Fragment Orbitals for Transition Metal Complexes

Transcription

1 Fragment Orbitals for Transition Metal Complees Introduction so far we have concentrated on the MO diagrams for main group elements, and the first 4 lectures will link into our Main Group chemistr course now we will concentrate on the MO diagrams for TM complees, and the net 4 lectures will link into our TM and Organometallic and our Crstal Architecture chemistr courses areas we don t have the space to cover are cluster MOs (ver interesting!) and etended sstem MOs (solid state, polmers, conjugated sstems). However with the knowledge gained from this course ou should be able to delve into these areas if ou are interested IMPOTANT! Fragment Orbitals of the Metal transition metals (TM) are electropositive thus the valence FAOs are high in energ the energ levels included for the TMs differ from the main group o the active electrons for bonding are in the 3d (or 4d) shell, and thus these AOs are included in the valence MO diagram o the occupied 3s and 3p AOs are too deep in energ to participate in bonding and are ignored o however the vacant 4s and 4p AOs are ver close in energ to the 3dAOs and we do include these AOs in valence MO diagrams that include TMs the smmetr labels s, p and d refer to spherical smmetr and in an MO diagram the new smmetr labels for the TM AOs must be determined using the point group smmetr of the molecule and our character tables o for eample, metals are often in an octahedral environment (si coordinating ligands, Figure 1) o determining the smmetr of the daos is eas; read the smmetr from the character table, d, d and d Þ t 2g and d 2-2 and d 2 must be degenerate so we choose Þ e g Figure 2 o the sao must be totall smmetric Þ a 1g and paos transform as the, and aes Þ t 1u smmetr ou should know the shape and phase of the daos o positive along the ais associated with the label o ie d 2-2 positive on ais and negative on ais o positive in the quadrant associated with the label o ie d is positive in the positive quadrant d d 2 d Figure 1 coordinate sstem 4p 4s 3d e g Figure 2 Metal orbital energies and smmetr for the O h point group Figure 3 daos M t 1u a 1g t 2g d 2-2 d Hunt / ecture 5 1

2 metal so include the unoccupied s and p orbitals in MO diagram p -> σ u, π u M M s -> σ g smmetr lables from the D h character table (using short cuts) d -> σ g, π g, δ g Metallic Dimers before we move on to octahedral TM complees we will consider the simpler case of a metallic dimer. Metals do not generall form unsupported dimers, however M-M bonds are a relevant feature of a significant number of multicentred TM complees M M M homonuclear diatomic -ais is the principle ais and lies along the bond M dao-dao splitting is ver small epand Figure 4 building the M 2 energ diagram to understand M-M fragment bonding we start b building a fragment energ diagram, Figure 4 o a fragment energ diagram includes all the energ levels and perhaps some of the ke MOs, this is in contrast to a MO diagram which includes illustrations of all MOs. o M 2 is a homonuclear diatomic and has D h smmetr, as a first guess orbital smmetries can be read off the character table, daos have s g p g and d g smmetr labels. o d-d AO interactions are ver weak compared to sao and pao interactions, tpicall we artificiall epand the d-d region of the diagram for ease of interpretation Figure 5 is a MO diagram showing the epanded d-d region of the M 2 energ diagram o as with main group elements FOs are combined once in-phase and once out-ofphase d -> σ g, π g, δ g δ-tpe d d 2-2 π-tpe d d σ-tpe d 2 Figure 5 epanded dao region of the M 2 MO diagram Hunt / ecture 5 2

3 IMPOTANT! determining the smmetr of the final MOs can be daunting initiall, however if ou know where to look and use short-cuts it becomes easier o first remember that the labels s and p are often applied to represent the changes in phase of orbitals on rotation around a bond (Figure 6) even when the molecule does not have D h smmetr! (just think of organic chemistr) o use the phase pattern of the orbitals closest to the centre of the bond where the ais origin resides, to determine the MO smmetr, Figure 7a σ-tpe smmetric for rotation about -ais π-tpe single phase change on rotation about -ais δ-tpe two phase changes on rotation about -ais Figure 6 smmetr labels σ-tpe σ u -ais phase pattern π-tpe π g d and d phase pattern δ-tpe δ-tpe π-tpe σ-tpe d d 2 d d 2-2 d δ u δ g π u σ g must be δ and inverts under i d and d 2-2 phase pattern -ais and -ais phase pattern totall smmetric M M Figure 7 (a) smmetr labels of the MOs for M 2. Ais origin shown b black dot in the centre of the bond, and (b) the first ambient conditions stable quintuple bond =isopropl. Cr Cr The quintuple M-M bond!! (bond order of 5) o understanding the MO structure of TMs lead to the prediction of M-M dimers that π u could bond orders of 4, 5 and 6! o in a metal if all the bonding dao MOs are occupied (and all the antibonding MOs are δ u vacant) then the bond order can potentiall d -> σ g, π g, δ g reach a maimum of 5, the electronic configuration for the dao based δ g manifold of MOs is s 2 p 4 d 4, (Figure 8) o a quintuple bond at ambient temperature π u was first reported for a stable dichromium M M compound in 2005 (Figure 7b), links to the original Science paper on m web-site σ g o if the higher 4s (or 5s) also interact and the M M M M bonding MO is occupied a potential bond Figure 8 quintuple M-M bond order of 6 can be obtained o [e 2 Cl 8 ] 2- forms a quadruple M-M bond, and Mo 2 and W 2 form a setuple bond at ver low temperatures. Hunt / ecture 5 3 σ u

4 H 1s AO IMPOTANT! igand Fragment Orbitals and Smmetr Adapted Orbitals smmetr can be used to determine smmetr adapted orbitals Figure 9 smmetr adapted orbitals for a ring smmetr adapted p AOs smmetr adapted saos Figure 10 smmetr adapted FOs based on paos, and miing of degenerate orbitals degenerate equivalent set of degenerate orbitals if ou want to know more about how these are derived look on m web-site under the first problems class from Figure 9 ou need to know the smmetr adapted orbitals up to 4 and ou should be familar with those up to 6 o smmetr adapted orbitals are general and can be used with an tpe of MO diagram; organic, main group and TM o ou have alread meet those for 2 and 3, we will be using those for 4 in the net few lectures useful facts about smmetr adapted orbitals: o once ou know the smmetr adapted orbitals for the saos ou also know them for the p AOs, Figure 10a o degenerate orbitals can be rotated or mied with no cost in energ, ou will see this most often for the degenerate smmetr adapted orbitals of 4, Figure 10b the 6 orbitals above are for a planar molecule like benene. However in a TM the 6 orbitals are 3D! the smmetr adapted 6 orbitals for ligands in an octahedral (O h ) comple are shown in Figure 11, ou need to know these orbitals. o there are tricks to help ou remember! o the first MO is all inphase and totall e g smmetric Þ a 1g t 1u o the net three MOs have the same phase pattern as a 1g the,, -aes Þ t 1u o the net MO has the same phase pattern as a d 2 AO Þ e g o the last MO has the same phase pattern as a d 2-2 AO Þ e g Figure 11 smmetr adapted orbitals for octahedral ligands Hunt / ecture 5 4

5 IMPOTANT! Isolobal Analog man ligands can be approimated b the orbital diagrams we have alread seen; E 2, E 2, E 3, for eample CO, OH 2 and NH 3 and the more comple analogues EX, EX 2 and EX 3 (X=an element with paos) to form the TM MO diagram we use the MO diagrams of the ligands as fragments however, not all of the orbitals of a ligand will interact with a central TM, the energ of the TM daos is high, tpicall onl the highest energ FOs of a ligand contribute to the TM diagram for man ligands the ke MO is an orbital which has "sigma" like characteristics o for eample in [Co(NH 3 ) 6 ] 3 the HOMO of the ammonia molecule, has s-like characteristics, Figure 12 o however the high energ orbital must have the right smmetr to interact, so it is not alwas the HOMO, for eample, in the case of OH 2 it is the HOMO- 1 that is important we sa these s-like orbitals are isolobal to the simpler saos o from the perspective of the metal "looking out toward" the ligand, the ligand FO looks like an sao. o isolobal with the orbitals of EH 3 are those of NH 3, N 3, PH 3, P 3 and even C 3 and Si 3 where there is onl a single electron in this FO we build the TM MO diagram using a smmetr adapted combination of the ligand s-like FOs, Figure 13, compare this diagram with Figure 11. o these smmetr adapted sigma orbitals are ver important, we will be using them etensivel, memorie them! 1b 2 3a 1 Figure 12 the HOMO of EH 3 and HOMO-2 of EH 2 ligands e g t 1u a 1g Figure 13 isolobal smmetr adapted orbitals for octahedral ligands what energ ordering can we epect for the ligand orbitals? o the orbitals are "two bonds" apart, ie the are distant and so will not interact strongl, thus the will all be ver close in energ o the a 1g is totall bonding and will lie deepest due to through space interactions o the t 1u FO are essentiall non-bonding o the e g FOs will be slightl higher in energ due to through space antibonding interactions ligands that have p and p* FOs are also important, we will be looking at these in a later lecture Hunt / ecture 5 5

6 The Octahedral Point Group to understand TM bonding we need to understand the O h point group (Figure 14) as this will determine the smmetr of the orbitals. O h E 8C 3 6C 2 6C 4 3C 2 i 6S 4 8S 6 3σ h 6σ d h=48 A 1g A 2g Eg T 1g T 2g A 1u A 2u Eu T 1u T 2u ( ) ( , 2-2 ) (,, ) (T, T,T ) 2 nd ear Crstal and Molecular Architecture course Figure 14 O h character table as an inorganic or materials chemist the octahedral point group is one of the most important, Figure 15 o a vast number of TM or organometallic compounds are octahedral, or are complees that can be related to octahedral such as square planar o man clusters can be understood using smmetr arguments developed from octahedral cage clusters. o an octahedral arrangement is one of the fundamental building blocks for solid state structures particularl that for the face centred cubic cell. o the centre of a cube of atoms is the equivalent of an octahedral interstitial site for solid state structures Figure 15 (a) transition metals compounds, (b) cluster compounds, (c) face centred cubic (d) octahedral interstical sites there are two useful was of drawing an octahedral molecule, Figure 16 each places emphasis is on a different aspect of smmetr o a "cube" where the molecular atoms or ligands occuping the centre of each face, emphasising the C 4 and C 2 aes, Figure 16(a) o the "double prism" emphasises the C 3 aes, Figure 16(b) (b) Figure 16 Octahedral geometries Hunt / ecture 5 6 M M (a)

7 the ke smmetr operations in this group are E 8C 3 6C 2 6C 4 3C 2 i 6S 4 8S 6 2s h 6s d o remember from ecture 1 and the D 3h point group that the number in front tells us the number smmetr elements o there can be multiple smmetr elements (ie 3C 2 aes in D 3h ) or there can be a single element with multiple operations (ie 2C 3 where C 3 1, C 3 2 operations about a single C 3 ais are counted in D 3h ) o onl new unique smmetr operations are counted in a character table, thus if a smmetr element has alread been found (and recorded in the smmetr operations to the left) it is not added to the character table. I epect ou to know and be able to show all the operations of the O h point group, if ou need some help there is an etra document on the web-site that steps through these in detail! Decent in Smmetr TM complees are not alwas octahedral o mied s-donor ligand complees can occur such as [Co(H 2 O) 2 (NH 3 ) 4 ] 3 o some complees have onl 4 s-donor ligands, for eample NiCl(PPh 3 ) 2 o it is important to be able to determine the MO and energ diagrams for complees with a lower smmetr than O h a higher smmetr group has more smmetr operations, a lower smmetr group has fewer smmetr operations o a lower smmetr group can be a sub-group of a higher smmetr group o when different smmetr elements are lost, different sub-groups occur o we sa there has been a descent in smmetr, Table 1 C 2v C 2 C s C 3v C 3 C s C 4v C 4 C 2v D 3h C 3h C 3v D 3 C 3 also C 2v D 4h D 2d D 2h D 2 C 4h C 4v C 2v D 4 C 4 S 4 C 2h C 2 C s C i D 6h D 3d D 2h C 6v C 3v C 2v C 2h D 6 D 3h C 6h C 6 C 3h D 3 S 6 D 2 C 3 T d D 2d C 3v C 2v also S 4 D 2 C 3 C 2 C s O h T d D 4h D 4 D 2d C 4h C 4v D 2h D 2 C 2h D 3d D 3 C 3v S 6 C 3 also C 4 S 4 C 2v Table 1 A selection of eamples showing descent in smmetr, descent after C 2v, C 3v are assumed for the higher point groups. for eample, the D 3h point group has man different sub-groups: C 3h, C 3v, C 3, C s, D 3, C 3, C 2v and C 2 o the D 3 point group has operations E, C 3 and C 2 where the smmetr elements s h, S 3 and s v have been lost o the C 3h point group has operations E, C 3, s h and S 3 where the smmetr elements s v and C 2 have been lost Hunt / ecture 5 7

8 ou have alread seen descent in smmetr in action in the correlation diagrams (D h ->C 2v and D 3h ->C 3v ), the effect of a distortion is to eliminate one or more smmetr elements in the contet of TM ' σ chemistr we are interested M σ M σ in the descent of smmetr M σ of the octahedral point group, Figure 17 O h ' σ D 4h D 4h as the ligands in the TM ' σ comple are differentiated M σ σ M σ the smmetr drops we work out the reduction in smmetr of the FOs and O h C 4v then MOs from O h to the Figure 17 drop in smmetr for TM complees new point group Ke Points be able to draw MO diagrams that include daos be able to eplain s, p and d interactions for daos be able to draw energ and/or MO diagrams for homonuclear and heteronuclear diatomics including M 2, MM and ME (as well as EE and E 2 ) where M,M are metals and E,E are main group elements. be able to discuss bond order with respect to diatomic molecules, and be able to eplain wh bond order cannot be etended to larger molecules be able to draw and use the ligand smmetr adapted fragment orbitals for rings n n=1-4, and 6 in an octahedral arrangement be able to eplain and use the isolobal analog be able to eplain wh the octahedral point group is ver important for inorganic chemistr be able to locate all of the smmetr elements of the O h point group and be able to draw diagrams showing the action of the O h point group smmetr operations on molecules and fragment orbitals be able to describe a descent in smmetr Self-Stud Problems / Eam Preparation Draw the MO diagram for Mo 2 and show that a setuple bond order is potentiall possible. Use the long method to show that the M 2 dimer d/d combination of AOs has p u smmetr. Clearl show using diagrams that S 4 2 = C 2 and S 4 4 = E Thus, showing that there are 2 unique operations per S 4 ais in the O h point group. Clearl show using diagrams that S 61 and S 6 5 = S 6 1 are the onl unique operations for each S 6 ais in the O h point group. Which smmetr operations are lost from the D 6h point group to generate the C 3v point group? Hunt / ecture 5 8