 5. combine fragment orbitals of the same smmetr, estimate the splitting energ and draw in the MO energ levels and MOs (in pencil!) 6. determine the number of electrons in each fragment and hence the central MO region, add them to the diagram 7. identif if an MO miing occurs, determine the mied orbitals and redraw the MO diagram with shifted energ levels and the mied MOs 8. use this checklist! 9. analse the MO diagram determine molecular shape identif the point group of the molecule: D2h convince ourself of this for homework define the aial sstem find all of the smmetr elements 3 2 aes 3 σ planes centre of inversion, i convince ourself of this for homework 2 () σ() 2 () σ() σ() 2 () Fig Revision: MO checklist Intermediate Diagram Steps to construct a MO diagram 1. determine the molecular shape and identif the point group of the molecule 2. define the aial sstem and find all of the smmetr operations on the molecule 3. identif the chemical fragments, and put them along the bottom of the diagram 4. determine the energ levels and smmetr labels of the fragment orbitals 5. combine fragment orbitals of the same smmetr, estimate the splitting energ and draw in the MO energ levels and MOs (in pencil!) 6. determine the number of electrons in each fragment and hence the central MO region, add them to the diagram 7. identif if an MO miing occurs, determine the mied orbitals and redraw the MO diagram with shifted energ levels and the mied MOs 8. use this checklist! 9. analse the MO diagram treat two 2 fragments first know orbitals for E2 combine these two in intermediate diagram include orbitals up to LUMO+1 requires electronic configuration of fragment =3 valence e and 2=2 valence e fragment =5e therefor keep up to b2 orbital Fig

10 Revision: MO checklist Form 2 4 Fragment π-interaction is weak Steps to construct a MO diagram 1. determine the molecular shape and identif the point group of the molecule 2. define the aial sstem and find all of the smmetr operations on the molecule 3. identif the chemical fragments, and put them along the bottom of the diagram 4. determine the energ levels and smmetr labels of the fragment orbitals 5. combine fragment orbitals of the same smmetr, estimate the splitting energ and draw in the MO energ levels and MOs (in pencil!) 6. determine the number of electrons in each fragment and hence the central MO region, add them to the diagram 7. identif if an MO miing occurs, determine the mied orbitals and redraw the MO diagram with shifted energ levels and the mied MOs 8. use this checklist! 9. analse the MO diagram combine fragment orbitals of the same smmetr FIRST work out the MOs TEN the splitting energ: degenerate orbitals have a large interaction but 2 units are NOT directl bonded and hence have a weaker interaction still moderated b overlap strength: s vs pσ vs pπ make an educated guess that can be justified eact ordering will require computation p σ-interaction large => directed π-interaction is weaker σ-interaction is large Fig Smmetr Labels? Smmetr Labels? totall bonding MO totall bonding MO which smmetr label is associated with each of the aes? -ais = b3u -ais = b2u -ais = b1u see the character table Fig Fig

11 Smmetr Labels? -ais Smmetr Labels? b d 2g totall bonding MO which smmetr label is associated with each of the aes? -ais = b3u -ais = b2u -ais = b1u -ais -ais u totall bonding MO which smmetr label is associated with each of the aes? -ais = b3u -ais = b2u -ais = b1u which MOs have the same phase pattern as daos? d 2 d u Fig Fig Smmetr Labels? g Fragments: totall bonding MO which smmetr label is associated with each of the aes? use the molecular fragments because it is easier to work out the interactions of degenerate fragments -ais = b3u -ais = b2u -ais = b1u which MOs have the same phase pattern as daos? final MO: use representation table u two 2 fragments we alread know MOs for A 2 from 2O add 2 across MOs for 2 are ver simple! Γ D 2h E 2 () 2 () 2 () i σ() σ() σ () smmetr Fig Fig

12 2 Set-Up Fig. 20 MO Diagram 4 g 3 Where will the 2 orbitals lie? the atoms are not directl bonded means small splitting energ means fragments are almost nonbonding so the will lie near non-bonding orbitals of 24 fragment u non-bonding FO ombine orbitals of the same smmetr ag lowest 24 ag orbital is too deep and will not interact the energ levels are not ver close, but overlap is good stabilisation is medium g u 1b2g 1 1u 3 1 the FOs are further apart in energ and interact strongl, there are two nodal planes eact energ odering difficult to predict, require a calculation 2 the FOs are close in energ and interact strongl, the have a single nodal plane MO Diagram 4 Revision: MO checklist 3 g 1b2g ombine orbitals of the same smmetr b3u there is onl one b3u orbital on 24 fragment the energ levels are almost degenerate, stabilisation is large u 1 1u the FOs are further apart in energ and interact strongl, there are two nodal planes eact energ odering difficult to predict, require a calculation the FOs are close in energ and interact strongl, the have a single nodal plane Steps to construct a MO diagram 1. determine the molecular shape and identif the point group of the molecule 2. define the aial sstem and find all of the smmetr operations on the molecule 3. identif the chemical fragments, and put them along the bottom of the diagram 4. determine the energ levels and smmetr labels of the fragment orbitals 5. combine fragment orbitals of the same smmetr, estimate the splitting energ and draw in the MO energ levels and MOs (in pencil!) 6. determine the number of electrons in each fragment and hence the central MO region, add them to the diagram 7. identif if an MO miing occurs, determine the mied orbitals and redraw the MO diagram with shifted energ levels and the mied MOs 8. use this checklist! 9. analse the MO diagram

13 2 MO Diagram 4 Revision: MO checklist 3 g 1b2g onfiguration Steps to construct a MO diagram 10e from 24 fragment and 2e from 2 =12e Onl MOs of the same smmetr mi must also be close in energ greatest between occupied and unoccupied orbitals ag and b1u? b1u too far apart in energ ag both occupied u 1 1u determine the molecular shape and identif the point group of the molecule 2. define the aial sstem and find all of the smmetr operations on the molecule 3. identif the chemical fragments, and put them along the bottom of the diagram 4. determine the energ levels and smmetr labels of the fragment orbitals 5. combine fragment orbitals of the same smmetr, estimate the splitting energ and draw in the MO energ levels and MOs (in pencil!) 6. determine the number of electrons in each fragment and hence the central MO region, add them to the diagram 7. identif if an MO miing occurs, determine the mied orbitals and redraw the MO diagram with shifted energ levels and the mied MOs 8. use this checklist! 9. analse the MO diagram NO miing! Analsis 4 Analsis of the occupied MOs are non-bonding with respect to the bridging atoms g u 1b2g 1 1u 3 4 of the occupied MOs are non-bonding with respect to the bridging atoms 2 of the occupied MOs describe bonding with the bridging atoms natural description which doesn t require us to invoke add-hoc corrections to a theor g u 1b2g 1 1u

14 2b3u Analsis 2b3u Analsis 4ag b1u b2 g 4 of the occupied MOs are non-bonding with respect to the bridging atoms 2 of the occupied MOs describe bonding with the bridging atoms natural description which doesn t require us to invoke add-hoc corrections to a theor LUMO is essentiall nonbonding between 2 units (and 2) low energ for a LUMO can accept electrons without destabilising the molecule b2 4ag b1u 3b1u b3u 1b2 g ag b3u b2 g qualitative MO diagram b2 ing der r o ct r ea an va c a1 ag 1b3g b3g b3u 1b2 g ag b3u the ag FOs are further apart in energ and interact strongl, there are two nodal planes a1 ag 1b3g b3g 3ag b1 3b1u 3ag b1 1b2u b2u eact energ odering difficult to predict, require a calculation 1b2u b2u 1b3u 1b3u b1u b1u 2b1u a is stable! a1 ag 2ag Fig Ke Points Finall be able to differentiate between smmetr and molecular fragments and be able to choose fragments that make generating the MO diagram easier be able to quickl determine the smmetr of MOs using character tables and short-cuts be able to eplain the bonding/antibonding qualities of a set of MOs and annotate a diagram showing the ke characteristics ag 2ag See m web-site notes AND slides link to panopto when it becomes available optional background support for beginners optional material to take ou a little further links to interesting people and web-sites links to relevant research papers on MOs model answers!! be able to represent complicated computed MOs in terms of LAOs be able to discuss the bonding in 26 with respect to VSEPR theor, delocalisation, and MO theor. e able to justif the stabilit of 262be able to form a MO diagram for A22, A24, A26 and analse the MO diagram for information relating to structure and bonding 55 the b3u FOs are close in energ and interact strongl, the have a single nodal plane 2b1u 56