x find all of the symmetry operations/elements: o character table headings: E, 2C φ σ v, i, S φ C 2 φ

Transcription

1 Construct and annotate a valence molecular orbital diagram for the linear molecule Mg 2. Assume the 3pAOs lie deeper in energ than the Mg 3sAO and that the Mg and orbitals interact onl slightl. Mg is a main group metal so the valence AOs are included in the MO diagram are the 3s and 3p AOs. Etension (ver advanced!) Eperimentall it has been found that the heavier group II (Ca, Mg, Ba) halides deviate from linear, and are increasingl bent. A number of theoretical models have been proposed to account for this behaviour, one of them suggests that occupied daos on the heavier group II element can participate in bonding via miing with the HOMO region MOs. Another suggests that π-bonding interactions are enhanced on bending. Consider onl the HOMO region occupied MOs, distort the molecule b reducing the L-M-L angle and analse the resulting changes in these MOs, does the molecule appear overall stabilised or destabilised? Introduce dao contributions on the central element, and evaluate their effect on the stabilit of the distorted molecule. (I will be happ to look at and discuss our answers to this question with ou) 1

2 Forming a MO diagram 1. determine the molecular shape and identif the point group of the molecule 2. define the aial sstem 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 the MO diagram check-list! 9. analse the MO diagram 1. Determine the molecular shape and identif the point group of the molecule shape has been given: linear point group: D h 2. Define the aial sstem find all of the smmetr operations on the molecule define aial sstem: -ais aligns along the principle ais (highest smmetr ais) C Mg find all of the smmetr operations/elements: o character table headings: E, 2C φ σ v, i, S φ C 2 φ o the C ais is also a C 2, C 3, C 4, C 5... up to C ais, this is represented b the angle φ in C o smmetr elements each C 2 has an associated σ v plane infinte number C 2 therefore an infinite number σ v C 2 σ h σ v Mg C (), S Mg Mg σ v 3. Identif the chemical fragments, and put them along the bottom of the diagram Chemical fragments as, with atoms far apart and Mg a central Mg atom. First we need to construct an intermediate diagram for the 2 unit,, this is shown below. Then we will add the Mg cation fragment. 4. Determine the energ levels and smmetr labels of the fragment orbitals Intermediate diagram for fragment this is not 2 so looking for o good separation between atoms o orbitals that do not touch o almost degenerate energ levels in both 3s and 3p manifolds, the 3p π split less than the 3p σ because the individual are not smmetr fragments we combine FOs of the same smmetr (s, p, p and p ) and then we have to determine the smmetr of the resultant MO under the point group of the molecule o 1 totall smmetric is eas o the 1 has the same smmetr as the -ais 2

3 o the 2 has the same phase pattern as a d 2 AO o the π bonding MOs ( ) formed from the p and p AOs have the same smmetr as the and aes o the π anti-bonding MOs (π g ) formed from the p and p AOs have the same smmetr as the d and d AOs o the 2 MO maps onto itself under rotation about the -ais, so must be of σ tpe. It inverts under i so must be un-gerade (u) and is anti-smmetric under C 2 rotation so must be "plus" (). Thus this is a MO. smmetr labels for MOs are ALWAYS small letters, not capitals (important point!) (from talking with students it appears man of ou do not know the Greek letters, these can be found in the front of Atkins phsical chemistr (or look them up on-line). Greek letters are used commonl in equations in phsical chemistr and ou should know them (both capitols and normal)! looking for a large sp gap, the 1 and 2 should not be close, ideall a written comment on this either in tet or as an annotation there will be no s-p miing because (a) the large sp gap (cf O 2 and F 2 ) and (b) there are two bonds between the atoms. Thus the σ and π interactions will not split enough to drive the orbitals into a region where the can mi. AO contributions are equal because the fragments orbitals are degenerate 2 π g 3p 2 the MO splitting is etremel small becuase the atoms are far apart (1 mark) for this annotation these orbitals should not touch... the atoms are two far apart. 3p lies to the right of the PT, therefor sp splitting is ver large 3s 1 1 Figure 1 Intermediate diagram 3s the MO splitting is etremel small becuase the atoms are far apart, and these are saos (which are dense and do not etend far from the nucleus) (1 mark) for this annotation Then for the full MO diagram the question states that "the 3pAOs lie deeper in energ than the Mg 3sAO" o thus the Mg 3sAO must lie above the 3pAOs (the fragment barel interacts and so the Mg 3s will lie above the 2 fragment FO) the question states "a valence molecular orbital diagram" this implies: 3

4 o the use of all and onl the last shell principle quantum number orbitals, for this will be the 3s and 3p, for Mg this will be the 3s and 3p ONLY o Mg lies to the left of the PT, the sp gap is ver small, thus both the 3s and 3p AOs should be shown o Mg is a main group metal so we do not show the daos the question states "Construct and annotate " o 5 out of 20 marks were assigned for ke annotations o for eample from Lecture 3: I have annotated this MO diagram (the gre bits). I epect ou to annotate our MO diagrams, eplaining ke features. IMPORTANT! antibonding MO is alwas destabilised more than the bonding MO is stabilised 2b 1 b 1 4 FO left nonbonding in the first stage diagram 1b 2 3 1b 1 b 2 FOs are closer in energ and so the interaction between the orbitals is larger for the b 1 MO b 1 H O H 2 1 is the O 1sAO which is not shown because this is a valence MO diagram O O H H H H H 2 O Figure 2 Figure 8 from Lecture 3 showing annotations 4

5 use same molecular structure for all orbitals (important point!) o the nuclei are assumed stationar re the Born-Oppenheimer approimation UNLESS doing a correlation diagram. You cannot have nuclei in one position for one MO and then bonds stretched, contracted or moved out-of-plane for other MOs. Be consistent! o use place holders in the fragments and in the MOs this will stop ou from making mistakes when ou add FOs to form the full MO (a) (b) (c) Figure 3 (a) show change of alignment of molecule between MOs, (b) showing significant increase in atomic positions between MOs, (c) showing combination of AOs that is not linear 5

6 5. combine fragment orbitals of the same smmetr, estimate the splitting energ and draw in the MO energ levels and MOs (in pencil!) Mg 3p AO contribution is much larger because the orbital lies much higher in energ than the " 2 " FOs and this is an antibonding MO 3p 3s pi tpe interactions have a smaller splitting energ than sigma tpe interactions π g π g Mg MO splitting is small because of the large energ difference between the FOs (almost an ionic compound) " 2 " FO contributions to the final MO are much larger because these orbitals lie much deeper than the Mg ones, and this is a bonding MO Mg 2e Mg 16e 14e Figure 4 Annotated MO diagram the electronegative atom orbitals are too deep to interact with the electropositive Mg orbitals 6. determine the number of electrons in each fragment and hence the central MO region 2 fragment has 14e Mg fragment has 2e total is 16e 7. identif if an MO miing occurs, and redraw the MO diagram with the mied MOs miing must be between orbitals of the same smmetr that are not part of the same bondingantibonding pair, and is largest when the orbitals are close in energ, in the HOMO-LUMO region, and when one of the MOs is non-bonding or unoccupied. The π g MO could mi (occupied, non-bonding, in HOMO-LUMO region), but there is no unoccupied MO orbital of the correct smmetr to mi with this MO -> no miing 6

7 Marking Scheme Setup o 1 mark for point group o 1 mark for smmetr elements o 1 mark for define aial sstem and molecule orientation with respect to the aial sstem (0.5 if onl aial sstem is shown) o 1 mark for chemical fragments (0.5 if place-holders are not shown) Fragment Orbitals o 1 mark for 2 fragment energies (-0.5 if no saos or if saos are not deep, -0.5 splitting too large) o 1 mark for eplaining wh the splitting is so small, preferabl as an annotation o 1 mark for 2 FOs (-0.5 AOs too close or if orientation changes, -1 if LCAOs not used) o 1 mark for Mg fragment energies and FOs o 1 mark smmetr labels (-0.5 if capitols used, -0.5 for simple mistakes like missing u or g) Molecular Orbitals o 0.5 marks for interaction o 0.5 marks for interaction o 0.5 marks for interaction o 0.5 marks for rest o 1 mark for altering the AO sie to reflect epected coefficient sie o 1 mark for an annotation eplaining that the bonding MO has a larger contribution from the lower energ FO and the antibonding MO has a larger contribution from the higher energ FO o 1 mark smmetr labels (-0.5 if capitols used, -0.5 for simple mistakes like missing u or g) o 1 mark MO energies (-1 if the interaction is not small, -0.5 for using deep saos, -0.5 for not using Mg paos, or using Mg 2pAOs, -0.5 for onl using Mg 2p(σ) and not 2p(π), maimum loss is 1 mark) o 1 mark MO for eplaining, ideall as an annotation, wh there is onl a slight stabilisation, that is the MOs are far apart in energ o 1 mark for eplaining, ideall as an annotation, that the saos are too deep in energ to interact with the Mg FOs o 1 mark for eplaining, ideall as an annotation, that there is no miing because miing must be between orbitals of the same smmetr that are not part of the same bonding-antibonding pair, and is largest when the orbitals are close in energ, in the HOMO-LUMO region, and when one of the MOs is non-bonding or unoccupied. None of these conditions are satisfied for Mg 2 MOs. (Lecture 3) o 1 mark for correct electronic configuration o 1 mark for a diagram I could read that was relativel neat and tid Feedback given to students last ear which ma be helpful for ou. o The MO diagrams we create are based on the "linear combination of atomic orbitals (LCAOs) so ou should not combine the orbitals from different centers, see Lecture 4 Figure 7. If ou do this ou cannot accuratel determine bonding and antibonding interactions, and if forming intermediate diagrams ou will run into problems. o Deep AOs lead to a large electronegativit, the orbitals are deep and so it is hard to remove the electrons from the atom, the electronegativit is a result of orbital stabilit o Miing onl occurs between MOs, MOs do not mi with FOs o Use each FO ONLY ONCE, then invoke miing o It is ecellent that man students tried to interpret their diagram, however it is not appropriate to tr and work out the bond order for anthing other than a diatomic. 7

8 Etension for eperts! (voluntar). Eperimentall it has been found that the heavier group II (Ca, Mg, Ba) halides deviate from linear, and are increasingl bent. A number of theoretical models have been proposed to account for this behaviour, one of them suggests that occupied daos on the heavier group II element can participate in bonding via miing with the HOMO region MOs. Another suggests that π-bonding interactions are enhanced on bending. Consider onl the HOMO region occupied MOs, distort the molecule b reducing the L-M-L angle and analse the resulting changes in these MOs, does the molecule appear overall stabilised or destabilised? Introduce dao contributions on the central element, and evaluate their effect on the stabilit of the distorted molecule. (I will be happ to look at and discuss our answers to this question with ou) stabilisation of pi orbitals due to increased L-L through space bonding overlap b 1 there ma be additional interactions but it is difficult to determine these d 2-2 -> d -> a 2 a 2 π g b 2 d -> b 2 b 1 d -> b 1 in general stabilisation primaril due to increased L-L through space bonding overlap d 2 -> in general stabilisation occurs due to in-phase overlap of dao lobes with L FOs L M L D h without miing L M C 2v L with miing L M C 2v overall stabilisation is approimatel equal to destabilisation Figure 5 Correlation MO diagram L overall dao miing has increased bonding overlap and stabilised these orbitals 8