MO Diagrams for O 2 and N 2

Transcription

1 MO Diagrams for O 2 and N 2 Drawing MO diagrams - always same number of MOs as AOs. - more electronegative element on the right - lower in energy O 2 σ* 2p Paramagnetic Bond order of 2 (O=O) 2p π* 2p π 2p 2p larger ΔE σ 2p σ* 2s 2s 2s σ 2s O O 2 O N 2 σ* 2p Diamagnetic Bond order of 3 (N N) 2p smaller ΔE π* 2p σ 2p π 2p 2p Very strong NN bond Unlike O 2, the σ 2p and π 2p orbitals are switched in energy (see next page) HOMO = σ 2p, LUMO = π* 2p 2s σ* 2s 2s σ 2s N N 2 N

2 MO Diagram for CO σ* 2p 2p π* 2p LUMO σ 2p 2p HOMO (slightly antibonding) π 2p 2s σ* 2s 2s σ 2s C CO O - CO is isoelectronic with N 2 (C has one less electron than N, O has one more) MO diagram is very similar to that of N 2. - Diamagnetic, Bond order of 3 (C O) - Important: HOMO = σ 2p (weakly antibonding), LUMO = π* 2p (strongly antibonding) - Since O is far more electronegative than C, would expect a large dipole moment with δ- on O. However, CO actually has only a small dipole moment (0.1 Debye) with the δ- on Carbon! Usually electronegativities are a good indication of the direction and magnitude of the dipole on a molecule, but especially in molecules where orbitals with antibonding character are occupied, things are not so straightforward Ordering of MOs in O 2 is σ 2p, π 2p, π* 2p, σ* 2p but in N 2 and CO, the order is π 2p, σ 2p, π* 2p, σ* 2p Reason - O 2 - larger ΔE between s and p orbitals less orbital mixing - larger ΔE because across the period (B,C,N,O,F) more protons added to the nucleus, which pulls the electrons in closer to the nucleus (lower energy). This effect is felt more strongly by the s-orbitals than the p-orbitals, so the energy of the s-orbitals drops more rapidly than that of the p-orbitals. - N 2 and CO - mixing between the σ 2p and the σ* 2s orbitals raises the energy of the σ 2p above the π 2p.

3 Crystal Field Theory Very wrong theory (for transition metal organometallic chemistry), but quite useful. Easy way to roughly predict the ordering of the energy levels for a TM compound. - Ligand lone pair thought of as a point charge (e.g. for Cl -, H - or CN - ) or the partial negative charge of a dipole (e.g. for :OH 2, :NH 3 or :PF 3 ). - Ligands attracted to the TM cation since they are point charges purely electrostatic bonding assumed. - Any interactions between the electrons of the ligand and those of the metal are repulsive no covalent bonding (σ, π or δ) exists according to this theory!!! d z2, d x2-y2 axial, e g Δ o TM d-orbitals inter-axial, d xz, d yz, d xy - The axial orbitals (e g symmetry in an octahedral environment) point directly towards the ligands so according to crystal field theory, are raised in energy (unfavourable interaction between the electrons of the ligands and those of the metal) - The inter-axial orbitals ( symmetry in an octahedral environment) do not point directly towards the ligands, so are lower in energy than the axial orbitals.

4 Crystal Field Theory Square pyramidal and Square Planar Geometry from Octahedral d x2-y2 d z2, d x2-y2 d x2-y2 large ΔE d z2 Δ o d xy d z2 TM d-orbitals d xz, d yz, d xy d xy d xz, d yz d xz, d yz M M M octahedral square pyramidal square planar - From the octahedral crystal field splitting diagram, pull off one of the ligands along the z-axis. - Since this partly removes an unfavourable (according to CF theory) interaction in the z-direction, all orbitals with a z-component (d z2, d xz and d yz ) fall in energy. The others go up in energy. - Removing the other ligand on the z-axis has the same effect, leading to the energy level diagram for a square planar complex. Note the large energy gap between the d xy and d x2-y2 orbitals. As a result, square planar complexes are almost exclusively those of d 8 metals (all metal orbitals are filled except the d x2-y2 ) and so have 16 electrons rather than 18. See later. - Crystal field theory is therefore quite useful for quickly predicting the order of the energy levels in transition metal complexes. However, the assumption that all bonding is ionic and no covalent interactions occur is unrealistic. According to this assumption, CO (an excellent ligand for reasonably electron rich metals) would be predicted to be a terrible ligand (no negative charge and v. small dipole), ligands would not be expected to bond to metals that do not have a formal positive charge (i.e. Pd(PPh 3 ) 4 and Fe(CO) 4 2- would definitely not exist), ligands cannot be σ-donors, π-donors or π-acceptors, and it is therefore impossible to assess why Δ o varies with the ligands as it does.

5 Crystal Field Splitting Diagram for Tetrahedral Geometry OCTAHEDRAL TETRAHEDRAL Inter-axial orbitals point more directly at the 4 ligands more of an unfavourable interaction between the ligand electrons and those of the metal higher in energy Axial orbitals point less directly at the 4 ligands less of an unfavourable interaction between the ligand electrons and those of the metal lower in energy t 2 d orbitals Δ t ~ 4/9 Δ o e Δ t is much smaller than Δ o partly because none of the metal orbitals point directly at the ligands, so overlap is less efficient. M [ML 4 ] The same type of approach can be extended in order to figure out the splitting pattern of the d-orbitals for a variety of other common geometries. Starting from octahedral, one can derive Jahn-Teller distorted octahedral geometry, square pyramidal and square planar geometry. By placing the ligands either in the 8 corners or on the 12 edges of a cube, one can derive the crystal field splitting diagram for 8-coordinate cubic or 12-coordinate cube-octahedral geometry (similar approach to that used for tetrahedral geometry). The splitting pattern for trigonal planar geometry can be derived by considering which orbitals or groups of orbitals point most directly towards the ligands. A similar approach can be used for trigonal bipyramidal geometry, although the actual ordering of the orbitals is more difficult to rationalise using such simple arguments.

6 MO theory ~ Ligand Field Theory Constructing an MO diagram for an octahedral complex Symmetry Adapted combinations of Ligand σ-orbitals in an Octahedral Complex - In an octahedral environment, the metal orbitals (3d, 4s, 4p for a 1 st row TM) divide by symmetry into 4 sets: s = a 1g, p = t 1u, axial d = e g, inter-axial d =. - The orbitals of the six ligands can be combined to give six symmetry-adapted linear combinations which are of the correct symmetry to interact with the s, 3 x p and 2 x axial-d orbitals, but not the inter-axial d orbitals. - The result is that 3 orbitals (the inter-axial d-orbitals) are non-bonding, while the rest (6 metal orbitals and 6 ligand orbitals) combine to form six bonding and six anti-bonding MOs. See next page. - This is a much more correct approach than crystal field theory, but is not as easy to use.

7 MO energy levels for an octahedral complex (only σ-bonding considered) t 1u * 4p (t 1u ) a 1g * 4s (a 1g ) e g * Δ O 3d (e g + ) (a 1g + t 1u + e g ) e g TM t 1u 6 L a 1g The six bonding orbitals are filled with 12 electrons from the six ligands Orbitals shown in red ( and e g *) are the frontier orbitals where d-electrons reside.

8 π-bonding ligands (the above MO diagram does not take into account π-bonding) filled orbital empty orbital M L M L M L σ-donor π-donor π-acceptor NH 3, CH - 3, H - Cl -, OH -, NR - 2, OH 2 CO, NO +, CN - For π-acceptor ligands, the bonding is SYNERGIC: σ-donation to the metal strengthens π-backbonding to the ligand, and π-donation from the metal to the ligand strengthens the σ-donor component of bonding. This is because σ-donation leads to increased electron density on the metal, which allows increased π-backdonation. Conversely, π-backdonation reduces the amount of electron density on the metal, which allows more σ-donation from the ligand to the metal. Cr(CO) 6 : Octahedral complex with good π-acceptor ligands σ-interaction π-interaction M lobe of acceptor orbital (whole orbital not shown) C O slightly antibonding HOMO of CO M C O M C O axial d-orbitals strongly antibonding π* orbitals of CO Note: The 12 empty π*-orbitals of the six CO ligands in a molecule like [Cr(CO) 6 ] can be combined to form 12 linear combinations of orbitals (3 x T, 3 x T, 3 x T, 3 x T ). Only the three linear combinations with T 2g symmetry are of the correct symmetry to interact with the orbitals (d, d and d ) on the metal. xy xz yz 1u 2g 1g 2u

9 MO energy levels for an octahedral complex with π-acceptor ligands (e.g. [Cr(CO) 6 ]) t 1u * 4p (t 1u ) a 1g * 4s (a 1g ) * e g * π* orbitals of CO ( ) 3d (e g + ) large Δ O e g (a 1g + t 1u + e g ) Cr t 1u 6 CO a 1g π-backdonation to CO from the orbitals (which are non-bonding in the absence of π-interactions between the metal and the ligands). The 3 orbitals and 3 high lying π* orbitals of the CO ligands form 3 bonding MOs and 3 antibonding MOs. Since the CO π* orbitals are empty, the d-electrons occupy the bonding MO from this interaction. The result is (1) a very large Δ o, so the e g orbital is likely to remain empty. (2) the orbital is strongly bonding (wants to be filled with 6 electrons) complexes of strong π-acceptor ligands are the most likely to obey the 18 electron rule

10 Simplified picture of how π-acceptor and π-donor interactions affect the MO diagram - Only the frontier orbitals are shown * e g * e g * π* ( ) L TM complex with σ-bonding only large Δ O [Cr(CO) 6 ] with π-backdonation from Cr to CO π-acceptor ligands increase Δ O e g * e g * small Δ O π-donor ligands decrease Δ O * TM complex with σ-bonding only TM complex with π- donation from LigandtoMetal L π -donor ligands π-donation from the ligands to the orbitals the 3 metal orbitals and 3 low lying, filled ligand orbitals of π-symmetry form 3 bonding MOs and 3 antibonding MOs. Since the interacting ligand orbitals are full, these electrons occupy the bonding MO from this interaction, and the d-electrons occupy the antibonding MO. The result is (1) a small Δ o (2) the orbital is weakly antibonding

11 The Spectrochemical Series of Ligands Using MO theory (Ligand Field Theory) instead of Crystal Field Theory, we have seen that ligands can be σ-donors, π-donors or π-acceptors, and that the nature of the ligands strongly affects Δ o in octahedral complexes. This effect can often be seen visually: e.g. for [Co III X(NH 3 ) 5 ] n+ (a d 6, 18-electron complex). X n Colour of Colour the absorbed complex I - 2 Purple Yellow Cl - 2 Pink Green NH 3 3 Yellow Blue d Δ o e g The colo ur of the complexes above results from promotion of an electron from the orbital to the e g orbital. The energy of light absorbed therefore corresponds to the size of Δ o. [Note: this type of simple treatment can only be applied in certain cases (e.g. d 1 or d 9 complexes and octahedral 3d complexes with a d 4 or d 6 configuration). For other configurations, it is necessary to consult a Tanabe-Sugano diagram and apply a more rigorous treatment]. For complexes with a single absorption in the visible region of the spectrum, the colour of light absorbed can be determined from the colour wheel (the colour of the light absorbed is found opposite the colour of the complex) Since the order of energy is blue > green > yellow, then the NH 3 complex can be seen to have a larger Δ o than the Cl - complex, which has a larger Δ o than the I - complex. Since the effect of the ligands on the size of Δ o is a visible change, the resulting series of ligands is called the spectrochemical series. The order of ligands in the spectrochemical series follows their behaviour as π-donors, σ-donors or π-acceptors very nicely. For Δ o : I - < Br - < S 2- < SCN - < Cl - < F - < OH - < OH 2 < MeCN < NH 3 < PR 3 < CN - < CO < NO + good π-donors OK π-donors σ-donors good π-acceptors However, these π-affects are not the whole story, because organometallic ligands such as CH 3 - or H - are located high in the spectrochemical series (H - is similar to CO). Both H - and CH 3 - (in the absence of α-agostic interactions) are purely σ-donor ligands, so their ability to act as high field ligands is a result of their extremely high σ-donor ability.

12 The Spectrochemical Series of Metals Δ o depends not only on the nature of the ligands, but also on the metal and its oxidation state. The spectrochemical series for metal ions (approximate) is shown below: Mn 2+ < Ni 2+ < Co 2+ < Fe 2+ < V 2+ < Co 3+ < Mn 4+ < Mo 3+ < Rh 3+ < Ru 3+ < Pd 4+ < Ir 3+ < Pt 4+ This series is not quite as regular as the spectrochemical series of ligands, but there are obvious trends: (1) Δ o increases with increasing oxidation number (Co 2+ < Co 3+ etc.) Reason - Metal ions in a higher oxidation state have greater polarising power bonding becomes more covalent and less ionic (the nephelauxetic effect = Latin for cloud expanding). (2) Δ o increases down a group (Co 3+ << Rh 3+ < Ir 3+ ) Reasons - Improved M-L bonding for larger 4d and 5d orbitals relative to the 3d orbitals. - Higher effective nuclear charge (i.e. the actual charge on the metal in a Rh(III) complex will be higher than in an analogous Co(III) complex because heavier congeners are easier to oxidise).