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

Molecular Orbitals in Inorganic Chemistr Dr. P. unt p.hunt@imperial.ac.uk Rm 167 (Chemistr) http://www.ch.ic.ac.uk/hunt/

Outline choosing fragments orbital smmetr (again!) bonding and antibonding character of orbitals complex MOs -> decompose into LCAOs a complex MO diagram: B26

Complex Fragments MO diagrams combine two fragments Smmetr Fragments Molecular Fragments Smmetr fragments atoms that transform onto each other under operations of the point group equivalent atoms in terms of NMR Molecular fragments small molecules for which the MOs are well known like A2 or liner AB or A3

Example: C2O formaldehde molecular fragments C2 and O smmetr fragments 2 and CO use molecular fragments as there is a single atom preferred C 2 O O O x Fig. 1 C C C C 2 fragment like 2 O will have the same MOs s map onto each other under C 2

Example: B3 boron trihdride molecular fragments 2 and B smmetr fragments 3 and B use the smmetr fragments as there is a single atom preferred x B x B B Fig. 2 2 and B fragments will have the same MOs as diatomics s map onto each other under C 2

In-Class Activit C24 ethane determine the smmetr fragments determine the molecular fragments which is the better one to use and wh? x C C Fig. 3

In-Class Activit C24 ethane molecular fragments? molecular C 2 x C C C C C C C 2 C 2 fragment like 2 O will have the same MOs

In-Class Activit C24 ethane molecular fragments? smmetr fragments? s map onto each other under C 2 molecular C 2 x C C C C C C C 2 smmetr C 2 fragment like 2 O will have the same MOs C s map onto each other under C 2

In-Class Activit C24 ethane molecular fragments? smmetr fragments? use the molecular fragments because it is easier to work out the interactions of degenerate fragments preferred molecular C 2 x C C C C C C C 2 C 2 fragment like 2 O will have the same MOs

Orbital Smmetr Short-cuts D 2h look at the phase pattern! orbitals with the same phase pattern as an axis have the same smmetr label as the axis Fig. 4 b 1u same smmetr as the x-axis

Orbital Smmetr Short-cuts look at the phase pattern! orbitals with the same phase pattern as a dao have the same smmetr as the corresponding cartesian function look at the last column on our character tables: it gives the smmetr label (IR) of the binar cartesian functions Fig. 5 x 2 p π orbitals d x orbital b 2g same smmetr as the dx AO

Orbital Smmetr if there are no short-cuts possible => use a representation table D 2h E C 2 () C 2 () C 2 (x) i σ(x) σ(x) σ () Γ Fig. 6 1 1-1 -1-1 -1 1 1 b 1u

In-Class Activit test ourself! socrative qui socrative qui! WZ9KBWC3 1 2 3 Fig. 7 x determine the smmetr of these MOs these are MOs from C24 which belongs to the D2h point group assume the centre of the axis sstem lies on the centre of inversion for the molecule

In-Class Activit determine the smmetr of these MOs same smmetr as the d AO b 3g d p d 2 same smmetr as the d 2 AO same smmetr as the p AO b 2u

Bonding vs Anti-bonding Bonding bonding => in-phase overlap anti-bonding => out-of-phase overlap out-of-phase E E in-phase Fig. 2 Fig. 8

Bonding vs Anti-bonding Bonding bonding => in-phase overlap anti-bonding => out-of-phase overlap 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 nodes where phase changes in the internuclear region

More Complex MOs Complex MO has both bonding and anti-bonding components Bonding 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) orbitals are close => strong (antibonding) interaction this MO has onl saos so interactions are stronger than π or p interactions Important! Fig. 8 orbitals are far apart => weak (bonding) interaction

In-Class Activit test ourself! 1 2 3 Fig. 9 x identif the bonding/antibonding interactions in these MOs and annotate the diagrams what is the relative energ ordering of these MOs? INTS 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-Class Activit nodal plane in the internuclear region: strong antibonding node on an atom: lesser node not ver antibonding

In-Class Activit atoms directl bonded, π-tpe: strong antibondng other orbitals from Fig 7 details on m web-site atoms medium distance apart: medium antibondng atoms directl bonded p-s overlap: strong bondng atoms far apart: weak antibonding overall: weak antibonding

In-Class Activit what is the relative energ ordering of these MOs? 1 2 3 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 x

LCAO for complex 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 exam this file is available on m web-site Fig. 10

LCAO for complex 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 es to valence MOs! es to lower energ unoccupied MOs this file is available on m web-site Fig. 10

LCAO for complex MOs decompose the real MOs into LCAO components examine MO look for AO contributions ver small contributions are ignored relate to known fragment orbitals relative sie is important larger contribution combined b 1 MOs from E 2 fragments "built" from E 2 FOs MO15

LCAO for complex MOs decompose the real MOs into LCAO components examine 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

LCAO for complex MOs Fig. 12

In-Class Activit draw the LCAO for MO14, M24 and MO25 MO 14 MO 24 OMO MO 25 LUMO

In-Class Activit draw the LCAO for MO14, M24 and MO25 small and ignored pao is polarised MO14 combined MOs from E 2 fragments MO24 MO25

Complex MO Diagrams complex molecules are built up b combining a series of fragments 1. know the B 2 fragment B B 2. combine two B 2 fragments => intermediate MO diagram 3 fragments!! form intermediate MO diagram B B B B 3. add 2 across centre =>final MO diagram Fig. 13

Diborane We could expect the bonding in B26 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 explained missing bonds B B B B 3-center-2e bond B B B B Fig. 14

Revision: MO checklist Steps to construct a MO diagram 1.determine the molecular shape and identif the point group of the molecule 2.define the axial 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 mixing occurs, determine the mixed orbitals and redraw the MO diagram with shifted energ levels and the mixed MOs 8.use this checklist! 9.analse the MO diagram

Setting Up determine molecular shape identif the point group of the molecule: D2h convince ourself of this for homework B B C 2 () define the axial sstem find all of the smmetr elements 3 C2 axes 3 σ planes centre of inversion, i convince ourself of this for homework C 2 (x) σ(x) B B σ() σ(x) C 2 () Fig. 15

Intermediate Diagram treat two B2 fragments first know orbitals for E2 combine these two in intermediate diagram include orbitals up to LUMO+1 requires electronic configuration of fragment B=3 valence e and 2=2 valence e fragment =5e therefor keep up to b2 orbital b 2 x b 1 Fig. 16 B 2

Form B 2 4 Fragment π-interaction is weak combine fragment orbitals of the same smmetr FIRST work out the MOs TEN the splitting energ: degenerate orbitals have a large interaction but B2 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 exact ordering will require computation b 2 p σ -interaction large => directed b 1 π-interaction is weaker σ-interaction is large Fig. 16 x B 2 4

Smmetr Labels? b 2 totall bonding MO b 1 Fig. 16 x B 2 4

Smmetr Labels? b 2 totall bonding MO which smmetr label is associated with each of the axes? x-axis = b3u -axis = b2u -axis = b1u see the character table b 1 Fig. 16 x B 2 4

Smmetr Labels? b 2 x-axis b 3u totall bonding MO which smmetr label is associated with each of the axes? x-axis = b3u -axis = b2u -axis = b1u b 1 -axis b 2u -axis b 1u Fig. 16 x B 2 4

Smmetr Labels? b 2 b 2g dx b 3u totall bonding MO which smmetr label is associated with each of the axes? x-axis = b3u -axis = b2u -axis = b1u which MOs have the same phase pattern as daos? b 3g b 1 d 2 d b 2u b 1u Fig. 16 x B 2 4

Smmetr Labels? b 2 b 2g b 3u totall bonding MO which smmetr label is associated with each of the axes? x-axis = b3u -axis = b2u -axis = b1u which MOs have the same phase pattern as daos? final MO: use representation table b 1 b 1u b 3g b 2u b 1u Fig. 19 D 2h E C 2 () C 2 () C 2 (x) i σ(x) σ(x) σ () Γ 1 1-1 -1-1 -1 1 1 b 1u smmetr Fig. 16 x B 2 4

Fragments: use the molecular fragments because it is easier to work out the interactions of degenerate fragments two B 2 fragments B B we alread know MOs for A 2 from 2 O B B add 2 across MOs for 2 are ver simple! B B Fig. 15

Set-Up b 1u Fig. 20 b 2g b 3u b 2 non-bonding FO b 3u 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 B24 fragment b 1 b 3g b 2u b 1u Fig. 19 x B 2 4 B 2 6 2

2b 3u MO Diagram 4 b 1u 3b 1u Combine orbitals of the same smmetr ag lowest B24 ag orbital is too deep and will not interact the energ levels are not ver close, but overlap is good stabilisation is medium b 2 b 1 b 2g b 3u b 3g b 2u 1b2g 1b 3g 1b 2u 3 b 3u the FOs are further apart in energ and interact strongl, there are two nodal planes exact energ odering difficult to predict, require a calculation 1b 3u b 1u 2b 1u the b 3u FOs are close in energ and interact strongl, the have a single nodal plane Fig. 19 x B 2 4 2 B 2 6 2

2b 3u MO Diagram 4 b 1u 3b 1u Combine orbitals of the same smmetr b3u there is onl one b3u orbital on B24 fragment the energ levels are almost degenerate, stabilisation is large b 2 b 1 b 2g b 3u b 3g b 2u 1b2g 1b 3g 1b 2u 3 b 3u the FOs are further apart in energ and interact strongl, there are two nodal planes exact energ odering difficult to predict, require a calculation 1b 3u b 1u 2b 1u the b 3u FOs are close in energ and interact strongl, the have a single nodal plane Fig. 19 x B 2 4 2 B 2 6 2

2b 3u MO Diagram 4 b 1u 3b 1u b 2g 1b2g b 3u Configuration b 2 b 3u 10e from B24 fragment and 2e from 2 =12e Onl MOs of the same smmetr mix 1b 3g must also be close in energ greatest between occupied and unoccupied orbitals b 1 b 3g b 2u 1b 2u 3 ag and b1u? 1b 3u b1u too far apart in energ ag both occupied b 1u 2b 1u NO mixing! 2 x B 2 4 B 2 6 2

2b 3u Analsis 4 b 1u 3b 1u b 2g 1b2g b 3u 4 of the occupied MOs are non-bonding with respect to the bridging atoms b 2 b 3u 1b 3g b 3g 3 b 1 1b 2u b 2u 1b 3u b 1u 2b 1u 2 Fig. 19 x B 2 4 B 2 6 2

2b 3u Analsis 4 b 1u 3b 1u b 2g 1b2g b 3u 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 B2 units (and 2) low energ for a LUMO can accept electrons without destabilising the molecule b 2 b 1 b 3u b 3g b 2u b 1u 1b 3g 1b 2u 2b 1u 3 1b 3u B26 2- is stable! 2 Fig. 19 x B 2 4 B 2 6 2

2b 3u Analsis 4 b 1u 3b 1u qualitative MO diagram b 2 b 2g 1b2g b 3u b 3u exact ordering can var 1b 3g the FOs are further apart in energ and interact strongl, there are two nodal planes b 3g 3 b 1 b 2u 1b 2u exact energ odering difficult to predict, require a calculation 1b 3u b 1u 2b 1u the b 3u FOs are close in energ and interact strongl, the have a single nodal plane Fig. 20 Fig. 19 x B 2 4 2 B 2 6 2

Ke Points 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 explain the bonding/antibonding qualities of a set of MOs and annotate a diagram showing the ke characteristics be able to represent complicated computed MOs in terms of LCAOs be able to discuss the bonding in B26 with respect to VSEPR theor, delocalisation, and MO theor. Be able to justif the stabilit of B26 2- be able to form a MO diagram for A22, A24, A26 and analse the MO diagram for information relating to structure and bonding

Finall 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!! http://www.huntresearchgroup.org.uk/