Figure 1 Correlation diagram for BeH 2

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1 Self-Stud Problems / Eam Preparation revise our computational chemistr workshop from last ear: o make sure ou have checked that the molecule is optimised o carr out the frequenc analsis and ensure that all the vibrational modes are positive o then perform the calculation which stores all the molecular orbital information pop=(full,nbo use qualitative MO theor to predict if e 2 will be bent or linear. o assume that we can appl the same MO diagram as generated for 2 O o note that because e is less electronegative than the orbital coefficients for the MOs will change, Figure 1 o the occupation is different! Figure 1 Correlation diagram for e 2 o e 2 will be linear o the stabilisation of the MO which occurs in 2 O because of miing does not occur in e 2 because the the 1 orbitals are not occupied and hence significant miing cannot occur o in addition it is the stabilit or instabilit of the and 1b 1 under the distortion which determine the structure o in the diagram above I have shown a slight miing of the and, this is because all orbitals of the same smmetr actuall interact slightl, thus on an distortion a slight amount of stablisation ma occur, however in this case this should be tin. 1

2 o on moving awa from linear the is stabilised b overlap of the 1sAO contributions, but the 1b 1 is destabilised b more due to the antibonding overlap of the 1sAO and reduction in overlap with the pao on the e. optimise e 2 using the 3LYP method and 6-311G(d,p basis set, confirm ou have a minimum structure. Compute the MOs using pop=(full,nbo, visualise orbitals 1-7 and compare them to our qualitative MO diagram o the orbitals for the optimised linear structure are shown on the MO diagram above, Figure 1 draw and annotate the MO diagram for linear water O, using this diagram eplain if linear C 2 is epected to diagmagnetic or paramagnetic o the MO diagram for linear water O is shown in, Figure 2a o note that I have not annotated this diagram, students are epected to annotate diagrams in the eam O 2 C 2 O C O C Figure 2 MO diagrams for (a linear 2 O and (b linear C 2. o C is more electronegative than and thus the linear 2 O MO diagram can be used to understand C 2 fragments (MO diagrams appl to molecular fragments as well as stable molecules, Figure 2b o in linear C 2 two electrons go into a degenerate set of π orbitals, the electrons will remain unpaired and thus linear C 2, if it eisted would be paramagnetic o however as we have a partiall filled degenerate orbital we could epect vibronic coupling to lower the smmetr and then orbital miing (analogous to that found in 2 O to split the degenerac. In this case these electrons would now pair in the lower ling MO and bent is C 2 diamagnetic. (bent C 2 MO diagram not given 2

3 (do AFTER the problems class draw a MO diagram for planar D 3h 3 o The problems class involved the first step in this process, drawing the MO diagram of 3, however, is less electronegative than and so we need to alter the diagram, Figure 3 o ke differences are ² shifting of orbital levels, valence moves down ² larger sp gap in ² has more electrons than and so now the 1a 2 level is filled o note carefull the changes in orbital composition (ie the largest contributing FO to each MO, the shift in energies and that in the D 3h structure the OMO and LUMO cannot mi because the are of different smmetr antibonding MO is destabilised more than bonding MO is stablised 2 e e out-of-phase overlap =>antibonding MO e 3 1 a 2 a 2 larger contribution from 3 becuase this FO is closer in energ non-bonding MO 1 e p (p,p e a 2 e in-phase overlap => bonding MO FOs are close in energ hence roughl equal contribution to the MO the large sp gap and electronegative nature of mean the 1s is relativel deep 2 significantl larger contribution from becuase this FO is much closer in energ Figure 3 MO diagram for D 3h 3 3

4 (do AFTER the problems class draw the correlation diagram for the distortion of 3 from D 3h to C 3v o The above question involved the first step, drawing the high smmetr MO diagram o Then we have two options: 1. determine the MO diagram for trigonal pramidal A 3 from scratch 2. use the MO diagram we have constructed and evaluate changes to MOs o Option 2 is often more useful when forming a correlation diagram, Figure 4 o the far right column of Figure 4 shows the centre of the MO diagram for trigonal planar A 3, A more electronegative than o remember when the shape of a molecule is distorted the AO components move with their atoms, the do not change direction or orientation. 2 e maimium distortion will occur for occupied and empt 3 1 a 2 1 e 2 A θ >90 θ =90 θ=pramidalisation angle C 3v D 3h A Figure 4 Correlation diagram for pramidalisation o first the shift in the energ levels can be determined solel b evaluating changes that occur in overlap and overall bonding character of a MO on distortion. ² the ' MO is slightl stabilised due to an increase in the (through space sao bonding overlap, this is a result of the atoms getting slightl closer together as the molecule distorts. There is also a slight decrease in the bonding overlap of the central element sao with the saos and so overall the stabilisation is not large. ² the ' MOs are destabilised due to a reduction in the bonding overlap of the central element pao with the saos, and an increase in the through space sao antibonding interaction, both interactions contribute to destabilisation and hence the shift in energ is larger than for the ' MO. The converse is true for the ' MOs. ² the 1a 2 " MO is non-bonding and so the energ of this MO does not change 4

5 o there is also a change in point group on distortion from D 3h to C 3v, and the smmetr labels of the orbitals change ² there is no significant effect on the e'->e MOs, or in the deep ling ' -> MO ² however 1a 2 " (D 3h MO becomes (C 3v, and ' (D 3h MO becomes (C 3v. ² these orbitals now have the same smmetr and can potentiall mi, the etent of miing is determined b the rules outlined in Lecture 3: o Rules for MO miing: ² onl MOs of the same smmetr can mi ² miing must stabilise the total energ of the molecule ² miing tends to be large when at least one of the following criteria are met: o MOs are close in energ o one of the MOs is non-bonding or unoccupied o MOs are in the OMO-LUMO region o we evaluate the effects of miing between the and (C 3v MOs (Figure 5 and include them on our diagram (Figure 3. ψ ( ψ ( ψ 1 = ψ ( ψ ( 3 ψ ( ψ ( ψ 2 = ψ ( ψ ( Figure 5 Miing of the and MOs for 3 o It is important to realise that miing will be small unless there are electrons in the LUMO, this is wh 3 is pramidal while 3 is planar! o 3 has 6e (3 from and 3 from 3 which fill this diagram to the ' (or level. On distortion the ' level is destabilised, more than the ' is stabilised and hence 3 prefers to remain planar. o 3 has 8e (5 from and 3 from 3 which fill this diagram to the level. While the MO is not stabilised b the geometr change, the loss of smmetr means that miing can now occur between the occupied and unoccupied MO. This miing is ver strong and stabilises the MO substantiall and hence 3 is trigonal pramidal and not planar. o comparing the orbitals that mi from 3 to 3 it is clear there is a stronger bonding and antibonding interaction between the and 3 than found between and 3, Figure 6 ψ ( ψ ( ψ 1 = ψ ( ψ ( 3 ψ ( ψ ( ψ 2 = ψ ( ψ ( Figure 6 Miing of the and MOs for 3 5

6 (do AFTER the problems class discuss the bonding and structure of the acid-base aduct 3 3 o 3 in the gas phase is planar while 3 is trigonal pramidal, on forming the aduct the overall smmetr of the molecules will be reduced, the smmetr becomes C 3v, this will change the smmetr of the contributing orbitals. σ v σ v σ v σ( σ v mirror in the plane with each pair of C 3 ( Figure 7 Smmetr of 3 3 o to a first approimation we can consider 3 3 as the MO diagram between two fragments 3 and 3. o the reduced local smmetr of the 3 fragment changes the smmetr labels for the MOs allowing the OMO and LUMO to mi, nevertheless without an occupation in the 2a 2 (now the this is not favoured o however there will be an interaction between the OMO of 3, and the low ling 2a 2 LUMO on 3, electrons will flow downhill and the resulting MO that forms can be thought of as partiall occuping the empt 2a 2 LUMO (now the on 3 4e 3e 6 5 LUMO OMO 1 Figure 8 Smmetr of 3 3 6

7 ² thus the base has donated electrons into the D 3h 1a 2 LUMO if 3 and miing is now favoured leading to distortion of the 3 molecule. The more electron densit transferred into the 1a 2 " LUMO of 3 the greater the miing that can occur and the larger the stabilisation and the greater the structural distortion. ² the electrons removed from the on 3 ma lead to a reduction in miing and the molecule will become less pramidal. The etent of distortion of the 3 and 3 molecules in an acid-base adduct can be correlated with the basicit of the base! ie the amount of electron densit donated from the base into the LUMO of 3 o the realit of the orbital interactions is more comple than this simple argument would present. All of the MOs can mi, and this leads to a rather comple set of MOs. Moreover the OMO of 3 is ver stable. One wa to rationalise the final computed MOs is to consider the interaction of the 3 OMO with the MO of 3. oth of these orbitals are occupied however it is the stabilisation of the antibonding pair b MO miing with the 3 LUMO that leads to the stabilisation of the molecule, Figure 9 4e 6 5 3e miing LUMO OMO Figure 9 Computed MOs of 3 3 7